# Patent

## Title
Method for determining precoding matrix and corresponding communication methods and devices

## Abstract

A method for determining precoding matrix for the sub-band precoding in a transmitter with M transmitting antennas. The method includes determining an optimized first matrix W1 according to wideband and/or long-term channel properties, multiplying the optimized first matrix W1, with each second matrix W2, in a second codebook, to obtain a plurality of candidate precoding matrices, the second matrix W2 corresponds to frequency-selective and/or short-term channel properties; selecting an optimized one from the plurality of candidate preceding matrices for precoding the data to be transmitted, according to a frequency selection and/or a short-term channel state information. The amount of DFT beams may be increased to improve the spatial resolution; a diagonal matrix is involved in the first matrix W1; and phase adjustment is involved in the second matrix W2, so as to guarantee the adjusted phase is evenly distributed among the whole phase space.

## Background
TECHNICAL FIELD
The invention relates to multi-antenna technology, particularly relates to precoding method in the multi-antenna technology.
BACKGROUND OF THE ART
According to the agreed way forward for Rel-10 feedback [R1-101683], a precoding matrix for a sub-band is composed of two matrices. One matrix denoted by W1 targets wideband and/or long-term channel properties, and the other matrix denoted by W2 targets frequency-selective and/or short-term channel properties. The multiplication product of these two matrices is taken as the precoding matrix for precoding the data.
In proposal R1-105011, a two-stage feedback approach is proposed, with W1 being a M×Nb matrix and W2 being a Nb×r matrix. In the W2 codebook design of this approach, there is a co-phasing factor trying to match the phase between antennas 1 ̃M/2 and antennas M/2 ̃M. Therefore, this proposal needs to carry out data feedback for such as the co-phasing factor for the uniform linear array (ULA) antennas. This results in a certain amount of overhead, and the performance of the proposal is not satisfying.
SUMMARY OF THE INVENTION
The invention aims to propose a precoding scheme based on a new codebook. According to a first aspect of the invention, it is provided a method for determining precoding matrix for the sub-band precoding in a transmitter, wherein the transmitter has M transmitting antennas, and the method comprises: a. determining an optimized first matrix W1 according to wideband and/or long-term channel properties, with the first matrix W1 corresponding to wideband and/or long-term channel properties; b. multiplying the optimized first matrix W1 with each second matrix W2 in a second codebook, so as to obtain a plurality of candidate precoding matrices, with the second matrix W2 corresponding to frequency-selective and/or short-term channel properties; c. selecting an optimized one from the plurality of candidate precoding matrices for precoding the data to be transmitted, according to a frequency selection and/or a short-term channel state information; characterized in that, the amount of DFT beams is increased to improve the spatial resolution; a diagonal matrix is involved in said first matrix W1; and co-phasing adjustment is involved in said second matrix W2, so as to guarantee the adjusted phase is evenly distributed among the whole phase space.
According to the above aspect, a diagonal matrix is involved in said first matrix W1 such that the corresponding column constitutes a complete DFT beam. Compared with the art R1-105011, the amount of DFT beams suitable for ULA is increased, while the spatial resolution is increased and therefore the performance of ULA is improved. Additionally, phase adjustment is involved in said second matrix W2, such that the adjustable phase for each beam is evenly distributed among the whole phase space.
According to an preferred embodiment, the amount of DFT beams is increased to improve the spatial resolution, the first matrix W1 is selected from the following first codebook C1:




  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            
              p
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              
                X
                
                  (
                  k
                  )
                
              
              ⁢
              
                Λ
                
                  (
                  k
                  )
                
              
            
          
        
      
      ]
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    p
    -
    1
  




    
    
        Wherein, p is the amount of the first matrix in the first codebook C1, and
    
    






  
    
      X
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              f
              
                k
                1
              
            
          
          
            
              f
              
                k
                2
              
            
          
          
            ...
          
          
            
              
                f
                k
              
              q
            
          
        
      
      ]
    
  
  ,
  
    

  
  ⁢
  
    
      Λ
      
        (
        k
        )
      
    
    =
    
      diag
      [
      
        (
        
          
            e
            
              
                jθ
                
                  k
                  1
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            e
            
              
                jθ
                
                  k
                  2
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            ...
            ⁢
            
              
            
            ⁢
            
              e
              
                
                  jθ
                  
                    k
                    q
                  
                
                ·
                
                  (
                  
                    M
                    /
                    2
                  
                  )
                
              
            
          
        
        ]
      
      )
    
  
  ,




    
    
        Wherein, q is the amount of each group of beam,
    
    






  
    
      f
      
        k
        n
      
    
    =
    
      
        [
        
          
            
              1
            
            
              
                e
                
                  
                    jθ
                    
                      k
                      n
                    
                  
                  ·
                  1
                
              
            
            
              ...
            
