# Patent

## Title
Method for configuring codebook in multi-antenna wireless communication system and device therefor

## Abstract

The present invention relates to a method and device for transmitting a signal by a transmitting end in a wireless communication system supporting multiple antennas including a plurality of vertical domain antennas and a plurality of horizontal domain antennas. Specifically, the present invention comprises the steps of: pre-coding a signal for multiple antennas, using a specific pre-coding matrix selected on the basis of a first codebook for the plurality of vertical domain antennas and a second codebook for the plurality of horizontal domain antennas; and transmitting the pre-coded signal to a receiving end, wherein the specific pre-coding matrix is defined by using a Kronecker product of a first pre-coding matrix selected from the first codebook according to at least one first selection vector and a second pre-coding matrix selected from the second codebook according to at least one second selection vector.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is the National Stage filing under 35 U.S.C. 371 of International Application No. PCT/KR2015/005935, filed on Jun. 12, 2015, which claims the benefit of U.S. Provisional Application No. 62/011,032, filed on Jun. 12, 2014, the contents of which are all hereby incorporated by reference herein in their entirety.


TECHNICAL FIELD
The present invention relates to a wireless communication system, and more particularly, to a method for configuring a codebook in a multi-antenna wireless communication system and apparatus therefor.
BACKGROUND ART
Multiple-Input Multiple-Output (MIMO) technology is a technology capable of improving data transmission/reception efficiency using multiple transmit (Tx) antennas and multiple receive (Rx) antennas instead of using a single Tx antenna and a single Rx antenna. In particular, a transmitting end or a receiving end of a wireless communication system can increase capability or improve performance using multiple antennas. Accordingly, the MIMO technology can also be referred to as a multi-antenna technology.
In order to support multi-antenna transmission, it may be able to apply a precoding matrix to appropriately distribute transmission information to each antenna according to a channel status and the like. A legacy 3GPP (3rd Generation Partnership Project) LTE (Long Term Evolution) system supports maximum 4 transmission antennas (4 Tx) to perform downlink transmission and defines a precoding codebook according to the transmission antennas.
In a multi-antenna system-based cellular communication environment, data transfer rate can be enhanced via beamforming between a transmitting end and a receiving end. Whether to apply a beamforming scheme is managed based on channel information. In general, it may be able to use a scheme that a receiving end appropriately quantizes a channel estimated by a reference signal and the like using a codebook and gives a transmitting end feedback on the quantized channel.
In the following, a spatial channel matrix (simply, channel matrix) capable of being used for generating a codebook is briefly explained. The spatial channel matrix (or, channel matrix) can be represented as follows.




  
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In this case, H (i, k) corresponds to a spatial channel matrix, Nr corresponds to the number of reception antennas, Nt corresponds to the number of transmission antennas, r corresponds to an index of an reception antenna, t corresponds to an index of a transmission antenna, i corresponds to an index of an OFDM (or SC-FDMA) symbol, and k corresponds to an index of a subcarrier.
hr,t (i, k) corresponds to an element of a channel matrix H (i, k) indicating a state of an rth channel and a tth antenna on an ith symbol and kth subcarrier.
A spatial channel covariance matrix capable of being used in the present invention is briefly explained in the following. The spatial channel covariance matrix can be represented by such a sign as R. In particular, the spatial channel covariance matrix can be represented as




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In this case, H and R correspond to a spatial channel matrix and a spatial channel covariance matrix, respectively. E[ ] corresponds to a mean, i corresponds to a symbol index, and k corresponds to a frequency index.

SVD (singular value decomposition) is one of important methods for decomposing a rectangular matrix. The SCD is widely used in signal processing and statistics. The SVD generalizes a spectrum theory of a matrix in response to a random rectangular matrix. An orthogonal square matrix can be decomposed to a diagonal matrix using the spectrum theory based on an Eigen value. Assume that a channel matrix H corresponds to m x n matrix consisting of a set element of real numbers or complex numbers. In this case, the matrix H can be represented by multiplication of three matrixes described in the following.

Hm×n=Um×mΣm×nVn×nH 

In this case, U and V correspond to unitary matrixes and Σcorresponds to m×n diagonal matrix including a singular value which is not a negative value. The singular value corresponds to Σ=diag(σ1 . . . σr), σi=√{square root over (λi)}. As mentioned above, when a matrix is represented by multiplication of three matrixes, it is referred to as singular value decomposition. It may be able to handle a much more general matrix using the singular value decomposition compared to Eigen value decomposition capable of decomposing an orthogonal squre matrix only. The singular value decomposition and the Eigen value decomposition are related to each other.
When a matrix H corresponds to an Hermite matrix which is positive definite, all Eigen values of the H correspond to real numbers which are not negative numbers. In this case, a singular value and a singular vector of the H correspond to real numbers which are not negative numbers. In particular, the singular value and the singular vector of the H become identical to the Eigen value and the Eigen vector of the H. Meanwhile, EVD (Eigen value Decomposition) can be represented as follows (in this case, Eigen value may correspond to λ1, . . . , λr).

HHH=(UΣVH)(UΣVH)H=UΣΣTUH 

HHH=(UΣVH)H(UΣVH)H=VΣTΣV 

In this case, Eigen value may correspond to λ1, . . . , λr. When singular value decomposition is performed on HHH, it is able to know information on U among U and V that indicate channel direction. When singular value decomposition is performed on HHH , it is able to know information on V. In general, each of a transmitting end and a receiving end performs beamforming to achieve a higher transfer rate in MU-MIMO (multi user-MIMO). If a beam of the receiving end and a beam of the transmitting end are represented by a matrix T and a matrix W, respectively, a channel to which beamforming is applied can be represented as THW=TU(Σ)VW. Hence, it may be preferable to generate a reception beam on the basis of the U and generate a transmission beam on the basis of the V to achieve a higher transfer rate.
In general, main concern in designing a codebook is to reduce feedback overhead using the number of bits as small as possible and precisely quantify a channel to achieve sufficient beamforming gain. One of schemes of designing a codebook, which is proposed or selected by recent communication standard such as 3GPP LTE (3rd Generation Partnership Project Long Term Evolution), LTE-Advanced, IEEE 16m system, etc. corresponding to an example of a mobile communication system, is to transform a codebook using a long-term covariance matrix of a channel as shown in equation 1 in the following.

Wt=norm(RW)   [Equation 1]

In this case, W corresponds to a legacy codebook for reflecting short-term channel information, R corresponds to a long-term covariance matrix of a channel H, and norm (A) corresponds to a normalized matrix that norm is normalized by 1 according to each column of a matrix A. W′ corresponds to a final codebook transformed from the legacy codebook W using the channel matrix H, the long-term covariance matrix R of the channel matrix H and a norm function.
The R, which is the long-term covariance matrix of the channel matrix H, can be represented as equation 2 in the following.




  
    
      
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In this case, if the singular value decomposition is performed on the R, which is the long-term covariance matrix of the channel matrix H, the R is decomposed to VΛVH. V corresponds to Nt×Nt unitary matrix and has Vi as an ith column vector. Λ corresponds to a diagonal matrix and has σi as an ith diagonal component. VH corresponds to an Hermitian matrix of the V. And, σi, vi respectively correspond to an ith singular value and an ith singular column vector corresponding to the ith singular value (σ1≧σ2≧ . . . ≧σNt).
DISCLOSURE OF THE INVENTION
Technical Task
The technical task of the present invention is to provide a method for configuring a codebook in a multi-antenna wireless communication system and apparatus therefor.
It will be appreciated by persons skilled in the art that the objects that could be achieved with the present invention are not limited to what has been particularly described hereinabove and the above and other objects that the present invention could achieve will be more clearly understood from the following detailed description.
Technical Solutions
In one aspect of the present invention to resolve the aforementioned problem, provided herein is a method of transmitting a signal by a transmitting end in a wireless communication system supporting multiple antennas including a multitude of vertical domain antennas and a multitude of horizontal domain antennas, including precoding a signal for the multiple antennas using a specific precoding matrix selected on the basis of a first codebook for a multitude of the vertical domain antennas and a second codebook for a multitude of the horizontal domain antennas and transmitting the precoded signal to a receiving end, wherein the specific precoding matrix is defined by using a Kronecker product of a first precoding matrix selected from the first codebook according to at least one first selection vector and a second precoding matrix selected from the second codebook according to at least one second selection vector.
In another aspect of the present invention to resolve the aforementioned problem, provided herein is an apparatus for transmitting a signal in a wireless communication system supporting multiple antennas including a multitude of vertical domain antennas and a multitude of horizontal domain antennas, including a radio frequency unit and a processor, wherein the processor is configured to precode a signal for the multiple antennas using a specific precoding matrix selected on the basis of a first codebook for a multitude of the vertical domain antennas and a second codebook for a multitude of the horizontal domain antennas and transmit the precoded signal to a receiving end and wherein the specific precoding matrix is defined by using a Kronecker product of a first precoding matrix selected from the first codebook according to at least one first selection vector and a second precoding matrix selected from the second codebook according to at least one second selection vector.
Advantageous Effects
According to the present invention, there is provided a method for configuring a codebook in a wireless communication system and apparatus therefor.
It will be appreciated by persons skilled in the art that that the effects achieved by the present invention are not limited to what has been particularly described hereinabove and other advantages of the present invention will be more clearly understood from the following detailed description.



DESCRIPTION OF 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 specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention.
FIG. 1 is a diagram showing a network structure of an Evolved Universal Mobile Telecommunications System (E-UMTS) as an example of a wireless communication system;
FIG. 2 is a block diagram illustrating configurations of a base station 205 and a user equipment 210 in a wireless communication system 200 according to the present invention;
FIG. 3 is a diagram for a configuration of a general MIMO communication system;
FIG. 4 is a diagram for an example of a general CDD structure in a MIMO system;
FIG. 5 is a diagram for explaining a basic concept of a codebook-based precoding;
FIG. 6 is a diagram for examples of configuring 8 transmission antennas;
FIG. 7 is a diagram for an active antenna system (AAS);
FIG. 8 is a reference diagram to describe feedback periods of a vertical PMI and a horizontal PMI.



