Patent Publication Number: US-8526538-B2

Title: Uplink precoding method in 4-Tx system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Pursuant to 35 U.S.C. 119, this application claims the benefit of earlier filing date and right of priority to Korean Patent Application No. 10-2009-0127920, filed on Dec. 21, 2009, and also claims the benefit of U.S. Provisional Application Nos. 61/152,476, 61/153,943, 61/156,544, 61/163,056, 61/171,071, 61/176,094 and 61/218,437, filed on Feb. 13, 2009, Feb. 19, 2009, Mar. 2, 2009, Mar. 25, 2009, Apr. 20, 2009, May 6, 2009 and Jun. 19, 2009, respectively, the contents of which are all hereby incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a technology for transmitting/receiving signals through precoding in a mobile communication system, and more particularly, to a method for a user equipment to precode and transmit an uplink signal efficiently in a 4-antenna system and a method for a base station to receive the transmitted signal efficiently. 
     2. Discussion of the Related Art 
     In a multi-antenna or MIMO system, precoding provides high peak/average system throughput by providing a beamforming gain and a diversity gain to a transmitting/receiving side. Yet, a precoding scheme needs to be appropriately designed in consideration of antenna setting, channel configuration, system structure and the like. 
     Generally, an MIMO system performs precoding to minimize complexity and control signaling overhead using a codebook based precoding scheme. In this case, a codebook includes a scribed number of precoding vectors/matrixes predetermined between transmitting and receiving sides according to a transmission rank and the number of antennas. The transmitting side selects a specific vector/matrix within the codebook according to channel status information received from the receiving side, perform precoding on a transmission signal, and then transmits the precoded signal. Occasionally, the transmitting side selects a precoding matrix according to a predetermined rule instead of receiving the channel status information from the receiving side, performs precoding and is then able to transmit a corresponding signal. 
       FIG. 1  is a diagram for explaining a basic concept of codebook based precoding. 
     According to a codebook based precoding scheme, as mentioned in the foregoing description, a transmitting side and a receiving side share codebook information including a prescribed number of precoding matrixes predetermined according to a transmission rank, the number of antennas and the like with each other. The receiving side measures a channel status via a received signal and is then able to feed back preferred precoding matrix information to the transmitting side based on the aforesaid codebook information.  FIG. 1  shows that the receiving side transmits preferred precoding matrix information per codeword to the transmitting side, for example. 
     Having received the feedback information from the receiving side, the transmitting side is able to select a specific precoding matrix from the codebook based on the received information. Having selected the precoding matrix, the transmitting side performs precoding in a manner of multiplying layer signals, of which number corresponds to a transmission rank, by the selected precoding matrix. And, the transmitting side is able to transmit the precoded transmission signal via a plurality of antennas. Having received the signal precoded and transmitted by the transmitting side, the receiving side is able to reconstruct the received signal by performing a process reverse to the precoding performed by the transmitting side. As a precoding matrix generally meets such a condition of a unitary matrix (U) as U*U H =I, the reverse processing of the above precoding can be performed in a manner of multiplying a received signal by Hermitian (P H ) of a precoding matrix (P) used for the precoding of the transmitting side. 
     In LTE (3 RD  Generation Partnership Project Long Term Evolution) release 8 system, in case of applying MIMO scheme to an uplink signal transmission to a base station from a user equipment, an MIMO transmission scheme is prescribed for a downlink signal transmission from a base station to a user equipment only due to such a problem as PAPR/CM (peak-to-average ratio/cubic metric) property degradation and the like. Yet, an uplink signal transmitted by a user equipment to a base station is ongoing to be discussed in a direction of applying MIMO scheme for transmission rate increase, diversity gain acquisition and the like. And, a next standard of 3GPP LTE system is ongoing to discuss about a detailed method of applying MIMO scheme to an uplink signal transmission. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention is directed to an uplink precoding method in 4 Tx system that substantially obviates one or more problems due to limitations and disadvantages of the related art. 
     An object of the present invention is to provide a codebook for uplink precoding, and more particularly, a codebook suitable for a user equipment to precode and transmit a signal efficiently using 4 antennas. 
     Another object of the present invention is to provide a method of transmitting a signal to a base station from a user equipment using 4 antennas. 
     The technical objects realized and attained by the present invention are non-limited to the above mentioned objects. And, other unmentioned technical tasks can be taken into consideration by those having ordinary skill in the art, to which the present invention pertains, upon examination of the following embodiments of the present invention. 
     To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method of transmitting a signal, which is transmitted to a base station by a user equipment configured to use 4 antennas, according to the present invention includes the steps of obtaining transmission rank information, outputting a precoded signal by selecting one precoding matrix corresponding to the transmission rank from a 4-antenna codebook and then performing precoding on layer signals of which number corresponds to the transmission rank, and transmitting the precoded signal to the base station, wherein the 4 antennas are grouped into a first antenna group including two of the 4 antennas and a second antenna group including the rest of the 4 antennas and wherein the 4-antenna codebook includes a first type precoding matrix, in which two components corresponding to the first antenna group are zero and two components corresponding to the second antenna group construct a DFT matrix, and a second type precoding matrix, in which two components corresponding to the first antenna group and two components corresponding to the second antenna group construct DFT matrixes, respectively, for a rank 1. 
     Preferably, the first type precoding matrix is an antenna group selection matrix and wherein the second type precoding matrix is a DFT matrix. 
     Preferably, the second type precoding matrix includes a code in which the two components corresponding to the first antenna group and the two components corresponding to the second antenna group are mutually orthogonal. 
     Preferably, the 4-antenna codebook includes a precoding matrix, in which two components corresponding to either the first antenna group or the second antenna group are 0 in a first column and two components corresponding to either the second antenna group or the first antenna group are 0 in a second column, for a rank 2. 
     More preferably, the 4-antenna codebook includes at least one selected from the group consisting of a precoding matrix for performing a layer swapping function of changing positions of two layer signals and an antenna permutation precoding matrix for changing a position of an antenna, for the rank 2. 
     In another aspect of the present invention, a method of transmitting a signal, which is transmitted to a base station by a user equipment using 4 antennas, includes the steps of obtaining transmission rank information, outputting a precoded signal by selecting one precoding matrix corresponding to the transmission rank from a 4-antenna codebook including a first type precoding matrix of 4*3 matrix type including 2 non-zero components in each row for a rank 3 and 2 zero components in first and second columns and then performing precoding on layer signals of which number corresponds to the transmission rank and transmitting the precoded signal to the base station. 
     Preferably, the first type precoding matrix has a type of 
                 W       N   t     ×   3     n     =     [             v   _     i           z   _             v   _     k               z   _             v   _     j           v   l           ]       ,           ν   i ,  ν   k ,  ν   j  and  ν   l  are 2*1 vectors including non-zero components only, and  z  is 2*1 vector including zero components only.
 
     More preferably, the  ν   i  and the  ν   k  are mutually orthogonal and the  ν   j  and the  ν   l  are mutually orthogonal. In this case, if a normalization coefficient for the  ν   i  and the  ν   j  is set to 1/√{square root over (α)} and a normalization coefficient for the  ν   k  and the  ν   l  is set to 1/√{square root over (β)}, it meets α=2β. If a normalization coefficient for the  ν   i  and the  ν   j  is set to 1/√{square root over (α)} and a normalization coefficient for the  ν   k  and the  ν   l  is set to 1/√{square root over (β)}, it meets α=β. 
     Preferably, the first type precoding matrix has a type resulting from multiplying 
               W       N   t     ×   3     n     =       [         1       0       1             ⅇ     jθ   1           0         -     ⅇ     jθ   1                 0       1       1           0         ⅇ     jθ   2             -     ⅇ     jθ   2               ]     ⁢           ⁢   or                   W       N   t     ×   3     n     =     [         1       0       1             -     ⅇ     jθ   1             0         ⅇ     jθ   1               0         ⅇ     jθ   2             ⅇ     jθ   2               0         -     ⅇ     jθ   3               ⅇ     jθ   3             ]           
by a normalization coefficient, the N t  is 4, the θ 1 , θ 2  meet a condition of
 
                 θ   2     ∈     {           2   ⁢   π     N     ⁢   i     ,     i   =   0     ,   …   ⁢           ,     N   -   1       }       ,         
and the N is set to 4 or 8.
 