            
              
                e
                
                  
                    jθ
                    
                      k
                      n
                    
                  
                  ·
                  
                    (
                    
                      
                        M
                        /
                        2
                      
                      -
                      1
                    
                    )
                  
                
              
            
          
        
        ]
      
      T
    
  
  ,




θkn is the phase difference between two neighboring element in the DFT vector with a value range of [0,2π);

    
    
        and when the amount of data flows is 1, said second codebook comprises second matrices W2 as follows:
    
    






  
    
      C
      2
    
    =
    
      {
      
        
          W
          2
          
            (
            0
            )
          
        
        ,
        
          W
          2
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          2
          
            (
            
              q
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




    
    
        and when the amount of data flows is 2, said second codebook comprises second matrices W2 as follows:
    
    






  
    
      C
      2
    
    =
    
      {
      
        
          W
          2
          
            (
            0
            )
          
        
        ,
        
          W
          2
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          2
          
            (
            
              q
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
            
              
                
                  -
                  a
                
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




Wherein, ek is an elementary vector with the (k+1)th element being 1 and other elements being zero, and a is a parameter related with the polarization manner of the antennas.

According a second aspect of the invention, it is proposed a method, in the user equipments, for feeding precoding matrix for sub-band precoding back to an eNodeB, comprising the steps of: determining the optimized first matrix W1 and the precoding matrix, by using a method according to the first aspect of the invention; determining an optimized second matrix W2 corresponding to said optimized precoding matrix; providing, for the eNodeB, identifications of said optimized first matrix W1 and said second matrix W2.
According to a third aspect of the invention, it is proposed a method, in eNodeBs, for precoding data, comprising: receiving identifications of an optimized first matrix W1 and an optimized second matrix W2, fed back by user equipments; determining, from the first codebook and the second code book in a method according to any one of claims 1 to 5, the optimized first matrix W1 and the optimized second matrix W2, according to the identifications; multiplying the optimized first matrix W1 and the optimized second matrix W2, and obtaining an optimized precoding matrix; precoding the data to be transmitted, by using the optimized precoding matrix, so as to transmit the data to the user equipment.
According to the fourth aspect of the invention, it is provided a device, in user equipments, for feeding precoding matrix for sub-band precoding back to an eNodeB, comprising: a determining means, for determining the optimized first matrix W1 and the precoding matrix, by using a method according to the first aspect of the invention, and for determining an optimized second matrix W2 corresponding to said optimized precoding matrix; a sender, for providing, for the eNodeB, identifications of said optimized first matrix W1 and said second matrix W2.
According to a fifth aspect of the invention, it is provided a device, in eNodeBs, for precoding data, comprising: a receiver, for receiving identifications of an optimized first matrix W1 and an optimized second matrix W2, fed back by user equipments; an inquiring means, for determining, from the first codebook and the second code book in a method according to the first aspect of the invention, the optimized first matrix W1 and the optimized second matrix W2, from the identifications; a calculating means, for multiplying the optimized first matrix W1 and the optimized second matrix W2, and obtaining an optimized precoding matrix for the sub-band precoding; a precoder, for precoding the data to be transmitted, by using the optimized precoding matrix.
The above and other features of the invention will be elucidated in the detailed embodiments below.


DETAILED EMBODIMENTS
Firstly, the design of the codebook according to the invention will be elucidated as following.
At first, multiple-input multiple-output with M transmitting antennas of uniform linear array (ULA) is taken as example. It is supposed that codeword W1∈C1 targets wideband/long-term channel properties, and W2∈C2 targets frequency-selective/short-term channel properties. The amount of W1, namely the size of the codebook C1 is denoted by p, and the amount of W2, namely the size of the codebook C2 is denoted by q respectively. The precoding matrix for a sub-band has the form of W=W1W2. For closely-spaced ULA (for example, the mode of the co-relation factor of the antennas is greater than a predetermined threshold, or the distance between the antennas is smaller than or equals to half of the signal wavelength), the dominated eigen-vector of the channel matrix can be approximated by a DFT vector. Hence, the invention proposes the codewords for W1 and W2 to satisfy that W is a M×1 DFT vector. And the specific W1 and W2 are proposed as follows.
(1) W1 Codebook Design
Define (M/2)×1 DFT vector




  
    f
    
      k
      n
    
  
  =
  
    
      [
      
        
          
            1
          
          
            
              e
              
                
                  jθ
                  
                    k
                    n
                  
                
                ·
                1
              
            
          
          
            ...
          