BEST MODE FOR INVENTION
Hereinafter, the preferred embodiments of the present invention will be described with reference to the accompanying drawings. It is to be understood that the detailed description, which will be disclosed along with the accompanying drawings, is intended to describe the exemplary embodiments of the present invention, and is not intended to describe a unique embodiment with which the present invention can be carried out. The following detailed description includes detailed matters to provide full understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention can be carried out without the detailed matters. For example, the following detailed description is given under the assumption that 3GPP LTE mobile communication systems are used. However, the description may be applied to any other mobile communication system except for specific features inherent to the 3GPP LTE systems.
In some cases, to prevent the concept of the present invention from being ambiguous, structures and apparatuses of the known art will be omitted, or will be shown in the form of a block diagram based on main functions of each structure and apparatus. Also, wherever possible, the same reference numbers will be used throughout the drawings and the specification to refer to the same or like parts.
Moreover, in the following description, it is assumed that a terminal refers to a mobile or fixed type user equipment such as a user equipment (UE), and an advanced mobile station (AMS). Also, it is assumed that a base station refers to a random node of a network terminal, such as Node B, eNode B, and an access point (AP), which performs communication with the user equipment.
In a mobile communication system, a user equipment may receive information from a base station through a downlink and transmit information to the base station through an uplink. The information that the user equipment transmits or receives includes data and various types of control information. There are various physical channels according to the types and usages of information that the user equipment transmits or receives.
As an example of a mobile communication system to which the present invention is applicable, a 3rd Generation Partnership Project Long Term Evolution (hereinafter, referred to as LTE) communication system is described in brief
FIG. 1 is a view schematically illustrating a network structure of an E-UMTS as an exemplary radio communication system.
An Evolved Universal Mobile Telecommunications System (E-UMTS) is an advanced version of a conventional Universal Mobile Telecommunications System (UMTS) and basic standardization thereof is currently underway in the 3GPP. E-UMTS may be generally referred to as a Long Term Evolution (LTE) system. For details of the technical specifications of the UMTS and E-UMTS, reference can be made to Release 7 and Release 8 of “3rd Generation Partnership Project; Technical Specification Group Radio Access Network”.
Referring to FIG. 1, the E-UMTS includes a User Equipment (UE), eNodeBs (eNBs), and an Access Gateway (AG) which is located at an end of the network (E-UTRAN) and connected to an external network. The eNBs may simultaneously transmit multiple data streams for a broadcast service, a multicast service, and/or a unicast service.
One or more cells may exist per eNB. The cell is set to operate in one of bandwidths such as 1.25, 2.5, 5, 10, 15, and 20 MHz and provides a downlink (DL) or uplink (UL) transmission service to a plurality of UEs in the bandwidth. Different cells may be set to provide different bandwidths. The eNB controls data transmission or reception to and from a plurality of UEs. The eNB transmits DL scheduling information of DL data to a corresponding UE so as to inform the UE of a time/frequency domain in which the DL data is supposed to be transmitted, coding, a data size, and hybrid automatic repeat and request (HARQ)-related information.
In addition, the eNB transmits UL scheduling information of UL data to a corresponding UE so as to inform the UE of a time/frequency domain which may be used by the UE, coding, a data size, and HARQ-related information. An interface for transmitting user traffic or control traffic may be used between eNBs. A core network (CN) may include the AG and a network node or the like for user registration of UEs. The AG manages the mobility of a UE on a tracking area (TA) basis. One TA includes a plurality of cells.
Although wireless communication technology has been developed to LTE based on wideband code division multiple access (WCDMA), the demands and expectations of users and service providers are on the rise. In addition, considering other radio access technologies under development, new technological evolution is required to secure high competitiveness in the future. Decrease in cost per bit, increase in service availability, flexible use of frequency bands, a simplified structure, an open interface, appropriate power consumption of UEs, and the like are required.
Recently, 3GPP has standardized technology subsequent to LTE. In this specification, the technology will be referred to as “LTE-Advanced” or “LTE-A”. A main difference between the LTE system and the LTE-A system is a system bandwidth. The LTE-A system aims to support a wideband of up to 100 MHz. To achieve this, the LTE-A system employs carrier aggregation or bandwidth aggregation that accomplishes a wideband using a plurality of frequency blocks. Carrier aggregation uses a plurality of frequency blocks as a large logical frequency band in order to achieve a wider frequency band. The bandwidth of each frequency block can be defined on the basis of a system block bandwidth used in the LTE system. Each frequency block is transmitted using a component carrier.
FIG. 2 is a block diagram illustrating configurations of a base station 205 and a user equipment 210 in a wireless communication system 200.
Although one base station 205 and one user equipment 210 are shown for simplification of a wireless communication system 200, the wireless communication system 200 may include one or more base stations and/or one or more user equipments.
Referring to FIG. 2, the base station 105 may include a transmitting (Tx) data processor 215, a symbol modulator 220, a transmitter 225, a transmitting and receiving antenna 230, a processor 280, a memory 285, a receiver 290, a symbol demodulator 295, and a receiving (Rx) data processor 297. The user equipment 210 may include a Tx data processor 265, a symbol modulator 270, a transmitter 275, a transmitting and receiving antenna 235, a processor 255, a memory 260, a receiver 240, a symbol demodulator 255, and an Rx data processor 250. Although the antennas 230 and 235 are respectively shown in the base station 205 and the user equipment 210, each of the base station 205 and the user equipment 210 includes a plurality of antennas. Accordingly, the base station 205 and the user equipment 210 according to the present invention support a multiple input multiple output (MIMO) system. Also, the base station 205 according to the present invention may support both a single user-MIMO (SU-MIMO) system and a multi user-MIMO (MU-MIMO) system.
On a downlink, the Tx data processor 215 receives traffic data, formats and codes the received traffic data, interleaves and modulates (or symbol maps) the coded traffic data, and provides the modulated symbols (“data symbols”). The symbol modulator 220 receives and processes the data symbols and pilot symbols and provides streams of the symbols.
The symbol modulator 220 multiplexes the data and pilot symbols and transmits the multiplexed data and pilot symbols to the transmitter 225. At this time, the respective transmitted symbols may be a signal value of null, the data symbols and the pilot symbols. In each symbol period, the pilot symbols may be transmitted continuously. The pilot symbols may be frequency division multiplexing (FDM) symbols, orthogonal frequency division multiplexing (OFDM) symbols, time division multiplexing (TDM) symbols, or code division multiplexing (CDM) symbols.
The transmitter 225 receives the streams of the symbols and converts the received streams into one or more analog symbols. Also, the transmitter 225 generates downlink signals suitable for transmission through a radio channel by additionally controlling (for example, amplifying, filtering and frequency upconverting) the analog signals. Subsequently, the downlink signals are transmitted to the user equipment through the antenna 230.
In the user equipment 210, the antenna 235 receives the downlink signals from the base station 205 and provides the received signals to the receiver 240. The receiver 240 controls (for example, filters, amplifies and frequency downcoverts) the received signals and digitalizes the controlled signals to acquire samples. The symbol demodulator 245 demodulates the received pilot symbols and provides the demodulated pilot symbols to the processor 255 to perform channel estimation.
Also, the symbol demodulator 245 receives a frequency response estimation value for the downlink from the processor 255, acquires data symbol estimation values (estimation values of the transmitted data symbols) by performing data demodulation for the received data symbols, and provides the data symbol estimation values to the Rx data processor 250. The Rx data processor 250 demodulates (i.e., symbol de-mapping), deinterleaves, and decodes the data symbol estimation values to recover the transmitted traffic data.
Processing based on the symbol demodulator 245 and the Rx data processor 250 is complementary to processing based on the symbol demodulator 220 and the Tx data processor 215 at the base station 205.
On an uplink, the Tx data processor 265 of the user equipment 210 processes traffic data and provides data symbols. The symbol modulator 270 receives the data symbols, multiplexes the received data symbols with the pilot symbols, performs modulation for the multiplexed symbols, and provides the streams of the symbols to the transmitter 275. The transmitter 275 receives and processes the streams of the symbols and generates uplink signals. The uplink signals are transmitted to the base station 205 through the antenna 235.
The uplink signals are received in the base station 205 from the user equipment 210 through the antenna 230, and the receiver 290 processes the received uplink signals to acquire samples. Subsequently, the symbol demodulator 295 processes the samples and provides data symbol estimation values and the pilot symbols received for the uplink. The Rx data processor 297 recovers the traffic data transmitted from the user equipment 210 by processing the data symbol estimation values.
The processors 255 and 280 of the user equipment 210 and the base station 205 respectively command (for example, control, adjust, manage, etc.) the operation at the user equipment 210 and the base station 205. The processors 255 and 280 may respectively be connected with the memories 260 and 285 that store program codes and data. The memories 260 and 285 respectively connected to the processor 280 store operating system, application, and general files therein.
Each of the processors 255 and 280 may be referred to as a controller, a microcontroller, a microprocessor, and a microcomputer. Meanwhile, the processors 255 and 280 may be implemented by hardware, firmware, software, or their combination. If the embodiment of the present invention is implemented by hardware, application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), and field programmable gate arrays (FPGAs) configured to perform the embodiment of the present invention may be provided in the processors 255 and 280. Meanwhile, if the embodiment according to the present invention is implemented by firmware or software, firmware or software may be configured to include a module, a procedure, or a function, which performs functions or operations of the present invention. Firmware or software configured to perform the present invention may be provided in the processors 255 and 280, or may be stored in the memories 260 and 285 and driven by the processors 255 and 280.
Layers of a radio interface protocol between the user equipment 110 or the base station 105 and a wireless communication system (network) may be classified into a first layer L1, a second layer L2 and a third layer L3 on the basis of three lower layers of OSI (open system interconnection) standard model widely known in communication systems. A physical layer belongs to the first layer L1 and provides an information transfer service using a physical channel. A radio resource control (RRC) layer belongs to the third layer and provides control radio resources between the user equipment and the network. The user equipment and the base station may exchange RRC messages with each another through the RRC layer.
The term, base station used in the present invention may refer to a “cell or sector” when used as a regional concept. A serving base station (or serving cell) may be regarded as a base station which provides main services to UEs and may transmit and receive control information on a coordinated multiple transmission point. In this sense, the serving base station (or serving cell) may be referred to as an anchor base station (or anchor cell). Likewise, a neighboring base station may be referred to as a neighbor cell used as a local concept.
Multiple Antenna System
In the multiple antenna technology, reception of one whole message does not depend on a single antenna path. Instead, in the multiple antenna technology, data fragments received through multiple antennas are collected and combined to complete data. If the multiple antenna technology is used, a data transfer rate within a cell region of a specific size may be improved, or system coverage may be improved while ensuring a specific data transfer rate. In addition, this technology can be broadly used by mobile communication devices and relays. Due to the multiple antenna technology, restriction on mobile communication traffic based on a legacy technology using a single antenna can be solved.
FIG. 3(a) shows the configuration of a wireless communication system including multiple antennas. As shown in FIG. 3(a), the number of transmit (Tx) antennas and the number of Rx antennas respectively to NT and NR, a theoretical channel transmission capacity of the MIMO communication system increases in proportion to the number of antennas, differently from the above-mentioned case in which only a transmitter or receiver uses several antennas, so that transmission rate and frequency efficiency can be greatly increased. In this case, the transfer rate acquired by the increasing channel transmission capacity can theoretically increase by a predetermined amount that corresponds to multiplication of a maximum transfer rate (Ro) acquired when one antenna is used and a rate of increase (Ri). The rate of increase (Ri) can be represented by the following equation 3.

