Patent Publication Number: US-2021194549-A1

Title: Enhanced Beam-Based Codebook Subset Restriction Signaling

Description:
CROSS-REFERENCE TO PRIORITY APPLICATION 
     The present application is a Continuation of application Ser. No. 16/789,759 filed 13 Feb. 2020, which is a Continuation of application Ser. No. 16/518,462 filed on 22 Jul. 2019, now U.S. patent Ser. No. 10/608,715, which is Continuation of application Ser. No. 16/235,273 filed on 28 Dec. 2018, now U.S. patent Ser. No. 10/411,773, which is a Continuation of the International Application No. PCT/SE2018/050794 filed on 6 Aug. 2018, which in its turn claims priority to U.S. Provisional Application No. 62/544,761 filed on 11 Aug. 2017. The disclosures of each of these references are incorporated in their entireties by reference herein. 
    
    
     TECHNICAL FIELD 
     The application relates to systems, methods, and apparatus for wireless communication, and in particular, for enhanced codebook subset restriction (CBSR) signaling. 
     BACKGROUND 
     Fifth-Generation (5G) air-interface protocols, also referred to as New Radio (NR), are currently being developed by the Third Generation Partnership Project (3GPP). The beam-based rank-agnostic CBSR approach used in Long Term Evolution (LTE) cannot be directly re-used for NR as the same beam-based quantity is not a constituent component of the precoders for all ranks. Namely, the precoder codebooks for ranks 3 and 4 in LTE are constructed with a different beam-based quantity than the remaining ranks. An alternative is to use the pre-LTE full dimension multiple-input, multiple-output (FD-MIMO) CBSR approach based on precoding matrix indicator (PMI)-based per-rank CBSR, however this would lead to around 8 times more signaling overhead compared to LTE. 
     NR codebooks use a generalized co-phasing behavior that is different from prior art codebooks in LTE, as there are now two parameters (φ_n and θ_p) used to co-phase the two-dimensional discrete Fourier transform (2D DFT) beams. The co-phasing behavior depends on the number of Channel State Information Reference Signal (CSI-RS) ports used in the codebook and may be different for codebooks of different ranks. Consequently, new mechanisms are needed in NR for codebook restriction of co-phasing and rank. 
     SUMMARY 
     The present disclosure describes techniques for codebook subset restriction and precoder selection in wireless telecommunications systems. Generally, the techniques involve a first component common to precoders of a first group of codebooks mapping to a second component different from the first component and common to precoders of a second group of codebooks. For instance, the present disclosure presents in an example method for codebook subset restriction at a user equipment (UE). According to the method, the UE can receive, from a network node (e.g., gNB, eNB, etc.), codebook subset restriction CBSR signaling for a first component common to precoders in a first group of codebooks. In an aspect of this example method, a restriction of the first component maps to a restriction of a second component common to precoders in a second group of codebooks. Several other example embodiments performed by the UE are also included herein will be described further below. 
     The present disclosure also discloses a method performed by a network node for codebook subset restriction that includes generating CBSR signaling that indicates a first component common to precoders in a first group of codebooks. In an aspect, the first component maps to a second component common to precoders in a second group of codebooks. Additionally, the CBSR signaling can be configured to cause a UE to restrict precoders selectable from a codebook in the second group of codebooks based on the second component. In a further aspect of the example method, the network node can transmit the CBSR signaling to the UE. 
     Embodiments herein also include corresponding apparatus, computer programs, and carriers (e.g., computer program products), as well as network-side aspects performed by a network node. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a spatial multiplexing operation that underlies example embodiments of the present disclosure. 
         FIG. 2  illustrates an example array with cross-polarized antenna elements utilized in example embodiments of the present disclosure. 
         FIG. 3  illustrates an example scenario where dynamic elevation beamforming may cause interference. 
         FIG. 4  is a graph illustrating a transmission gap at a particular elevation angle according to some embodiments of the present disclosure. 
         FIG. 5  illustrates a wireless communication system corresponding to example embodiments of the present disclosure. 
         FIG. 6  illustrates an example of how a first component maps to a second component in one or more embodiments. 
         FIG. 7A  illustrates a method performed by a UE according to one or more embodiments. 
         FIG. 7B  illustrates a method performed by a UE according to one or more embodiments. 
         FIG. 7C  illustrates a method performed by a UE according to one or more embodiments. 
         FIG. 7D  illustrates a method performed by a UE according to one or more embodiments. 
         FIG. 7E  illustrates a method performed by a UE according to one or more embodiments. 
         FIG. 8A  illustrates a method performed by a network node according to one or more embodiments. 
         FIG. 8B  illustrates a method performed by a network node according to one or more embodiments. 
         FIG. 8C  illustrates a method performed by a network node according to one or more embodiments. 
         FIGS. 9A and 9B  illustrate aspects of a UE in example embodiments of the present disclosure. 
         FIGS. 10A and 10B  illustrate aspects of a network node in example embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure describes example techniques for codebook subset restriction and precoder selection. For instance, in some examples, a UE can receive, from a network node, CBSR signaling that indicates a first component (or components) common to precoders in a first group of codebooks. The UE can map the first component to a second component that is different than the first component and that is common to precoders in a second group of codebooks, and can restrict precoders selectable from a codebook in the second group of codebooks based on the second component. 
     Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is in particular improved if both the transmitter and the receiver are equipped with multiple antennas, which results in a multiple-input multiple-output (MIMO) communication channel. Such systems and/or related techniques are commonly referred to as MIMO. 
     The NR standard is currently being specified. A core aspect of NR is the support of MIMO antenna deployments and MIMO related techniques. NR will support an 8-layer spatial multiplexing mode for up to 32 TX antenna ports with channel dependent precoding. The spatial multiplexing mode aims for high data rates in favorable channel conditions. 
     An illustration of the spatial multiplexing operation is provided in  FIG. 1 . As shown in the figure, an information carrying symbol vector s  10  is multiplied by an NT×r precoder matrix W  11 , which serves to distribute the transmit energy in a subspace of the NT (corresponding to NT antenna ports  12 )-dimensional vector space. The precoder matrix  11  is typically selected from a codebook of possible precoder matrices, and typically indicated by means of a precoder matrix indicator (PMI), which specifies a unique precoder matrix in the codebook for a given number of symbol streams. The r symbols in symbol vector s  10  each correspond to a layer and r is referred to as the transmission rank. In this way, spatial multiplexing is achieved since multiple symbols can be transmitted simultaneously over the same time/frequency resource element (TFRE). The number of symbols r is typically adapted to suit the current channel properties. 
     NR uses OFDM in the downlink and hence the received N R ×1 vector y n  for a certain TFRE on subcarrier n (or alternatively data TFRE number n) is thus modeled by: 
     