     Preferably, the 4-antenna codebook further includes a second type precoding matrix of a 4*3 type including one non-zero component in each row. 
     More preferably, the second type precoding matrix has a type resulting from multiplying 
               W       N   t     ×   3     n     =     [         1       0       0           0       1       0           0       0       1           0       0         ⅇ   jθ           ]           
by a normalization coefficient, the N t  is 4, the θ meets a condition of
 
               θ   ∈     {           2   ⁢   π     N     ⁢   i     ,     i   =   0     ,   …   ⁢           ,     N   -   1       }       ,         
and the N is set to 4 or 8. In this case, the second type precoding matrix has a type multiplied by either a coefficient for inter-antenna power normalization or inter-layer power normalization.
 
     In another aspect of the present invention, a method of receiving a signal, which is received by a base station from a user equipment configured to use 4 antennas, includes the steps of receiving a reception signal from the user equipment, obtaining transmission rank and precoding matrix identification information used by the user equipment for the reception signal transmission, and performing reverse processing of precoding on the reception signal by selecting one precoding matrix corresponding to the transmission rank and precoding matrix identification information from a 4-antenna codebook, wherein the 4 antennas are grouped into a first antenna group including two of the 4 antennas and a second antenna group including the rest of the 4 antennas and wherein the 4-antenna codebook includes a first type precoding matrix, in which two components corresponding to the first antenna group are zero and two components corresponding to the second antenna group construct a DFT matrix, and a second type precoding matrix, in which two components corresponding to the first antenna group and two components corresponding to the second antenna group construct DFT matrixes, respectively, for a rank 1. 
     In another aspect of the present invention, a method of receiving a signal, which is received by a base station from a user equipment using 4 antennas, includes the steps of receiving a reception signal from the user equipment, obtaining transmission rank and precoding matrix identification information used by the user equipment for the reception signal transmission, and performing reverse processing of precoding on the reception signal by selecting one precoding matrix corresponding to the transmission rank and precoding matrix identification information from a 4-antenna codebook including a first type precoding matrix of 4*3 matrix type including 2 non-zero components in each row for a rank 3 and 2 zero components in first and second columns. 
     In another aspect of the present invention, a user equipment includes a first antenna group including a first antenna and a second antenna, a second antenna group including a third antenna and a fourth antenna, a memory configured to store a 4-antenna codebook including a first type precoding matrix, in which two components corresponding to the first antenna group are zero and two components corresponding to the second antenna group construct a DFT matrix, and a second type precoding matrix, in which two components corresponding to the first antenna group and two components corresponding to the second antenna group construct DFT matrixes, respectively, for a rank 1, and a precoder outputting a signal precoded by selecting one precoding matrix corresponding to a transmission rank from the 4-antenna codebook stored in the memory and then performing precoding on layer signals of which number corresponds to the transmission rank, wherein the signal precoded by the precoder is transmitted to a base station via at least one selected from the group consisting of the first antenna group and the second antenna group. 
     In another aspect of the present invention, a user equipment includes a memory configured to store a 4-antenna codebook including a first type precoding matrix of 4*3 matrix type including 2 non-zero components in each row for a rank 3 and 2 zero components in first and second columns, a precoder outputting a precoded signal by selecting one precoding matrix corresponding to the transmission rank from the 4-antenna codebook, the precoder performing precoding on layer signals of which number corresponds to the transmission rank, and four antennas configured to transmit the signal precoded by the precoder to a base station. 
     In another aspect of the present invention, a base station includes an antenna configured to receive a reception signal transmitted from a user equipment configured to transmit a signal using four antennas grouped into a first antenna group including two of the 4 antennas and a second antenna group including the rest of the 4 antennas, a memory configured to store a 4-antenna codebook including a first type precoding matrix, in which two components corresponding to the first antenna group are zero and two components corresponding to the second antenna group construct a DFT matrix, and a second type precoding matrix, in which two components corresponding to the first antenna group and two components corresponding to the second antenna group construct DFT matrixes, respectively, for a rank 1, and a precoder performing reverse processing of precoding on the reception signal by selecting one precoding matrix corresponding to transmission rank and precoding matrix identification information used by the user equipment from the 4-antenna codebook. 
     In another aspect of the present invention, a base station includes an antenna configured to receive a reception signal transmitted from a user equipment configured to use four antennas, a memory configured to store a 4-antenna codebook including a first type precoding matrix of 4*3 matrix type including 2 non-zero components in each row for a rank 3 and 2 zero components in first and second columns, and a precoder performing reverse processing of precoding on the reception signal received via the antenna by selecting one precoding matrix corresponding to transmission rank and precoding matrix identification information used by the user equipment from the 4-antenna codebook stored in the memory. 
     Besides, it is apparent that the above-mentioned embodiments for the rank 1, rank 2 and rank 3 of the 4-antenna codebook are usable in a manner of being combined into a type including a prescribed number of precoding matrixes for each of the ranks in one codebook. 
     Accordingly, the present invention provides the following effects and/or advantages. 
     First of all, if a codebook according to one of embodiments of the present invention is used, it is able to efficiently perform a transmission control per antenna group. 
     Secondly, in uplink signal transmission, the present invention is able to maintain a sensitive PAPR/CM property well. 
     Effects attainable from the embodiments of the present invention are non-limited to the above-mentioned effects. Other unmentioned effects can be clearly derived and understood from the description of the following embodiments of the present invention by those having ordinary skill in the art to which the present invention pertains. Namely, effects unintended in the application stage of the present invention can be derived from the embodiments of the present invention by those having ordinary skill in the art to which the present invention pertains. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principle of the invention. In the drawings: 
         FIG. 1  is a diagram for explaining a basic concept of codebook based precoding; 
         FIG. 2  is a diagram for explaining ULA antenna setup and X-pol antenna setup; 
         FIG. 3  is a diagram for explaining general SC-FDMA; 
         FIG. 4  is a diagram for detailed configuration of a processor of a user equipment according to one embodiment of the present invention; and 
         FIG. 5  is a diagram for configurations of a base station and a user equipment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. In the following detailed description of the invention includes details to help the full understanding of the present invention. Yet, it is apparent to those skilled in the art that the present invention can be implemented without these details. For instance, the following description is made with reference to predetermined terminologies, by which the present invention is non-limited. Even if an arbitrary terminology is used, it can have the same meaning of the predetermined terminology. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. 
     In the following description, ‘rank’ indicates the number of paths for carrying signals independently and ‘the number of layers’ indicates the number of signal streams transmitted via each path. Generally, as a transmitting side transmits layers of which number corresponds to the rank number used for signal transmission, a rank has the same meaning of the layer number (i.e., the number of layers) unless there is a special note. In a precoding matrix, assume that a row corresponds to each antenna and that a column corresponds to a rank or each layer signal. 
     Table 1 shows 4-antenna codebook structure in LTE release 8. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Codebook 
                   
                 Number of layers υ 
               
            
           
           
               
               
               
               
               
               
            
               
                 index 
                 u n   
                 1 
                 2 
                 3 
                 4 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 u 0  = [1 −1 −1 −1] T   
                 W 0   {1}   
                 W 0   {14} /{square root over (2)} 
                 W 0   {124} /{square root over (3)} 
                 W 0   {1234} /2 
               
               
                 1 
                 u 1  = [1 −j 1 j] T   
                 W 1   {1}   
                 W 1   {12} /{square root over (2)} 
                 W 1   {123} /{square root over (3)} 
                 W 1   {1234} /2 
               
               
                 2 
                 u 2  = [1 1 −1 1] T   
                 W 2   {1}   
                 W 2   {12} /{square root over (2)} 
                 W 2   {123} /{square root over (3)} 
                 W 2   {3214} /2 
               
               
                 3 
                 u 3  = [1 j 1 −j] T   
                 W 3   {1}   
                 W 3   {12} /{square root over (2)} 
                 W 3   {123} /{square root over (3)} 
                 W 3   {3214} /2 
               
               
                 4 
                 u 4  = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}] T   
                 W 4   {1}   
                 W 4   {14} /{square root over (2)} 
                 W 4   {124} /{square root over (3)} 
                 W 4   {1234} /2 
               