Ri=min (NT, NR)   [Equation 3]

For example, provided that a MIMO system uses four Tx antennas and four Rx antennas, the MIMO system can theoretically acquire a high transfer rate which is four times higher than that of a single antenna system. After the above-mentioned theoretical capacity increase of the MIMO system was demonstrated in the mid-1990s, many developers began to conduct intensive research into a variety of technologies which can substantially increase data transfer rate using the theoretical capacity increase. Some of the above technologies have been reflected in a variety of wireless communication standards, for example, third-generation mobile communication or next-generation wireless LAN, etc.
A variety of MIMO-associated technologies have been intensively researched by many companies or developers, for example, research into information theory associated with MIMO communication capacity under various channel environments or multiple access environments, research into a radio frequency (RF) channel measurement and modeling of the MIMO system, and research into a space-time signal processing technology.
Mathematical modeling of a communication method for use in the above-mentioned MIMO system will hereinafter be described in detail. As can be seen from FIG. 7, it is assumed that there are NTTx antennas and NR Rx antennas. In the case of a transmission signal, a maximum number of transmission information pieces is NT under the condition that NTTx antennas are used, so that the transmission information can be represented by a specific vector shown in the following equation 4.

s=[s1, s2, . . . , sNT]T   [Equation 4]

In the meantime, individual transmission information pieces s1, s2, . . . , sNT may have different transmission powers. In this case, if the individual transmission powers are denoted by P1, P2, . . . , PNT, transmission information having an adjusted transmission power can be represented by a specific vector shown in the following equation 5.

ŝ=└ŝ1, ŝ2, . . . , ŝNT┘T=[Ps1, Ps2, . . . , PsNT]T   [Equation 5]

In Equation 5, Ŝ is a transmission vector, and can be represented by the following equation 6 using a diagonal matrix P of a transmission power.




  
    
      
        
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In the meantime, the information vector Ŝ having an adjusted transmission power is applied to a weight matrix W, so that NT transmission signals x1, x2, . . . , xNT to be actually transmitted are configured. In this case, the weight matrix W is adapted to properly distribute transmission information to individual antennas according to transmission channel situations. The above-mentioned transmission signals x1, x2, . . . , xNT can be represented by the following equation 7 using the vector X. Here, Wij denotes a weight corresponding to i-thTx antenna and j-th information. W represents a weight matrix or precoding matrix.



  
    
      
    
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                    12
                  
                
                
                  
                    w
                    12
                  
                
                
                  ...
                
                
                  
                    w
                    
                      2
                      ⁢
                      
                        N
                        T
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    w
                    
                      i
                      ⁢
                      2
                    
                  
                
                
                  
                    w
                    
                      i
                      ⁢
                      2
                    
                  
                
                
                  ...
                
                
                  
                    w
                    
                      iN
                      T
                    
                  
                
              
              
                
                  ⋮
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    w
                    
                      N
                      
                        T
                        1
                      
                    
                  
                
                
                  
                    w
                    
                      N
                      
                        T
                        2
                      
                    
                  
                
                
                  ...
                
                
                  
                    w
                    
                      
                        N
                        T
                      
                      ⁢
                      
                        N
                        T
                      
                    
                  
                
              
            
            ]
          
          ⁡
          
            [
            
              
                
                  
                    
                      s
                      ^
                    
                    1
                  
                
              
              
                
                  
                    
                      s
                      ^
                    
                    2
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      s
                      ^
                    
                    j
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      s
                      ^
                    
                    
                      N
                      T
                    
                  
                
              
            
            ]
          
        
        =
        
          
            W
            ⁢
            
              s
              ^
            
          
          =
          WPs
        
      
    
  



Given NR Rx antennas, signals received at the respective Rx antennas, y1, y2, . . . , yNR may be represented as the following vector.

y=[y1, y2, . . . , yNR]T   [Equation 8]

When channels are modeled in the MIMO communication system, they may be distinguished according to the indexes of Tx and Rx antennas and the channel between a jthTx antenna and an ith Rx antenna may be represented as hij. It is to be noted herein that the index of the Rx antenna precedes that of the Tx antenna in hij.
The channels may be represented as vectors and matrices by grouping them. Examples of vector expressions are given as below. FIG. 3(b) illustrates channels from NTTx antennas to an ith Rx antenna.
As illustrated in FIG. 3(b), the channels from the NTTx antennas to an ith Rx antenna may be expressed as follows.

hiT=[hi1, hi2, . . . , hiNT]  [Equation 9]

Also, all channels from the NTTx antennas to the NR Rx antennas may be expressed as the following matrix.




  
    
      
        H
        =
        
          
            [
            
              
                
                  
                    h
                    1
                    T
                  
                
              
              
                
                  
                    h
                    2
                    T
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    h
                    i
                    T
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    h
                    
                      N
                      R
                    
                    T
                  
                
              
            
            ]
          
          =
          
            [
            
              
                
                  
                    h
                    11
                  
                
                
                  
                    h
                    12
                  
                
                
                  ...
                
                
                  
                    h
                    
                      1
                      ⁢
                      
                        N
                        T
                      
                    
                  
                
              
              
                
                  
                    h
                    12
                  
                
                
                  
                    h
                    12
                  
                
                
                  ...
                
                
                  
                    h
                    
                      2
                      ⁢
                      
                        N
                        T
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    h
                    
                      i
                      ⁢
                      2
                    
                  
                
                
                  
                    h
                    
                      i
                      ⁢
                      2
                    
                  
                
                
                  ...
                
                
                  
                    h
                    
                      iN
                      T
                    
                  
                
              
              
                
                  ⋮
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    h
                    
                      N
                      
                        R
                        1
                      
                    
                  
                
                
                  
                    h
                    
                      N
                      
                        R
                        2
                      
                    
                  
                
                
                  ...
                
                
                  
                    h
                    
                      
                        N
                        R
                      
                      ⁢
                      
                        N
                        T
                      
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          10
        
        ]
      
    
  




Actual channels experience the above channel matrix H and then are added with Additive White Gaussian Noise (AWGN). The AWGN n1, n2, . . . , nNR added to the NR Rx antennas is given as the following vector.

n=[n1, n2, . . . , nNR]T   [Equation 11]

 From the above modeled equations, the received signal can be expressed as follows.



  
    
      
    
    ⁢
    
      [
      
        Equation
        ⁢
        
          
        
        ⁢
        12
      
      ]
    
  




  
    y
    =
    
      
        [
        
          
            
              
                y
                1
              
            
          
          
            
              
                y
                2
              
            
          
          
            
              ⋮
            
          
          
            
              
                y
                i
              
            
          
          
            
              ⋮
            
          
          
            
              
                y
                
                  N
                  R
                
              
            
          
        
        ]
      
      =
      
        
          
            
              [
              
                
                  
                    
                      h
                      11
                    
                  
                  
                    
                      h
                      12
                    
                  
                  
                    ...
                  
                  
                    
                      h
                      
                        1
                        ⁢
                        
                          N
                          T
                        
                      
                    
                  
                
                
                  
                    
                      h
                      12
                    
                  
                  
                    
                      h
                      12
                    
                  
                  
                    ...
                  
                  
                    
                      h
                      
                        2
                        ⁢
                        
                          N
                          T
                        
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    
                      
                    
                  
                  
                    ⋱
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      h
                      
                        i
                        ⁢
                        2
                      
                    
                  
                  
                    
                      h
                      
                        i
                        ⁢
                        2
                      
                    
                  
                  
                    ...
                  
                  
                    
                      h
                      
                        iN
                        T
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    
                      
                    
                  
                  
                    ⋱
                  
                  
                    
                      
                    
                  
                
                
                  
                    
                      h
                      
                        
                          N
                          R
                        
                        ⁢
                        1
                      
                    
                  
                  
                    
                      h
                      
                        
                          N
                          R
                        
                        ⁢
                        2
                      
                    
                  
                  
                    ...
                  
                  
                    
                      h
                      
                        
                          N
                          R
                        
                        ⁢
                        
                          N
                          T
                        
                      
                    
                  
                
              
              ]
            
            ⁡
            
              [
              
                
                  
                    
                      x
                      1
                    
                  
                
                
                  
                    
                      x
                      2
                    
                  
                
                
                  
                    ⋮
                  
                
                
                  
                    
                      x
                      j
                    
                  
                
                
                  
                    ⋮
                  
                
                
                  
                    
                      x
                      
                        N
                        T
                      
                    
                  
                
              
              ]
            
          
          +
          
            [
            
              
                
                  
                    n
                    1
                  
                
              
              
                
                  
                    n
                    2
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    n
                    i
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    n
                    
                      N
                      R
                    
                  
                
              
            
            ]
          
        
        =
        
          Hx
          +
          n
        
      
    
  



In the meantime, the numbers of rows and columns in the channel matrix H representing channel states are determined according to the numbers of Tx and Rx antennas. The number of rows is identical to that of Rx antennas, NR and the number of columns is identical to that of Tx antennas, NT. Thus, the channel matrix H is of size NRxNT. In general, the rank of a matrix is defined as the smaller between the numbers of independent rows and columns. Accordingly, the rank of the matrix is not larger than the number of rows or columns. The rank of the matrix H, rank(H) is limited as follows.

rank(H)≦min(NT, NR)   [Equation 13]