       
      
       y 
       n 
       =H 
       n 
       Ws 
       n 
       +e 
       n  
      
     
     where e n  is a noise/interference vector obtained as realizations of a random process. The precoder W can be a wideband precoder, which is constant over frequency, or frequency selective. 
     The precoder matrix W is often chosen to match the characteristics of the NR×NT MIMO channel matrix H n , resulting in so-called channel dependent precoding. This is also commonly referred to as closed-loop precoding and essentially strives for focusing the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the UE. In addition, the precoder matrix may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the UE, the interlayer interference is reduced. 
     One example method for a UE to select a precoder matrix W can be to select the W k  that maximizes the Frobenius norm of the hypothesized equivalent channel: 
     
       
         
           
             
               max 
               k 
             
              
             
               
                  
                 
                   
                     
                       H 
                       ^ 
                     
                     n 
                   
                    
                   
                     W 
                     k 
                   
                 
                  
               
               F 
               2 
             
           
         
       
     
     where:
         Ĥ n  is a channel estimate;   W k  is a hypothesized precoder matrix with index k; and   Ĥ n W k  is the hypothesized equivalent channel.       

     In closed-loop precoding for the NR downlink, the UE transmits (based on channel measurements in the forward link/downlink) recommendations to the gNB (also referred to herein as a gNB, eNB, base station, or the like) regarding a suitable precoder to use. For example, by transmitting or sending a PMI to the gNB. The gNB may configure the UE to provide feedback, and may transmit CSI-RS and/or may configure the UE to use measurements of CSI-RS to feedback recommended precoding matrices that the UE selects from a codebook. A single precoder or indication thereof that is supposed to cover a large bandwidth (wideband precoding) may be fed back. It may also be beneficial to match the frequency variations of the channel and instead feedback a frequency-selective precoding report, e.g. several precoders or indications thereof, one per subband. This is an example of the more general case of CSI feedback, which also encompasses feeding back other information than recommended precoders to assist the gNB in subsequent transmissions to the UE. Such other information may include channel quality indicators (CQIs) as well as transmission rank indicator (RI). 
     Given the CSI feedback from the UE, the gNB determines the transmission parameters it wishes to use to transmit to the UE, including the precoding matrix or precoder, transmission rank, and modulation and coding state (MCS). These transmission parameters may differ from the recommendations the UE makes. Therefore, a rank indicator and MCS may be signaled in downlink control information (DCI), and the precoding matrix or precoder or indication thereof can be signaled in DCI or the gNB can transmit a demodulation reference signal from which the equivalent channel can be measured. The transmission rank, and thus the number of spatially multiplexed layers, is reflected in the number of columns of the precoder W. For efficient performance, it is important that a transmission rank that matches the channel properties is selected. 
     The example embodiments presented in this disclosure may be used with two-dimensional antenna arrays and some of the presented embodiments use such antennas. Such antenna arrays may be (partly) described by the number of antenna columns corresponding to the horizontal dimension N h , the number of antenna rows corresponding to the vertical dimension N v  and the number of dimensions corresponding to different polarizations N p . The total number of antennas is thus N=N h N v N p . It should be pointed out that the concept of an antenna is non-limiting in the sense that it can refer to any virtualization (e.g., linear mapping) of the physical antenna elements. For example, pairs of physical sub-elements could be fed the same signal, and hence share the same virtualized antenna port.  FIG. 2  illustrates a two-dimensional (4×4) array  13  with cross-polarized antenna elements having N h =4 horizontal antenna elements and N v =4 vertical antenna elements. 
     Precoding may be interpreted as multiplying the signal with different beamforming weights for each antenna prior to transmission. A typical approach is to tailor the precoder to the antenna form factor, i.e. taking into account N h , N v  and N p  when designing the precoder codebook. 
     A common type of precoding is to use a DFT-precoder, where the precoder vector used to precode a single-layer transmission using a single-polarized uniform linear array (ULA) with N antennas is defined as: 
     
