Abstract:
The present disclosure relates 5G or pre-5G communication systems for supporting higher data transmission rate than those by LTE or other post-4G communication systems. According to the present disclosure, a method for operating a beamformed reference signal by a base station and terminal in a communication system, and the terminal, are provided. The method includes transmitting, to a terminal, control information indicating whether a first codebook is used for generating feedback information on a downlink reference signal. The first codebook is used if generating feedback information on the beamformed reference signal and is generated based on a number of antenna ports and a number of ranks.

Description:
[0001]    CROSS-REFERENCE TO RELATED APPLICATION(S) 
         [0002]    This application claims the benefit under 35 U.S.C. §119(e) of a U.S. Provisional application filed on Aug. 13, 2015 in the U.S. Patent and Trademark Office and assigned Ser. No. 62/204,582, of a U.S. Provisional application filed on Sep. 24, 2015 in the U.S. Patent and Trademark Office and assigned Ser. No. 62/232,016, of a U.S. Provisional application filed on Oct. 13, 2015 in the U.S. Patent and Trademark Office and assigned Ser. No. 62/240,744 and of a U.S. Provisional application filed on Oct. 23, 2015 in the U.S. Patent and Trademark Office and assigned Ser. No. 62/245,630, the entire disclosure of each of which is hereby incorporated by reference. 
     
    
     TECHNICAL FIELD 
       [0003]    The present disclosure relates to methods and apparatuses for operating beamformed reference signals in communication systems. 
       BACKGROUND 
       [0004]    In order to meet the demand for wireless data traffic soring since the fourth generation (4G) communication system came to the market, there are ongoing efforts to develop enhanced fifth generation (5G) communication systems or pre-5G communication systems. For the reasons, the 5G communication system or pre-5G communication system is called the beyond 4G network communication system or post long term evolution (LTE) system. 
         [0005]    For higher data transmit rates, 5G communication systems are considered to be implemented on ultra-high frequency bands (mmWave), such as, e.g., 60 GHz. To mitigate pathloss on the ultra-high frequency band and increase the reach of radio waves, the following techniques are taken into account for the 5G communication system: beamforming, massive multi-input multi-output (MIMO), full dimensional MIMO (FD-MIMO), array antenna, analog beamforming, and large scale antenna. 
         [0006]    Also being developed are various technologies for the 5G communication system to have an enhanced network, such as evolved or advanced small cell, cloud radio access network (cloud RAN), ultra-dense network, device-to-device (D2D) communication, wireless backhaul, moving network, cooperative communication, coordinated multi-point (CoMP), and interference cancellation. 
         [0007]    There are also other various schemes under development for the 5G system including, e.g., hybrid FSK and QAM modulation (FQAM) and sliding window superposition coding (SWSC), which are advanced coding modulation (ACM) schemes, and filter bank multi-carrier (FBMC), non-orthogonal multiple access (NOMA) and sparse code multiple access (SCMA), which are advanced access schemes. 
         [0008]    Meanwhile, MIMO technology increases channel capacity within limited frequency resources by using multiple antennas and provides channel capacity theoretically proportional to the number of antennas by multiple antennas having an excellent scattering environment. 
         [0009]    However, MIMO technology has a limited space and area where antennas may be installed, and the inter-antenna interval has a significant influence on communication capability. That is, as the inter-antenna interval decreases, radio channels present a higher correlation. In particular, when antennas have the same polarization, radio channels have a significantly high correlation, and interference between radio channels reduces reliability and data transmission ratio of data communication. 
         [0010]    Accordingly, various polarization directions of antennas need to be used in order to increase channel capacity while decreasing the area where multiple antennas are installed. This is why interference between radio channels may be decreased when antennas have multiple polarizations. 
         [0011]    MIMO technology requires a precoding task for previously coding data in order to efficiently transmit data. Further, a data precoding rule represented as a matrix is called precoding matrix, and a set of precoding matrixes is called codebook. 
         [0012]    Although various codebooks have been suggested for operation of non-beamformed reference signals, there is no suggestion as to efficient codebooks regarding operation of beamformed reference signals. Therefore, a need exists for low-complexity, high-performance schemes for generating codebooks when operating beamformed reference signals. 
         [0013]    The above information is presented as background information only to assist with an understanding of the present disclosure. No determination has been made, and no assertion is made, as to whether any of the above might be applicable as prior art with regard to the present disclosure. 
       SUMMARY 
       [0014]    Aspects of the present disclosure are to address at least the above-mentioned problems and/or disadvantages and to provide at least the advantages described below. Accordingly, an aspect of the present disclosure is to provide a method and apparatus for operating beamformed reference signals in a communication system. 
         [0015]    According to an embodiment of the present disclosure, there are provided a method and apparatus for generating codebooks used when generating feedback information for beamformed reference signals in a communication system. 
         [0016]    In accordance with an aspect of the present disclosure, a method for operating a beamformed reference signal by a base station in a communication system is provided. The method includes transmitting, to a terminal, control information indicating whether a first codebook is used for generating feedback information on a downlink reference signal. The first codebook is used if generating feedback information on the beamformed reference signal and is generated based on a number of antenna ports and a number of ranks. 
         [0017]    In accordance with another aspect of the present disclosure, a method for operating a beamformed reference signal by a terminal in a communication system is provided. The method includes receiving, from a base station, control information indicating whether a first codebook is used for generating feedback information on a downlink reference signal. The first codebook is used if generating feedback information on the beamformed reference signal and is generated based on a number of antenna ports and a number of ranks. 
         [0018]    In accordance with another aspect of the present disclosure, a base station for operating a beamformed reference signal in a communication system is provided. The base station includes a communication unit configured to transmit and receive a relevant signal and at least one processor configured to control to transmit, to a terminal, control information indicating whether a first codebook is used for generating feedback information on a downlink reference signal. The first codebook is used if generating feedback information on the beamformed reference signal and is generated based on a number of antenna ports and a number of ranks. 
         [0019]    In accordance with another aspect of the present disclosure, a terminal for operating a beamformed reference signal in a communication system is provided. The terminal includes a communication unit configured to transmit and receive a relevant signal and at least one processor configured to control to receive, from a base station, control information indicating whether a first codebook is used for generating feedback information on a downlink reference signal. The first codebook is used if generating feedback information on the beamformed reference signal and is generated based on a number of antenna ports and a number of ranks. 
         [0020]    According to an embodiment of the present disclosure, beamformed reference signals may be operated in a communication system. 
         [0021]    According to an embodiment of the present disclosure, codebooks may be generated which are used when generating feedback information for beamformed reference signals in a communication system. 
         [0022]    Other aspects, advantages, and salient features of the disclosure will become apparent to those skilled in the art from the following detailed description, which, taken in conjunction with the annexed drawings, discloses various embodiments of the present disclosure. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]    The above and other aspects, features, and advantages of certain embodiments of the present disclosure will be more apparent from the following description taken in conjunction with the accompanying drawings, in which: 
           [0024]      FIG. 1  is a view illustrating a scenario in which a beamformed reference signal is operated in a communication system according to an embodiment of the present disclosure; 
           [0025]      FIG. 2  is a view illustrating an example of a configuration of a reference signal port used upon transmission of a beamforming information-applied reference signal by a base station according to an embodiment of the present disclosure; 
           [0026]      FIG. 3  is a flowchart illustrating an example of operation of a beamformed reference signal by a base station in a communication system according to an embodiment of the present disclosure; 
           [0027]      FIG. 4  is a flowchart illustrating an example of operation of a beamformed reference signal by a base station in a communication system according to an embodiment of the present disclosure; 
           [0028]      FIG. 5  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure; 
           [0029]      FIG. 6  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure; 
           [0030]      FIG. 7  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure; 
           [0031]      FIG. 8  is a view illustrating an internal configuration of a terminal operating a beamformed reference signal in a communication system according to an embodiment of the present disclosure; and 
           [0032]      FIG. 9  is a view illustrating an internal configuration of a base station operating a beamformed reference signal in a communication system according to an embodiment of the present disclosure. 
       
    
    