          
            
              e
              
                
                  jθ
                  
                    k
                    n
                  
                
                ·
                
                  (
                  
                    
                      M
                      /
                      2
                    
                    -
                    1
                  
                  )
                
              
            
          
        
      
      ]
    
    T
  




Wherein, θkn is the phase difference between two neighboring elements in the DFT vector, the value range of which is [0,2π);
Define p DFT sets with a dimension of (M/2)×q

X(k)=[fk1fk2 . . . fkq], k=0,1, . . . , p−1.

And define p diagonal matrices




  
    
      Λ
      
        (
        k
        )
      
    
    =
    
      diag
      [
      
        (
        
          
            e
            
              
                jθ
                
                  k
                  1
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            e
            
              
                jθ
                
                  k
                  2
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            ...
            ⁢
            
              
            
            ⁢
            
              e
              
                
                  jθ
                  
                    k
                    q
                  
                
                ·
                
                  (
                  
                    M
                    /
                    2
                  
                  )
                
              
            
          
        
        ]
      
      )
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    p
    -
    1.
  




Then W1 is designed as




  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              
                X
                
                  (
                  k
                  )
                
              
              ⁢
              
                Λ
                
                  (
                  k
                  )
                
              
            
          
        
      
      ]
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    p
    -
    1
  




That is to say the codebook C1 is

C1={W1(0), W1(1), . . . , W1(p−1)}

(2) W2 Codebook Design

Define ek as the elementary vector, i.e. the (k+1) th column of identity matrix.
For one data flow, namely rank 1, W2 is




  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
          
          
            
              
                e
                k
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




For two data flows, namely rank 2, W2 is




  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
            
              
                e
                k
              
            
          
          
            
              
                e
                k
              
            
            
              
                -
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




The codebook C2 is

C2={W2(0), W2(1), . . . , W2(q−1)}

Based on the W1 and W2 designed above, the corresponding precoding matrix W=W1W2 has the form of DFT vector, which matches channel characteristics well for closely-spaced co-polarized antennas. It should be noted that although the precoding matrix is written as the multiplication of W1 and W2, in practice W can be easily obtained without doing matrix multiplication by selecting corresponding elements in W1 based on the positions of 1 in W2. Thus, even if the dimension of W1 is large, the practical computational complexity is low.
For cross-polarized linear array (CLA) antennas, the codebook C1 and codeword W1 stay as they are, and codeword W2 is adjusted by a co-phasing factor a.
Specifically, for one data flow, namely rank 1, W2 is




  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




For two data flows, namely rank 2, W2 is




  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
            
              
                
                  -
                  a
                
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  




Codebook C2 is

C2={W2(0), W2(1), . . . , W2(q−1)}

When it is used for ULA antennas, a=1. When it is used for CLA or when the same codebook is used for various polarization manner of the antennas, the value of a is selected from a set {ejβ1, ejβ2, . . . , ejβm}, wherein, m is the amount of values of a, the values of β1, β2, . . . , βm are selected in a range of [0,2π), generally selected as evenly distributed among [0,2π) namely




  
    
      β
      k
    
    =
    
      
        2
        ⁢
        
          
        
        ⁢
        
          π
          ⁡
          
            (
            
              k
              -
              1
            
            )
          
        
      
      m
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    1
  
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    m
    .
  




The following part describes the design of the above codewords W1 and W2. In this embodiment, eNB has 8 antenna elements.
(1) Codebook C1



  
    
      
    
    ⁢
    
      
        B
        =
        
          [
          
            
              b
              0
            
            ⁢
            
              
            
            ⁢
            
              b
              1
            
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              b
              31
            
          
          ]
        
      
      ,
      
        

      
      ⁢
      
        
      
      ⁢
      
        
          
            [
            B
            ]
          
          
            
              1
              +
              m
            
            ,
            
              1
              +
              n
            
          
        
        =
        
          e
          
            j
            ⁢
            
              
                2
                ⁢
                
                  
                
                ⁢
                π
                ⁢
                
                  
                
                ⁢
                mn
              
              32
            
          
        
      
      ,
      
        

      
      ⁢
      
        
      
      ⁢
      
        m
        =
        0
      
      ,
      1
      ,
      2
      ,
      3
      ,
      
        n
        =
        0
      
      ,
      1
      ,
      ...
      ⁢
      
        
      