               
                 5 
                 u 5  = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}] T   
                 W 5   {1}   
                 W 5   {14} /{square root over (2)} 
                 W 5   {124} /{square root over (3)} 
                 W 5   {1234} /2 
               
               
                 6 
                 u 6  = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}] T   
                 W 6   {1}   
                 W 6   {13} /{square root over (2)} 
                 W 6   {134} /{square root over (3)} 
                 W 6   {1324} /2 
               
               
                 7 
                 u 7  = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}] T   
                 W 7   {1}   
                 W 7   {13} /{square root over (2)} 
                 W 7   {134} /{square root over (3)} 
                 W 7   {1324} /2 
               
               
                 8 
                 u 8  = [1 −1 1 1] T   
                 W 8   {1}   
                 W 8   {12} /{square root over (2)} 
                 W 8   {124} /{square root over (3)} 
                 W 8   {1234} /2 
               
               
                 9 
                 u 9  = [1 −j −1 −j] T   
                 W 9   {1}   
                 W 9   {14} /{square root over (2)} 
                 W 9   {134} /{square root over (3)} 
                 W 9   {1234} /2 
               
               
                 10 
                 u 10  = [1 1 1 −1] T   
                 W 10   {1}   
                 W 10   {13} /{square root over (2)} 
                 W 10   {123} /{square root over (3)} 
                 W 10   {1324} /2 
               
               
                 11 
                 u 11  = [1 j −1 j] T   
                 W 11   {1}   
                 W 11   {13} /{square root over (2)} 
                 W 11   {134} /{square root over (3)} 
                 W 11   {1324} /2 
               
               
                 12 
                 u 12  = [1 −1 −1 1] T   
                 W 12   {1}   
                 W 12   {12} /{square root over (2)} 
                 W 12   {123} /{square root over (3)} 
                 W 12   {1234} /2 
               
               
                 13 
                 u 13  = [1 −1 1 −1] T   
                 W 13   {1}   
                 W 13   {13} /{square root over (2)} 
                 W 13   {123} /{square root over (3)} 
                 W 13   {1324} /2 
               
               
                 14 
                 u 14  = [1 1 −1 −1] T   
                 W 14   {1}   
                 W 14   {13} /{square root over (2)} 
                 W 14   {123} /{square root over (3)} 
                 W 14   {3214} /2 
               
               
                 15 
                 u 15  = [1 1 1 1] T   
                 W 15   {1}   
                 W 15   {12} /{square root over (2)} 
                 W 15   {123} /{square root over (3)} 
                 W 15   {1234} /2 
               
               
                   
               
            
           
         
       
     
     In Table 1, W n   {s}  can be prescribed as W n =I−2u n u n   H /u n   H u n  for a set including a column indicated by {s}. In this case, I indicates 4*4 identity matrix. Referring to Table 1, 4-Tx codebook prescribed in LTE release 8 is constructed with total 64 precoding matrixes including 16 precoding matrixes for each rank. The codebook shown in Table 1 has the following properties.
         Constant modulus property: each component of each precoding vector/matrix has uniform power.   Nested property: a precoding vector/matrix at a low rank is included in a column of a precoding vector/matrix of a high rank.   Limited number of components: component (precoding alphabet) of precoding matrix is limited to       

     
       
         
           
             
               { 
               
                 
                   ± 
                   1 
                 
                 , 
                 
                   ± 
                   j 
                 
                 , 
                 
                   ± 
                   
                     
                       ( 
                       
                         1 
                         + 
                         j 
                       
                       ) 
                     
                     
                       2 
                     
                   
                 
                 , 
                 
                   ± 
                   
                     
                       ( 
                       
                         
                           - 
                           1 
                         
                         + 
                         j 
                       
                       ) 
                     
                     
                       2 
                     
                   
                 
               
               } 
             
             . 
           
         
       
     
     In consideration of the above mentioned features, a codebook structure for uplink signal transmission in LTE-A system is explained as follows. 
       FIG. 2  is a diagram for explaining ULA antenna setup and X-pol antenna setup. 
     The codebook structure shown in Table 1 is designed in consideration of ULA (uniform linear array) antenna setup shown in a left part of  FIG. 2 . Generally, the ULA antenna type needs a big antenna space to maintain antenna correlation over a predetermined level. Accordingly, in order to use a number of antennas like 4Tx, 8Tx or the like, a cross-pol (X-pol) antenna setup shown in a right part of  FIG. 2  is used. In case of the X-pol antenna setup, it is able to reduce an antenna space smaller than that of the ULA antenna setup. Therefore, the X-pol antenna setup is taken into consideration in designing 4-Tx system codebook for LTE-A. 
     A precoding matrix can be represented as N t ×R matrix. In this case, N t  indicates the number of antennas and R indicates a rank. A codebook for the rank R can be represented as W N     t     ×R   i , i=0, . . . , N rank . In this case, N rank  indicates the number of precoding matrixes for the rank R. 
     According to one embodiment of the present invention, N t  antennas can be divided into at least two groups. For instance, antenna port  1  and antenna port  3  can be grouped into one antenna group in the setup shown in the right part of  FIG. 2 , while antenna port  2  and antenna port  4  can be grouped into another antenna group in the setup shown in the right part of  FIG. 2 . 
     A recoding matrix can be designed to be suitable for each of the above-mentioned antennas groups. For instance, 2Tx codebook is usable for each of the above-mentioned antenna groups and is also usable by being combined for 4Tx codebook. In order to completely separate these two antenna groups from each other, one embodiment of the present invention proposes to use a zero vector/matrix. If 4Tx system includes two antenna groups each of which includes two antennas, Table 2 shows vectors/matrixes usable for each of the antenna groups. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Number of layers 
                 Precoding 
                 Zero 
               
               
                 υ 
                 vectors/matrices 
                 vector/matrix 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     1 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     1 
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               1 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     2 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     2 
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               2 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     3 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     3 
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               3 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     4 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     4 
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               4 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                               
                             
                             ] 
                           
                           ︸ 
                         
                         
                           z 
                           _ 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         
                           ︸ 
                           w 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                         
                           ︸ 
                           z 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     In Table 2, ν i   j , i=1, . . . , 4, j=1, 2, indicates a complex number value having a unit power. If a component of each precoding matrix is limited to {±1, ±j}, precoding vector/matrix candidates for each antenna group can be represented as follows. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Number of layers 
                 Precoding 
                 Zero 
               
               
                 υ 
                 vectors/matrices 
                 vector/matrix 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   1 
                                 
                               
                               
                                 
                                   1 
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               1 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               2 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   1 
                                 
                               
                               
                                 
                                   j 
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               3 
                             
                           
                         
                         , 
                         
                           
                             [ 
                             
                               
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     - 
                                     j 
                                   
                                 
                               
                             
                             ] 
                           
                           
                             ︸ 
                             
                               
                                 v 
                                 _ 
                               
                               4 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                               
                             
                             ] 
                           
                           ︸ 
                         
                         
                           z 
                           _ 
                         
                       
                     
                   
                 
               
               
                   
               
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         
                           ︸ 
                           w 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                         
                           ︸ 
                           z 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     According to another embodiment of the present invention, it is able to design a codebook using the following precoding vector/matrix candidates. 
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                 Precoding 
                   
               
               
                 Number of layers υ 
                 vectors/matrices 
                 Zero vector/matrix 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               v 
                               _ 
                             
                             1 
                           
                         
                         , 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               v 
                               _ 
                             
                             2 
                           
                         
                         , 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     j 
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               v 
                               _ 
                             
                             3 
                           
                         
                         , 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       j 
                                     
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               v 
                               _ 
                             
                             4 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     0 
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             z 
                             _ 
                           
                         
                         , 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               γ 
                               _ 
                             
                             1 
                           
                         
                         , 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     0 
                                   
                                 
                               
                               ] 
                             
                             ︸ 
                           
                           
                             
                               γ 
                               _ 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     In Table 3 and Table 4, matrixes except zero vector/matrix can be called DFT matrixes. In the following description, 4Tx uplink codebook is described in detail per rank. 
     Rank-1 Codebook 
     First of all, it is able to design a rank-1 precoding matrix of 4Tx system by combining two vectors/matrixes for 1 layer in Table 3 or Table 4 in one column. 
     Total combinations of precoding vectors/matrixes per antenna except zero vector/matrix in Table 3 or Table 4 can be represented as follows. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Number of 
                   
               
               
                   
                 layers υ 
                 Layer-1 codebook (W n   N×1 ) 
               
               
                   
                   
               
             
            
               
                   
                 1 
                 
                   
                     
                       
                         
                           
                             
                               
                                   
                                 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             3 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             4 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             1 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             3 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               v 
                                               _ 
                                             
                                             4 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   , 
                                 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               1 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               2 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               1 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               2 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               3 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     , 
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 v 
                                                 _ 
                                               
                                               4 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                     
                                 
                                 ⁢ 
                                 
                                     
                                     
                                 
                               
                             
                           
                         
                           
                       
                     
                   
                 
               
               
                   
                   
               
            
           
         
       
     
     Meanwhile, it is able to design a codebook in consideration of antenna permutation. In this case, it is able to permutate all precoding vectors/matrixes within the codebook using the same antenna permutation matrix Π. According to this embodiment, the precoding matrixes shown in Table 5 can be represented as follows using a permutation matrix.
 