       [0033]    Throughout the drawings, like reference numerals will be understood to refer to like parts, components, and structures. 
       DETAILED DESCRIPTION 
       [0034]    The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of various embodiments of the present disclosure as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the various embodiments described herein can be made without departing from the scope and spirit of the present disclosure. In addition, descriptions of well-known functions and constructions may be omitted for clarity and conciseness. 
         [0035]    The terms and words used in the following description and claims are not limited to the bibliographical meanings, but, are merely used by the inventor to enable a clear and consistent understanding of the present disclosure. Accordingly, it should be apparent to those skilled in the art that the following description of various embodiments of the present disclosure is provided for illustration purpose only and not for the purpose of limiting the present disclosure as defined by the appended claims and their equivalents. 
         [0036]    It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces. 
         [0037]    For example, the electronic device may be a smartphone, a tablet personal computer (PC), a PC, a mobile phone, a video phone, an e-book reader, a desktop PC, a laptop PC, a netbook PC, a personal digital assistant (PDA), a portable multimedia player (PMP), an Moving Picture Experts Group phase 1 or phase 2 (MPEG-1 or MPEG-2) audio layer 3 (MP3) player, a mobile medical device, a camera, a wearable device (e.g., a head-mounted device (HMD)), electronic clothes, an electronic bracelet, an electronic necklace, an electronic appcessory, an electronic tattoo, or a smart watch. 
         [0038]    Further, according to an embodiment of the present disclosure, the electronic device may include, e.g., a smart home device, e.g., a television, a digital versatile disc (DVD) player, an audio player, a refrigerator, an air conditioner, a vacuum cleaner, an oven, a microwave oven, a washer, a dryer, an air cleaner, a set-top box, a television (TV) box, a gaming console, an electronic dictionary, a camcorder, or an electronic picture frame. 
         [0039]    Further, according to an embodiment of the present disclosure, the electronic device includes, e.g., a medical device, a navigation device, a global positioning system (GPS) receiver, an event data recorder (EDR), a flight data recorder (FDR), an automotive infotainment device, a sailing electronic device, an aviation electronic device, a security device, or an industrial or home robot. 
         [0040]    According to various embodiments of the disclosure, an electronic device may be a combination of the above-listed devices. It should be appreciated by one of ordinary skill in the art that the electronic device is not limited to the above-described devices. 
         [0041]      FIG. 1  is a view illustrating a scenario in which a beamformed reference signal is operated in a communication system according to an embodiment of the present disclosure. 
         [0042]    Referring to  FIG. 1 , the communication system shown includes a base station (also denoted herein as evolved nodeB (eNB))  100  and a terminal (also denoted herein as user equipment (UE))  110 . 
         [0043]    eNB  100  transmits control information, including a field indicating whether a first codebook is used to generate a channel state information (CSI) feedback, to UE  110  in operation  101 . The first codebook means a brand-new codebook generated by a brand-new scheme as provided according to an embodiment of the present disclosure, and it is here assumed that the field contained in the control information indicates that the first codebook is used to generate the CSI feedback. 
         [0044]    When the field contained in the control information received by UE  110  indicates that the first codebook is not used to generate the CSI feedback, UE  110  uses a second codebook, not the first codebook, to generate the CSI feedback. Here, the second feedback means a legacy codebook. 
         [0045]    In order to use signal transmission utilizing massive multi-input multi-output (MIMO) technology, eNB  100  must determine beamforming appropriate for a channel between eNB  100  and UE  110 . Time division duplexing (TDD) systems primarily determine per-UE beamforming appropriate for data transmission based on a sounding reference signal (SRS) received from UE  110 , and frequency division duplexing (FDD) systems primarily determine per-UE beamforming based on CSI transmitted from UE  110 . 
         [0046]    In order to increase beamforming accuracy in a full dimensional MIMO (FD-MIMO) system, eNB  100  generates first beamforming information using feedback information on a CSI-reference signal (CSI-RS) transmitted at a long period or a sounding reference signal (SRS) transmitted from UE  110 , and transmits an additional reference signal having the first beamforming information applied thereto. Here, CSI-RS means a reference signal transmitted for CSI computation. Thereafter, eNB  100  may generate more accurate second beamforming information using feedback information on CSI transmitted for the additional reference signal and may apply the second beamforming information to data transmission. 
         [0047]      FIG. 1  illustrates an example of generating beamforming information using an SRS that eNB  100  receives from UE  110 . That is, eNB  100  receives a SRS periodically transmitted from UE  110  at operation  105 . Thus, eNB  100  receiving the SRS performs precoding per UE and determines first beamforming information at operation  107 . 
         [0048]    When beamforming information is generated using a CSI-RS transmitted at a long period, operation  105  of  FIG. 1  may be replaced with a configuration in which eNB  100  transmits CSI-RS to UE  110  at a long period and in response receives feedback information containing CSI from UE  110 . 
         [0049]    Having determined first beamforming information, eNB  100  transmits CSI-RS having beamforming information related per transmission port applied thereto, i.e., beamforming CSI-RS (BF-CSI-RS), to UE  110  at operation  109 . 
         [0050]    UE  110  computes CSI based on the received BF-CSI-RS at operation  111 . That is, UE  110  selects a precoding matrix index (PMI) and rank index (RI) based on the first codebook according to the control information received in operation  101  and computes a channel quality indicator (CQI) based on the selected PMI and RI. 
         [0051]    Thereafter, UE  110  reports the CSI computed in operation  111  to eNB  100  at operation  113 , and eNB  100  compensates for RI and CQI based on the CSI and performs precoding adjustment and determines second beamforming information at operation  115 . The eNB  100  having determined second beamforming information transmits a physical downlink shared channel (PDSCH) signal having beamforming information related per transmission port applied thereto to UE  110  at operation  117 . 
         [0052]    A configuration in which control information containing a field indicating whether the first codebook is used to generate CSI feedback is transmitted before operation  105  where SRS is received has been described in connection with  FIG. 1 , for example. However, the control information may also be sent after operation  105  where SRS is received. 
         [0053]      FIG. 2  is a view illustrating an example of a configuration of a reference signal port used upon transmission of a beamforming information-applied reference signal by a base station. 
         [0054]    Referring to  FIG. 2 , eNB  100  may apply various schemes to configure a reference signal port, and in one embodiment, eNB  100  may configure a BF-CSI-RS per antenna polarization to utilize the characteristics of a cross polarization antenna. Here, BF-CSI-RS corresponding to each polarization may be configured in pairs. That is, eNB  100  configures a total of eight reference signal ports including four pairs (A 1 , B 1 ), (A 2 , B 2 ), (A 3 , B 3 ), and (A 4 , B 4 ) and trnasmits BF-CSI-RS through each port. 
         [0055]    Beamforming information applied to BF-CSI-RS sent through each port, e.g., beamforming weight, is determined to form a signal transmission in a dominant direction considering the radio environment channel between eNB  100  and UE  110 . 
         [0056]    Generally, beam for generating codebook is a major approach for configuring a beam direction in a correlated MIMO environment as a discrete Fourier transform (DFT) vector. 
         [0057]    However, since in operation of beamforming information-applied CSI-RS, i.e., BF-CSI-RS, a beam is used in generating a reference signal, a codebook for selecting a beam preferred by UE among received beams, rather than information configuring a beam, is necessary. In the following embodiment, a method for generating a brand new codebook used for beam selection is described. 
       First Embodiment 
       [0058]    scheme for generating brand new codebook by utilizing a legacy eight transmit antenna port (8Tx) codebook structure 
         [0059]    According to a first embodiment of the present disclosure, described is a scheme for generating a brand new codebook utilizing legacy 8Tx codebook structure and using an appropriate v m  vector as a beam for generating the codebook. Here, 8Tx codebook means a codebook used for eight antenna ports. 
         [0060]    Table 1 to Table 8 represent an 8Tx codebook used according to the first embodiment of the present disclosure, and each PMI corresponds to a pair of codebook indices, where the quantities φ n  and v m  are shown by Equation 1 below. A first PMI value of i 1 ∈{0,1,Λ, f(ν)−1} and a second PMI value of i 2 ∈{0,1,Λ,g(ν)−1} correspond to the codebook indices i 1  and i 2  given in Table 1 to Table 8, where f(ν)={16,16,4,4,4,4,4,1} and g(ν)={16,16,16,8,1,1,1,1}. 
         [0000]      φ n =e jπn/2  
 
         [0000]      v m =[1e j2πm/32 e j4πm/32 e j6πm/32 ] T    Equation 1
 
         [0061]    Table 1 represents rank-1 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 0-15 
                 W 2i     1     ,0   (1)   
                 W 2i     1     ,1   (1)   
                 W 2i     1     ,2   (1)   
                 W 2i     1     ,3   (1)   
                 W 2i     1     +1,0   (1)   
                 W 2i     1     +1,1   (1)   
                 W 2i     1     +1,2   (1)   
                 W 2i     1     +1,3   (1)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 0-15 
                 W 2i     1     +2,0   (1)   
                 W 2i     1     +2,1   (1)   
                 W 2i     1     +2,2   (1)   
                 W 2i     1     +2,3   (1)   
                 W 2i     1     +3,0   (1)   
                 W 2i     1     +3,1   (1)   
                 W 2i     1     +3,2   (1)   
                 W 2i     1     +3,3   (1)   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             W 
                             
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                               , 
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                               ( 
                               1 
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                         = 
                         
                           
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                               8 
                             
                           
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         [0062]    Table 2 represents rank-2 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 0-15 
                 W 2i     1     ,2i     1     ,0   (2)   
                 W 2i     1     ,2i     1     ,1   (2)   
                 W 2i     1     +1,2i     1     +1,0   (2)   
                 W 2i     1     +1,2i     1     +1,1   (2)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 0-15 
                 W 2i     1     +2,2i     1     +2,0   (2)   
                 W 2i     1     +2,2i     1     +2,1   (2)   
                 W 2i     1     +3,2i     1     +3,0   (2)   
                 W 2i     1     +3,2i     1     +3,1   (2)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 0-15 
                 W 2i     1     ,2i     1     +1,0   (2)   
                 W 2i     1     ,2i     1     +1,1   (2)   
                 W 2i     1     +1,2i     1     +2,0   (2)   
                 W 2i     1     +1,2i     1     +2,1   (2)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 0-15 
                 W 2i     1     ,2i     1     +3,0   (2)   
                 W 2i     1     ,2i     1     +3,1   (2)   
                 W 2i     1     +1,2i     1     +3,0   (2)   
                 W 2i     1     +1,2i     1     +3,1   (2)   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
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                               m 
                               , 
                               
                                 m 
                                 ′ 
                               
                               , 
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                               2 
                               ) 
                             
                           
                         
                         = 
                         
                           
                             1 
                             4 
                           
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         [0063]    Table 3 represents rank-3 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 0-3 
                 W 8i     1     , 8i     1     , 8i     1     +8   (3)   
                 W 8i     1     +8, 8i     1     , 8i     1     +8   (3)   
                 {tilde over (W)} 8i     1     , 8i     1     +8, 8i     1     +8   (3)   
                 {tilde over (W)} 8i     1     +8, 8i     1     , 8i     1     (3)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 0-3 
                 W 8i     1     +2, 8i     1     +2, 8i     1     +10   (3)   
                 W 8i     1     +10, 8i     1     +2, 8i     1     +10   (3)   
                 {tilde over (W)} 8i     1     +2, 8i     1     +10, 8i     1     +10   (3)   
                 {tilde over (W)} 8i     1     +10, 8i     1     +2, 8i     1     +2   (3)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 0-3 
                 W 8i     1     +4, 8i     1     +4, 8i     1     +12   (3)   
                 W 8i     1     +12, 8i     1     +4, 8i     1     +12   (3)   
                 {tilde over (W)} 8i     1     +4, 8i     1     +12, 8i     1     +12   (3)   
                 {tilde over (W)} 8i     1     +12, 8i     1     +4, 8i     1     +4   (3)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 0-3 
                 W 8i     1     +6, 8i     1     +6, 8i     1     +14   (3)   
                 W 8i     1     +14, 8i     1     +6, 8i     1     +14   (3)   
                 {tilde over (W)} 8i     1     +6, 8i     1     +14, 8i     1     +14   (3)   
                 {tilde over (W)} 8i     1     +14, 8i     1     +6, 8i     1     +6   (3)   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         
                           
                             where 
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                                   ″ 
                                 
                               
                               
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                                 3 
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                         , 
                         
                           
                             
                               W 
                               ~ 
                             
                             
                               m 
                               , 
                               
                                 m 
                                 ′ 
                               
                               , 
                               
                                 m 
                                 ″ 
                               
                             
                             
                               ( 
                               3 
                               ) 
                             
                           
                           = 
                           
                             
                               1 
                               
                                 24 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       v 
                                       m 
                                     
                                   
                                   
                                     
                                       v 
                                       
                                         m 
                                         ′ 
                                       
                                     
                                   
                                   
                                     
                                       v 
                                       
                                         m 
                                         ″ 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       v 
                                       m 
                                     
                                   
                                   
                                     
                                       v 
                                       
                                         m 
                                         ′ 
                                       
                                     
                                   
                                   
                                     
                                       - 
                                       
                                         v 
                                         
                                           m 
                                           ″ 
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0064]    Table 4 represents rank-4 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 0-3 
                 W 8i     1     , 8i     1     +8, 0   (4)   
                 W 8i     1     , 8i     1     +8, 1   (4)   
                 W 8i     1     +2, 8i     1     +10, 0   (4)   
                 W 8i     1     +2, 8i     1     +10,1   (4)   
               
               
                   
               
             
          
           
               
                   
                 i 2   
               
             
          
           
               
                 i 1   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 0-3 
                 W 8i     1     +4, 8i     1     +12, 0   (4)   
                 W 8i     1     +4, 8i     1     +12, 1   (4)   
                 W 8i     1     +6, 8i     1     +14, 0   (4)   
                 W 8i     1     +6, 8i     1     +14, 1   (4)   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             W 
                             