       
         
           
             
               
                 
                   w 
                   
                     1 
                      
                     D 
                   
                 
                  
                 
                   ( 
                   k 
                   ) 
                 
               
               = 
               
                 
                   1 
                   
                     N 
                   
                 
                  
                 
                   [ 
                   
                     
                       
                         
                           e 
                           
                             j 
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             
                               π 
                               · 
                               0 
                               · 
                               
                                 k 
                                 QN 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           e 
                           
                             j 
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             
                               π 
                               · 
                               1 
                               · 
                               
                                 k 
                                 QN 
                               
                             
                           
                         
                       
                     
                     
                       
                         ⋮ 
                       
                     
                     
                       
                         
                           e 
                           
                             j 
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             
                               π 
                               · 
                               
                                 ( 
                                 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               · 
                               
                                 k 
                                 QN 
                               
                             
                           
                         
                       
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
     where k=0, 1, . . . QN−1 is the precoder index and Q is an integer oversampling factor. A corresponding precoder vector for a two-dimensional uniform planar array (UPA) can be created by taking the Kronecker product of two precoder vectors as w 2D (k,l)=w 1D (k)⊗w 1D (l). Extending the precoder for a dual-polarized UPA may then be done as: 
     
       
         
           
             
               
                 W 
                 
                   
                     2 
                      
                     D 
                   
                   , 
                   DP 
                 
               
                
               
                 ( 
                 
                   k 
                   , 
                   l 
                   , 
                   φ 
                 
                 ) 
               
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         1 
                       
                     
                     
                       
                         
                           e 
                           
                             j 
                              
                             φ 
                           
                         
                       
                     
                   
                   ] 
                 
                 ⊗ 
                 
                   
                     w 
                     
                       2 
                        
                       D 
                     
                   
                    
                   
                     ( 
                     
                       k 
                       , 
                       l 
                     
                     ) 
                   
                 
               
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           
                             w 
                             
                               2 
                                
                               D 
                             
                           
                            
                           
                             ( 
                             
                               
                                 k 
                                 ′ 
                               
                                
                               l 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         
                           
                             e 
                             
                               j 
                                
                               φ 
                             
                           
                            
                           
                             
                               w 
                               
                                 2 
                                  
                                 D 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 , 
                                 l 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               w 
                               
                                 2 
                                  
                                 D 
                               
                             
                              
                             
                               ( 
                               
                                 k 
                                 , 
                                 l 
                               
                               ) 
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           
                             
                               w 
                               
                                 2 
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                              
                             
                               ( 
                               
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                               ) 
                             
                           
                         
                       
                     
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                    
                   
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                           1 
                         
                       
                       
                         
                           
                             e 
                             
                               j 
                                
                               φ 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
     where e jϕ  is a co-phasing factor that may for instance be selected from QPSK alphabet ϕ∈ 
     
       
         
           
             
               { 
               
                 0 
                 , 
                 
                   π 
                   2 
                 
                 , 
                 π 
                 , 
                 
                   
                     3 
                      
                     π 
                   
                   2 
                 
               
               } 
             
             . 
           