Π· W   N     t     ×1   , n= 0, . . . ,  N   c −1  [Formula 1]
 
     In Formula 1, N c  indicates the number of precoding vectors/matrixes per layer. The above-described permutation matrix can be represented as follows. 
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Π 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Π 1  
         [         1       0       0       0           0       0       1       0           0       1       0       0           0       0       0       1         ]             
 
                 Π 2  
         [         1       0       0       0           0       1       0       0           0       0       0       1           0       0       1       0         ]             
 
                 Π 3  
         [         1       0       0       0           0       0       1       0           0       0       0       1           0       1       0       0         ]             
 
                 Π 4  
         [         1       0       0       0           0       0       0       1           0       1       0       0           0       0       1       0         ]             
 
               
               
                   
               
               
                 Π 5  
         [         1       0       0       0           0       0       0       1           0       0       1       0           0       1       0       0         ]             
 
                 Π 6  
         [         0       1       0       0           1       0       0       0           0       0       1       0           0       0       0       1         ]             
 
                 Π 7  
         [         0       1       0       0           1       0       0       0           0       0       0       1           0       0       1       0         ]             
 
                 Π 8  
         [         0       1       0       0           0       0       1       0           0       0       0       1           1       0       0       0         ]             
 
               
               
                   
               
               
                 Π 9  
         [         0       1       0       0           0       0       1       0           1       0       0       0           0       0       0       1         ]             
 
                 Π 10  
         [         0       1       0       0           0       0       0       1           1       0       0       0           0       0       1       0         ]             
 
                 Π 11  
         [         0       1       0       0           0       0       0       1           0       0       1       0           1       0       0       0         ]             
 
                 Π 12  
         [         0       0       1       0           1       0       0       0           0       1       0       0           0       0       0       1         ]             
 
               
               
                   
               
               
                 Π 13  
         [         0       0       1       0           1       0       0       0           0       0       0       1           0       1       0       0         ]             
 
                 Π 14  
         [         0       0       1       0           0       1       0       0           1       0       0       0           0       0       0       1         ]             
 
                 Π 15  
         [         0       0       1       0           0       1       0       0           0       0       0       1           1       0       0       0         ]             
 
                 Π 16  
         [         0       0       1       0           0       0       0       1           1       0       0       0           0       1       0       0         ]             
 
               
               
                   
               
               
                 Π 17  
         [         0       0       1       0           0       0       0       1           0       1       0       0           1       0       0       0         ]             
 
                 Π 18  
         [         0       0       0       1           1       0       0       0           0       1       0       0           0       0       1       0         ]             
 
                 Π 19  
         [         0       0       0       1           1       0       0       0           0       0       1       0           0       1       0       0         ]             
 
                 Π 20  
         [         0       0       0       1           0       1       0       0           1       0       0       0           0       0       1       0         ]             
 
               
               
                   
               
               
                 Π 21  
         [         0       0       0       1           0       1       0       0           0       0       1       0           1       0       0       0         ]             
 
                 Π 22  
         [         0       0       0       1           0       0       1       0           1       0       0       0           0       1       0       0         ]             
 
                 Π 23  
         [         0       0       0       1           0       0       1       0           0       1       0       0           1       0       0       0         ]             
 
               
               
                   
               
            
           
         
       
     
     For clarity of the following description, assume that Π 1  is used as a permutation matrix. Yet, other permutation matrixes are available as well. 
     If the precoding vector/matrix per antenna shown in Table 4 is applied to Table 5, it is able to configure the following rank-1 (layer-1) codebook. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Number of 
                   
               
               
                   
                 layers υ 
                 Layer-1 codebook (W n   N     t     ×1 ) 
               
               
                   
                   
               
             
            
               
                   
                 1 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                     
                                   
                                     [ 
                                     
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                               
                             
                           
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                           
                       
                     
                   
                 
               
               
                   
                   
               
            
           
         
       
     
     Moreover, if a permutation using antenna permutation matrix Π 1  is additionally taken into consideration for Table 7, it is able to design the following rank-1 codebook. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 Number of 
                   
               
               
                   
                 layers υ 
                 Layer-1 codebook (Π· W n   N     t     ×1 ) 
               
               
                   
                   
               
             
            
               
                   
                 1 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                     
                                   
                                     [ 
                                     
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                       
                                         
                                           1 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                               
                             
                           
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           1 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         j 
                                       
                                     
                                   
                                   ] 
                                 
                                 , 
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           j 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                           
                       
                     
                   
                 
               
               
                   
                   
               
            
           
         
       
     
     According to another embodiment of the present invention, only part of precoding matrixes in the rank-1 codebook can be configured in a type that uses a permutation matrix as follows. 
     
       
         
           
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Meanwhile, according to one preferred embodiment of the present invention, proposed is a method of designing a codebook to have a mutually orthogonal property between vectors/matrixes corresponding to each antenna group in a precoding matrix within a codebook. Table 11 shows an example for configuring a codebook by selecting precoding matrixes meeting the mutually orthogonal property between the corresponding antenna groups shown in Table 5. 
     
       
         
           
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Meanwhile, according to one embodiment of the present invention, proposed is a method of configuring a codebook that includes an antenna group selection matrix. In particular, in case that 4 antennas are grouped into a first antenna group including 2 of the 4 antennas and a second antenna group including the rest, the codebook is designed in a manner that 2 components corresponding to one of the antenna groups are set to 0 and that 2 components corresponding to the other antenna group construct a DFT matrix. Through this, it is able to turn off antennas by an antenna group unit at a timing point of transmitting an uplink signal to a base station from a user equipment. 
     Table 12 shows an example of the above-described antenna group selection matrix. 
     
       
         
           
               
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   z 
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   z 
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   z 
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   z 
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     According to a preferred embodiment of the present invention, proposed is a method of configuring 4Tx rank-1 codebook in a manner that the corresponding codebook includes both of the antenna group selection matrix shown in Table 12 and the DFT matrix shown in Table 5. Table 13 and Table 14 are examples for the 4Tx rank-1 codebook according to this embodiment. 
     
       
         
           
               
               
             
               
                 TABLE 13 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 z 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 14 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-1 codebook (W N     t     ×1   n ) 
               
               
                   
               
             
            
               
                 1 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 z 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   z 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Rank-2 Codebook 
     According to one embodiment of the present invention, proposed is a method of setting a rank-2 codebook to further include a precoding matrix of a permutated type of the precoding matrix within the codebook shown in Table 15. In this case, if a used permutation matrix is represented as Π, a permutated precoding matrix can be represented as follows.
 
Π· W   N     t     ×2   n   , n= 0, . . . ,  N   c −1  [Formula 2]
 
     The above permutation matrix can be selected from Table 6. 
     In case that Table 4 is used as a precoding vector/matrix for each antenna group, Table 15 can be modified into Table 16. 
     