                               m 
                               , 
                               
                                 m 
                                 ′ 
                               
                               , 
                               n 
                             
                             
                               ( 
                               4 
                               ) 
                             
                           
                         
                         = 
                         
                           
                             1 
                             
                               32 
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     m 
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       m 
                                       ′ 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     m 
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       m 
                                       ′ 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       ϕ 
                                       n 
                                     
                                      
                                     
                                       v 
                                       m 
                                     
                                   
                                 
                                 
                                   
                                     
                                       ϕ 
                                       n 
                                     
                                      
                                     
                                       v 
                                       
                                         m 
                                         ′ 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
                                         ϕ 
                                         n 
                                       
                                     
                                      
                                     
                                       v 
                                       m 
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
                                         ϕ 
                                         n 
                                       
                                     
                                      
                                     
                                       v 
                                       
                                         m 
                                         ′ 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0065]    Table 5 represents rank-5 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                   
                 i 2   
               
               
                   
                 i 1   
                 0 
               
               
                   
                   
               
             
             
               
                   
                 0-3 
                 
                   
                     
                       
                         
                           W 
                           
                             i 
                             1 
                           
                           
                             ( 
                             5 
                             ) 
                           
                         
                         = 
                         
                           
                             1 
                             
                               40 
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       16 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                         + 
                                         8 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       16 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
             
          
         
       
     
         [0066]    Table 6 represents rank-6 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                   
                 i 2   
               
               
                   
                 i 1   
                 0 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 0-3 
                 
                   
                     
                       
                         
                           W 
                           
                             i 
                             1 
                           
                           
                             ( 
                             6 
                             ) 
                           
                         
                         = 
                         
                           
                             1 
                             
                               48 
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       16 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       16 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       2 
                                        
                                       
                                         i 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                         + 
                                         8 
                                       
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
                                         2 
                                          
                                         
                                           i 
                                           1 
                                         
                                       
                                       + 
                                       16 
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                         + 
                                         16 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
             
          
         
       
     
         [0067]    Table 7 represents rank-7 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                   
                 i 2   
               
               
                 i 1   
                 0 
               
               
                   
               
             
             
               
                 0-3 
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                 
                                   W 
                                   
                                     i 
                                     1 
                                   
                                   
                                     ( 
                                     7 
                                     ) 
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   
                                     56 
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           v 
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             8 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             8 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             16 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             16 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             24 
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           v 
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             8 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               
                                                 2 
                                                  
                                                 
                                                   i 
                                                   1 
                                                 
                                               
                                               + 
                                               8 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             16 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               
                                                 2 
                                                  
                                                 
                                                   i 
                                                   1 
                                                 
                                               
                                               + 
                                               16 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             24 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0068]    Table 8 represents rank-8 codebook used according to the first embodiment of the present disclosure. 
         [0000]    
       
         
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                   
                 i 2   
               
               
                 i 1   
                 0 
               
               
                   
               
             
             
               
                 0 
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                 
                                   W 
                                   
                                     i 
                                     1 
                                   
                                   
                                     ( 
                                     8 
                                     ) 
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   8 
                                 
                                 [ 
                                 
                                   
                                     
                                       
                                         v 
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           8 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           8 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           16 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           16 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           24 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           24 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         v 
                                         
                                           2 
                                            
                                           
                                             i 
                                             1 
                                           
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           8 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             8 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           16 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             16 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           
                                             2 
                                              
                                             
                                               i 
                                               1 
                                             
                                           
                                           + 
                                           24 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             
                                               2 
                                                
                                               
                                                 i 
                                                 1 
                                               
                                             
                                             + 
                                             24 
                                           
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0069]    A beam set as shown in Equation 2 below is generated upon generating a rank-1 and rank-2 codebook by applying a beam for generating codebook, e.g., DFT vector v m =[1e j2πm/32 e j4πm/32 e j6πm/32 ] T , to the 8Tx codebook shown in Table 1 to Table 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               b 
                               0 
                             
                           
                           
                             
                               b 
                               1 
                             
                           
                           
                             Λ 
                           
                           
                             
                               b 
                               31 
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     
                       
                         [ 
                         B 
                         ] 
                       
                       
                         
                           1 
                           + 
                           m 
                         
                         , 
                         
                           1 
                           + 
                           n 
                         
                       
                     
                     = 
                     
                        
                       
                         j 
                          
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             mn 
                           
                           32 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     m 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   3 
                   , 
                   
                     n 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   Λ 
                   , 
                   31 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0070]    In Equation 2, the B matrix is a 4×32-size matrix, and a W1 and W2 codebook is generated based on the B matrix. 
         [0071]    In the following embodiment of the present disclosure, described is a method in which a v m  vector of a proper size, e.g., 4×1 size, is utilized as a beam for generating codebook to generate an 8Tx codebook appropriate for operation of BF-CSI-RS. The v m  vector may be defined by various methods, and it may be defined by applying the following rules. 
         [0072]    Rule 1) Matrix having 1&#39;s in a ratio of 1/4 and 0&#39;s in a ratio of 3/4 in each row 
         [0073]    Rule 2) Matrix constituted of vectors having one 1 and three 0&#39;s for all the rows 
         [0074]    Rule 3) Matrix in which among a total of 32 rows, 16 sub matrixes are repeatedly or symmetrically constituted 
         [0075]    Rule 4) Matrix in which among a total of 32 rows, four consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0076]    Rule 5) Matrix in which among a total of 32 rows, eight consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0077]    Rule 6) Matrix utilizing the columns of the identity matrix for all the rows 
         [0078]    Further, a beam set as shown in Equation 3 below is generated upon generating a rank-1 and rank-2 codebook by applying a beam for generating codebook, e.g., DFT vector v m =[1e j2πm/32 e j4πm/32 e j6πm/32 ] T , to the 8Tx codebook shown in Table 1 to Table 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               b 
                               0 
                             
                           
                           
                             
                               b 
                               1 
                             
                           
                           
                             Λ 
                           
                           
                             
                               b 
                               31 
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     
                       
                         [ 
                         B 
                         ] 
                       
                       
                         
                           1 
                           + 
                           m 
                         
                         , 
                         
                           1 
                           + 
                           n 
                         
                       
                     
                     = 
                     
                        
                       
                         j 
                          
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             mn 
                           
                           32 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     m 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   3 
                   , 
                   
                     n 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   Λ 
                   , 
                   31 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0079]    In Equation 3, the B matrix is a 4×32-size matrix, and a W1 and W2 codebook is generated based on the B matrix. 
         [0080]    In the following embodiment of the present disclosure, described is a method in which a v m  vector of a proper size, e.g., 2×1 size, is utilized as a beam for generating codebook to generate an 4Tx codebook appropriate for operation of BF-CSI-RS. Here, 4Tx codebook means a codebook used for four antenna ports. The v m  vector may be defined by various methods, and it may be defined by applying the following rules. 
         [0081]    Rule 1) Matrix having 1&#39;s in a ratio of 1/2 and 0&#39;s in a ratio of 1/2 in each row 
         [0082]    Rule 2) Matrix constituted of vectors having one 1 and one 0 for all the rows 
         [0083]    Rule 3) Matrix in which among a total of 32 rows, 16 sub matrixes are repeatedly or symmetrically constituted 
         [0084]    Rule 4) Matrix in which among a total of 32 rows, four consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0085]    Rule 5) Matrix in which among a total of 32 rows, eight consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0086]    Rule 6) Matrix utilizing the columns of the identity matrix for all the rows 
         [0087]    Further, a beam set as shown in Equation 4 below is generated upon generating a rank-3 and rank-8 codebook by applying a beam for generating codebook, e.g., DFT vector v m =[1e j2πm/32 e j4πm/32 e j6πm/32 ] T , to the 8Tx codebook shown in Table 1 to Table 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               b 
                               0 
                             
                           
                           
                             
                               b 
                               1 
                             
                           
                           
                             Λ 
                           
                           
                             
                               b 
                               15 
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                   
                     
                       
                         [ 
                         B 
                         ] 
                       
                       
                         
                           1 
                           + 
                           m 
                         
                         , 
                         
                           1 
                           + 
                           n 
                         
                       
                     
                     = 
                     
                        
                       
                         j 
                          
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             mn 
                           
                           16 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     m 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   3 
                   , 
                   
                     n 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   Λ 
                   , 
                   15 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0088]    In Equation 4, the B matrix is a 4×16-size matrix, and a W1 and W2 codebook is generated based on the B matrix. 
         [0089]    In the following embodiment of the present disclosure, described is a method in which a v m  vector of a proper size, e.g., 4×1 size, is utilized as a beam for generating codebook to generate an 8Tx codebook appropriate for operation of BF-CSI-RS. The v m  vector may be defined by various methods, and it may be defined by applying the following rules. 
         [0090]    Rule 1) Matrix having 1&#39;s in a ratio of 1/4 and 0&#39;s in a ratio of 3/4 in each row 
         [0091]    Rule 2) Matrix constituted of vectors having one 1 and three 0&#39;s for all the rows 
         [0092]    Rule 3) Matrix in which among a total of 16 rows, 8 sub matrixes are repeatedly or symmetrically constituted 
         [0093]    Rule 4) Matrix in which among a total of 16 rows, four consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0094]    Rule 5) Matrix in which among a total of 16 rows, eight consecutive rows are repeatedly configured with the order of rows recursively changed 
         [0095]    Rule 6) Matrix utilizing the columns of the identity matrix for all the rows 
       Second Embodiment 
       [0096]    scheme for generating brand new codebook by utilizing a predetermined codebook structure 
         [0097]    According to a second embodiment of the present disclosure, described is a scheme for generating a brand new codebook utilizing a codebook structure other than the legacy 8Tx codebook structure and using an appropriate v m  vector as beam for generating codebook. 
         [0098]    In one embodiment, when a codebook other than the legacy 8Tx codebook is used in future standards, the v m  vector used in the codebook may be utilized as a proper beam for generating a codebook to generate a brand-new codebook. For example, a future standard may use the rank-1 and rank-2 codebook as shown in Tables 9 and 10 below. 
         [0099]    Equation 5 and Table 9 represent rank-1 codebook. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       W 
                       
                         
                           m 
                           1 
                         
                         , 
                         
                           m 
                           2 
                         
                         , 
                         n 
                       
                       
                         ( 
                         1 
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           Q 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ϕ 
                                   n 
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         ϕ 
                         n 
                       
                       = 
                       
                          
                         
                           j 
                            
                           
                             
                               π 
                                
                               
                                   
                               
                                
                               n 
                             
                             2 
                           
                         
                       
                     
                     , 
                     
                       
                         v 
                         
                           m 
                           1 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           1 
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             1 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 1 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         u 
                         
                           m 
                           2 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           2 
                                         
                                       
                                       
                                         
                                           o 
                                           2 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 2 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           2 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                     , 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   5 
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 Rank-1 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 i′ 2   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 Precoder 
                 W s     1     i     1,1     , s     2     i     1,2     , 0   (1)   
                 W s     1     i     1,1     , s     2     i     1,2     , 1   (1)   
                 W s     1     i     1,1     , s     2     i     1,2     , 2   (1)   
                 W s     1     i     1,1     , s     2     i     1,2     , 3   (1)   
               