      ,
      31
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              [
              
                
                  b
                  
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    k
                    ⁢
                    
                      
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        1
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        2
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        3
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
              
              ]
            
            ⁢
            
              :
            
            ⁢
            
              
            
            ⁢
            k
          
          =
          0
        
        ,
        1
        ,
        ...
        ⁢
        
          
        
        ,
        15
      
      }
    
  




  
    
      
    
    ⁢
    
      
        W
        1
        
          (
          k
          )
        
      
      =
      
        [
        
          
            
              
                X
                
                  (
                  k
                  )
                
              
            
            
              0
            
          
          
            
              0
            
            
              
                
                  X
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  Λ
                  
                    (
                    k
                    )
                  
                
              
            
          
        
        ]
      
    
  




  
    
      Λ
      
        (
        k
        )
      
    
    =
    
      diag
      (
      
        [
        
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  k
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      1
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      2
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      3
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
        
        ]
      
      )
    
  




  
    
      
    
    ⁢
    
      
        C
        1
      
      =
      
        {
        
          
            W
            1
            
              (
              0
              )
            
          
          ,
          
            W
            1
            
              (
              1
              )
            
          
          ,
          
            W
            1
            
              (
              2
              )
            
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            W
            1
            
              (
              15
              )
            
          
        
        }
      
    
  



(2) Codebook C2 

For one data flow, namely rank 1,



  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        [
        
          
            
              Y
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                Y
              
            
          
        
        ]
      
      }
    
  




  
    
      Y
      ∈
      
        {
        
          
            e
            0
          
          ,
          
            e
            1
          
          ,
          
            e
            2
          
          ,
          
            e
            3
          
        
        }
      
    
    ,
    
      

    
    ⁢
    
      a
      =
      
        {
        
          
            
              1
            
            
              
                U
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
              
            
          
          
            
              
                {
                
                  l
                  ,
                  
                    -
                    l
                  
                  ,
                  j
                  ,
                  
                    -
                    j
                  
                
                }
              
            
            
              
                U
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
                ⁢
                
                  
                
                ⁢
                and
                ⁢
                
                  
                
                ⁢
                C
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
              
            
          
        
      
    
  



Wherein, ek is the elementary vector with all zeros except for the (k+1)th element with value 1.
For two data flows, namely rank 2,



  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        [
        
          
            
              
                
                  Y
                  1
                
              
            
            
              
                
                  a
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Y
                    1
                  
                
              
            
          
          ⁢
          
            
              
                
                  Y
                  2
                
              
            
            
              
                
                  
                    -
                    a
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    Y
                    2
                  
                
              
            
          
        
        ]
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              0
            
            ,
            
              e
              0
            
          
          )
        
        ,
        
          (
          
            
              e
              1
            
            ,
            
              e
              1
            
          
          )
        
        ,
        
          (
          
            
              e
              2
            
            ,
            
              e
              2
            
          
          )
        
        ,
        
          (
          
            
              e
              3
            
            ,
            
              e
              3
            
          
          )
        
      
      }
    
  




  
    a
    =
    
      {
      
        
          
            1
          
          
            
              U
              ⁢
              
                
              
              ⁢
              L
              ⁢
              
                
              
              ⁢
              A
            
          
        
        
          
            
              {
              
                l
                ,
                
                  -
                  l
                
                ,
                j
                ,
                
                  -
                  j
                
              
              }
            
          
          
            
              U
              ⁢
              
                
              
              ⁢
              L
              ⁢
              
                
              
              ⁢
              A
              ⁢
              
                
              
              ⁢
              and
              ⁢
              
                
              
              ⁢
              C
              ⁢
              
                
              
              ⁢
              L
              ⁢
              
                
              
              ⁢
              A
            
          
        
      
    
  