       
         
           
               
               
             
               
                 TABLE 16 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 W N     t     ×2   0   
                 W N     t     ×2   1   
                 W N     t     ×2   2   
                 W N     t     ×2   3   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   4   
                 W N     t     ×2   5   
                 W N     t     ×2   6   
                 W N     t     ×2   7   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   8   
                 W N     t     ×2   9   
                 W N     t     ×2   10   
                 W N     t     ×2   11   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   12   
                 W N     t     ×2   13   
                 W N     t     ×2   14   
                 W N     t     ×2   15   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     If a permutation matrix is applied to Table 16, a rank-2 codebook can be represented as follows. 
     
       
         
           
               
               
             
               
                 TABLE 17 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (Π · W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 2 
                 Π · 
                 Π · 
                 Π · 
                 Π · 
               
               
                   
                 W N     t     ×2   0   
                 W N     t     ×2   1   
                 W N     t     ×2   2   
                 W N     t     ×2   3   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π · 
                 Π · 
                 Π · 
                 Π · 
               
               
                   
                 W N     t     ×2   4   
                 W N     t     ×2   5   
                 W N     t     ×2   6   
                 W N     t     ×2   7   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π · 
                 Π · 
                 Π · 
                 Π · 
               
               
                   
                 W N     t     ×2   8   
                 W N     t     ×2   9   
                 W N     t     ×2   10   
                 W N     t     ×2   11   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π · 
                 Π · 
                 Π · 
                 Π · 
               
               
                   
                 W N     t     ×2   12   
                 W N     t     ×2   13   
                 W N     t     ×2   14   
                 W N     t     ×2   15   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Meanwhile, according to one embodiment of the present invention, proposed is a method of designing a codebook to apply a physical antenna permutation and virtual swapping in addition. Formula 3 shows a precoding matrix type to which virtual antenna swapping is applied.
 
 W   N     t     ×2   n ·Ξ  [Formula 3]
 
     In Formula 3, Ξ indicates a virtual antenna swapping matrix. And, this virtual antenna swapping matrix can be represented as follows. 
     
       
         
           
             
               
                 
                   Ξ 
                   = 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           1 
                         
                         
                           0 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     If the above-described virtual antenna swapping matrix is applied to Table 16/Table 17, Table 18/Table 19 can be generated. 
     
       
         
           
               
               
             
               
                 TABLE 18 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (W N     t     ×2  · Θ) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 2 
                 W N     t     ×2   0  · 
                 W N     t     ×2   1  · 
                 W N     t     ×2   2  · 
                 W N     t     ×2   3  · 
               
               
                   
                 Θ 
                 Θ 
                 Θ 
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   4  · 
                 W N     t     ×2   5  · 
                 W N     t     ×2   6  · 
                 W N     t     ×2   7  · 
               
               
                   
                 Θ 
                 Θ 
                 Θ 
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   8  · 
                 W N     t     ×2   9  · 
                 W N     t     ×2   10  · 
                 W N     t     ×2   11  · 
               
               
                   
                 Θ 
                 Θ 
                 Θ 
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 j 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   12  · 
                 W N     t     ×2   13  · 
                 W N     t     ×2   14  · 
                 W N     t     ×2   15  · 
               
               
                   
                 Θ 
                 Θ 
                 Θ 
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   - 
                                   j 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 19 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (Π · W N     t     ×2   n  · Θ) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 2 
                 Π 1  · W N     t     ×2   0 · 
                 Π 1  · 
                 Π 1  · W N     t     ×2   2  · 
                 Π 1  · 
               
               
                   
                 Θ 
                 W N   ×2   1  · Θ 
                 Θ 
                 W N     t     ×2   3  · Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π 1  · W N     t     ×2   4  · 
                 Π 1  · 
                 Π 1  · W N     t     ×2   6  · 
                 Π 1  · 
               
               
                   
                 Θ 
                 W N   ×2   5  · Θ 
                 Θ 
                 W N     t     ×2   7  · Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π 1  · W N     t     ×2   8  · 
                 Π 1  · 
                 Π 1  · W N     t     ×2   10  · 
                 Π 1  · 
               
               
                   
                 Θ 
                 W N   ×2   9  · Θ 
                 Θ 
                 W N     t     ×2   11  · 
               
               
                   
                   
                   
                   
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
               
                   
                 Π 1  · W N     t     ×2   12  · 
                 Π 1  · 
                 Π 1  · W N     t     ×2   14  · 
                 Π 1  · 
               
               
                   
                 Θ 
                 W N   ×2   13  · Θ 
                 Θ 
                 W N     t     ×2   15  · 
               
               
                   
                   
                   
                   
                 Θ 
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 j 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   j 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Meanwhile, according to one embodiment of the present invention, proposed is a rank-2 codebook of a type to which a physical antenna permutation is partially applied. In particular, parts of Table 16 and Table 17 can be included in a combined codebook type. Table 20/Table 21 shows a case that one permutation matrix is used per codebook, while table 22/Table 23 shows a case that two permutation matrixes are used per codebook. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 20 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   0   ,  Π 1  · W N     t     ×2   1   ,  Π 1  · W N     t     ×2   4   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   5   ,   
               
               
                   
                   
                 Π 1 ·  W N     t     ×2   6   ,  Π 1  · W N     t     ×2   7   ,  Π 1  · W N     t     ×2   10   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   11   ,   
               
               
                   
                   
               
            
           
         
       
     
     Table 20 is characterized in that a subset of a total combination codebook is combined with a subset of a permutated codebook. All permutated elements do not originate from the subset of the total combination codebook. And, Table 20 shows a case that one permutation matrix is used only. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 21 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   2   ,  Π 1  · W N     t     ×2   3   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   6   ,  Π 1  · W N     t     ×2   7   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   8   ,  Π 1  · W N     t     ×2   9   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   12   ,  Π 1  · W N     t     ×2   13   ,   
               
               
                   
                   
               
            
           
         
       
     
     Table 21 is characterized in that a subset of a total combination codebook is combined with a subset of a permutated codebook. All permutated elements originate from the subset of the total combination codebook. And, Table 21 shows a case that one permutation matrix is used only. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 22 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   0   ,  Π 1  · W N     t     ×2   1   ,  Π 1  · W N     t     ×2   4   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   5   ,   
               
               
                   
                   
                 Π 3  · W N     t     ×2   8   ,  Π 3  · W N     t     ×2   9   ,  Π 3  · W N     t     ×2   12   ,   
               
               
                   
                   
                 Π 3  · W N     t     ×2   13   ,   
               
               
                   
                   
               
            
           
         
       
     
     Table 22 is characterized in that a subset of a total combination codebook is combined with a subset of a permutated codebook. All permutated elements do not originate from the subset of the total combination codebook. And, Table 22 shows a case that a plurality of permutation matrixes is used. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 23 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,   
               
               
                   
                   
                 W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   2   ,  Π 1  · W N     t     ×2   3   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   6   ,  Π 1  · W N     t     ×2   7   ,   
               
               
                   
                   
                 Π 3  · W N     t     ×2   8   ,  Π 3  · W N     t     ×2   9   ,   
               
               
                   
                   
                 Π 3  · W N     t     ×2   12   ,  Π 3  · W N     t     ×2   13   ,   
               
               
                   
                   
               
            
           
         
       
     
     Table 23 is characterized in that a subset of a total combination codebook is combined with a subset of a permutated codebook. All permutated elements originate from the subset of the total combination codebook. And, Table 22 shows a case that a plurality of permutation matrixes is used. 
     Meanwhile, according to another embodiment of the present invention, proposed is a codebook of a type in which permutation and swapping are combined with each other. Examples of a rank-2 codebook according to the present embodiment are shown as follows. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 24 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   0   ,  · Ξ ,  Π 1  · W N     t     ×2   1   ,  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   4   ,  · Ξ ,  Π 1  · W N     t     ×2   5   ,  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   6   ,  · Ξ ,  Π 1  · W N     t     ×2   7   ,  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   10   ,  · Ξ ,  Π 1  · W N     t     ×2   11   ,  · Ξ ,   
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 25 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   2   ,  · Ξ ,  Π 1  · W N     t     ×2   3  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   2  · Ξ ,  Π 1  · W N     t     ×2   7  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   6  · Ξ ,  Π 1  · W N     t     ×2   9  · Ξ ,   
               
               
                   
                   
                 Π 1  · W N     t     ×2   12  · Ξ ,  Π 1  · W N     t     ×2   13  · Ξ ,   
               
               
                   