               
                   
               
               
                 i′ 2   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 Precoder 
                 W s     1     i     1,1     + 1, s     2     i     1,2     , 0   (1)   
                 W s     1     i     1,1     + 1, s     2     i     1,2     , 1   (1)   
                 W s     1     i     1,1     + 1, s     2     i     1,2     , 2   (1)   
                 W s     1     i     1,1     + 1, s     2     i     1,2     , 3   (1)   
               
               
                   
               
               
                 i′ 2   
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 Precoder 
                 W s     1     i     1,1     + 2, s     2     i     1,2     , 0   (1)   
                 W s     1     i     1,1     + 2, s     2     i     1,2     , 1   (1)   
                 W s     1     i     1,1     + 2, s     2     i     1,2     , 2   (1)   
                 W s     1     i     1,1     + 2, s     2     i     1,2     , 3   (1)   
               
               
                   
               
               
                 i′ 2   
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 Precoder 
                 W s     1     i     1,1     + 3, s     2     i     1,2     , 0   (1)   
                 W s     1     i     1,1     + 3, s     2     i     1,2     , 1   (1)   
                 W s     1     i     1,1     + 3, s     2     i     1,2     , 2   (1)   
                 W s     1     i     1,1     + 3, s     2     i     1,2     , 3   (1)   
               
               
                   
               
             
          
           
               
                 i′ 2   
                 16-31 
               
               
                   
               
               
                 Precoder 
                 Entries 16-31 constructed with replacing the second subscript  s   2   i   1,2   
               
               
                   
                 with  s   2   i   1,2    + 1  in entries 0-15. 
               
               
                   
               
             
          
         
       
     
         [0100]    Equation 6 and Table 10 represent rank-2 codebook. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       W 
                       
                         
                           m 
                           1 
                         
                         , 
                         
                           m 
                           2 
                         
                         , 
                         
                           m 
                           1 
                           ′ 
                         
                         , 
                         
                           m 
                           2 
                           ′ 
                         
                         , 
                         n 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             2 
                              
                             
                                 
                             
                              
                             Q 
                           
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                   
                                 
                               
                             
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                     ′ 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                     ′ 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ϕ 
                                   n 
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     ϕ 
                                     n 
                                   
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       
                         ϕ 
                         n 
                       
                       = 
                       
                          
                         
                           j 
                            
                           
                             
                               π 
                                
                               
                                   
                               
                                
                               n 
                             
                             2 
                           
                         
                       
                     
                     , 
                     
                       
                         v 
                         
                           m 
                           1 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           1 
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             1 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 1 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         u 
                         
                           m 
                           2 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           2 
                                         
                                       
                                       
                                         
                                           o 
                                           2 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 2 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           2 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         i 
                         
                           1 
                           , 
                           1 
                         
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         
                           O 
                           1 
                         
                          
                         
                           
                             N 
                             1 
                           
                           / 
                           
                             s 
                             1 
                           
                         
                       
                       - 
                       1 
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         i 
                         
                           1 
                           , 
                           2 
                         
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       
                         
                           O 
                           2 
                         
                          
                         
                           
                             N 
                             2 
                           
                           / 
                           
                             s 
                             2 
                           
                         
                       
                       - 
                       1 
                     
                     , 
                     
                       
                         p 
                         1 
                       
                       = 
                       1 
                     
                     , 
                     
                       
                         and 
                          
                         
                             
                         
                          
                         
                           p 
                           2 
                         
                       
                       = 
                       1 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Rank-2 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 i′ 2   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     , s     2     i     1,2     , 1   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     , 1   (2)   
               
               
                   
               
               
                 i′ 2   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     + 2p     1     , s     2     i     1,2     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     + 2p     1     , s     2     i     1,2     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     , 1   (2)   
                 W s     1     i     1,1     + 3p     1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     + 3p     1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 1   (2)   
               
               
                   
               
               
                 i′ 2   
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     , 1   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     , 1   (2)   
               
               
                   
               
               
                 i′ 2   
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 1   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 0   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     , 1   (2)   
               
               
                   
               
               
                 i′ 2   
                 16 
                 17 
                 18 
                 19 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     , s     2     i     1,2     + p     2     , s     1     i     1,1     , s     2     i     1,2     + p     2     , 0   (2)   
                 W s     1     i     1,1     , s     2     i     1,2     + p     2     , s     1     i     1,1     , s     2     i     1,2     + p     2     , 1   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
               
               
                   
                   
                   
                 
                   p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                   p     1     , s     2     i     1,2     + p     2     , 1 (2) 
               
               
                   
               
               
                 i′ 2   
                 20 
                 21 
                 22 
                 23 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     + 3p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     + 3p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     , s     2     i     1,     2 + p     2     , s     1     i     1,1     + p     1     , s     2     i     1,2     +    
               
               
                   
                 
                   3p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                 
                   3p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + p 
                   
                     2 
                   
                   , 1 
                   (2) 
                 
                 
                   p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                 
                   p 
                   
                     2 
                   
                   , 1 
                   (2) 
                 
               
               
                   
               
               
                 i′ 2   
                 24 
                 25 
                 26 
                 27 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     + p     2     , s     1     i     1,1     +    
               
               
                   
                 
                   2p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                 
                   2p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + 
                   p 
                   
                     2 
                   
                   , 1 
                   (2) 
                 
                 
                   3p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + 
                   p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                 
                   3p 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + 
                   p 
                   
                     2 
                   
                   , 1 
                   (2) 
                 
               
               
                   
               
               
                 i′ 2   
                 28 
                 29 
                 30 
                 31 
               
               
                   
               
               
                 i 1,1 , i 1,2   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     , s     2     i     1,2     + p     2     , 0   (2)   
                 W s     1     i     1,1     , s     2     i     1,2     , s     1     i     1,1     , s     2     i     1,2     + p     2     , 1   (2)   
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     +    
                 W s     1     i     1,1     + p     1     , s     2     i     1,2     , s     1     i     1,1     + p     1     , s     2     i     1,2     +    
               
               
                   
                   
                   
                 
                   p 
                   
                     2 
                   
                   , 0 
                   (2) 
                 
                 
                   p 
                   
                     2 
                   
                   , 1 
                   (2) 
                 
               
               
                   
               
             
          
         
       
     
         [0101]    An eNB may designate an additional configuration as shown in Tables 11 and 12 based on the codebook shown in Tables 9 and 10. A portion of the codebook shown in Tables 9 and 10 may be used as a brand new codebook according to each configuration. 
         [0102]    Table 11 represents a portion of the rank-1 codebook shown in Table 9 as a brand-new codebook. 

 
         [0103]    Table 12 represents a portion of the rank-2 codebook shown in Table 10 as a brand-new codebook. 

 
         [0104]    According to the second embodiment of the present disclosure, v m     1   = 
         [0000]    
       
         
           
             
               
                 Q 
                 2 
               
             
              
             
               e 
               
                 m 
                 1 
               
               
                 ( 
                 
                   
                     N 
                     p 
                   
                   / 
                   2 
                 
                 ) 
               
             
           
         
       
     
         [0000]    and u m     2   =1 may be used as beams for generating codebook to generate a brand-new assuming configuration 4 in the codebook shown in Tables 11 and 12. Here, N p  denotes the number of antenna ports, and the e i   (N)  vector is a vector of N size in which the ith element is 1, and the other elements are 0&#39;s. 
         [0105]    Table 13 represents a 4Tx codebook generated for each of rank-1 and rank-2 generated based on the codebook shown in Tables 11 and 12. Here, 4Tx codebook means a codebook used for four antenna ports. It is assumed in Table 13 below that the brand-new codebook starts from element index 0. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 Codebook 
                 Rank-1 
                 Rank-2 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
             
             
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 1 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 3 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 4 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 5 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 6 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 7 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0106]    Table 14 represents the 8Tx codebook generated for each of rank-1 and rank-2 generated based on the codebook shown in Tables 11 and 12. Here, the 8Tx codebook means a codebook used for eight antenna ports, and the brand new codebook shown in Table 14 below is assumed to start from element index 0. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 Codebook 
                 Rank-1 
                 Rank-2 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 1 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 3 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 4 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 e 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 5 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 6 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 7 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 8 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 9 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 10 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 11 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 12 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 13 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 14 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   j 
                                   · 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 15 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                   · 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0107]    Other than the rank-1 and rank-2 codebook described above, rank-3 and rank-4 codebook as shown in Tables 15 and 16 below may be used in the future standard. 
         [0108]    Equation 7 and Table 15 represent Rank-3 codebook. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         W 
                         
                           
                             m 
                             1 
                           
                           , 
                           
                             m 
                             1 
                             ′ 
                           
                           , 
                           
                             m 
                             2 
                           
                           , 
                           
                             m 
                             2 
                             ′ 
                           
                         
                         
                           ( 
                           3 
                           ) 
                         
                       
                       = 
                       
                         
                           1 
                           
                             
                               3 
                                
                               Q 
                             
                           
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         m 
                                         1 
                                       
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         m 
                                         1 
                                         ′ 
                                       
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                     , 
                     
                         
                     
                      
                     or 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           W 
                           ~ 
                         
                         
                           
                             m 
                             1 
                           
                           , 
                           
                             m 
                             1 
                             ′ 
                           
                           , 
                           
                             m 
                             2 
                           
                           , 
                           
                             m 
                             2 
                             ′ 
                           
                         
                         
                           ( 
                           3 
                           ) 
                         
                       
                       = 
                       
                         
                           1 
                           
                             
                               3 
                                
                               Q 
                             
                           
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     - 
                                     
                                       v 
                                       
                                         m 
                                         1 
                                         ′ 
                                       
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         ϕ 
                         n 
                       
                       = 
                       
                          
                         
                           jπ 
                            
                           
                               
                           
                            
                           
                             n 
                             / 
                             2 
                           
                         
                       
                     
                     , 
                     
                       
                         v 
                         
                           m 
                           1 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           1 
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             1 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 1 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           1 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         u 
                         
                           m 
                           2 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           m 
                                           2 
                                         
                                       
                                       
                                         
                                           o 
                                           1 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 … 
                               
                               
                                 
                                    
                                   
                                     j 
                                      
                                     
                                       
                                         2 
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             m 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 2 
                                               
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           o 
                                           2 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         t 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
             
           
               
                 TABLE 15 
               
               
                   
               
               
                 Rank-3 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 i′ 2   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     , s     1     i     1,1     +    
                 W s     1     i     1,1     + δ     1     , s     1     i     1,1     , s     2     i     1,2     + δ     2     , s     2     i     1,2     (3)   
                 {tilde over (W)} s     1     i     1,1     , s     1     i     1,1     + δ     1     , s     2     i     1,2     , s     2     i     1,2     +   
                 {tilde over (W)} s     1     i     1,1     + δ     1     , s     1     i     1,1     , s     2     i     1,2     + δ     2     , s     2     i     1,2     (3)   
               