When the codebook C2 is used for ULA, C2 comprises four second matrices W2, and when the codebook C2 is used for both ULA and CLA simultaneously, C2 comprises sixteen second matrices W2.
It should be noted that in the art R1-105011, since there are only 4 choices for co-phasing factor, the number of the DFT beams of the 8 antennas is only 16 and could not be increased to 32. The above example proposed by the invention increases the number of the DFT beams of the 8 antennas from 16 to 32, so as to increase the spatial resolution.
The codewords determined according to the invention are described in the above example. It should be noted that the invention is not limited by the above codeword design. In case that the number of at least one of antenna elements, codeword W1, codeword W2, phase θkn and co-phasing factor a changes, the codewords can be adjusted accordingly.
The above part discusses the codewords proposed by the invention. The following part will describe the embodiment of carrying out precoding communication based on the codewords determined by the invention.
Firstly, the determining means in the user equipment (UE) measures wideband and/or long-term channel related information, and selects, from the first codebook C1 an first matrix, namely the codeword W1, according to the channel related information. The UE can determine the optimized codeword corresponding to the wideband and/or long-term channel related information, according to the criteria of maximum capacity or minimum distance with the eigen-vector of the channel correlation matrix.
After that, the determining means multiplies the first matrix W1 with each second matrix W2 in the second codebook C2, so as to obtain a plurality of candidate precoding matrices.
Then, the determining means selects an optimized precoding matrix from the plurality of candidate precoding matrices based on the predefined rules, according to the measured frequency selection and/or short-term channel state information. The predefined rules are for example rules that can select a candidate precoding matrix enabling a maximum channel capacity, or select a candidate precoding matrix with a minimum distance with the eigen-vector of the channel correlation matrix. It should be noted that other rules are also applicable, and the description will not give unnecessary details.
Then, the determining means can determine an optimized second matrix W2 corresponding to the optimized precoding matrix.
At last, the sender of the UE provides, for the eNodeB, identifications, such as the serial numbers of the matrix in the codebook, of the optimized first matrix W1 and the optimized second matrix W2.
At the eNodeB, the receiver of the eNodeB receives identifications of the optimized first matrix W1 and the optimized second matrix W2, fed back by user equipments.
Then, the inquiring means of the eNodeB determines, from the first codebook C1 and the second code book C2, the optimized first matrix W1 and the optimized second matrix W2, according to the identifications.
After that, the calculator of the eNodeB obtains an optimized precoding matrix for sub-band precoding in the manner illustrated above, according to the first matrix W1 and the second matrix W2.
At last, the precoder of the eNodeB precodes the data to be transmitted, by using the optimized precoding matrix, so as to transmit the precoded data to the user equipment.
The inventor simulates the performance of the codebook proposed by the invention, and compares it with the simulation results of R1-105011 in the art. The simulation uses 19 cells/57 pentagon sectors. The following table 1 shows the assumed wireless network environment, based on which the simulation is carried out.








TABLE 1





Parameter
Assumptions used for evaluation







Deployment scenario
3GPP case 1 3D, SCM-UMa with low angle spread (8 deg)


Cell number
19 cells with 3 sectors per cell


Wrap-around model
Yes


Duplex method and bandwidths
FDD: 10 MHz for downlink


Network synchronization
Synchronized


Traffic model
Full-buffer


UE number per sector
10


Maximal number of co-scheduled UE
4


Handover margin
1.0 dB


eNB Antenna assumptions
8Tx: Co-polarized antennas with 0.5-lambda spacing: Vertically



polarized


UE antenna assumptions
2Rx: A single co-polarized ULA with 0.5-lambda spacing with vertical



polarization


UE antenna orientation
Random distribution within range [−90, 90] degrees


Calibrated antenna array
Ideal













Downlink transmission scheme


Dynamic SU/MU-



Approach
Max rank per UE
MIMO switching






Proposed approach
SU: 2
Yes




MU: 1




Approach in R1-105011
SU: 2
Yes




MU: 1












Note: All MU-MIMO schemes are based on low-bound MU CQI, DMRS, ZF



precoding, w/SU and MU MIMO switching


Downlink scheduler
Proportional fair, frequency selective


Feedback assumptions (feedback
long-term/wideband W1 and short-term/sub-band W2, and sub-band CQI


periodicity in time domain, feedback
Sub-band CQI report: 5 ms periodicity, 6 ms delay, with measurement


granularity in frequency domain)
error: N(0.1 dB) per PRB



W1 and W2 report:



5 ms periodicity for both W1 and W2, and 6 ms feedback delay


CQI
SU-CQI for SU-MIMO and low-bound MU-CQI for MU-MIMO


Downlink HARQ scheme
Synchronous HARQ, Chase combining


Downlink receiver type
MMSE


CSI-RS based CSI estimation error
Real


DM-RS channel estimation
Real


Feedback error
Yes, 1% codeword error rate


HARQ
Chase combing with max 4 retransmissions


Control channel and reference signal
Fixed 0.3063 (As agreed in ITU evaluation)


overhead



test configuration
800 subframes









The simulation results are listed in the following table 2:









TABLE 2






average cell spectral
5% Cell edge spectral



efficiency
efficiency


Codebook type
(bits/s/Hz/cell)
(bits/s/Hz/user)







Proposed codebooks
4.4563 (100%)
0.1433 (100%)


Codebooks in R1-105011
5.0596 (113.54%)
0.1506 (105.09%)









It can be seen that the invention achieves better performance than the art.
Those ordinary skilled in the art could understand and realize modifications to the disclosed embodiments, through studying the description, drawings and appended claims. The word “comprising” does not exclude the presence of elements or steps not listed in a claim or in the description. The word “a” or “an” preceding an element does not exclude the presence of a plurality of such elements. In the practice of present invention, several technical features in the claim can be embodied by one component.