                   
               
            
           
         
       
     
     Besides, various combinations are possible as follows. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 26 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π · W N     t     ×2   0   ,  Π · W N     t     ×2   1   ,  Π · W N     t     ×2   4   ,   
               
               
                   
                   
                 Π · W N     t     ×2   5   ,   
               
               
                   
                   
                 W N     t     ×2   6  · Ξ ,  W N     t     ×2   7  · Ξ ,  W N     t     ×2   10  · Ξ ,   
               
               
                   
                   
                 W N     t     ×2   11  · Ξ ,   
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 27 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,   
               
               
                   
                   
                 W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,   
               
               
                   
                   
                 W N     t     ×2   13   ,   
               
               
                   
                   
                 Π · W N     t     ×2   0   ,  Π · W N     t     ×2   1   ,   
               
               
                   
                   
                 Π · W N     t     ×2   4   ,  Π · W N     t     ×2   5   ,   
               
               
                   
                   
                 W N     t     ×2   6  · Ξ ,  W N     t     ×2   7  · Ξ ,   
               
               
                   
                   
                 W N     t     ×2   10  · Ξ ,  W N     t     ×2   11  · Ξ ,   
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 28 
               
               
                   
                   
               
               
                   
                 Number of layers 
                   
               
               
                   
                 ν 
                 Layer-2 codebook 
               
               
                   
                   
               
             
            
               
                   
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                   
                 Π · W N     t     ×2   0   ,  Π · W N     t     ×2   1   ,  Π · W N     t     ×2   4   ,   
               
               
                   
                   
                 Π · W N     t     ×2   5  · Ξ ,   
               
               
                   
                   
                 Π · W N     t     ×2   6  · Ξ ,  Π · W N     t     ×2   7  · Ξ ,  W N     t     ×2   10  · Ξ ,   
               
               
                   
                   
                 W N     t     ×2   11  · Ξ ,   
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 29 
               
               
                   
               
               
                 Number of layers 
                   
               
               
                 ν 
                 Layer-2 codebook 
               
               
                   
               
             
            
               
                 2 
                 W N     t     ×2   2   ,  W N     t     ×2   3   ,  W N     t     ×2   6   ,  W N     t     ×2   7   ,   
               
               
                   
                 W N     t     ×2   8   ,  W N     t     ×2   9   ,  W N     t     ×2   12   ,  W N     t     ×2   13   ,   
               
               
                   
                 Π · W N     t     ×2   2   ,  Π · W N     t     ×2   3   ,  Π · W N     t     ×2   6   ,   
               
               
                   
                 Π 1  · W N     t     ×2   7  · Ξ ,   
               
               
                   
                 Π 1  · W N     t     ×2   8  · Ξ ,  Π 1  · W N     t     ×2   9  · Ξ ,  W N     t     ×2   12  · Ξ ,   
               
               
                   
                 W N     t     ×2   13  · Ξ ,   
               
               
                   
               
            
           
         
       
     
     According to another embodiment of the present invention, an antenna group selection matrix is configured as Table 30 or can be configured by being combined with other precoding matrixes as Tables 31 to 33. 
     
       
         
           
               
               
             
               
                 TABLE 30 
               
               
                   
               
               
                 Number of layers 
                   
               
               
                 ν 
                 Layer-2 codebook (W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
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                                     _ 
                                   
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                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                               
                                 
                                   
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                           · 
                           
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                                       _ 
                                     
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                                     _ 
                                   
                                 
                                 
                                   
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                         , 
                         
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                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     3 
                                   
                                 
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     z 
                                     _ 
                                   
                                 
                                 
                                   
                                     z 
                                     _ 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     z 
                                     _ 
                                   
                                 
                                 
                                   
                                     z 
                                     _ 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     1 
                                   
                                 
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
                                     2 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         , 
                         
                           Π 
                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     z 
                                     _ 
                                   
                                 
                                 
                                   
                                     z 
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                                       v 
                                       _ 
                                     
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                                       _ 
                                     
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                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 31 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   2 , W N     t     ×2   3 , W N     t     ×2   6 , W N     t     ×2   7 , 
               
               
                   
                 W N     t     ×2   8 , W N     t     ×2   9 , W N     t     ×2   12 , W N     t     ×2   13 , 
               
               
                   
                 Π 1  · W N     t     ×2   2 , Π 1  · W N     t     ×2   3 , Π 1  · W N     t     ×2   6 , 
               
               
                   
                 Π 1  · W N     t     ×2   7 , 
               
               
                   
                 Π 1  · W N     t     ×2   8 , Π 1  · W N     t     ×2   9 , Π 1  · W N     t     ×2   12 , 
               
               
                   
                 Π 1  · W N     t     ×2   13 , 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 32 
               
               
                   
               
               
                 Number of layers ν 
                 Layer-2 codebook (W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
                           [ 
                           
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   3 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   4 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   2 , W N     t     ×2   3 , W N     t     ×2   6 , W N     t     ×2   7 , 
               
               
                   
                 Π · W N     t     ×2   0 , Π · W N     t     ×2   1 , Π · W N     t     ×2   4 , 
               
               
                   
                 Π · W N     t     ×2   5 , 
               
               
                   
                 Π · W N     t     ×2   6 , Π · W N     t     ×2   7 , Π · W N     t     ×2   10 , 
               
               
                   
                 Π · W N     t     ×2   11 , 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 33 
               
               
                   
               
               
                 Number of layers  
                   
               
               
                 ν 
                 Layer-2 codebook (W N     t     ×2   n ) 
               
               
                   
               
             
            
               
                 2 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   1 
                                 
                               
                               
                                 
                                   
                                     v 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   _ 
                                 
                               
                               
                                 
                                   z 
                                   _ 
                                 
                               
                             
                           
                           ] 
                         
                         , 
                         
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                                     v 
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                                   3 
                                 
                               
                               
                                 
                                   
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                                     _ 
                                   
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                         , 
                         
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                           ] 
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           Π 
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                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     z 
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                                     1 
                                   
                                 
                                 
                                   
                                     
                                       v 
                                       _ 
                                     
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                             ] 
                           
                         
                         , 
                         
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                           · 
                           
                             [ 
                             
                               
                                 
                                   
                                     z 
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                                       _ 
                                     
                                     4 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 W N     t     ×2   2 , W N     t     ×2   3 , W N     t     ×2   6 , W N     t     ×2   7 , 
               
               
                   
                 Π · W N     t     ×   0 , Π · W N     t     ×   1 , Π · W N     t     ×   4 , 
               
               
                   
                 Π · W N     t     ×   5 , 
               
               
                   
                 Π · W N     t     ×   6 , Π · W N     t     ×   7 , Π · W N     t     ×   10 , 
               
               
                   
                 Π · W N     t     ×   11 , 
               
               
                   
               
            
           
         
       
     
     Rank-3 Codebook 
     According to one embodiment of the present invention, 4Tx rank-3 codebook design is approached in two viewpoints. 
     (1) Viewpoint of Antenna Power Balance 
     A most feasible type of 4Tx rank-3 codebook is explained as follows. First of all, the zero vector/matrix shown in Table 3 is usable for antenna group separation. 
     
       
         
           
             
               
                 
                   
                     W 
                     
                       
                         N 
                         t 
                       
                       × 
                       3 
                     
                     n 
                   
                   ∈ 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 v 
                                 _ 
                               
                               i 
                             
                           
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               k 
                             
                           
                         
                         
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               j 
                             
                           
                           
                             
                               z 
                               _ 
                             
                           
                         
                       
                       ] 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       or 
                       ⁢ 
                       
                           
                       
                       [ 
                       
                         
                           
                             
                               
                                 v 
                                 _ 
                               
                               i 
                             
                           
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               z 
                               _ 
                             
                           
                         
                         
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               j 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               k 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     It is able to consider a matrix type that is normalized by multiplying the precoding matrix type of Formula 5 by a same scaling coefficient. In this case, i, j, k can include independent numbers, respectively. Physical antenna permutation (e.g., Π·W N     t     ×3   n ), virtual antenna permutation (e.g., W N     t     ×3   n ·Θ), and total permutation (e.g., Π·W N     t     ×3   n ·Θ) can be applied to the rank-3 codebook in the same manner of the rank-2 codebook. And, virtual antenna permutation Θ can be prescribed as follows. 
     