               
                 i 1,2 , 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                   
                 
                   δ 
                   
                     2 
                   
                   (3) 
                 
                   
               
               
                 k 
               
               
                   
               
               
                 i′ 2   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     + p     1     , s     1     i     1,1     + p     1     +    
                 W s     1     i     1,1     + p     1     + δ     1     , s     1     i     1,1     + p     1     , s     2     i     1,2     + δ     2     , s     2     i     1,2     (3)   
                 {tilde over (W)} s     1     i     1,1     + p     1     , s     1     i     1,1     + p     1     +    
                 {tilde over (W)} s     1     i     1,1     + p     1     + δ     1     , s     1     i     1,1     + p     1     , s     2     i     1,2     + δ     2     , s     2     i     1,2     (3)   
               
               
                 i 1,2 , 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                   
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                   
               
               
                 k 
               
               
                   
               
               
                 i′ 2   
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     + 2p     1     , s     1     i     1,1     + 2p     1     +    
                 W s     1     i     1,1     + 2p     1     + δ     1     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     +    
                 {tilde over (W)} s     1     i     1,1     + 2p     1     , s     1     i     1,1     + 2p     1     +    
                 {tilde over (W)} s     1     i     1,1     + 2p     1     + δ     1     , s     1     i     1,1     + 2p     1     , s     2     i     1,2     +    
               
               
                 i 1,2 , 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   (3) 
                 
               
               
                 k 
               
               
                   
               
               
                 i′ 2   
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     + 3p     1     , s     1     i     1,1     +    
                 W s     1     i     1,1     + 3p     1     + δ     1,      s     1     i     1,1     + 3p     1     , s     2     i     1,2     +    
                 {tilde over (W)} s     1     i     1,1     + 3p     1     , s     1     i     1,1     + 3p     1     +    
                 {tilde over (W)} s     1     i     1,1     + 3p     1     + δ     1     , s     1     i     1,1     + 3p     1     , s     2     i     1,2     +    
               
               
                 i 1,2 , 
                 
                   3p 
                   
                     1 
                   
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   (3) 
                 
                 
                   δ 
                   
                     2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   (3) 
                 
               
               
                 k 
               
               
                   
               
             
          
           
               
                 i′ 2   
                 16-31 
               
               
                   
               
               
                 i 1,1 , 
                 Entries 16-31 constructed with replacing  s   2   i   1,2  in third and fourth subscripts with 
               
               
                 i 1,2 , 
                   s   2   i   1,2    + p   2  in entries 0-15. 
               
               
                 k 
               
               
                   
               
             
          
         
       
     
         [0109]    Equation 8 and Table 16 represent rank-4 codebook. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       W 
                       
                         
                           m 
                           1 
                         
                         , 
                         
                           m 
                           1 
                           ′ 
                         
                         , 
                         
                           m 
                           2 
                         
                         , 
                         
                           m 
                           2 
                           ′ 
                         
                         , 
                         n 
                       
                       
                         ( 
                         4 
                         ) 
                       
                     
                     = 
                     
                       Equation 
                        
                       
                           
                       
                        
                       8 
                        
                       
                         
                           1 
                           
                             
                               4 
                                
                               Q 
                             
                           
                         
                         [ 
                         
                             
                         
                          
                         
                           
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                   
                                 
                               
                             
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                     ′ 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                     ′ 
                                   
                                 
                               
                             
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                   
                                 
                               
                             
                             
                               
                                 
                                   v 
                                   
                                     m 
                                     1 
                                     ′ 
                                   
                                 
                                 ⊗ 
                                 
                                   u 
                                   
                                     m 
                                     2 
                                     ′ 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ϕ 
                                   n 
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   ϕ 
                                   n 
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     ϕ 
                                     n 
                                   
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     ϕ 
                                     n 
                                   
                                 
                                  
                                 
                                   
                                     v 
                                     
                                       m 
                                       1 
                                       ′ 
                                     
                                   
                                   ⊗ 
                                   
                                     u 
                                     
                                       m 
                                       2 
                                       ′ 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       ϕ 
                       n 
                     
                     = 
                     
                        
                       
                         jπ 
                          
                         
                             
                         
                          
                         
                           n 
                           / 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
                       v 
                       
                         m 
                         1 
                       
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     
                                       2 
                                        
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       
                                         m 
                                         1 
                                       
                                     
                                     
                                       
                                         o 
                                         1 
                                       
                                        
                                       
                                         N 
                                         1 
                                       
                                     
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     
                                       2 
                                        
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           m 
                                           1 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               N 
                                               1 
                                             
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         o 
                                         1 
                                       
                                        
                                       
                                         N 
                                         1 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       t 
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       u 
                       
                         m 
                         2 
                       
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     
                                       2 
                                        
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       
                                         m 
                                         2 
                                       
                                     
                                     
                                       
                                         o 
                                         1 
                                       
                                        
                                       
                                         N 
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                  
                                 
                                   j 
                                    
                                   
                                     
                                       2 
                                        
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           m 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               N 
                                               2 
                                             
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         o 
                                         2 
                                       
                                        
                                       
                                         N 
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       t 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
             
           
               
                 TABLE 16 
               
               
                   
               
               
                 Rank-4 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 i′ 2   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     , s     1     i     1,1     + δ     1     , s     2     i     1,2     ,      s       2     i     1,2     +    
                 W s     1     i     1,1     , s     1     i     1,1     + δ     1     , s     2     i     1,2     , s     2     i     1,2     +    
                 W s     1     i     1,1     + p     1     , s     1     i     1,1     + p     1     +    
                 W s     1     i     1,1     + p     1     , s     1     i     1,1     + p     1     +    
               
               
                 i 1,2 , 
                 
                   δ 
                   
                     2 
                   
                   , 0 
                   (4) 
                 
                 
                   δ 
                   
                     2 
                   
                   , 1 
                   (4) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + 
                   δ 
                   
                     2 
                   
                   , 0 
                   (4) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   , 1 
                   (4) 
                 
               
               
                 k 
               
               
                   
               
               
                 i′ 2   
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 i 1,1 , 
                 W s     1     i     1,1     + 2p     1     , s     1     i     1,1     + 2p     1     +    
                 W s     1     i     1,1     + 2p     1     , s     1     i     1,1      + 2p     1     +    
                 W s     1     i     1,1     + 3p     1     , s     1     i     1,1     + 3p     1     +    
                 W s     1     i     1,1     + 3p     1     , s     1     i     1,1     + 3p     1     +    
               
               
                 i 1,2 , 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   , 0 
                   (4) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   , 1 
                   (4) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   , 0 
                   (4) 
                 
                 
                   δ 
                   
                     1 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   , s 
                   
                     2 
                   
                   i 
                   
                     1,2 
                   
                   + δ 
                   
                     2 
                   
                   , 1 
                   (4) 
                 
               
               
                 k 
               
               
                   
               
             
          
           
               
                 i′ 2   
                 8-15 
               
               
                   
               
               
                 i 1,1 , 
                 Entries 8-15 constructed with replacing  s   2   i   1,2  in the third and fourth subscripts with 
               
               
                 i 1,2 , 
                   s   2   i   1,2    + p   2  in entries 0-7. 
               
               
                 k 
               
               
                   
               
             
          
         
       
     
         [0110]    An eNB and UE may designate an additional configuration as shown in Table 17 below based on the codebook shown in Tables 15 and 16. A portion of the codebook shown in Tables 15 and 16 may be used as a brand new codebook according to each configuration. 
         [0111]    Table 17 represents orthogonal beam type for δ 1  and δ 2 . 
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 17 
               
             
             
               
                   
               
               
                   
                   
                 k 
               
             
          
           
               
                   
                 δ 
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 If N 1  &gt; 1 and N 2  &gt; 1 
                 δ 1   
                 O 1   
                 0 
                 O 1   
                 (N 1  − 1)O 1   
               
               
                   
                 δ 2   
                 0 
                 O 2   
                 O 2   
                 0 
               
               
                 If N 2  = 1 
                 δ 1   
                 O 1   
                 2O 1   
                 3O 1   
                 (N 1  − 1)O 1   
               
               
                   
                 δ 2   
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
         
       
     
         [0112]    Table 18 represents configurations 1 to 4 for index i′ 2  selected to report rank-3 CSI, and Table 19 represents configurations 1 to 4 for index i′ 2  selected to report rank-4 CSI. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 18 
               
             
             
               
                   
               
               
                 Selected i′ 2  indices for rank-3 CSI reporting 
               
             
          
           
               
                   
                 Config 
                 Selected i′ 2  indices 
                 (s1, s2) 
                 (p 1 , p 2 ) 
               
               
                   
                   
               
               
                   
                 1 
                 0, 2 
                 (1, 1) 
                 (1, 1) 
               
               
                   
                   
               
               
                   
                 2 
                 0-7, 16-23 
                 (O 1 , O 2 ) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             2 
                           
                           , 
                           
                             
                               O 
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 3 
                 0-3, 8-11, 20-23, 28-31 
                 (O 1 , O 2 ) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             4 
                           
                           , 
                           
                             
                               O 
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 4 
                 0-15 
                 (O 1 , 2) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             4 
                           
                           , 
                           - 
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 19 
               
             
             
               
                   
               
               
                 Selected i′ 2  indices for rank-4 CSI reporting 
               
             
          
           
               
                   
                 Config 
                 Selected i′ 2  indices 
                 (s1, s2) 
                 (p 1 , p 2 ) 
               
               
                   
                   
               
               
                   
                 1 
                 0, 1 
                 (1, 1) 
                 (1, 1) 
               
               
                   
                   
               
               
                   
                 2 
                 0-3, 8-11 
                 (O 1 , O 2 ) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             2 
                           
                           , 
                           
                             
                               O 
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 3 
                 0-1, 4-5, 10-11, 14-15 
                 (O 1 , O 2 ) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             4 
                           
                           , 
                           
                             
                               O 
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 4 
                 0-7 
                 (O 1 , 2) 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               O 
                               1 
                             
                             4 
                           
                           , 
                           - 
                         
                         ) 
                       
                     
                   
                 
               
               
                   
                   
               
             
          
         
       
     
         [0113]    In the second embodiment of the present disclosure, a brand-new codebook may be generated using 
         [0000]    
       
         
           
             
               v 
               
                 m 
                 1 
               
             
             = 
             
               
                 
                   Q 
                   2 
                 
               
                
               
                 e 
                 
                   mod 
                    
                   
                     ( 
                     
                       
                         m 
                         1 
                       
                       , 
                       
                         
                           N 
                           p 
                         
                         / 
                         2 
                       
                     
                     ) 
                   
                 
                 
                   ( 
                   
                     
                       N 
                       p 
                     
                     / 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    and u m     2   =1 as beams for generating codebook assuming configuration 4 and δ 1 =1 and p 1 =1 in the codebook shown in Tables 18 and 19. Here, N p  denotes the number of antenna ports, and the e i   (N)  vector is a vector of N size in which the ith element is 1, and the other elements are 0&#39;s. 
         [0114]    Table 20 represents the 4Tx codebook generated for each of rank-3 and rank-4 generated based on the codebook shown in Tables 18 and 19. It is assumed in Table 20 below that the brand-new codebook starts from element index 0. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 Codebook 
                 Rank-3 
                 Rank-4 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
             