## Claims

1. A method for determining precoding matrix for the sub-band precoding in a transmitter, wherein the transmitter has M transmitting antennas, and the method comprises:
determining an optimized first matrix W1 according to wideband and/or long-term channel properties, with the first matrix W1 corresponding to wideband and/or long-term channel properties;
multiplying the optimized first matrix W1 with a second matrix W2 in a second codebook, so as to obtain a plurality of candidate precoding matrices, with the second matrix W2 corresponding to frequency-selective and/or short-term channel properties;
selecting an optimized one from the plurality of candidate precoding matrices for precoding the data to be transmitted, according to a frequency selection and/or a short-term channel state information;
wherein, the amount of discrete Fourier transform (DFT) beams is increased to improve the spatial resolution; a diagonal matrix is involved in said first matrix W1; and phase adjustment is involved in said second matrix W2, so as to guarantee the adjusted phase is evenly distributed among the whole phase space.

2. A method as claimed in claim 1, wherein the amount of DFT beams is increased to improve the spatial resolution,
the first matrix W1 is selected from the following first codebook C1:





  
    
      C
      1
    
    =
    
      {
      
        
          W
          1
          
            (
            0
            )
          
        
        ,
        
          W
          1
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          1
          
            (
            
              p
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      1
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              X
              
                (
                k
                )
              
            
          
          
            0
          
        
        
          
            0
          
          
            
              
                X
                
                  (
                  k
                  )
                
              
              ⁢
              
                Λ
                
                  (
                  k
                  )
                
              
            
          
        
      
      ]
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    p
    -
    1
  



wherein, p is the amount of the first matrix in the first codebook C1, and





  
    
      X
      
        (
        k
        )
      
    
    =
    
      [
      
        
          
            
              f
              
                k
                1
              
            
          
          
            
              f
              
                k
                2
              
            
          
          
            ...
          
          
            
              
                f
                k
              
              q
            
          
        
      
      ]
    
  
  ,
  
    

  
  ⁢
  
    
      Λ
      
        (
        k
        )
      
    
    =
    
      diag
      [
      
        (
        
          
            e
            
              
                jθ
                
                  k
                  1
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            e
            
              
                jθ
                
                  k
                  2
                
              
              ·
              
                (
                
                  M
                  /
                  2
                
                )
              
            
          
          ,
          
            ...
            ⁢
            
              
            
            ⁢
            
              e
              
                
                  jθ
                  
                    k
                    q
                  
                
                ·
                
                  (
                  
                    M
                    /
                    2
                  
                  )
                
              
            
          
        
        ]
      
      )
    
  
  ,



Wherein, q is the amount of each group of beam,





  
    
      f
      
        k
        n
      
    
    =
    
      
        [
        
          
            
              1
            
            
              
                e
                
                  
                    jθ
                    
                      k
                      n
                    
                  
                  ·
                  1
                
              
            
            
              ...
            
            
              
                e
                
                  
                    jθ
                    
                      k
                      n
                    
                  
                  ·
                  
                    (
                    
                      
                        M
                        /
                        2
                      
                      -
                      1
                    
                    )
                  
                
              
            
          
        
        ]
      
      T
    
  
  ,



θkn is the phase difference between two neighboring element in the DFT vector with a value range of [0,2π);
and when the amount of data flows is 1, said second codebook comprises second matrices W2 as follows:





  
    
      C
      
        2
        ⁢
        
          
        
      
    
    =
    
      {
      
        
          W
          2
          
            (
            0
            )
          
        
        ,
        
          W
          2
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          2
          
            (
            
              q
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  



and when the amount of data flows is 2, said second codebook comprises second matrices W2 as follows:





  
    
      C
      
        2
        ⁢
        
          
        
      
    
    =
    
      {
      
        
          W
          2
          
            (
            0
            )
          
        
        ,
        
          W
          2
          
            (
            1
            )
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          W
          2
          
            (
            
              q
              -
              1
            
            )
          
        
      
      }
    
  
  ,
  
    

  
  ⁢
  
    
      W
      2
      
        (
        k
        )
      
    
    =
    
      
        1
        
          2
        
      
      ⁡
      
        [
        
          
            
              
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
            
              
                e
                k
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
            
              
                
                  -
                  a
                
                ⁢
                
                  
                
                ⁢
                
                  e
                  k
                
              
            
          
        
        ]
      
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    0
  
  ,
  1
  ,
  ...
  ⁢
  
    
  
  ,
  
    q
    -
    1
  



Wherein, ek is an elementary vector with the (k+1)th element being 1 and other elements being zero, and a is a parameter related with the polarization manner of the antennas.