As a multi-antenna transmission and reception scheme used for operating a multi-antenna system, it may be able to use FSTD (frequency switched transmit diversity), SFBC (Space Frequency Block Code), STBC (Space Time Block Code), CDD (Cyclic Delay Diversity), TSTD (time switched transmit diversity) and the like. In a rank 2 or higher, SM (Spatial Multiplexing), GCDD (Generalized Cyclic Delay Diversity), S-VAP (Selective Virtual Antenna Permutation) and the like can be used.
The FSTD corresponds to a scheme of obtaining a diversity gain by assigning a subcarrier of a different frequency to a signal transmitted by each of multiple antennas. The SFBC corresponds to a scheme capable of securing both a diversity gain in a corresponding dimension and a multi-user scheduling gain by efficiently applying selectivity in a spatial domain and a frequency domain. The STBC corresponds to a scheme of applying selectivity in a spatial domain and a time domain. The CDD corresponds to a scheme of obtaining a diversity gain using path delay between transmission antennas. The TSTD corresponds to a scheme of distinguishing signals transmitted by multiple antennas from each other on the basis of time. The spatial multiplexing (SM) corresponds to a scheme of increasing a transfer rate by transmitting a different data according to an antenna. The GCDD corresponds to a scheme of applying selectivity in a time domain and a frequency domain. The S-VAP corresponds to a scheme of using a single precoding matrix. The S-VAP can be classified into an MCW (multi codeword) S-VAP for mixing multiple codewords between antennas in spatial diversity or spatial multiplexing and an SCW (single codeword) S-VAP for using a single codeword.
Among the aforementioned MIMO transmission schemes, the STBC scheme corresponds to a scheme of obtaining time diversity in a manner that an identical data symbol is repeated in a time domain to support orthogonality. Similarly, the SFBC scheme corresponds to a scheme of obtaining frequency diversity in a manner that an identical data symbol is repeated in a frequency domain to support orthogonality. Examples of a time block code used for the STBC and a frequency block code used for the SFBC can be represented as equation 14 and equation 15, respectively. The equation 14 indicates a block code in case of 2 transmission antennas and the equation 15 indicates a block code in case of 4 transmission antennas.




  
    
      
        
          1
          
            2
          
        
        ⁢
        
          (
          
            
              
                
                  S
                  1
                
              
              
                
                  S
                  2
                
              
            
            
              
                
                  -
                  
                    S
                    2
                    *
                  
                
              
              
                
                  S
                  1
                  *
                
              
            
          
          )
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          14
        
        ]
      
    
  








  
    
      
        
          1
          
            2
          
        
        ⁢
        
          (
          
            
              
                
                  S
                  1
                
              
              
                
                  S
                  2
                
              
              
                0
              
              
                0
              
            
            
              
                0
              
              
                0
              
              
                
                  S
                  3
                
              
              
                
                  S
                  4
                
              
            
            
              
                
                  -
                  
                    S
                    2
                    *
                  
                
              
              
                
                  S
                  1
                  *
                
              
              
                0
              
              
                0
              
            
            
              
                0
              
              
                0
              
              
                
                  -
                  
                    S
                    4
                    *
                  
                
              
              
                
                  -
                  
                    S
                    3
                    *
                  
                
              
            
          
          )
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          15
        
        ]
      
    
  




In the equations 14 and 15, Si (i=1, 2, 3, 4) corresponds to a modulated data symbol. And, in the equations 14 and 15, a row of a matrix corresponds to an antenna port and a column of the matrix corresponds to time (STBC) or frequency (SFBC).
Meanwhile, among the aforementioned MIMO transmission schemes, the CDD scheme corresponds to a scheme of increasing frequency diversity by increasing delay propagation on purpose. FIG. 4 shows an example of a general CDD structure in a multi-antenna system. FIG. 4(a) shows a scheme of applying cyclic delay in time domain. As shown in FIG. 4(b), the CDD scheme applying the cyclic delay of FIG. 4(a) can also be implemented by applying phase-shift diversity.
Codebook-based Precoding Scheme
In order to support MIMO antenna transmission, it may be able to apply precoding configured to appropriately distribute transmission information to each of multiple antennas according to a channel status and the like. A codebook-based precoding scheme corresponds to a scheme that a transmitting end and a receiving end determine a set of precoding matrixes in advance, the receiving end measures channel information from the transmitting end and gives feedback on a most suitable precoding matrix (i.e., precoding matrix index (PMI) to the transmitting end, and the transmitting end applies appropriate precoding to signal transmission based on the PMI.
Since the codebook-based precoding scheme is a scheme of selecting an appropriate precoding matrix from the predetermined set of precoding matrixes, although an optimized precoding is not always applied, feedback overhead can be reduced compared to a case of explicitly giving feedback on optimized precoding information to actual channel information.
FIG. 5 is a diagram for explaining a basic concept of a codebook-based precoding.
In case of following a codebook-based precoding scheme, a transmitting end and a receiving end share codebook information including the prescribed number of precoding matrixes, which are predetermined according to a transmission rank, the number of antennas, and the like. In particular, when feedback information is finite, the codebook-based precoding scheme can be used. The receiving end measures a channel state via a reception signal and may be then able to give feedback on information on the finite number of preferred precoding matrixes (i.e., an index of a corresponding precoding matrix) to the transmitting end based on the aforementioned codebook information. For instance, the receiving end measures a reception signal using ML (maximum likelihood) or MMSE (minimum mean square error) scheme and may be then able to select an optimized precoding matrix. Although FIG. 5 shows a case that the receiving end transmits precoding matrix information to the transmitting end according to a codeword, by which the present invention may be non-limited.
Having received the feedback information from the receiving end, the transmitting end can select a specific precoding matrix from a codebook based on the received information. The transmitting end, which has selected the precoding matrix, performs precoding in a manner of multiplying the number of layer signals corresponding to a transmission rank by the selected precoding matrix and may be then able to transmit a transmission signal on which the precoding is performed via a plurality of antennas. In a precoding matrix, the number of rows is identical to the number of antennas and the number of columns is identical to a rank value. Since the rank value is identical to the number of layers, the number of columns is identical to the number of layers. For instance, if the number of transmission antennas corresponds to 4 and the number of transmission layers corresponds to 2, a precoding matrix can be configured by a 4×2 matrix. Information transmitted via each layer can be mapped to each antenna through the precoding matrix.
Having received a signal, which is transmitted from the transmitting end in a manner of being pre-coded, the receiving end can restore the received signal in a manner of performing reverse processing on the precoding processed in the transmitting end. In general, since a precoding matrix satisfies a unitary matrix (U) condition such as U*UH=I, the reverse processing performed on the precoding can be performed using a scheme of multiplying Hermite matrix (PH) of a precoding matrix (P) used in the precoding of the transmitting end by the received signal.
For instance, Table 1 in the following shows a codebook used for downlink transmission using 2 transmission antennas in 3GPP LTE release-8/9 and Table 2 in the following shows a codebook used for downlink transmission using 4 transmission antennas in 3GPP LTE release-8/9.








TABLE 1








Number of rank









Codebook index
1
2





0




  
    1
    
      2
    
  
  ⁡
  
    [
    
      
        
          1
        
      
      
        
          1
        
      
    
    ]
  








  
    1
    
      2
    
  
  ⁡
  
    [
    
      
        
          1
        
        
          0
        
      
      
        
          0
        
        
          1
        
      
    
    ]
  






 


1




  
    1
    
      2
    
  
  ⁡
  
    [
    
      
        
          1
        
      
      
        
          
            -
            1
          
        
      
    
    ]
  








  
    1
    2
  
  ⁡
  
    [
    
      
        
          1
        
        
          1
        
      
      
        
          1
        
        
          
            -
            1
          
        
      
    
    ]
  






 


2




  
    1
    
      2
    
  
  ⁡
  
    [
    
      
        
          1
        
      
      
        
          j
        
      
    
    ]
  








  
    1
    2
  
  ⁡
  
    [
    
      
        
          1
        
        
          1
        
      
      
        
          j
        
        
          
            -
            j
          
        
      
    
    ]
  






 


3




  
    1
    
      2
    
  
  ⁡
  
    [
    
      
        
          1
        
      
      
        
          
            -
            j
          
        
      
    
    ]
  




—


















TABLE 2







Codebook

Number of layers ν












index
un
1
2
3
4















0
u0 = [1 −1 −1 −1]T
W0{1}
W0{14}/{square root over (2)}
W0{124}/{square root over (3)}
W0{1234}/2


1
u1 = [1 −j 1 j]T
W1{1}
W1{12}/{square root over (2)}
W1{123}/{square root over (3)}
W1{1234}/2


2
u2 = [1 1 −1 1]T
W2{1}
W2{12}/{square root over (2)}
W2{123}/{square root over (3)}
W2{3214}/2


3
u3 = [1 j 1 −j]T
W3{1}
W3{12}/{square root over (2)}
W3{123}/{square root over (3)}
W3{3214}/2


4
u4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}]T
W4{1}
W4{14}/{square root over (2)}
W4{124}/{square root over (3)}
W4{1234}/2


5
u5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}]T
W5{1}
W5{14}/{square root over (2)}
W5{124}/{square root over (3)}
W5{1234}/2


6
u6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]T
W6{1}
W6{13}/{square root over (2)}
W6{134}/{square root over (3)}
W6{1324}/2


7
u7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}]T
W7{1}
W7{13}/{square root over (2)}
W7{134}/{square root over (3)}
W7{1324}/2


8
u8 = [1 −1 1 1]T
W8{1}
W8{12}/{square root over (2)}
W8{124}/{square root over (3)}
W8{1234}/2


9
u9 = [1 −j −1 −j]T
W9{1}
W9{14}/{square root over (2)}
W9{134}/{square root over (3)}
W9{1234}/2


10
u10 = [1 1 1 −1]T
W10{1}
W10{13}/{square root over (2)}
W10{123}/{square root over (3)}
W10{1324}/2


11
u11 = [1 j −1 j]T
W11{1}
W11{13}/{square root over (2)}
W11{134}/{square root over (3)}
W11{1324}/2


12
u12 = [1 −1 −1 1]T
W12{1}
W12{12}/{square root over (2)}
W12{123}/{square root over (3)}
W12{1234}/2


13
u13 = [1 −1 1 −1]T
W13{1}
W13{13}/{square root over (2)}
W13{123}/{square root over (3)}
W13{1324}/2


14
u14 = [1 1 −1 −1]T
W14{1}
W14{13}/{square root over (2)}
W14{123}/{square root over (3)}
W14{3214}/2


15
u15 = [1 1 1 1]T
W15{1}
W15{12}/{square root over (2)}
W15{123}/{square root over (3)}
W15{1234}/2









In Table 2, Wn{s} can be obtained by a set {s} configured from an equation represented as Wn=I−2ununH/unHun. In this case, I indicates a 4×4 single matrix and uu is a value given in Table 2.
As shown in Table 1, in case of a codebook for 2 transmission antennas, it may have total 7 precoding vectors/matrixes. In this case, since a single matrix is used for an open-loop system, total 6 precoding vectors/matrixes are used for a close-loop system. And, in case of a codebook for 4 transmission antennas shown in Table 2, it may have total 64 precoding vectors/matrixes.
The aforementioned codebook has a common property such as a CM (constant modulus) property, a nested property, a constrained alphabet property, and the like. The CM property corresponds to a property that each element of all precoding matrixes in a codebook does not include ‘0’ and has a same size. The nested property corresponds to a property that a precoding matrix of a lower rank is configured by a subset of a specific column of a precoding matrix of a higher rank. The constrained alphabet property corresponds to a property that an alphabet of each element of all precoding matrixes in a codebook is configured by




  
    {
    
      
        ±
        1
      
      ,
      
        ±
        j
      
      ,
      
        ±
        
          
            (
            
              1
              +
              j
            
            )
          
          
            2
          
        
      
      ,
      
        ±
        
          
            (
            
              
                -
                1
              
              +
              j
            
            )
          
          
            2
          
        
      
    
    }
  
  .