       
         
           
               
             
               
                 TABLE 34 
               
               
                   
               
               
                 Θ 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Θ 1   
                 Θ 2   
                 Θ 3   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 Θ 4   
                 Θ 5   
               
               
                   
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                           
                       
                     
                   
                 
               
               
                   
                   
               
            
           
         
       
     
     Yet, one preferred embodiment of the present invention proposes that a precoding matrix of a following type, which enables perfect power balance per antenna, is included in a rank-3 codebook. 
     
       
         
           
             
               
                 
                   
                     W 
                     
                       
                         N 
                         t 
                       
                       × 
                       3 
                     
                     n 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               v 
                               _ 
                             
                             i 
                           
                         
                         
                           
                             z 
                             _ 
                           
                         
                         
                           
                             
                               v 
                               _ 
                             
                             k 
                           
                         
                       
                       
                         
                           
                             z 
                             _ 
                           
                         
                         
                           
                             
                               v 
                               _ 
                             
                             j 
                           
                         
                         
                           
                             v 
                             l 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     In Formula 6, i, j and k can be arbitrary independent indexes in Table 2 or Table 3, respectively. According to one embodiment of the present invention, if a normalization coefficient for  ν   i  and  ν   j  is set to 1/√{square root over (α)} and a normalization coefficient for  ν   k  and the  ν   l  is set to 1/√{square root over (β)}, the two coefficients can differ from each other. For instance, if α=2β, it is able to simultaneously match power balance per layer and power balance per antenna both. 
     If it is set to α=β, it becomes a precoding matrix of a type that matches the power balance per antenna only. In this case, Formula 6 can be represented as follows. 
     
       
         
           
             
               
                 
                   
                     W 
                     
                       
                         N 
                         t 
                       
                       × 
                       3 
                     
                     n 
                   
                   = 
                   
                     
                       1 
                       
                         δ 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 v 
                                 _ 
                               
                               i 
                             
                           
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               k 
                             
                           
                         
                         
                           
                             
                               z 
                               _ 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               j 
                             
                           
                           
                             
                               
                                 v 
                                 _ 
                               
                               l 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     According to the present embodiment, physical antenna permutation (e.g., Π·W N     t     ×3   n ), virtual antenna permutation (e.g., W N     t     ×3   n ·Θ), and total permutation (e.g., Π·W N     t     ×3   n ·Θ) can be applied in the same manner of the rank-2 codebook. And, virtual antenna permutation Θ can be prescribed as Table 34. 
     In the precoding matrix type represented by Formula 6 or Formula 7,  ν   i  and  ν   k  are preferably orthogonal to each other. And,  ν   j  and  ν   l  are preferably orthogonal to each other as well. 
     An example for a rank-3 precoding matrix, which meets the above-mentioned conditions, can be represented as follows. 
     
       
         
           
             
               
                 
                   
                     
                       W 
                       
                         
                           N 
                           t 
                         
                         × 
                         3 
                       
                       n 
                     
                     = 
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   1 
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 - 
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     1 
                                   
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   2 
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     2 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       or 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       W 
                       
                         
                           N 
                           t 
                         
                         × 
                         3 
                       
                       n 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                         
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   jθ 
                                   1 
                                 
                               
                             
                           
                           
                             0 
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 1 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 2 
                               
                             
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 2 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   jθ 
                                   3 
                                 
                               
                             
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 3 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
     Of course, a rank-3 codebook includes a type generated from multiplying the type of Formula 8 by a normalization coefficient. In this case, N t  is 4, θ 1 , θ 2  meets the condition of 
                 θ   2     ∈     {           2   ⁢   π     N     ⁢   i     ,     i   =   0     ,   …   ⁢           ,     N   -   1       }       ,   ,         
and N is 4 or 8.
 
     Moreover, it is able to consider a type generated from multiplying Formula 8 by one of various permutations. Theses types can be represented as follows. 
     
       
         
           
             
               
                 
                   
                     
                       ∏ 
                       
                         · 
                         
                           W 
                           
                             
                               N 
                               t 
                             
                             × 
                             3 
                           
                           n 
                         
                       
                     
                     = 
                     
                       ∏ 
                       
                         
                           · 
                           
                             [ 
                             
                               
                                 
                                   1 
                                 
                                 
                                   0 
                                 
                                 
                                   1 
                                 
                               
                               
                                 
                                   
                                     ⅇ 
                                     
                                       jθ 
                                       1 
                                     
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     - 
                                     
                                       ⅇ 
                                       
                                         jθ 
                                         1 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   1 
                                 
                                 
                                   1 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   
                                     ⅇ 
                                     
                                       jθ 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     - 
                                     
                                       ⅇ 
                                       
                                         jθ 
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         or 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     ∏ 
                     
                       · 
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     1 
                                   
                                 
                               
                             
                             
                               0 
                             
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   1 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   2 
                                 
                               
                             
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   2 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 - 
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     3 
                                   
                                 
                               
                             
                             
                               
                                 ⅇ 
                                 
                                   jθ 
                                   3 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       ∏ 
                       
                         · 
                         
                           W 
                           
                             
                               N 
                               t 
                             
                             × 
                             3 
                           
                           n 
                         
                         · 
                         Θ 
                       
                     
                     = 
                     
                       ∏ 
                       
                         · 
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     1 
                                   
                                 
                               
                               
                                 0 
                               
                               
                                 
                                   - 
                                   
                                     ⅇ 
                                     
                                       jθ 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                               
                                 1 
                               
                             
                             
                               
                                 0 
                               
                               
                                 
                                   ⅇ 
                                   
                                     jθ 
                                     2 
                                   
                                 
                               
                               
                                 
                                   - 
                                   
                                     ⅇ 
                                     
                                       jθ 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                         · 
                         Θ 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             
                               W 
                               
                                 
                                   N 
                                   t 
                                 
                                 × 
                                 3 
                               
                               n 
                             
                             · 
                             Θ 
                           
                           = 
                             
                           ⁢ 
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                   
                                     0 
                                   
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     
                                       ⅇ 
                                       
                                         jθ 
                                         1 
                                       
                                     
                                   
                                   
                                     0 
                                   
                                   
                                     
                                       - 
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           1 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     0 
                                   
                                   
                                     1 
                                   
                                   
                                     1 
                                   
                                 
                                 
                                   
                                     0 
                                   
                                   
                                     
                                       ⅇ 
                                       
                                         jθ 
                                         2 
                                       
                                     
                                   
                                   
                                     
                                       - 
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                             · 
                             Θ 
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             ∏ 
                             
                               · 
                               
                                 [ 
                                 
                                   
                                     
                                       1 
                                     
                                     
                                       0 
                                     
                                     
                                       1 
                                     
                                   
                                   
                                     
                                       
                                         - 
                                         
                                           ⅇ 
                                           
                                             jθ 
                                             1 
                                           
                                         
                                       
                                     
                                     
                                       0 
                                     
                                     
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           1 
                                         
                                       
                                     
                                   
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           2 
                                         
                                       
                                     
                                   
                                   
                                     
                                       0 
                                     
                                     
                                       
                                         - 
                                         
                                           ⅇ 
                                           
                                             jθ 
                                             3 
                                           
                                         
                                       
                                     
                                     
                                       
                                         ⅇ 
                                         
                                           jθ 
                                           3 
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                               · 
                               Θ 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       W 
                       
                         
                           N 
                           t 
                         
                         × 
                         3 
                       
                       n 
                     
                     · 
                     Θ 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                         
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   jθ 
                                   1 
                                 
                               
                             
                           
                           
                             0 
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 1 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 2 
                               
                             
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 2 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               - 
                               
                                 ⅇ 
                                 
                                   jθ 
                                   3 
                                 
                               
                             
                           
                           
                             
                               ⅇ 
                               
                                 jθ 
                                 3 
                               
                             
                           
                         
                       
                       ] 
                     