         
       
     
     A precoder matrix W 2D,DP  for multi-layer transmission may be created by appending columns of DFT precoder vectors as: 
         W   2D,DP =[ w   2D,DP ( k   1   ,l   1 ,ϕ 1 ) w   2D,DP ( k   2   ,l   2 ,ϕ 2 ) . . .  w   2D,DP ( k   R   ,l   R ,ϕ R )],
 
     where R is the number of transmission layers, i.e. the transmission rank. In a common special case for a rank-2 DFT precoder, k 1 =k 2 =k and l 1 =l 2 =l, meaning that: 
     
       
         
           
             
               W 
               
                 
                   2 
                    
                   D 
                 
                 , 
                 DP 
               
             
             = 
             
               
                 [ 
                 
                   
                     
                       
                         
                           w 
                           
                             
                               2 
                                
                               D 
                             
                             , 
                             DP 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             , 
                             l 
                             , 
                             
                               φ 
                               1 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         
                           w 
                           
                             
                               2 
                                
                               D 
                             
                             , 
                             DP 
                           
                         
                          
                         
                           ( 
                           
                             k 
                             , 
                             l 
                             , 
                             
                               φ 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 ] 
               
               = 
               
                   
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 w 
                                 
                                   2 
                                    
                                   D 
                                 
                               
                                
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   l 
                                 
                                 ) 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               
                                 w 
                                 
                                   2 
                                    
                                   D 
                                 
                               
                                
                               
                                 ( 
                                 
                                   k 
                                   , 
                                   l 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                  
                                 
                                   φ 
                                   1 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                  
                                 
                                   φ 
                                   2 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Elevation beamforming, which can be achieved by using codebook-based precoding from a 2D or vertical antenna array, is a powerful tool for directing the transmitted energy towards the UE of interest, thereby increasing the received signal level. Interference is another aspect that should be taken into consideration to maximize system performance. For instance, in some urban topologies, dynamic elevation beamforming can cause significant interference, as illustrated in  FIG. 3 . As show, when a gNB  14  directs its transmitted power towards a UE  15 A it may at the same time also direct the transmitted energy towards another UE  15 B currently receiving a signal from another gNB  18 B. Hence, gNBs  14  may cause interference to their neighboring cells when performing elevation beamforming and this interference may be very harmful for the system. In fact, if this interference is not mitigated, it is possible that employing elevation beamforming in a communication system will not lead to a system-level gain, since the increase in received signal level by dynamic beam selection may be less than the simultaneous increase in the interference level. 
     The concept of angular gap constrained transmission has been introduced to avoid beamforming in certain angular intervals where the caused interference to other cells would be large. Such transmission characteristics may be achieved by not offering an elevation beam in said critical directions, thereby creating a transmission “gap.”  FIG. 4  shows such a gap  16  as gap  16 , where normalized antenna gain (y-axis) drops off in a range of elevation zenith angles (x-axis) compared to the antenna gain levels of adjacent zenith angles. 
     When elevation beamforming is used with codebook-based precoding, such a transmission gap  16  can be attained by codebook subset restriction, in which the gNB instructs the UE to not use a subset of the precoding matrices in that codebook which would correspond to beam directions causing excessive inter-cell interference. Note that there may also be azimuthal directions which can cause excessive inter-cell interference, and restricting the transmission in these directions may be beneficial as well. 
     The LTE precoder codebooks are based on DFT precoders as described above. Codebooks are defined for ranks 1-8 and are based on the quantities of: 
     
       
         
           
             
               ϕ 
               n 
             
             = 
             
               e 
               
                 j 
                  
                 
                     
                 
                  
                 π 
                  
                 
                     
                 
                  
                 
                   n 
                   / 
                   2 
                 
               
             
           
         
       
       
         
           
             
               u 
               m 
             
             = 
             
               [ 
               
                 
                   
                     1 
                   
                   
                     
                       e 
                       
                         j 
                          
                         
                           
                             2 
                              
                             π 
                              
                             m 
                           
                           
                             
                               O 
                               2 
                             
                              
                             
                               N 
                               2 
                             
                           
                         
                       
                     
                   
                   
                     … 
                   
                   
                     
                       e 
                       
                         j 
                          
                         
                           
                             2 
                              
                             π 
                              
                             
                               m 
                                
                               
                                 ( 
                                 
                                   
                                     N 
                                     2 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               O 
                               2 
                             
                              
                             
                               N 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               ] 
             
           
         
       
       
         
           
             
               v 
               
                 l 
                 , 
                 m 
               
             
             = 
             
               
                 [ 
                 
                   
                     
                       
                         
                           u 
                           m 
                         
                       
                       
                         
                           
                             e 
                             
                               j 
                                
                               
                                 
                                   2 
                                    
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                                    
                                   
                                       
                                   
                                    
                                   l 
                                 
                                 
                                   
                                     O 
                                     1 
                                   
                                    
                                   
                                     N 
                                     1 
                                   
                                 
                               
                             
                           
                            
                           
                             u 
                             m 
                           
                         
                       
                       
                         … 
                       
                       
                         
                           e 
                           
                             j 
                              
                             
                               
                                 2 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 
                                   l 
                                    
                                   
                                     ( 
                                     
                                       
                                         N 
                                         1 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   O 
                                   1 
                                 
                                  
                                 
                                   N 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                    
                   
                     u 
                     m 
                   
                 
                 ] 
               
               T 
             
           
         