In Table 2, Wn{s} can be obtained from a set {s} configured by an equation represented as Wn=I−2ununH/unHun. In this case, I corresponds to 4×4 single matrix and un corresponds to a value given by Table 2.
As shown in Table 1, a codebook for two transmission antennas includes 7 precoding vectors/matrixes in total. In this case, since a single matrix is used for an open-loop system, for precoding of a closed-loop system, there are 6 precoding vectors/matrixes in total. And, as shown in Table 2, a codebook for 4 transmission antennas has 64 precoding vectors/matrixes in total.
The aforementioned codebook has a common property such as a CM (constant modulus) property, a nested property, a constrained alphabet property, and the like. The CM property corresponds to a property that each element of all precoding matrixes in a codebook does not include ‘0’ and has a same size. The nested property corresponds to a property that a precoding matrix of a lower rank is configured by a subset of a specific column of a precoding matrix of a higher rank. The constrained alphabet property corresponds to a property that an alphabet of each element of all precoding matrixes in a codebook is configured by




  
    {
    
      
        ±
        1
      
      ,
      
        ±
        j
      
      ,
      
        ±
        
          
            (
            
              1
              +
              j
            
            )
          
          
            2
          
        
      
      ,
      
        ±
        
          
            (
            
              
                -
                1
              
              +
              j
            
            )
          
          
            2
          
        
      
    
    }
  
  .




Feedback Channel Structure
Basically, since a base station is unable to know information on a downlink channel in FDD (frequency division duplex) system, the base station uses channel information fed back by a UE for downlink transmission. In case of a legacy 3GPP LTE release-8/9 system, a UE can feedback downlink channel information via PUCCH or PUSCH. In case of the PUCCH, the PUCCH periodically feedbacks channel information. In case of the PUSCH, the PUSCH aperiodically feedbacks channel information according to a request of the base station. And, channel information can be fed back in response to the whole of assigned frequency bands (i.e., wideband (WB)) or the specific number of RBs (i.e., subband (SB)).
Extended Antenna Configuration
FIG. 6 is a diagram for examples of configuring 8 transmission antennas.
FIG. 6(a) shows a case that N numbers of antennas configure an independent channel without grouping. In general, this case is referred to as an ULA (uniform linear array). If a plurality of antennas are deployed in a manner of being apart from each other, a space of a transmitter and/or a receiver may not be sufficient enough for configuring channels independent from each other.
FIG. 6(b) shows an antenna configuration (paired ULA) of a ULA scheme that two antennas make a pair. In this case, an associated channel may exist between the two antennas making a pair and an independent channel may exist with an antenna of a different pair.
Meanwhile, unlike a legacy 3GPP LTE release-8/9 using 4 transmission antennas in downlink, 3GPP LTE release-10 system may use 8 transmission antennas in downlink. In order to apply the extended antennas configuration, it is necessary to install many antennas in an insufficient space. Hence, the ULA antenna configurations shown in FIGS. 6(a) and (b) may not be appropriate for the extended configuration. Hence, as shown in FIG. 6(c), it may consider applying a dual-pole (or cross-pole) antenna configuration. If transmission antennas are configured using the dual-pole (or cross-pole) antenna configuration, although a distance d between antennas is relatively short, it is able to transmit data of high throughput by lowering antenna correlation.
Codebook Structures
As mentioned in the foregoing description, if a predefined codebook is shared between a transmitting end and receiving end, it is able to reduce overhead of the receiving end resulted from making a feedback on precoding information to be used for MIMO transmission of the transmitting end. Hence, it is able to apply efficient precoding.
As an example of configuring a predetermined codebook, it may be able to configure a precoder matrix using a DFT (Discrete Fourier Transform) matrix or a Walsh matrix. Or, it may be able to configure a precoder of various forms in a manner of combining with a phase shift matrix or a phase shift diversity matrix.
In case of a co-polarization antenna system, a codebook of a DFT system shows good performance. In this case, when the DFT matrix-based codebook is configured, n×n DFT matrix can be defined as equation 16 in the following.




  
    
      
        
          
            DFTn
            ⁢
            
              :
            
            ⁢
            
              
            
            ⁢
            
              
                D
                n
              
              ⁡
              
                (
                
                  k
                  ,
                  l
                
                )
              
            
          
          =
          
            
              1
              
                n
              
            
            ⁢
            
              exp
              ⁡
              
                (
                
                  
                    -
                    j2π
                  
                  ⁢
                  
                    
                  
                  ⁢
                  k
                  ⁢
                  
                    
                  
                  ⁢
                  
                    l
                    /
                    n
                  
                
                )
              
            
          
        
        ,
        
          

        
        ⁢
        k
        ,
        
          l
          =
          0
        
        ,
        1
        ,
        ...
        ⁢
        
          
        
        ,
        
          n
          -
          1
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          16
        
        ]
      
    
  




The DFT matrix shown in the equation 14 exists as a single matrix in response to a specific size n. Hence, in order to define various precoding matrixes and appropriately use the various precoding matrixes according to a situation, it may consider additionally configuring and using a rotated version of a DFTn matrix. Equation 17 in the following shows an example of a rotated DFTn matrix.




  
    
      
        
          rotated
          ⁢
          
            
          
          ⁢
          DFTn
          ⁢
          
            :
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              
                D
                n
                
                  (
                  
                    G
                    ,
                    g
                  
                  )
                
              
              ⁡
              
                (
                
                  k
                  ,
                  l
                
                )
              
            
            =
            
              
                1
                
                  n
                
              
              ⁢
              exp
              ⁢
              
                (
                
                  
                    -
                    j2π
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      k
                      ⁡
                      
                        (
                        
                          l
                          +
                          
                            g
                            /
                            G
                          
                        
                        )
                      
                    
                    /
                    n
                  
                
                )
              
            
          
          ,
          
            

          
          ⁢
          k
          ,
          
            l
            =
            0
          
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            n
            -
            1
          
          ,
          
            g
            =
            0
          
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            G
            .
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          17
        
        ]
      
    
  




If a DFT matrix is configured using the equation 17, it may be able to generate G number of rotated DFTn matrixes and the generated matrixes satisfy a property of a DFT matrix.
In the following, a householder-based codebook structure is explained. The householder-based codebook structure corresponds to a codebook configured by a householder matrix. The householder matrix is a matrix used for householder transform. The householder transform is a sort of linear transformations and can be used for performing QR decomposition. The QR decomposition is to decompose a matrix into an orthogonal matrix (Q) and an upper triangular matrix (R). The upper triangular matrix corresponds to a square matrix that all components below a main diagonal line component are 0. An example of 4×4 householder matrix is shown in equation 18 in the following.




  
    
      
        
          
            M
            1
          
          =
          
            
              
                I
                4
              
              -
              
                2
                ⁢
                
                  
                
                ⁢
                
                  u
                  0
                
                ⁢
                
                  
                    u
                    1
                    H
                  
                  /
                  
                    
                      
                      
                        u
                        0
                      
                      
                    
                    2
                  
                
              
            
            =
            
              
                1
                
                  4
                
              
              *
              
                [
                
                  
                    
                      1
                    
                    
                      1
                    
                    
                      1
                    
                    
                      1
                    
                  
                  
                    
                      1
                    
                    
                      1
                    
                    
                      
                        -
                        1
                      
                    
                    
                      
                        -
                        1
                      
                    
                  
                  
                    
                      1
                    
                    
                      
                        -
                        1
                      
                    
                    
                      1
                    
                    
                      
                        -
                        1
                      
                    
                  
                  
                    
                      1
                    
                    
                      
                        -
                        1
                      
                    
                    
                      
                        -
                        1
                      
                    
                    
                      1
                    
                  
                
                ]
              
            
          
        
        ,
        
          

        
        ⁢
        
          
        
        ⁢
        
          
            u
            0
            T
          
          =
          
            [
            
              
                
                  1
                
                
                  
                    -
                    1
                  
                
                
                  
                    -
                    1
                  
                
                
                  
                    -
                    1
                  
                
              
            
            ]
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          18
        
        ]
      
    
  