                     · 
                     Θ 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     (2) CM Property Maintaining Viewpoint 
     If MIMO is applied to uplink signal transmission, it may cause such a problem that a power amplifier of high performance raises a cost of a user equipment. And, PAPR/CM property of the uplink signal transmission is more important than that of downlink signal transmission. Therefore, a codebook structure for maintaining a good PAPR/CM property needs to be taken into consideration. 
     PAPR (peak power to average power ratio) is a parameter that indicates a property of waveform. This value results from dividing a peak amplitude of waveform by a time-averaged RMS (root mean square) value of the waveform and is a dimensionless value. Normally, a PAPR of a single carrier signal is better than that of a multi-carrier signal. 
     In LTE-Advanced, it is able to implement MIMO (multiple input multiple output) using SC-FDMA (single carrier-frequency division multiple access) to maintain a good CM property. If general precoding is used, a signal carrying information corresponding to several layers is multiplexed and transmitted via a single antenna, the signal transmitted via this antenna can be regarded as a sort of multi-carrier signal. PAPR is associated with a dynamic range a power amplifier in a transmitting side should support. And, a CM (cubic metric) value is another numerical value indicating a numerical value represented by the PAPR. 
     In order to maintain the above-mentioned good PAPR/CM property for the uplink signal transmission, a combined type of SC-FDMA and MIMO is preferably taken into consideration. 
       FIG. 3  is a diagram for explaining general SC-FDMA. 
     Referring to  FIG. 3 , in both OFDM and SC-FDMA schemes, a serial signal is converted to a parallel signal, the parallel signal is mapped by a subcarrier, IDFT or IFFT is performed thereon, the signal is converted to a serial signal again, a CP is attached to the serial signal, and the corresponding signal is then transmitted via an RF module. Yet, the SC-FDMA scheme is characterized in reducing influence of IDFT or IFFT processing through DFP spreading after conversion to a serial signal from a parallel signal and maintaining a single signal property over a predetermined level. 
     When MIMO is applied to this SC-FDMA signal transmission, a processor configuration of a user equipment is explained as follows. 
       FIG. 4  is a diagram for detailed configuration of a processor of a user equipment according to one embodiment of the present invention. 
     Referring to  FIG. 4 , a processor of a user equipment according to one embodiment of the present invention includes a layer mapper  1401  mapping an uplink signal by layers of which number corresponding to a specific rank, a prescribed number of DFT modules  1402  performing DFT (discrete Fourier transform) spreading on a prescribed number of layer signals, and a precoder  1403  performing precoding on a transmission signal by selecting a precoding matrix from a codebook stored in a memory  22 . The DFT module  1402  for transmitting an uplink signal by SC-FDMA, as shown in  FIG. 4 , is arranged in front of the precoder  1403  and in rear of the layer mapper  1401 . The DFT-spread signal per layer passes through the precoding and is then transmitted by being IFFT inverse-spread. Therefore, it is able to maintain a good PAPR/CM property due to the cancellation effect between DFT spreading and IFFT inverse spreading. 
     According to one embodiment of the present invention, proposed is a method of designing a rank-3 codebook to maintain an optimal PAPR/CM property in a manner that each row of a precoding matrix is made to include one component except 0 only. In case of using such a precoding matrix including one component except 0 in each row, a plurality of data symbols are not combined with each antenna port. Therefore, it is able to maintain a good CM property. Moreover, as mentioned in the foregoing description with reference to  FIG. 4 , if one layer signal is set to be transmitted via one antenna in performing precoding after DFT spreading, it is able to directly cancel the effect of IFFT inverse spreading by DFT spreading. 
     A precoding matrix of a rank-3 codebook according to the present embodiment can be represented as follows. 
     
       
         
           
             
               
                 
                   
                     W 
                     
                       
                         N 
                         t 
                       
                       × 
                       3 
                     
                     n 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             ⅇ 
                             jθ 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     Of course, the rank-3 codebook can include a type that the above type represented by Formula 11 is multiplied by a normalization coefficient. In Formula 11, N t  is 4, θ meets the condition of 
                           ‵     ⁢   θ   ∈     {           2   ⁢   π     N     ⁢   i     ,     i   =   0     ,   …   ⁢           ,     N   -   1       }       ;     ,         
and N is 4 or 8.
 
     A precoding matrix according to the present embodiment can have various permutation types as follows. 
     
       
         
           
             
               
                 
                   
                     ∏ 
                     
                       · 
                       
                         W 
                         
                           
                             N 
                             t 
                           
                           × 
                           3 
                         
                         n 
                       
                     
                   
                   = 
                   
                     ∏ 
                     
                       · 
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 ⅇ 
                                 jθ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
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     In case of the precoding matrixes represented as Formulas 11 to 13, either antenna power balancing or layer power balancing can be performed. And, it is unable to simultaneously perform both of the antenna power balancing and the layer power balancing. 
     In viewpoint of CM property, the precoding matrixes shown in Formulas 7 to 10 can be regarded as matrixes for maintaining a good CM property in apart. Regarding the precoding matrixes shown in Formulas 7 to 10, two non-zero components are included in each row. Comparing the precoding matrixes shown in Formulas 7 to 10 to a precoding matrix, in which every component has a constant modulus, since two symbols are combined per antenna, it can be regarded as maintaining a good CM property. 
     Meanwhile, according to one preferred embodiment of the present invention for 4Tx rank-3 codebook, proposed is a combined type codebook, which includes a precoding matrix of an antenna power balance considered type as a first type precoding matrix and a precoding matrix of a type including one non-zero component in one row as a second type precoding matrix, for using both of the first and second type precoding matrixes. 
     It is understood that the above-mentioned embodiments of the rank-1, rank-2 and rank-3 of the 4Tx antenna codebook are usable by being combined into a type including a prescribed number of precoding matrixes per rank in one codebook. 
     In the following description, a base station and a user equipment, which use the above described codebook, are explained. 
       FIG. 5  is a diagram for configurations of a base station and a user equipment. 
     Referring to  FIG. 5 , a base station  10  can include a processor  11 , a memory  12  and an RF module  13  as a transceiving module for performing a reception of an uplink signal and a transmission of a downlink signal. The processor  11  of the base station  10  controls the downlink signal transmission using information, which is stored in the memory  12  for the downlink signal transmission, e.g., a specific precoding matrix within a codebook for the downlink signal transmission. And, the processor  11  of the base station  10  is able to control the downlink signal reception using information stored in the memory  12  for the uplink signal reception. For instance, the processor  11  is able to control a signal receiving process for multiplying an uplink signal by Hermitian matrix of the same precoding matrix used by a user equipment  20  as a reverse process of precoding. The memory  12  of the base station  10  according to the present embodiment is proposed to store the above-mentioned codebook as an uplink 4Tx codebook. Moreover, a functionality module for performing a precoding relevant function of the processor  11  can be separately configured with a precoder (not shown in the drawing). 
     The user equipment  20  can include a processor  21 , a memory  22  and an RF module  23  as a transceiving module for performing a transmission of an uplink signal and a reception of a downlink signal. The processor  21  controls the uplink signal transmission using information, which is stored in the memory  22  for the uplink signal transmission, e.g., a specific precoding matrix within a codebook for the uplink signal transmission, as mentioned in the foregoing description of the embodiment for the uplink signal transmission. And, the processor  21  is able to control the downlink signal reception using information stored in the memory  22  for the downlink signal reception. For instance, the processor  21  is able to control a signal receiving process for multiplying an uplink signal by Hermitian matrix of the same precoding matrix used by the base station  10  as a reverse process of precoding. The memory  22  of the user equipment  20  according to the present embodiment is proposed to store the above-mentioned codebook as an uplink 4Tx codebook. Moreover, the detailed configuration of the processor  21  can have the former configuration described with reference to  FIG. 4 . 
     While the present invention has been described and illustrated herein with reference to the preferred embodiments thereof, it will be apparent to those skilled in the art that various modifications and variations can be made therein without departing from the spirit and scope of the invention. Thus, it is intended that the present invention covers the modifications and variations of this invention that come within the scope of the appended claims and their equivalents. And, it is apparently understandable that an embodiment is configured by combining claims failing to have relation of explicit citation in the appended claims together or can be included as new claims by amendment after filing an application. 
     Accordingly, the above description is mainly made with reference to a case of a follow-up model of 3GPP LTE system, e.g., a case of 3GPP LTE-A system. And, the present invention is a next generation mobile communication technology and is applicable to IEEE series or systems according to other standards by the same principle.