       
     
     where v l,m  is defined for l=0, . . . , N 1 O 1 −1, m=0, . . . , N 2 O 2 −1, and is a 2D DFT precoder or beam that corresponds to W 2D (k,l) w 2D (l,m), the codebooks for all ranks are constructed based on the quantity v l,m . As an example, the definitions of the rank-2 and rank-4 codebooks are given in Table 1 and Table 2, below, where i 1,1  and i 1,2  are the 2D DFT beam indices in each dimension and i 2  is the corresponding co-phasing index: 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 2 Layers, Codebook-Config = 1 
               
               
                 i 1,2  = 0, . . . , N 2 O 2 −1 
               
            
           
           
               
               
            
               
                   
                 i2 
               
            
           
           
               
               
               
               
               
            
               
                 i 1,1   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                 0, . . . , N 1 O 1 −1 
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     ,0   (2)   
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     ,1   (2)   
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     ,2   (2)   
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     ,3   (2)   
               
               
                   
               
            
           
           
               
            
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             W 
                             
                               l 
                               , 
                               
                                 l 
                                 ′ 
                               
                               , 
                               m 
                               , 
                               
                                 m 
                                 ′ 
                               
                               , 
                               n 
                             
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                         = 
                         
                           
                             
                               1 
                               
                                 
                                   2 
                                    
                                   P 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       v 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                     
                                   
                                   
                                     
                                       v 
                                       
                                         
                                           l 
                                           ′ 
                                         
                                         , 
                                         
                                           m 
                                           ′ 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         ϕ 
                                         n 
                                       
                                        
                                       
                                         v 
                                         
                                           l 
                                           , 
                                           m 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         - 
                                         
                                           ϕ 
                                           n 
                                         
                                       
                                        
                                       
                                         v 
                                         
                                           
                                             l 
                                             ′ 
                                           
                                           , 
                                           
                                             m 
                                             ′ 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 4 Layers, Codebook-Config = 1, N 1  &gt;1, N 2  &gt;1 
               
               
                 i 1,2  = 0,1, . . . , N 2 O 2 −1 
               
            
           
           
               
               
            
               
                   
                 i 2   
               
            
           
           
               
               
               
            
               
                 i 1,1   
                 0 
                 1 
               
               
                   
               
               
                 0, . . . , N 1 O 1 −1 
                 W i     1,1     ,i     1,1     +O     1     ,i     1,2     ,i     1,2     ,0   (4)   
                 W i     1,1     ,i     1,1     +O     1     ,i     1,2     ,i     1,2     ,1   (4)   
               
               
                 O,N 1 , . . . , 2O 1 N 1 −1 
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     +O     2     ,0   (4)   
                 W i     1,1     ,i     1,1     ,i     1,2     ,i     1,2     +O     2     ,1   (4)   
               
               
                   
               
            
           
           
               
            
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             W 
                             
                               l 
                               , 
                               
                                 l 
                                 ′ 
                               
                               , 
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                               , 
                               
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                                 ′ 
                               
                               , 
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                               ( 
                               4 
                               ) 
                             
                           
                         
                         = 
                         
                           
                             1 
                             
                               
                                 4 
                                  
                                 P 
                               
                             
                           
                            
                           
                             [ 
                             
                               
                                 
                                   
                                     v 
                                     
                                       l 
                                       , 
                                       m 
                                     
                                   
                                 
                                 
                                   
                                     v 
                                     
                                       
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                                         ′ 
                                       
                                       , 
                                       
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                                         ′ 
                                       
                                     
                                   
                                 
                                 
                                   
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                                     v 
                                     
                                       
                                         l 
                                         ′ 
                                       
                                       , 
                                       
                                         m 
                                         ′ 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       ϕ 
                                       n 
                                     
                                      
                                     
                                       v 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       ϕ 
                                       n 
                                     
                                      
                                     
                                       v 
                                       
                                         
                                           l 
                                           ′ 
                                         
                                         , 
                                         
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                                           ′ 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
                                         ϕ 
                                         n 
                                       
                                     
                                      
                                     
                                       v 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
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                                         n 
                                       
                                     
                                      
                                     
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                                           l 
                                           ′ 
                                         