It may be able to generate 4×4 unitary matrix including a CM property by the householder transform. Similar to a codebook for 4 transmission antennas shown in Table 2, n×n precoding matrix can be generated using the householder transform and it may be able to configure the precoding matrix to be used for rank transmission less than n using a column subset of the generated precoding matrix.
Codebook for 8 Transmission Antennas
In 3GPP LTE release-10 system including an extended antenna configuration (e.g., 8 transmission antennas), it may be able to apply a feedback scheme previously used in a legacy 3GPP LTE release-8/9 system in a manner of extending the feedback scheme. For example, it may be able to feedback such channel state information (CSI) as an RI (rank indicator), a PMI (precoding matrix index), CQI (channel quality information) and the like. In the following, a method of designing a dual precoder-based feedback codebook capable of being used in a system supporting an extended antenna configuration is explained. In order to indicate a precoder to be used for MIMO transmission of a transmitting end in the dual precoder-based feedback codebook, a receiving end can transmit a precoding matrix index to the transmitting end. A precoding matrix can be indicated by a combination of two PMIs different from each other. In particular, if the receiving end feedbacks the two PMIs different from each other (i.e., a first PMI and a second PMI) to the transmitting end, the transmitting end determines a precoding matrix indicated by the first and the second PMI and may be then able to apply the determined precoding matrix to MIMO transmission.
In designing the dual precoder-based feedback codebook, it may consider MIMO transmission transmitted by 8 transmission antennas, whether or not single user-MIMO (SU-MIMO) and multiple user-MIMO (MU-MIMO) are supported, suitability of various antenna configurations, a reference of codebook design, a size of a codebook, and the like.
When a codebook is applied to MIMO transmission transmitted by 8 transmission antennas, if the codebook is greater than rank 2, SU-MIMO is supported only. If the codebook is equal to or less than the rank 2, it may consider designing a feedback codebook optimized to both the SU-MIMO and the MU-MIMO and the feedback codebook appropriate for various antenna configurations.
Regarding the MU-MIMO, it may be preferable to make UEs participating in the MU-MIMO to be separated from each other in a correlation domain. Hence, it is necessary to design a codebook for the MU-MIMO to be properly operated on a channel of high correlation. Since DFT vectors provide good performance on the channel of high correlation, it may consider including a DFT vector in a set of codebooks up to rank-2. And, in high scattering propagation environment (e.g., indoor environment including many reflected waves) capable of generating many spatial channels, a SU-MIMO operation may be more suitable as a MIMO transmission scheme. Hence, it may be able to configure a codebook for a rank greater than rank-2 to have good performance of identifying multiple layers.
When a precoder for MIMO transmission is designed, it may be preferable to make a precoder structure have good performance in response to various antenna configurations (low correlation, high correlation, cross-polarization, and the like). In case of arranging 8 transmission antennas, it may be able to configure a cross-polarization array including 4λantenna space as a low-correlation antenna configuration, a ULA including 0.5λantenna space as a high-correlation antenna configuration, or a cross-polarization array including 0.5λantenna space as a cross-polarization antenna configuration. A DFT-based codebook structure can provide good performance in response to the high-correlation antenna configuration.
Meanwhile, block diagonal matrixes may be more suitable for the cross-polarization antenna configuration. Hence, if a diagonal matrix is introduced to a codebook for 8 transmission antennas, it is able to configure a codebook capable of providing goof performance to all antenna configurations.
As mentioned in the foregoing description, a reference of codebook design is to satisfy a unitary codebook, a CM property, a constrained alphabet property, an appropriate codebook size, a nested property and the like. The reference is applied to 3GPP LTE release-8/9 codebook design. It may consider applying the reference of codebook design to 3GPP LTE release-10 codebook design supporting an extended antenna configuration as well.
In relation to a size of a codebook, in order to sufficiently support a merit of using 8 transmission antennas, it is necessary to increase the size of the codebook. In order to obtain a sufficient precoding gain from the 8 transmission antennas in low correlation environment, a codebook (e.g., a codebook of a size greater than 4 bits in response to a rank 1 and a rank 2) of a big size may be required. A codebook of a size of 4 bits may be sufficient in obtaining a precoding gain in high correlation environment. Yet, in order to achieve a multiplexing gain of the MU-MIMO, it may be able to increase a codebook size for the rank 1 and the rank 2.
Hereinafter, the present invention will be described based on the aforementioned description. In particular, the present invention proposes a codebook having a kronecker product configuration.
A discussion over whether to introduce an antenna system utilizing an AAS in a wireless communication system after LTE Rel-12 is underway. Since the AAS consists of active antennas, each of which includes an active circuit, it is a technology capable of reducing interference or supporting an effective performance of beamforming by changing an antenna pattern adaptively to a wireless communication environment.
If such AAS is structured two-dimensionally (i.e., 2D-AAS), in terms of an antenna pattern, a main lobe of an antenna can be adjusted with respect to a beam direction, not only for the existing horizontal surface, but also for a vertical surface, enabling three-dimensional beam adaptation more effectively. Accordingly, on the basis of the above, it is possible to change a transmission beam more actively according to a location of a UE.
FIG. 7 is a reference diagram to describe a 2D-AAS to which the present invention is applicable. In the 2D-AAS, as shown in FIG. 7, a plurality of antennas are installed in a vertical direction and a horizontal direction, whereby a multiple antenna systems can be established.
Namely, if the 2D-AAS shown in FIG. 7 is introduced, antennas are increasingly installed on an antenna domain in a vertical direction, thereby increasing the possibility of installing a multitude of antennas together. Yet, in order to effectively operate a multitude of the antennas, it is significantly important to design a reference signal (RS) for a channel measurement per antenna and a feedback for a UE to indicate channel information between an antenna and the UE. This is because, in general, a reference signal (RS) overhead and a feedback overhead increase linearly or exponentially in proportion to the number of antennas.
Furthermore, in the present invention, a precoding set represents a set of precoding matrices regarding specific domain antennas (e.g., a vertical antenna and a horizontal antenna), and may be replaced by a codebook in some cases.
Hence, the present invention proposes a 3D MIMO codebook for a rank 1 such as the following equation 19 or equation 20 to reduce a feedback overhead.




  
    
      
        
          (
          
            
              W
              V
            
            ⁢
            
              e
              V
            
          
          )
        
        ⊗
        
          
            [
            
              
                
                  
                    W
                    H
                  
                
                
                  0
                
              
              
                
                  0
                
                
                  
                    W
                    H
                  
                
              
            
            ]
          
          ⁡
          
            [
            
              
                
                  
                    e
                    H
                  
                
              
              
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      e
                      H
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          19
        
        ]
      
    
  
  
    
      
        
          (
          
            
              W
              H
            
            ⁢
            
              e
              H
            
          
          )
        
        ⊗
        
          
            [
            
              
                
                  
                    W
                    V
                  
                
                
                  0
                
              
              
                
                  0
                
                
                  
                    W
                    V
                  
                
              
            
            ]
          
          ⁡
          
            [
            
              
                
                  
                    e
                    V
                  
                
              
              
                
                  
                    α
                    ⁢
                    
                      
                    
                    ⁢
                    
                      e
                      V
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          20
        
        ]
      
    
  




Furthermore, the equation 19 may be transformed to be expressed as equation 21, and the equation 20 may be transformed to be expressed as equation 22.




  
    
      
        [
        
          
            
              
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      V
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      H
                    
                  
                  )
                
              
            
          
          
            
              
                
                  α
                  ⁡
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        V
                      
                    
                    )
                  
                
                ⊗
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      H
                    
                  
                  )
                
              
            
          
        
        ]
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          21
        
        ]
      
    
  
  
    
      
        [
        
          
            
              
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      H
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      V
                    
                  
                  )
                
              
            
          
          
            
              
                
                  α
                  ⁡
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        H
                      
                    
                    )
                  
                
                ⊗
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      V
                    
                  
                  )
                
              
            
          
        
        ]
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          22
        
        ]
      
    
  




In the aforementioned equations 19 to 22,  means a kronecker product operation.
In a codebook of the equation 19 or the equation 21, according to the present invention, WV means a precoding set of vertical antenna elements. eV is a factor for selecting a specific one from this precoding set (i.e., WV). Hence, WV is fed back in a long-term, and eV may be fed back in a short-term having a period shorter than that of WV.
In particular, WV may be selected as a subset of D matrices composed of columns in a DFT codebook D matrix. Herein, the DFT codebook can be represented as equation 23.




  
    
      
        
          
            D
            
              (
              mn
              )
            
            
              
                N
                V
              
              ×
              
                N
                V
              
              ⁢
              a
            
          
          =
          
            
              1
              
                
                  N
                  V
                
              
            
            ⁢
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                
                  
                    2
                    ⁢
                    
                      π
                      ⁡
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      (
                      
                        n
                        -
                        1
                      
                      )
                    
                  
                  
                    
                      N
                      V
                    
                    ⁢
                    a
                  
                
              
            
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          23
        
        ]
      
    
  




for m=1, 2, . . . , NV, n=1, 2, . . . , NVα

In a DFT codebook according to the equation 23, α is an oversampling factor, and NV is the number of vertical antenna elements.
In addition, eV is a selection vector, which is used for selecting a single column. Herein, eV is composed of a single vector, and only one of elements has a value of “1” and the rest of the elements have a value of “0”. For example, regarding eV, if only a second element has a value of “1” and the rest of the elements have a value of “0”, a second column of WV is selected.
Moreover, in a codebook according to the equation 20 or equation 22 according to the present invention, WH means a precoding set of horizontal antenna elements. eH is a factor for selecting a specific one from this precoding set (i.e., WH). Hence, WH is fed back in a long-term, and eH may be fed back in a short-term having a period shorter than that of WH.
In particular, WH may be selected as a subset of D matrices composed of columns in a DFT codebook D matrix. Herein, the DFT codebook can be represented as equation 24.