3. A method, in the user equipments, for feeding precoding matrix for sub-band precoding back to an eNodeB, comprising :
determining the optimized first matrix W1 and the precoding matrix, by using a method as claimed in claim 1;
determining an optimized second matrix W2 corresponding to said optimized precoding matrix;
providing, for the eNodeB, identifications of said optimized first matrix W1 and said second matrix W2.

4. A method, in eNodeBs, for precoding data, comprising:
receiving identifications of an optimized first matrix W1 and an optimized second matrix W2, fed back by user equipments;
determining, from the first codebook and the second code book in a method according to claim 1, the optimized first matrix W1 and the optimized second matrix W2, according to the identifications;
multiplying the optimized first matrix W1 and the optimized second matrix W2, and obtaining an optimized precoding matrix;
precoding the data to be transmitted, by using the optimized precoding matrix.

5. A device, in user equipments, for feeding precoding matrix for sub-band precoding back to an eNodeB, comprising:
a processor that determines the optimized first matrix W1 and the precoding matrix, by using a method as claimed in claim 1, and an optimized second matrix W2 corresponding to said optimized precoding matrix;
a transmitter that provides to the eNodeB identifications of said optimized first matrix W1 and said second matrix W2.

6. A device, in eNodeBs, for precoding data, comprising:
a receiver that receives identifications of an optimized first matrix W1 and an optimized second matrix W2, fed back by user equipments;
a processor that determines from the first codebook and the second code book in a method according to claim 1, the optimized first matrix W1 and the optimized second matrix W2, from the identifications;
a calculator that multiplies the optimized first matrix W1 and the optimized second matrix W2, and obtaining an optimized precoding matrix for the sub-band precoding;
a precoder that precodes the data to be transmitted, by using the optimized precoding matrix.

7. A method as claimed in claim 2, wherein the value of a is 1 when the polarization manner of the antennas is uniform linear array.

8. A method as claimed in claim 2, wherein when the polarization manner of the antennas is cross polarized linear array or when the same codebook is used for various polarization manner of the antennas, a is selected from a set {ejβ1, ejβ2, . . . ejβm}, wherein m is the amount of values of a, the values of β1, β2, . . . , βm are selected in a range of [0,2π), generally selected as evenly distributed among [0,2π) namely




  
    
      β
      k
    
    =
    
      
        2
        ⁢
        
          
        
        ⁢
        
          π
          ⁡
          
            (
            
              k
              -
              1
            
            )
          
        
      
      m
    
  
  ,
  
    

  
  ⁢
  
    k
    =
    1
  
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    m
    .

9. A method as claimed in claim 2, wherein, when the transmitter has 8 antenna elements, for codebook C1,



  
    
      
    
    ⁢
    
      
        B
        =
        
          [
          
            
              b
              0
            
            ⁢
            
              
            
            ⁢
            
              b
              1
            
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              b
              31
            
          
          ]
        
      
      ,
      
        

      
      ⁢
      
        
      
      ⁢
      
        
          
            [
            B
            ]
          
          
            
              1
              +
              m
            
            ,
            
              1
              +
              n
            
          
        
        =
        
          e
          
            j
            ⁢
            
              
                2
                ⁢
                
                  
                
                ⁢
                π
                ⁢
                
                  
                
                ⁢
                mn
              
              32
            
          
        
      
      ,
      
        

      
      ⁢
      
        
      
      ⁢
      
        m
        =
        0
      
      ,
      1
      ,
      2
      ,
      3
      ,
      
        n
        =
        0
      
      ,
      1
      ,
      ...
      ⁢
      
        
      
      ,
      31
    
  




  
    
      X
      
        (
        k
        )
      
    
    ∈
    
      {
      
        
          
            
              [
              
                
                  b
                  
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    k
                    ⁢
                    
                      
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        1
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        2
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
                ⁢
                
                  
                
                ⁢
                
                  b
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          k
                        
                        +
                        3
                      
                      )
                    
                    ⁢
                    mod
                    ⁢
                    
                      
                    
                    ⁢
                    32
                  
                
              