                                         , 
                                         
                                           m 
                                           ′ 
                                         
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     In order to reduce codebook subset restriction (CBSR) signaling overhead, LTE FD-MIMO uses beam-based rank-agnostic CBSR signaling as opposed to PMI-based per-rank CBSR as was used in earlier releases of LTE. In PMI-based per-rank CBSR, precoders are restricted by signaling one or more bitmaps for each rank (i.e. 8 sets of bitmaps for ranks 1-8) and each bit in the bitmap restricts one PMI index (e.g. i1 or i2) for the codebook of a specific rank. 
     With beam-based rank-agnostic CBSR, on the other hand, the constituent 2D DFT beams v l,m  are restricted instead, resulting in a size N 1 N 2 O 1 O 2  bitmap where each bit is associated with one oversampled 2D DFT beam, v l,m . When a bit in the bit map is set, the corresponding DFT beam is restricted or should not be used for CSI estimation. Since the quantity v l,m  are the constructing blocks for precoders of all ranks, a substantial overhead reduction in CBSR signaling is attained. Thus, a particular precoder in the codebook is restricted if any of the restricted beams v l,m  is present in the precoder. 
     Beam-based CBSR requires a second set of restrictions to control rank and/or i2. These restrictions are indicated by a joint rank-i2 restriction in LTE, where a bitmap of the combinations of rank υ and codebook index i2. As stated in 3GPP TS 36.213, bit b (g(υ-1)+i     2    is associated with the precoder for υ layers (υ∈{1, 2, 3, 4}) and codebook index i 2  where g(⋅) is given in Table 3, below: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Value of Codebook-Config 
                 g(•) 
               
               
                   
                   
               
             
            
               
                   
                 1 
                 {0, 4, 8, 10} 
               
               
                   
                 2 
                 {0, 16, 32, 48} 
               
               
                   
                 3 
                 {0, 16, 32, 48} 
               
               
                   
                 4 
                 {0, 16, 32, 48} 
               
               
                   
                   
               
            
           
         
       
     
     The NR Type I codebooks are similar in many ways to the LTE FD-MIMO codebooks, but contain some differences. One difference is that the rank-3 and rank-4 codebooks use “antenna grouping” when the number of antenna ports is larger than 16 (for the smaller than 16 port case, the rank-3 and rank-4 codebooks are similar to the LTE codebooks). This has led to the introduction of two quantities that correspond to 2D DFT beams: v l,m  and {tilde over (v)} l,m , where v l,m  is used for the ranks 1, 2, 5, 6, 7, 8 codebooks for 16 antenna ports and larger (and ranks 1-8 for smaller than 16 antenna ports) and {tilde over (v)} l,m  is used for rank-3 and rank-4 codebooks for larger than or equal to 16 antenna ports. Here, it can be observed that co-phasing behavior is generalized from LTE, as there are now two parameters φ n  and θ p  used to co-phase the 2D DFT beams {tilde over (v)} l,m : 
     
       
         
           
             
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             = 
             
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                 j 
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                 π 
                  
                 
                     
                 
                  
                 
                   n 
                   / 
                   2 
                 
               
             
           
         
       
       
         
           
             
               θ 
               p 
             
             = 
             
               
                 
                   e 
                   
                     j 
                      
                     
                         
                     
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                      
                     
                         
                     
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                  
                 
                   
 
                 
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                 { 
                 
                   
                     
                       
                         
                           
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                         ] 
                       
                       T 
                     
                   
                 
               
             
           
         
       
     
     As an example, the definitions of the rank-2 and the rank-4 codebooks are also given in Table 4 and Table 5, respectively: 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Codebook-Config = 1 
               
            
           
           
               
               
               
               
            
               
                 i 1,1   
                 i 1,2   
                 i 2   
                   
               
               
                   
               
               
                 0,1, . . . , N 1 O 1 −1 
                 0, . . . , N 2 O 2 −1 
                 0,1 
                 W i     1,1     ,i     1,1     +k     1     ,i     1,2     ,i     1,2     +k     2     ,i     2     (2)   
               
               
                   
               
            
           
           
               
            
               
                 
                   
                     
                       
                         
                           where 
                            
                           
                               
                           
                            
                           
                             W 
                             
                               l 
                               , 
                               
                                 l 
                                 ′ 
                               
                               , 
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                               ( 
                               2 
                               ) 
                             
                           
                         
                         = 
                         
                           
                             
                               1 
                               
                                 
                                   2 
                                    
                                   
                                     P 
                                     
                                       CSI 
                                       - 
                                       RS 
                                     
                                   
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       v 
                                       
                                         l 
                                         , 
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                                         ϕ 
                                         n 
                                       
                                        
                                       
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                                           m 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
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                                           n 
                                         
                                       
                                        
                                       
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                                             l 
                                             ′ 
                                           
                                           , 
                                           
                                             m 
                                             ′ 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Codebook-Config = 1-2, P CSI-RS  ≥16 
               
            
           
           
               
               
               
               
               
            
               
                 i 1,1   
                 i 1,2   
                 i 1,3   
                 i 2   
                   
               
               
                   
               
               
                 
                   
                     
                       
                         0 
                         , 
                         … 
                          
                         
                             
                         
                         , 
                         
                           
                             
                               
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                                 1 
                               
                             
                             2 
                           
                           - 
                           1 
                         
                       
                     
                   
                 