  
    
      
        
          
            D
            
              (
              mn
              )
            
            
              
                N
                H
              
              ×
              
                N
                H
              
              ⁢
              a
            
          
          =
          
            
              1
              
                
                  N
                  H
                
              
            
            ⁢
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                
                  
                    2
                    ⁢
                    
                      π
                      ⁡
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      (
                      
                        n
                        -
                        1
                      
                      )
                    
                  
                  
                    
                      N
                      H
                    
                    ⁢
                    a
                  
                
              
            
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          24
        
        ]
      
    
  




for m=1, 2, . . . , NH, n=1, 2, . . . , NHα

In a DFT codebook according to the equation 24, α is an oversampling factor, and NH is the number of horizontal antenna elements.
And, eH is a selection vector, which is used in selecting a single column from WH. Herein, eH is composed of a single vector, and only one of elements has a value of “1” and the rest of the elements have a value of “0”. For example, regarding eH, if only a second element has a value of “1” , and the rest of the elements have a value of “0” , a second column of WH is selected.
Moreover, in a codebook represented as the aforementioned equations 19 to 22, α plays a role in adjusting a phase between ‘/’ antenna and “\” antenna in a cross-polarization antenna (hereinafter, referred to as “X-pol antenna”). That is, α is selected from a set of




  α
  ∈
  
    {
    
      1
      ,
      
        exp
        ⁡
        
          (
          
            j
            ⁢
            
              
            
            ⁢
            
              
                2
                ⁢
                π
              
              
                2
                
                  N
                  
                    α
                    ⁢
                    
                      
                    
                  
                
              
            
          
          )
        
      
      ,
      
        exp
        ⁡
        
          (
          
            j
            ⁢
            
              
                
                  
                
                ⁢
                
                  4
                  ⁢
                  π
                
              
              
                2
                
                  N
                  
                    α
                    ⁢
                    
                      
                    
                  
                
              
            
          
          )
        
      
      ,
      ...
      ⁢
      
        
      
      ,
      
        exp
        (
        
          j
          ⁢
          
            
          
          ⁢
          
            
              2
              ⁢
              
                (
                
                  
                    2
                    
                      N
                      α
                    
                  
                  -
                  2
                
                )
              
              ⁢
              π
            
            
              2
              
                N
                α
              
            
          
        
        )
      
      ,
      
        exp
        (
        
          j
          ⁢
          
            
              2
              ⁢
              
                (
                
                  
                    2
                    
                      N
                      α
                    
                  
                  -
                  1
                
                )
              
              ⁢
              π
            
            
              2
              
                N
                α
              
            
          
        
        )
      
    
    }
  




Herein, Nα corresponds to the number of feedback bits for α. In case of Nα=2, α may be selected from a set of





  α
  ∈
  
    
      {
      
        1
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
              
              ⁢
              
                π
                2
              
            
            )
          
        
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                
                2
              
            
            )
          
        
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  3
                  ⁢
                  π
                
                2
              
            
            )
          
        
      
      }
    
    .
  




Furthermore, in a codebook represented as the aforementioned equations 19 to 22, WV may be fed back with a period longer than that of WH, and eV may be fed back with a period longer than that of eH.
FIG. 8 is a reference diagram to describe a feedback period of a Vertical Precoding Matrix Index (Vertical PMI) and a Horizontal Precoding Matrix Index (Horizontal PMI). FIG. 8 shows an experimental result measured on the Vertical PMI and the Horizontal PMI, based on 64 antennas composed of 8 vertical antennas and 8 horizontal antennas in a time interval in which 500 UEs correspond to 1,000 subframes.
With respect to FIG. 8, it is assumed that 4-bit and 8-bit DFT codebooks are used for a PMI, and FIG. 8 illustrates a cumulative distribution function (DCF) drawn by measuring a time atin which an optimal PMIs consecutively have the same index. It can be assumed that the 4-bit codebook and the 8-bit codebook are a codebook for a long-term feedback and a codebook for a short-term feedback, respectively. As shown in FIG. 8, it can be observed that the VPMI maintains the same PMI for a long time in comparison to the HPMI. This phenomenon appears in the 4-bit codebook for the long-term feedback further clearly.
According to the present invention, feedback amounts WV, WH, eV, eH and α possess may be predetermined in advance, or may be changed semi-statically by higher layer signaling.
Hereinafter, according to the present invention, a 3D MIMO codebook for a rank 2 for a purpose of reducing a feedback overhead is proposed as equation 25 and equation 26.




  
    
      
        [
        
          
            
              
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      
                        V
                        ⁢
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      
                        H
                        ⁢
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  )
                
              
            
            
              
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      
                        V
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      
                        H
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                  )
                
              
            
          
          
            
              
                β
                ×
                
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                
              
            
            
              
                
                  -
                  β
                
                ×
                
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                
              
            
          
        
        ]
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          25
        
        ]
      
    
  
  
    
      
        [
        
          
            
              
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      
                        H
                        ⁢
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      
                        V
                        ⁢
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  )
                
              
            
            
              
                
                  (
                  
                    
                      W
                      H
                    
                    ⁢
                    
                      e
                      
                        H
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                  )
                
                ⊗
                
                  (
                  
                    
                      W
                      V
                    
                    ⁢
                    
                      e
                      
                        V
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                  )
                
              
            
          
          
            
              
                β
                ×
                
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                
              
            
            
              
                
                  -
                  β
                
                ×
                
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                
              
            
          
        
        ]
      
    
    
      
        [
        
          Equaiton
          ⁢
          
            
          
          ⁢
          26
        
        ]
      
    
  




In the equation 25 and the equation 26,  means a kronecker product operation.
In a codebook represented as the equation 25, WV means a precoding set of vertical antenna elements. Each of eV1 and eV2 plays a role in selecting a single specific antenna element corresponding to each rank from this precoding set. Accordingly, WV is fed back in a long-term, and each of eV1 and eV2 may be fed back in a short-term having a period shorter than that of WV.
In particular, WV may be selected as a subset of D matrices composed of columns in a DFT codebook D matrix. Herein, the DFT codebook can be represented as equation 27.




  
    
      
        
          
            D
            
              (
              mn
              )
            
            
              
                N
                V
              
              ×
              
                N
                V
              
              ⁢
              a
            
          
          =
          
            
              1
              
                
                  N
                  V
                
              
            
            ⁢
            
              e
              
                j
                ⁢
                
                  
                
                ⁢
                
                  
                    2
                    ⁢
                    
                      π
                      ⁡
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      (
                      
                        n
                        -
                        1
                      
                      )
                    
                  
                  
                    
                      N
                      V
                    
                    ⁢
                    a
                  
                
              
            
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          27
        
        ]
      
    
  




for m=1, 2, . . . , NV, n=1, 2, . . . , NVα

In a DFT codebook according to the equation 27, α corresponds to an oversampling factor, and NV corresponds to the number of vertical antenna elements.
In addition, eV1 and eV2 are selection vectors, which are used for selecting a corresponding specific column from WV, respectively. Herein, each of the eV1 and the eV2 is composed of a single vector, and only a single value among elements has a value of “1” and the rest of values have a value of “0” each. For example, regarding WV, if only a second element has a value of “1” and the rest of elements have a value of “0” each, a second column of WV is selected.
Moreover, in a codebook according to the equation 26, WH means a precoding set of horizontal antenna elements. Each of eH1 and eH2 plays a role in selecting a single specific antenna element corresponding to each rank from this precoding set (i.e., WH). Hence, WH is fed back in a long-term, and each of eH1 and eH2 may be fed back in a short-term having a period shorter than that of WH.
In particular, WH may be selected as a subset of D matrices composed of columns in a DFT codebook D matrix. Herein, the DFT codebook can be represented as equation 28.




  
    
      
        
          
            D
            
              (
              mn
              )
            
            
              
                N
                H
              
              ×
              
                N
                H
              
              ⁢
              a
            
          
          =
          
            
              1
              
                
                  N
                  H
                
              
            
            ⁢
            
              e
              
                j
                ⁢
                
                  
                    2
                    ⁢
                    
                      π
                      ⁡
                      
                        (
                        
                          m
                          -
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      (
                      
                        n
                        -
                        1
                      
                      )
                    
                  
                  
                    
                      N
                      H
                    
                    ⁢
                    a
                  
                
              
            
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          28
        
        ]
      
    
  




for m=1, 2, . . . , NH, n=1, 2, . . . , NHα

In a DFT codebook according to the equation 28, α corresponds to an oversampling factor, and NV corresponds to the number of vertical antenna elements.
In addition, eH1 and eH2 are selection vectors, which are used for selecting corresponding specific columns from WH, respectively. Herein, each of eH1 and eH2 is composed of a single vector, and only a single value among elements has a value of “1” and the rest of values have a value of “0” each. For example, regarding eH1, if only a second element has a value of “1” and the rest of elements have a value of “0” each, a second column of WH is selected.
Furthermore, in a codebook represented as the aforementioned equation 27 or equation 28, β plays a role in adjusting a phase between ‘/’ antenna and “\” antenna in an X-pol antenna. That is, β is selected from a set of




  β
  ∈
  
    {
    
      1
      ,
      
        exp
        ⁡
        
          (
          
            j
            ⁢
            
              
            
            ⁢
            
              
                2
                ⁢
                π
              
              
                2
                
                  N
                  β
                
              
            
          
          )
        
      
      ,
      
        exp
        ⁡
        
          (
          
            j
            ⁢
            
              
            
            ⁢
            
              
                4
                ⁢
                π
              
              
                2
                
                  N
                  β
                
              
            
          
          )
        
      
      ,
      ...
      ⁢
      
        
      
      ,
      
        exp
        (
        
          j
          ⁢
          
            
          
          ⁢
          
            
              2
              ⁢
              
                (
                
                  
                    2
                    
                      N
                      β
                    
                  
                  -
                  2
                
                )
              
              ⁢
              π
            
            
              2
              
                N
                β
              
            
          
        
        )
      
      ,
      
        exp
        (
        
          j
          ⁢
          
            
          
          ⁢
          
            
              2
              ⁢
              
                (
                
                  
                    2
                    
                      N
                      β
                    
                  
                  -
                  1
                
                )
              
              ⁢
              π
            
            
              2
              
                N
                β
              
            
          
        
        )
      
    
    }
  




Nβ corresponds to the number of feedback bits for β. In case of Nβ=2, β may be selected from a set of





  β
  ∈
  
    
      {
      
        1
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
              
              ⁢
              
                π
                2
              
            
            )
          
        
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  π
                
                2
              
            
            )
          
        
        ,
        
          exp
          ⁡
          
            (
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  3
                  ⁢
                  π
                
                2
              
            
            )
          
        
      
      }
    
    .
  