             
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 1 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 3 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 4 
                 — 
                 — 
               
               
                 5 
                 — 
                 — 
               
               
                 6 
                 — 
                 — 
               
               
                 7 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
         [0115]    Table 21 represents the 8Tx codebook generated for each of rank-3 and rank-4 generated based on the codebook shown in Tables 18 and 19. It is assumed in Table 21 below that the brand-new codebook starts from element index 0. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 21 
               
               
                   
               
               
                 Codebook 
                 Rank-3 
                 Rank-4 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 1 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 3 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   1 
                                 
                               
                               
                                 
                                   je 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     1 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 4 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 5 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   2 
                                 
                               
                               
                                 
                                   je 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     2 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 6 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 7 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   je 
                                   3 
                                 
                               
                               
                                 
                                   je 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     je 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 8 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 9 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 10 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 11 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 12 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 13 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 14 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
               
                 15 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 — 
               
               
                   
               
             
          
         
       
     
         [0116]    Other than the rank-3 and rank-4 codebook described above, rank-5, rank-6, rank-7, and rank-8 codebook as shown in Equation 9 below may be used in the future standard. 
         [0000]    
       
         
           
             
               W 
               
                 
                   i 
                   
                     1 
                     , 
                     1 
                   
                 
                 , 
                 
                   i 
                   
                     1 
                     , 
                     2 
                   
                 
               
               
                 ( 
                 5 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   
                     5 
                      
                     Q 
                   
                 
               
                
               
                 [ 
                 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
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                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
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                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
       
         
           
             
               W 
               
                 
                   i 
                   
                     1 
                     , 
                     1 
                   
                 
                 , 
                 
                   i 
                   
                     1 
                     , 
                     2 
                   
                 
               
               
                 ( 
                 6 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   
                     6 
                      
                     Q 
                   
                 
               
                
               
                 [ 
                 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
       
         
           
             
               W 
               
                 
                   i 
                   
                     1 
                     , 
                     1 
                   
                 
                 , 
                 
                   i 
                   
                     1 
                     , 
                     2 
                   
                 
               
               
                 ( 
                 7 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   
                     7 
                      
                     Q 
                   
                 
               
                
               
                 [ 
                 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
       
         
           
             
               W 
               
                 
                   i 
                   
                     1 
                     , 
                     1 
                   
                 
                 , 
                 
                   i 
                   
                     1 
                     , 
                     2 
                   
                 
               
               
                 ( 
                 8 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   
                     8 
                      
                     Q 
                   
                 
               
                
               
                 [ 
                 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     s 
                                     1 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   i 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       i 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                     
                                   
                                   + 
                                   
                                     δ 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   v 
                                   
                                     
                                       
                                         s 
                                         1 
                                       
                                        
                                       
                                         i 
                                         
                                           1 
                                           , 
                                           1 
                                         
                                       
                                     
                                     + 
                                     
                                       δ 
                                       
                                         1 
                                         , 
                                         3 
                                       
                                     
                                   
                                 
                               
                               ⊗ 
                             
                           
                         
                         
                           
                             
                               u 
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                    
                                   
                                     i 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 + 
                                 
                                   δ 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
         [0117]    Table 22 represents rank-5, rank-6, rank-7, and rank-8 codebook for δ 1,1 , δ 1,2 , δ 1,3 , δ 2,1 , δ 2,2 , and δ 2,3 . 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 22 
               
               
                   
                   
               
               
                   
                 i′ 2   
                 0 
               
               
                   
                   
               
             
             
               
                   
                 Precoder 
                 W s     1     i     1,1   ,  s     2     i     1,2     (r)   
               
               
                   
                   
               
             
          
         
       
     
         [0118]    An eNB or UE may designate an additional configuration as shown in Tables 23 and 24 based on the codebook shown in Table 22. The codeword of the codebook may be varied according to each configuration. 
         [0119]    Table 23 defines δ 1,1 , δ 1,2 , δ 1,3 , δ 2,1 , δ 2,2 , and δ 2,3  for 16 antenna ports. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 23 
               
               
                   
               
               
                 k 
                 Antenna configuration 
                 δ 1,1   
                 δ 2,1   
                 δ 1,2   
                 δ 2,2   
                 δ 1,3   
                 δ 2,3   
               
               
                   
               
             
             
               
                 k = 0 
                 N1 ≧ N2 
                 O 1   
                 0 
                 2O 1   
                 0 
                 3O 1   
                 0 
               
               
                   
                 N1 &lt; N2 
                 0 
                 O 2   
                 0 
                 2O 2   
                 0 
                 3O 2   
               
               
                 k = 1 
                 N1 ≧ N2 
                 O 1   
                 O 2   
                 2O 1   
                 0 
                 3O 1   
                 O 2   
               
               
                   
                 N1 &lt; N2 
                 O 1   
                 O 2   
                 0 
                 2O 2   
                 0 
                 3O 2   
               
               
                 k = 2 
                 Both 
                 O 1   
                 0 
                 O 1   
                 O 2   
                 0 
                 O 2   
               
               
                   
               
             
          
         
       
     
         [0120]    Table 24 defines δ 1,1 , δ 1,2 , δ 1,3 , δ 2,1,  δ 2,2 , and δ 2,3  for 12 antenna ports. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 24 
               
               
                   
               
               
                 Type 
                 Antenna configuration 
                 δ 1,1   
                 δ 2,1   
                 δ 1,2   
                 δ 2,2   
                 δ 1,3   
                 δ 2,3   
               
               
                   
               
             
             
               
                 Orthogonal 
                 N1 ≧ N2 
                 O 1   
                 0 
                 2O1 
                 0 
                 0 
                 O2 
               
               
                 beam type 0 
                 N1 &lt; N2 
                 0 
                 O2 
                 0 
                 2O2 
                 O1 
                 0 
               
               
                 Orthogonal 
                 N1 ≧ N2 
                 O1 
                 0 
                 2O1 
                 0 
                 O1 
                 O2 
               
               
                 beam type 1 
                 N1 &lt; N2 
                 0 
                 O2 
                 0 
                 2O2 
                 O1 
                 O2 
               
               
                 Orthogonal 
                 Both 
                 O1 
                 0 
                 O1 
                 O2 
                 0 
                 O2 
               
               
                 beam type 2 
               
               
                   
               
             
          
         
       
     
         [0121]    In the second embodiment of the present disclosure, a brand-new codebook may be generated using 
         [0000]    
       
         
           
             
               v 
               
                 m 
                 1 
               
             
             = 
             
               
                 
                   Q 
                   2 
                 
               
                
               
                 e 
                 
                   m 
                   1 
                 
                 
                   ( 
                   
                     
                       N 
                       p 
                     
                     / 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    and u m     2   =1 as beams for generating codebook assuming that δ 1,1 =1, δ 1,2 =2, and δ 1,3 =3 in the codebook shown in Table 22. Here, N p  denotes the number of antenna ports, and the e i   (N)  vector is a vector of N size in which the ith element is 1, and the other elements are 0&#39;s. 
         [0122]    Table 25 represents 8Tx codebook for each of rank-5, rank-6, rank-7, and rank-8 generated based on the codebook shown in Table 22. The codebook for each of rank-5, rank-6, rank-7, and rank-8 in the codebook lacks W2 feedback, and thus, one codeword is used for the codebook. This means that information on PMI need not be fed back when rank-5, rank-6, rank-7, and rank-8 feedbacks are made. It is assumed in Table 25 below that the brand-new codebook starts from element index 0. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 25 
               
               
                   
               
             
             
               
                 Codebook 
                 Rank-5 
                 Rank-6 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 1-15 
                 — 
                 — 
               
               
                   
               
               
                 Codebook 
                 Rank-7 
                 Rank-8 
               
               
                 index 
                 codebook 
                 codebook 
               
               
                   
               
               
                 0 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         
                           [ 
                           
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   0 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     0 
                                   
                                 
                               
                               
                                 
                                   e 
                                   1 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     1 
                                   
                                 
                               
                               
                                 
                                   e 
                                   2 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     2 
                                   
                                 
                               
                               
                                 
                                   e 
                                   3 
                                 
                               
                               
                                 
                                   - 
                                   
                                     e 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 1-15 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
         [0123]    Conditions for using the codebook shown in Tables 13,14,20,21,25 are as follows: 
         [0124]    1) When class B of CSI report type applies (e.g., CSI-Reporting-Type=‘Class B’) 
         [0125]    2) When only one CSI-RS resource is configured in UE (e.g., only one CSI-RS-ConfigNZPId configuration) 
         [0126]    3) When UE is instructed to use the codebook shown in Tables 13,14,20,21,25 (e.g., PMI-Config=1) 
         [0127]    Further, the future standard may use rank-5, rank-6, rank-7, and rank-8 codebook as shown in Tables 21 to 24. 
         [0128]    Table 26 represents rank-5 codebook when configuration 4 is used. In Table 26, i 1,1  and i 1,2  represent W1 codebook index, and i 2  represents W2 codebook index. 
         [0000]    
       
         
               
               
               
             
               
               
             
           
               
                   
                 TABLE 26 
               
               
                   
                   
               
               
                   
                   
                 i 2   
               
               
                   
                 i 1,1 , i 1,2   
                 0 
               
               
                   
                   
               
             
             
               
                   
                 0, 1, Λ, O 1 N 1  − 1 
                 W (i     1,1     ,i     1,2     ),(i     1,1     +O     1     ,i     1,2     ),(i     1,1     +2O     1     ,i     1,2     )   (5)   
               
               
                   
                 0, 1, Λ, O 2 N 2  − 1 
                   
               
               
                   
                   
               
             
          
           
               
                   
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                 
                                   
                                     where 
                                      
                                     
                                         
                                     
                                      
                                     
                                       W 
                                       
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                             
                                           
                                           ) 
                                         
                                         , 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ′ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ′ 
                                             
                                           
                                           ) 
                                         
                                         , 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ″ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ″ 
                                             
                                           
                                           ) 
                                         
                                       
                                       
                                         ( 
                                         5 
                                         ) 
                                       
                                     
                                   
                                   = 
                                 
                               
                             
                             
                               
                                 
                                   
                                     1 
                                     
                                       
                                         10 
                                          
                                         
                                           N 
                                           1 
                                         
                                          
                                         
                                           N 
                                           2 
                                         
                                       
                                     
                                   
                                    
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ′ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ′ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ″ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ″ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             - 
                                             
                                               v 
                                               
                                                 ( 
                                                 
                                                   
                                                     m 
                                                     1 
                                                   
                                                   , 
                                                   
                                                     m 
                                                     2 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ′ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           
                                             - 
                                             
                                               v 
                                               
                                                 ( 
                                                 
                                                   
                                                     m 
                                                     1 
                                                     ′ 
                                                   
                                                   , 
                                                   
                                                     m 
                                                     2 
                                                     ′ 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ″ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ″ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                             
                           
                             
                         
                       
                     
                   
                 
               
               
                   
                   
               
             