              ]
            
            ⁢
            
              :
            
            ⁢
            
              
            
            ⁢
            k
          
          =
          0
        
        ,
        1
        ,
        ...
        ⁢
        
          
        
        ,
        15
      
      }
    
  




  
    
      
    
    ⁢
    
      
        W
        1
        
          (
          k
          )
        
      
      =
      
        [
        
          
            
              
                X
                
                  (
                  k
                  )
                
              
            
            
              0
            
          
          
            
              0
            
            
              
                
                  X
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  Λ
                  
                    (
                    k
                    )
                  
                
              
            
          
        
        ]
      
    
  




  
    
      Λ
      
        (
        k
        )
      
    
    =
    
      diag
      (
      
        [
        
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  k
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      1
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      2
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
          ,
          
            e
            
              j
              ⁢
              
                
              
              ⁢
              
                
                  2
                  ⁢
                  
                    
                  
                  ⁢
                  π
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
                32
              
              ⁢
              
                (
                
                  
                    (
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        k
                      
                      +
                      3
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  mod
                  ⁢
                  
                    
                  
                  ⁢
                  32
                
                )
              
            
          
        
        ]
      
      )
    
  




  
    
      
    
    ⁢
    
      
        
          C
          1
        
        =
        
          {
          
            
              W
              1
              
                (
                0
                )
              
            
            ,
            
              W
              1
              
                (
                1
                )
              
            
            ,
            
              W
              1
              
                (
                2
                )
              
            
            ,
            ...
            ⁢
            
              
            
            ,
            
              W
              1
              
                (
                15
                )
              
            
          
          }
        
      
      ,
    
  


for codebook C2,
when the amount of data flows is 1,





  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        [
        
          
            
              Y
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                Y
              
            
          
        
        ]
      
      }
    
  




  
    
      Y
      ∈
      
        {
        
          
            e
            0
          
          ,
          
            e
            1
          
          ,
          
            e
            2
          
          ,
          
            e
            3
          
        
        }
      
    
    ,
    
      

    
    ⁢
    
      a
      =
      
        {
        
          
            
              1
            
            
              
                U
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
              
            
          
          
            
              
                {
                
                  l
                  ,
                  
                    -
                    l
                  
                  ,
                  j
                  ,
                  
                    -
                    j
                  
                
                }
              
            
            
              
                U
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
                ⁢
                
                  
                
                ⁢
                and
                ⁢
                
                  
                
                ⁢
                C
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
              
            
          
        
      
    
  



wherein ek is an elementary vector with the (k+1)th element being 1 and other elements being zero,
when the amount of data flows is 2, namely rank 2,






  
    
      
        W
        2
      
      ∈
      
        C
        2
      
    
    =
    
      {
      
        
          1
          
            2
          
        
        [
        
          
            
              
                Y
                1
              
            
            
              
                Y
                2
              
            
          
          
            
              
                a
                ⁢
                
                  
                
                ⁢
                
                  Y
                  1
                
              
            
            
              
                
                  -
                  a
                
                ⁢
                
                  
                
                ⁢
                
                  Y
                  2
                
              
            
          
        
        ]
      
      }
    
  




  
    
      (
      
        
          Y
          1
        
        ,
        
          Y
          2
        
      
      )
    
    ∈
    
      {
      
        
          (
          
            
              e
              0
            
            ,
            
              e
              0
            
          
          )
        
        ,
        
          (
          
            
              e
              1
            
            ,
            
              e
              1
            
          
          )
        
        ,
        
          (
          
            
              e
              2
            
            ,
            
              e
              2
            
          
          )
        
        ,
        
          (
          
            
              e
              3
            
            ,
            
              e
              3
            
          
          )
        
      
      }
    
  




  
    a
    =
    
      {
      
        
          
            1
          
          
            
              U
              ⁢
              
                
              
              ⁢
              L
              ⁢
              
                
              
              ⁢
              A
            
          
        
        
          
            
              {
              
                l
                ,
                
                  -
                  l
                
                ,
                j
                ,
                
                  -
                  j
                
              
              }
            
          
          
            
              
                U
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
                ⁢
                
                  
                
                ⁢
                and
                ⁢
                
                  
                
                ⁢
                C
                ⁢
                
                  
                
                ⁢
                L
                ⁢
                
                  
                
                ⁢
                A
              
              ,
            
          
        
      
    
  



when the codebook C2 is used for ULA, C2 comprises four second matrices W2, and when the codebook C2 is used for both ULA and CLA simultaneously, C2 comprises sixteen second matrices W2.