In addition, in a codebook represented as the aforementioned equation 27 or equation 28, WV is fed back with a period longer than that of WH, or eV1 and eV2 (i.e., selection vectors associated with a vertical antenna element) may be fed back with a period longer than that of eH1 and eH2 (i.e., selection vectors associated with a horizontal antenna element).
Furthermore, according to the present invention, a feedback amounts that WV, WH, eV1, eV2, eH1, eH2 and β possess may be determined in advance, or changed semi-statically by higher layer signaling.
In addition, a combination of eV1 and eV2 may have too many values according to the number of antennas. Hence, a set related to combinations of eV1 and eV2 may be predetermined and used. Likewise, a combination of eH1 and eH2 may have too many values according to the number of antennas as well. Therefore, a set related to combinations of eH1 and eH2 may be predetermined and used, as well. Furthermore, a set related to combinations of eH1 and eH2 may be changed semi-statically by higher layer signaling.
The above-described embodiments may correspond to combinations of elements and features of the present invention in prescribed forms. And, it may be able to consider that the respective elements or features may be selective unless they are explicitly mentioned. Each of the elements or features may be implemented in a form failing to be combined with other elements or features. Moreover, it may be able to implement an embodiment of the present invention by combining elements and/or features together in part. A sequence of operations explained for each embodiment of the present invention may be modified. Some configurations or features of one embodiment may be included in another embodiment or can be substituted for corresponding configurations or features of another embodiment. And, it is apparently understandable that a new embodiment may be configured by combining claims failing to have relation of explicit citation in the appended claims together or may be included as new claims by amendment after filing an application.
In this disclosure, a specific operation explained as performed by an eNode B may be performed by an upper node of the eNode B in some cases. In particular, in a network constructed with a plurality of network nodes including an eNode B, it is apparent that various operations performed for communication with a user equipment can be performed by an eNode B or other network nodes except the eNode B. ‘Base station (BS)’ may be substituted with such a terminology as a fixed station, a Node B, an eNode B (eNB), an access point (AP) and the like.
Embodiments of the present invention may be implemented using various means. For instance, embodiments of the present invention may be implemented using hardware, firmware, software and/or any combinations thereof. In case of the implementation by hardware, one embodiment of the present invention may be implemented by at least one of ASICs (application specific integrated circuits), DSPs (digital signal processors), DSPDs (digital signal processing devices), PLDs (programmable logic devices), FPGAs (field programmable gate arrays), processor, controller, microcontroller, microprocessor and the like.
In case of the implementation by firmware or software, one embodiment of the present invention may be implemented by modules, procedures, and/or functions for performing the above-explained functions or operations. Software code may be stored in a memory unit and may be then drivable by a processor.
The memory unit is located at the interior or exterior of the processor and may transmit and receive data to and from the processor via various known means.
It will be apparent to those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit and essential characteristics of the invention. Thus, the above embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the invention should be determined by reasonable interpretation of the appended claims and all change which comes within the equivalent scope of the invention are included in the scope of the invention.
INDUSTRIAL APPLICABILITY
Although a method for configuring a codebook in a multi-antenna wireless communication system and apparatus therefor are described centering on examples applied to 3GPP LTE system, it may be applicable to various wireless communication systems as well as to the 3GPP LTE system.

## Claims

1. A method of transmitting a signal by a transmitting end in a wireless communication system supporting multiple antennas including a multitude of vertical domain antennas and a multitude of horizontal domain antennas, the method comprising:
precoding a signal for the multiple antennas using a specific precoding matrix selected on the basis of a first codebook for a multitude of the vertical domain antennas and a second codebook for a multitude of the horizontal domain antennas; and
transmitting the precoded signal to a receiving end,
wherein the specific precoding matrix is defined by using a Kronecker product of a first precoding matrix selected from the first codebook according to at least one first selection vector and a second precoding matrix selected from the second codebook according to at least one second selection vector, and
wherein a feedback period of the at least one first selection vector is set longer than that of the at least one second selection vector.

2. The method of claim 1,
wherein the first codebook is defined as according to Equation A,





  
    
      
        
          D
          
            (
            mn
            )
          
          
            
              N
              V
            
            ×
            
              N
              V
            
            ⁢
            a
          
        
        =
        
          
            1
            
              
                N
                V
              
            
          
          ⁢
          
            e
            
              j
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    (
                    
                      m
                      -
                      1
                    
                    )
                  
                  ⁢
                  
                    (
                    
                      n
                      -
                      1
                    
                    )
                  
                
                
                  
                    N
                    V
                  
                  ⁢
                  a
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          A
        
        ]
      
    
  



 for m=1, 2, . . . , NV, n=1, 2, . . . , NVα,
where D(mn)NV×NVα indicates a DFT (Discrete Fourier Transform) matrix, NV indicates a number of vertical antenna elements, and α indicates an oversampling factor.

3. The method of claim 1,
wherein the second codebook is defined as according to Equation B,





  
    
      
        
          D
          
            (
            mn
            )
          
          
            
              N
              H
            
            ×
            
              N
              H
            
            ⁢
            a
          
        
        =
        
          
            1
            
              
                N
                H
              
            
          
          ⁢
          
            e
            
              j
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    (
                    
                      m
                      -
                      1
                    
                    )
                  
                  ⁢
                  
                    (
                    
                      n
                      -
                      1
                    
                    )
                  
                
                
                  
                    N
                    H
                  
                  ⁢
                  a
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          B
        
        ]
      
    
  



 for m=1, 2, . . . , NH , n=1, 2, . . . , NHα,
where D(mn)NH×NHα indicates a DFT (Discrete Fourier Transform) matrix, NH indicates a number of vertical antenna elements, and α indicates an oversampling factor.

4. The method of claim 1,
wherein the specific precoding matrix is a precoding for a rank 1, being defined as according to Equation C,





  
    
      
        
          [
          
            
              
                
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        V
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        H
                      
                    
                    )
                  
                
              
            
            
              
                
                  
                    α
                    ⁡
                    
                      (
                      
                        
                          W
                          V
                        
                        ⁢
                        
                          e
                          V
                        
                      
                      )
                    
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        H
                      
                    
                    )
                  
                
              
            
          
          ]
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          C
        
        ]
      
    
  



where WV indicates a precoding set related to a vertical antenna element included in the first codebook, WH indicates a precoding set related to a horizontal antenna element included in the second codebook, eV indicates the first selection vector, eH indicates the second selection vector, and α indicates a phase adjustment factor.

5. The method of claim 4,
wherein the α is defined for a dual-polarization phase adjustment in a cross-polarization antenna, being selected on the basis of Equation D,





  
    
      
        
          α
          ∈
          
            {
            
              1
              ,
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        2
                        ⁢
                        π
                      
                      
                        2
                        
                          N
                          α
                        
                      
                    
                  
                  )
                
              
              ,
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        4
                        ⁢
                        π
                      
                      
                        2
                        
                          N
                          α
                        
                      
                    
                  
                  )
                
              
              ,
              ...
              ⁢
              
                
              
              ,
              
                exp
                (
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            2
                            
                              N
                              α
                            
                          
                          -
                          2
                        
                        )
                      
                      ⁢
                      π
                    
                    
                      2
                      
                        N
                        α
                      
                    
                  
                
                )
              
              ,
              
                exp
                (
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            2
                            
                              N
                              a
                            
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      π
                    
                    
                      2
                      
                        N
                        α
                      
                    
                  
                
                )
              
            
            }
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          D
        
        ]
      
    
  



where Nα a indicates a number of feedback bits for α.

6. The method of claim 1,
wherein the specific precoding matrix is a precoding matrix for a rank 2, being defined as according to Equation E,





  
    
      
        
          [
          
            
              
                
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          1
                        
                      
                    
                    )
                  
                
              
              
                
                  
                    (
                    
                      
                        W
                        V
                      
                      ⁢
                      
                        e
                        
                          V
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                  ⊗
                  
                    (
                    
                      
                        W
                        H
                      
                      ⁢
                      
                        e
                        
                          H
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                    )
                  
                
              
            
            
              
                
                  β
                  ×
                  
                    
                      (
                      
                        
                          W
                          V
                        
                        ⁢
                        
                          e
                          
                            V
                            ⁢
                            
                              
                            
                            ⁢
                            1
                          
                        
                      
                      )
                    
                    ⊗
                    
                      (
                      
                        
                          W
                          H
                        
                        ⁢
                        
                          e
                          
                            H
                            ⁢
                            
                              
                            
                            ⁢
                            1
                          
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    -
                    β
                  
                  ×
                  
                    
                      (
                      
                        
                          W
                          V
                        
                        ⁢
                        
                          e
                          
                            V
                            ⁢
                            
                              
                            
                            ⁢
                            2
                          
                        
                      
                      )
                    
                    ⊗
                    
                      (
                      
                        
                          W
                          H
                        
                        ⁢
                        
                          e
                          
                            H
                            ⁢
                            
                              
                            
                            ⁢
                            2
                          
                        
                      
                      )
                    
                  
                
              
            
          
          ]
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          E
        
        ]
      
    
  



where WV is a precoding set related to a vertical antenna element included in the first codebook, WH indicates a precoding set related to a horizontal antenna element included in the second codebook, each of eV1 and eV2 indicates the at least one first selection vector, each of eH1 and eH2 indicates the at least one second selection vector, and βindicates a phase adjustment factor.

7. The method of claim 6,
wherein the β is defined for a dual-polarization phase adjustment in a cross-polarization antenna, being selected on the basis of Equation F,





  
    
      
        
          β
          ∈
          
            {
            
              1
              ,
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      
                        
                          
                        
                        ⁢
                        
                          2
                          ⁢
                          π
                        
                      
                      
                        2
                        
                          N
                          
                            β
                            ⁢
                            
                              
                            
                          
                        
                      
                    
                  
                  )
                
              
              ,
              
                exp
                ⁡
                
                  (
                  
                    j
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        4
                        ⁢
                        π
                      
                      
                        2
                        
                          N
                          β
                        
                      
                    
                  
                  )
                
              
              ,
              ...
              ⁢
              
                
              
              ,
              
                exp
                (
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            2
                            
                              N
                              β
                            
                          
                          -
                          2
                        
                        )
                      
                      ⁢
                      π
                    
                    
                      2
                      
                        N
                        β
                      
                    
                  
                
                )
              
              ,
              
                exp
                (
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            2
                            
                              N
                              β
                            
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      π
                    
                    
                      2
                      
                        N
                        β
                      
                    
                  
                
                )
              
            
            }
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          F
        
        ]
      
    
  



where Nβ indicates a number of feedback bits for β.

8. The method of claim 1, wherein a feedback period of the first precoding matrix is set longer than that of the second precoding matrix.

9. An apparatus for transmitting a signal in a wireless communication system supporting multiple antennas including a multitude of vertical domain antennas and a multitude of horizontal domain antennas, the apparatus comprising:
a radio frequency unit; and
a processor coupled to the radio frequency unit,
wherein the processor is configured to precode a signal for the multiple antennas using a specific precoding matrix selected on the basis of a first codebook for a multitude of of the vertical domain antennas and a second codebook for a multitude of the horizontal domain antennas and transmit the precoded signal to a receiving end and
wherein the specific precoding matrix is defined by using a Kronecker product of a first precoding matrix selected from the first codebook according to at least one first selection vector and a second precoding matrix selected from the second codebook according to at least one second selection vector, and
wherein a feedback period of the at least one first selection vector is set longer than that of the at least one second selection vector.