                 0, . . . , N 2 O 2 −1 
                 0,1,2,3 
                 0,1 
                 W i     1,1     ,i     1,2     ,i     1,3     ,i     2     (4)   
               
               
                   
               
            
           
           
               
            
               
                 
                   
                     
                       
                         
                           where 
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                                           l 
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                               ] 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     The beam-based rank-agnostic CBSR approach used in LTE cannot be directly re-used for NR as the same beam-based quantity is not constituent component of the precoders for all ranks. An alternative is to use the pre-“LTE FD-MIMO” CBSR approach based on PMI-based per-rank CBSR, however this would lead to around eight times more signaling overhead compared to LTE. In addition, NR codebooks use a generalized co-phasing behavior that is different from prior art codebooks in LTE, as there are now two parameters φ n  and θ p  used to co-phase the 2D DFT beams {tilde over (v)} l,m . The co-phasing behavior depends on the number of CSI-RS ports used in the codebook and on the rank of the report. Consequently, new mechanisms, such as those described throughout the present disclosure, are needed in NR for codebook restriction of co-phasing and rank. 
     The present description further relates to techniques for compressing codebook subset restriction signaling and is applicable to precoder codebooks where the per-rank codebooks may be divided in two groups. The precoders in the per-rank codebooks of the first group are all constructed using a first component while the precoders in the per-rank codebooks of the second group are all constructed using a second component, where the second component is different from the first component. In addition, each component can take a number of different values. 
     In particular, the techniques disclosed by the present disclosure are applicable (in a non-limiting fashion) to the NR Type I codebooks (for larger and equal to 16 antenna ports). In this case, the first group contains the per-rank codebooks for ranks 1, 2, 5, 6, 7, 8, where the precoders are all constructed based on the component v l     1     ,m , which is defined for l 1 =0, . . . , N 1 O 1 −1, m=0, . . . , N 2 O 2 −1 and constitutes a size-N 1 N 2  2D DFT vector. The second group contains the per-rank codebooks for ranks 3 and 4, where the precoders are all constructed based on the component {tilde over (v)} l     2     ,m , defined for l 2 =0, . . . , (N 1 /2)O 1 −1, m=0, . . . , N 2 O 2 −1. 
     These groups of codebooks are illustrated in  FIG. 5 , which illustrates a wireless communication system  100  that includes a network node  106  and a UE  102  in wireless communication over one or more communication channels. As shown, the UE  102  may divide the codebooks possible for utilization by network node  106  into separate groups, such as first group of codebooks  118  and second group of codebooks  120 . The UE may receive CBSR signaling  114  from the network node on the downlink, and may restrict precoders of the codebooks from the first  118  and second  120  groups of codebooks based on one or more components indicated in the CBSR signaling  114  (also referred to herein simply as CBSR). The UE  102  can select a precoder from the restricted codebooks and report the selected precoder to the network node  106  in CSI message  116  in the uplink. The example embodiments described in reference to the figures that follow detail how the restriction and selection may be undertaken in the disclosed techniques. 
     In a first technique, a codebook subset restriction or indication thereof is signaled from a network node  106  to a UE  102  via CBSR signaling  114  containing a first component  128 , or an indication thereof, which is used for defining the CBSR for precoders  124  in the first group of codebooks  118 . The restricted first components  128  are then mapped or has a mapping to restricted second components  130  using or based on a predefined mapping. The CBSR of the precoders in the second group of codebooks  120  is defined based on the restricted second components  130 . Within the first group, beam-based rank-agnostic CBSR is applied to define the CBSR for the first per-rank codebooks according to existing techniques. Namely, each precoder in the first group of codebooks  118  that is constructed using one or more of the restricted first components  128  are not allowed to be used for CSI reporting by the UE. 
     To derive the restriction of the precoders  126  in the second group  120 , a mapping between first components and second components are made, wherein each first component can be mapped or maps to one or more second component. Or, equivalently, each second component  130  is mapped or maps to one or more first components  128 . Thus, each second component  130  can be mapped or maps to one or more first components  128  and each first component  128  can be mapped or maps to one or more second components  130 . Based on this mapping and the restricted first components  128 , a restriction of the second components  130  is determined such that if at least one restricted first component  128  is mapped to a second component  130 , that second component  130  is restricted. 
     This principle is illustrated in the example mapping diagram in  FIG. 6 , which illustrates how indices of a first component  128  (or restriction thereof) might map to those of a second component  130 . As can be seen in the diagram, the first components  128  with indices 2, 7, and 8 are restricted. The first component with index 2 maps to second components  130  with indices 1 and 2, which implies that these second components are restricted. Based on the determined restricted second components, the CBSR for the precoders of the per-rank codebooks in the second group can be determined by applying beam-based rank-agnostic CBSR within the second group. 
     Thus, with this method, only a restriction of the first component needs to be signaled to define the CBSR, which keeps down the overhead for CBSR signaling. In some embodiments, the NR Type I codebooks is used, where the first and second groups are defined as above. The signaling of the restriction of the first component may for instance be done using a length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit is mapped to a (l 1 ,m) value which in turn indicates the restriction of the first component  128 . For purposes of the present disclosure, the term “component” (e.g., as used in the terms “first component(s)” and “second component(s),” and the like) can correspond to a numerical vector. The first component  128 , for instance, may be referred to through the present disclosure mathematically as v l     1     ,m . Likewise, the second component may be represented mathematically in the present disclosure as {tilde over (v)} l     2     ,m . Generally, any component or entity described according to the format v l     x     ,m  or {tilde over (v)} l     x     ,m  identifies a vector representation of a component, as introduced above. Furthermore, though the term “component” is particularly defined for purposes of the present disclosure as well as a corresponding mathematical representation of the component/vector, it should also be appreciated that each component and mathematical representation thereof represents, in practical terms, a particular beam direction for wireless transmission. 
     The mapping between v l     1     ,m  and {tilde over (v)} l     2     ,m  will now be explained. First of all, v l     1     ,m , may be a 2D DFT vector that is applied to (each polarization of) the antenna array while {tilde over (v)} l     2     ,m  may be a 2D DFT beam of half-size compared to v l     1     ,m , which is applied to (each polarization of) each antenna group of the antenna array and where each of the two antenna groups are formed by splitting the antenna array in half along the first dimension (which is typically the horizontal dimension). Thus, {tilde over (v)} l     2     ,m  is applied to both the left half and the right half of the antenna array. This means that the corresponding beamwidth of v l     2     ,m  is twice that of v l     1     ,m  along the first dimension (since half the array is used to form the beam) while the beamwidth along the second dimension is the same. To form the rank-4 transmission, different cophasing between antenna groups and polarizations is applied for the different layers, but the resulting beam shape will be similar to the beam shape of {tilde over (v)} l     2     ,m . 
     In some example embodiments, the mapping between v l     1     ,m , and {tilde over (v)} l     2     ,m  is only performed when the number of antenna ports is greater or equal to 16, and the CBSR for rank-3 and rank-4 codebooks is achieved by applying beam-based CBSR using the restricted {tilde over (v)} l     2     ,m . In these examples, when the number of antenna ports is less than 16, for rank-3 and rank-4 codebooks, beam-based CBSR is applied using the set v l     1     ,m . 
     Thus, as the properties of the beam shape along the second dimension is the same for {tilde over (v)} l     2     ,m  and v l     1     ,m , the problem can be reduced to finding a mapping rule in the first dimension, i.e., to find a mapping rule between the indices l 1  and l 2 . To derive such relationship, one can study the entries of the array steering vector e j2π sin(ϕ)d     λ     n , where ϕ is the steering angle, d λ  the array element separation in wavelengths and n the array element index. This indicates that a beam is to be steered to angle −ϕ for an array with d λ  element separation, the phase e j2π sin(ϕ)d     λ     n  shall be applied to each array element n (i.e., the complex conjugate of the steering phase shall be applied). 
     The first component v l     1     ,m  has a phase progression of 
     