          
         
       
     
         [0129]    Table 27 represents rank-6 codebook when configuration 4 is used. In Table 20, i 1,1  and i 1,2  represent W1 codebook index, and i 2  represents W2 codebook index. 
         [0000]    
       
         
               
               
             
               
             
           
               
                 TABLE 27 
               
               
                   
               
               
                   
                 i 2   
               
               
                 i 1,1 , i 1,2   
                 0 
               
               
                   
               
             
             
               
                 0, 1, Λ, O 1 N 1  − 1 
                 W (i     1,1     ,i     1,2     ),(i     1,1     +O     1     ,i     1,2     ),(i     1,1     +2O     1     ,i     1,2     )   (6)   
               
               
                 0, 1, Λ, O 2 N 2  − 1 
                   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   where 
                                    
                                   
                                       
                                   
                                    
                                   
                                     W 
                                     
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ′ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ′ 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ″ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ″ 
                                           
                                         
                                         ) 
                                       
                                     
                                     
                                       ( 
                                       6 
                                       ) 
                                     
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   
                                     
                                       12 
                                        
                                       
                                         N 
                                         1 
                                       
                                        
                                       
                                         N 
                                         2 
                                       
                                     
                                   
                                 
                                 [ 
                                 
                                   
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ′ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ′ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ′ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ′ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ″ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ″ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ″ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ″ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ′ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ′ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     
                                       
                                         v 
                                         
                                           ( 
                                           
                                             
                                               m 
                                               1 
                                               ″ 
                                             
                                             , 
                                             
                                               m 
                                               2 
                                               ″ 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                          
                         
                             
                             
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0130]    Table 28 represents rank-7 codebook when configuration 4 is used. In Table 28, i 1,1  and i 1,2  represent W1 codebook index, and i 2  represents W2 codebook index. 
         [0000]    
       
         
               
               
             
               
             
           
               
                 TABLE 28 
               
               
                   
               
               
                   
                 i 2   
               
               
                 i 1,1 , i 1,2   
                 0 
               
               
                   
               
             
             
               
                 0, 1, Λ, O 1 N 1  − 1 
                 W (i     1,1     ,i     1,2     ),(i     1,1     +O     1     ,i     1,2     ),(i     1,1     +2O     1     ,i     1,2     ),(i     1,1     +3O     1     ,i     1,2     )   (7)   
               
               
                 0, 1, Λ, O 2 N 2  − 1 
                   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                 
                                   where 
                                    
                                   
                                       
                                   
                                    
                                   
                                     W 
                                     
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ′ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ′ 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ″ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ″ 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ′′′ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ′′′ 
                                           
                                         
                                         ) 
                                       
                                     
                                     
                                       ( 
                                       7 
                                       ) 
                                     
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   
                                     
                                       14 
                                        
                                       
                                         N 
                                         1 
                                       
                                        
                                       
                                         N 
                                         2 
                                       
                                     
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′′′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′′′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ′ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ″ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ″ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′′′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′′′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0131]    Table 29 represents rank-8 codebook when configuration 4 is used. In Table 29, i 1,1  and i 1,2  represent W1 codebook index, and i 2  represents W2 codebook index. 
         [0000]    
       
         
               
               
             
               
             
           
               
                 TABLE 29 
               
               
                   
               
               
                   
                 i 2   
               
               
                 i 1,1 , i 1,2   
                 0 
               
               
                   
               
             
             
               
                 0, 1, Λ, O 1 N 1  − 1 
                 W (i     1,1     ,i     1,2     ),(i     1,1     +O     1     ,i     1,2     ),(i     1,1     +2O     1     ,i     1,2     ),(i     1,1     +3O     1     ,i     1,2     )   (8)   
               
               
                 0, 1, Λ, O 2 N 2  − 1 
                   
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                 
                                   where 
                                    
                                   
                                       
                                   
                                    
                                   
                                     W 
                                     
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ′ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ′ 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ″ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ″ 
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         ( 
                                         
                                           
                                             m 
                                             1 
                                             ′′′ 
                                           
                                           , 
                                           
                                             m 
                                             2 
                                             ′′′ 
                                           
                                         
                                         ) 
                                       
                                     
                                     
                                       ( 
                                       8 
                                       ) 
                                     
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   
                                     
                                       16 
                                        
                                       
                                         N 
                                         1 
                                       
                                        
                                       
                                         N 
                                         2 
                                       
                                     
                                   
                                 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′′′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′′′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′′′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′′′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ′ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ″ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ″ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   1 
                                                   ″ 
                                                 
                                                 , 
                                                 
                                                   m 
                                                   2 
                                                   ″ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       
                                         
                                           v 
                                           
                                             ( 
                                             
                                               
                                                 m 
                                                 1 
                                                 ′′′ 
                                               
                                               , 
                                               
                                                 m 
                                                 2 
                                                 ′′′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             v 
                                             
                                               ( 
                                               
                                                 
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                                                   1 
                                                   ′′′ 
                                                 
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                                                   2 
                                                   ′′′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
         
       
     
         [0132]    In the second embodiment of the present disclosure, a brand-new codebook may be generated using 
         [0000]    
       
         
           
             
               v 
               
                 m 
                 1 
               
             
             = 
             
               
                 
                   Q 
                   2 
                 
               
                
               
                 e 
                 
                   m 
                   1 
                 
                 
                   ( 
                   
                     
                       N 
                       p 
                     
                     / 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    and u m     2   =1 as beams for generating codebook assuming O1=1 in the codebook shown in Tables 26 and 29. Here, N p  denotes the number of antenna ports, and the e i   (N)  vector is a vector of N size in which the ith element is 1, and the other elements are 0&#39;s. 
         [0133]    When 
         [0000]    
       
         
           
             
               v 
               
                 m 
                 1 
               
             
             = 
             
               
                 
                   Q 
                   2 
                 
               
                
               
                 e 
                 
                   m 
                   1 
                 
                 
                   ( 
                   
                     
                       N 
                       p 
                     
                     / 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    and u m     2   =1 are utilized as beams for generating codebook under the assumption that O 1 =1, an 8Tx codebook for each of rank-5, rank-6, rank-7, and rank-8 as shown in Table 25 may be generated. The codebook for each of rank-5, rank-6, rank-7, and rank-8 in the codebook lacks W2 feedback, and thus, one codeword is used for the codebook. This means that information on PMI need not be fed back when rank-5, rank-6, rank-7, and rank-8 feedbacks are made. 
       Third Embodiment 
       [0134]    scheme for generating feedback information other than PMI 
         [0135]    According to a third embodiment of the present disclosure, a scheme for generating feedback information other than PMI is described. 
         [0136]    In one embodiment, the system may assume the following feedback or may indicate the same to the terminal in order to feedback W1 codebook index. 
         [0137]    1) stop UE from performing W1 feedback 
         [0138]    2) allow UE to feedback particular W1 index (e.g., feedback “0” as W1 information) 
         [0139]    3) in order to instruct the 2) UE operation above, eNB instructs UE to do codebook subset restriction for the operation 
         [0140]    In another embodiment, in order to feed back a precoding type indicator (PTI), a relevant system may assume the following feedback or instruct UE to do the feedback. 
         [0141]    1) stop UE from performing PTI feedback 
         [0142]    2) allow UE to feedback particular PTI index (e.g., always feedback “1” as PTI information) 
         [0143]    3) in order to instruct the 2) UE operation above, eNB instructs UE to do codebook subset restriction on W1 codebook for the operation. In this case, the W1 codebook available to UE is limited to one value, and resultantly, UE always feeds back “1” as PTI information. 
         [0144]    According to an embodiment of the present disclosure, a communication system may use a legacy codebook or a brand-new codebook generated by a brand-new scheme as suggested herein when generating feedback information on downlink reference signal. Accordingly, eNB transmits control information indicating whether the brand-new codebook is used when generating feedback information to UE before transmitting the reference signal to UE. Here, the control information may be designed in the format as shown in Table 30 below. 
         [0000]    
       
         
               
               
             
           
               
                 TABLE 30 
               
               
                   
               
             
             
               
                 AntennaInfoDedicated-r1x ,,= 
                 SEQUENCE { 
               
               
                 alternativeCodebookEnabled-r1x  
                 BOOLEAN or ENUMERATED or BIT  
               
               
                   
                 STRING  
               
               
                 } 
               
               
                   
               
             
          
         
       
     
         [0145]    That is, the control information shown in Table 30 contains a field indicating whether the brand-new codebook is used to generate CSI feedback. When rring the control information, UE may use the legacy codebook or brand-new codebook according to the value indicated by the field contained in the control information. 
         [0146]    As another example, eNB transmits control information indicating the type of reference signal to UE before transmitting the reference signal. The type of reference signal includes type 1 and type 2, and type 1 denotes that the reference signal is not beamformed, and type 2 denotes that the reference signal is beamformed. Here, the control information may be designed in the format as shown in Table 31 below. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 31 
               
               
                   
                   
               
             
             
               
                   
                 NZP-CSI-RS-r1x ,,= 
                 SEQUENCE { 
               
               
                   
                 CSI-RS-Type-r1x 
                  {Class A, Class B} 
               
               
                   
                 } 
               
               
                   
                   
               
             
          
         
       
     
         [0147]    According to an embodiment of the present disclosure, the brand-new codebook has a high chance of being used in UE receiving BF-CSI-RS. Accordingly, when information on CSI-RS type is delivered to UE as shown in Table 31, UE may determine a codebook to be used for generating CSI feedback based on the CSI-RS type information. That is, when receiving control information containing type 1-related information, UE generates CSI feedback using the legacy codebook, and upon receiving control information including type 2-related information, UE generates CSI feedback using the brand-new codebook. 
         [0148]      FIG. 3  is a flowchart illustrating an example of operation of a beamformed reference signal by a base station in a communication system according to an embodiment of the present disclosure. Described in connection with  FIG. 3  is an operation in which eNB generates first beamforming information using SRS received from UE. 
         [0149]    Referring to  FIG. 3 , in operation  301 , eNB transmits, to UE, control information containing a field indicating whether a first codebook is used for generating CSI feedback. Here, the field contained in the control information is assumed to indicate that the first codebook, i.e., a brand-new codebook, is used for generating CSI feedback. 
         [0150]    In operation  305 , eNB waits to receive SRS periodically transmitted from UE, eNB goes to operation  307  to determine whether SRS is received. When it is determined in operation  307  that unless SRS is received, eNB goes to operation  305  to wait to receive SRS. When it is determined in operation  307  that SRS is received, eNB goes to operation  309  to determine first beamforming information based on the received SRS information. That is, eNB determines the first beamforming information by performing per-UE precoding on the received SRS information. In operation  311 , eNB transmits, to UE, a BF-CSI-RS having beamforming information applied thereto based on the first beamforming information. 
         [0151]    In operation  313 , eNB waits to receive feedback information on the BF-CSI-RS transmitted in operation  311 , e.g., a CSI report, and goes to operation  315  to determine whether the CSI report is received. When the CSI report is not determined to be received, eNB goes to operation  313  to wait to receive the CSI report, and when the CSI report is received, eNB goes to operation  317  to determine second beamforming information based on CSI report information. That is, eNB compensates for RI and CQI based on the CSI report and performs precoding adjustment to determine the second beamforming information. 
         [0152]    In operation  319 , eNB transmits, to UE, data having beamforming information applied thereto based on the second beamforming information. 
         [0153]      FIG. 4  is a flowchart illustrating an example of operation of a beamformed reference signal by a base station in a communication system according to an embodiment of the present disclosure. Described in connection with  FIG. 4  is an operation in which eNB generates first beamforming information using beamforming information received corresponding to a CSI-RS transmitted at a long period. 
         [0154]    Referring to  FIG. 4 , in operation  401 , eNB transmits, to UE, control information containing a field indicating whether a first codebook derives CSI feedback and is used for a report for a CSI process. Here, the field contained in the control information is assumed to indicate that the first codebook, i.e., a brand-new codebook, derives the CSI feedback and is used for a report for a CSI process. 
         [0155]    In operation  403 , eNB transmits a long term CSI-RS transmitted at a long period to UE and goes to operation  405  to wait to receive feedback information transmitted corresponding to the long-term CSI-RS. 
         [0156]    In operation  407 , eNB determines whether feedback information is received, and when no feedback information is received, eNB goes to operation  405  to wait to receive feedback information. When it is determined in operation  407  that the feedback information is received, eNB goes to operation  409  to determine first beamforming information based on the received feedback information. That is, eNB determines the first beamforming information by performing per-UE precoding on the received feedback information. In operation  411 , eNB transmits, to UE, a BF-CSI-RS having beamforming information applied thereto based on the first beamforming information. 
         [0157]    In operation  413 , eNB waits to receive feedback information on the BF-CSI-RS transmitted in operation  411 , e.g., a CSI report, and goes to operation  415  to determine whether the CSI report is received. When the CSI report is not determined to be received, eNB goes to operation  413  to wait to receive the CSI report, and when the CSI report is received, eNB goes to operation  417  to determine second beamforming information based on CSI report information. That is, eNB compensates for RI and CQI based on the CSI report and performs precoding adjustment to determine the second beamforming information. 
         [0158]    In operation  419 , eNB transmits, to UE, data having beamforming information applied thereto based on the second beamforming information. 
         [0159]      FIG. 5  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure. 
         [0160]    Referring to  FIG. 5 , in operation  501 , UE receives, from eNB, control information containing a field indicating whether a first codebook, i.e., brand-new codebook, is used for generating CSI feedback. In operation  503 , UE obtains codebook-related information indicated by the field contained in the control information. That is, UE obtains information indicating whether the brand-new codebook is used for generating CSI feedback. 
         [0161]    In operation  505 , UE receives beamforming information-applied BF-CSI-RS from eNB and estimates channel based on the received BF-CSI-RS. 
         [0162]    In operation  507 , UE configures feedback information on BF-CSI-RS, e.g., CSI, based on the codebook-related information obtained in operation  503 . That is, when the codebook-related information obtained in operation  503  indicates that the brand-new codebook is used for generating CSI feedback, UE configures a CSI based on the brand-new codebook, and when the codebook-related information indicates that the brand-new codebook is not used for generating CSI feedback, UE configures a CSI based on the legacy codebook. 
         [0163]    In operation  509 , UE transmits the CSI configured in operation  507  to eNB and goes to operation  511  to receive data from eNB. 
         [0164]      FIG. 6  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure. 
         [0165]    Referring to  FIG. 6 , in operation  601 , UE receives, from eNB, control information containing a field indicating whether a first codebook, i.e., brand-new codebook, is used for generating CSI feedback. In operation  603 , UE determines whether the brand-new codebook is used for generating CSI feedback based on the field information contained in the control information. 
         [0166]    When it is determined in operation  603  that the field contained in the control information indicates that the brand-new codebook is used for generating CSI feedback, UE goes to operation  605  to receive a beamforming information-applied BF-CSI-RS from eNB and estimates channel based on the received BF-CSI-RS. 
         [0167]    In operation  607 , UE configures feedback information on the BF-CSI-RS, e.g., CSI information, based on the brand-new codebook and goes to operation  609  to transmit the CSI information configured in operation  607 . 
         [0168]    On the other hand, when it is determined in operation  603  that the field contained in the control information indicates that the brand-new codebook is not used for generating CSI feedback, UE goes to operation  613  to receive a non-beamformed CSI-RS from eNB and estimates channel based on the received CSI-RS. Here, the non-beamformed CSI-RS means non-precoded CSI-RS. 
         [0169]    In operation  615 , UE configures feedback information on the BF-CSI-RS, e.g., CSI information, based on the legacy codebook and goes to operation  609  to transmit the CSI information configured in operation  615 . 
         [0170]    Thereafter, in operation  611 , UE receives data from eNB. 
         [0171]      FIG. 7  is a flowchart illustrating an example of operation of a beamformed reference signal by a terminal in a communication system according to an embodiment of the present disclosure. 
         [0172]    Referring to  FIG. 7 , in operation  701 , UE receives control information containing reference signal type information from eNB. Here, reference signal type information includes type 1 information indicating that reference signal is not beamformed and type 2 information indicating that reference signal is beamformed. 
         [0173]    In operation  703 , UE determines whether control information includes type 1 information or type 2 information, and when the control information includes type 1 information, UE goes to operation  705  to receive a type 1 reference signal, i.e., a non-beamformed reference signal, and estimates channel based on the received reference signal. 
         [0174]    In operation  707 , UE configures feedback information on the reference signal, e.g., CSI information, based on the legacy codebook and goes to operation  709  to transmit the CSI information configured in operation  707 . 
         [0175]    On the other hand, when it is determined in operation  703  that the control information includes type 2 information, UE goes to operation  713  to receive a type 2 reference signal, i.e., a beamformed BF-CSI-RS and estimates channel based on the received BF-CSI-RS. 
         [0176]    In operation  715 , UE configures feedback information on the BF-CSI-RS, e.g., CSI information, based on the brand-new codebook and goes to operation  709  to transmit the CSI information configured in operation  715 . 
         [0177]    Thereafter, in operation  711 , UE receives data from eNB. 
         [0178]      FIG. 8  is a view illustrating an internal configuration of a terminal operating a beamformed reference signal in a communication system according to an embodiment of the present disclosure. 
         [0179]    Referring to  FIG. 8 , a UE  800  as shown includes a controller  810 , a communication unit  820 , and a storage unit  830 , and controller  810  includes a reference signal detector  801  and a feedback information generator  803 . 
         [0180]    Controller  810  controls the overall operation of UE  800 . In particular, controller  810  controls UE  800  to perform the overall operation related to operation of beamformed reference signal according to an embodiment of the present disclosure. Further, reference signal detector  801  in controller  810  detects a reference signal from an eNB, and feedback information generator  803  generates feedback information on the reference signal. Here, the same description given above in connection with  FIGS. 1 and 5 to 7  applies to operation of the beamformed reference signal, and no further detailed description is given below. 
         [0181]    Communication unit  820  transmits and receives various messages under the control of controller  810 . Here, the same description given above in connection with  FIGS. 1 and 5 to 7  applies to various messages transmitted/received by communication unit  820 , and no further detailed description is given below. 
         [0182]    Storage unit  830  stores various information generated from UE  800 . Here, the same description given above in connection with  FIGS. 1 and 5 to 7  applies to various information stored in storage unit  830 , and no further detailed description is given below. 
         [0183]      FIG. 9  is a view illustrating an internal configuration of a base station operating a beamformed reference signal in a communication system according to an embodiment of the present disclosure. 
         [0184]    Referring to  FIG. 9 , an eNB  900  as shown includes a controller  910 , a communication unit  920 , and a storage unit  930 , and controller  910  includes a beamforming information generator  901 , a RI/CQI/precoding adjuster  903 , and a beamforming information applier  905 . 
         [0185]    Controller  910  controls the overall operation of eNB  900 . In particular, controller  910  controls eNB  900  to perform the overall operation related to operation of beamformed reference signal according to an embodiment of the present disclosure. Further, beamforming information generator  901  in controller  910  generates per-UE beamforming information, RI/CQI/precoding adjuster  903  compensates for RI and CQI based on a CSI received from a UE and performs precoding adjustment, and beamforming information applier  905  applies beamforming information to CSI-RS and/or data transmitted to UE. Here, the same description given above in connection with  FIGS. 1, 3, and 4  applies to operation of the beamformed reference signal, and no further detailed description is given below. 
         [0186]    Communication unit  920  transmits and receives various messages under the control of controller  910 . Here, the same description given above in connection with  FIGS. 1, 3, and 4  applies to various messages transmitted/received by communication unit  920 , and no further detailed description is given below. 
         [0187]    Storage unit  930  stores various information generated from eNB  900 . Here, the same description given above in connection with  FIGS. 1, 3, and 4  applies to various information stored in storage unit  930 , and no further detailed description is given below. 
         [0188]    Particular aspects of the present disclosure may be implemented in computer-readable codes on a computer-readable recording medium. The computer readable recording medium is a data storage device that may store data readable by a computer system. Examples of the computer readable recording medium may include read only memories (ROMs), random access memories (RAMs), compact disk-read only memories (CD-ROMs), magnetic tapes, floppy disks, optical data storage devices, and carrier waves (such as data transmission over the Internet). The computer readable recording medium may be distributed by computer systems over a network, and accordingly, the computer readable codes may be stored and executed in a distributed manner. Functional programs, codes, and code segments to attain the present disclosure may be readily interpreted by skilled programmers in the art to which the present disclosure pertains. 
         [0189]    The apparatuses and methods according to various embodiments of the present disclosure may be implemented in hardware, software, or a combination of hardware and software. Such software may be recorded in volatile or non-volatile storage devices, such as ROMs, memories, such as RAMs, memory chips, memory devices, or integrated circuit devices, compact disks (CDs), DVDs, magnetic disks, magnetic tapes, or other optical or magnetic storage devices while retained in machine (e.g., computer)-readable storage media. The methods according to various embodiments of the present disclosure may be implemented by a computer or a portable terminal including a controller and a memory, and the memory may be a machine-readable storage medium that may properly retain program(s) containing instructions for implementing the various embodiments of the present disclosure. 
         [0190]    Accordingly, the present disclosure encompasses a program containing codes for implementing the device or method set forth in the claims of this disclosure and a machine (e.g., computer)-readable storage medium storing the program. The program may be electronically transferred via any media such as communication signals transmitted through a wired or wireless connection and the present disclosure properly includes the equivalents thereof. 
         [0191]    The apparatuses according to various embodiments of the present disclosure may receive the program from a program providing device wired or wirelessly connected thereto and store the same. The program providing apparatus may include a memory for storing a program including instructions enabling a program processing apparatus to perform a method according to an embodiment of the present disclosure and data necessary for a method according to an embodiment of the present disclosure, a communication unit for performing wired or wireless communication with a graphic processing apparatus, and a controller transmitting the program to the graphic processing apparatus automatically or as requested by the graphic processing apparatus. 
         [0192]    While the present disclosure has been shown and described with reference to various embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present disclosure as defined by the appended claims and their equivalents.