       
         
           
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     should hold. This implies that l 2 =l 1 /2 results in the same beam direction. Thus, in an embodiment, the mapping between restricted first and second components is given as follows. If an (sub)-index l 1  of the first component is restricted, the (sub)-index l 2 =l 1 /2 is restricted for the second component. Note that for odd l 1 , 
     
       
         
           
             
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     is not an integer and so does not map to an l 2  index. In one embodiment, the odd l 1  values are simply ignored so that there is a one-to-one mapping between restricted first and restricted second components. In another embodiment, both l 2 =┌l 1 /2┐ and l 2 =└l 1 /2┘ are restricted if l 1  is restricted and l 1  is odd, meaning that one first component restricts two second components in that case. 
     In yet another embodiment, l 2 =└l 1 /2┘ is restricted if l 1  is restricted. For example, if l 1 =11 or l 1 =10 is restricted, then l 2 =5 is also restricted in rank 3 and rank 4 codebooks. Alternatively, l 2 =┌l 1 /2┐ is restricted if l 1  is restricted. For example, if l 1 =11 is restricted, then l 2 =6 is also restricted in rank 3 and rank 4 codebooks. 
     Since the beamwidth of {tilde over (v)} l     2     ,m  is twice that of v l     1     ,m , it would make sense that the restriction of {tilde over (v)} l     2     ,m  depends on several, adjacent, v l     1     ,m . Thus, in some embodiments, the second component corresponding to the index l 2  is restricted if any of the first components corresponding the interval [mod(2l 2 −Δ 1 ,N 1 O 1 ),mod(2l 2 +Δ z ,N 1 O 1 )] of index l 1  is restricted. Since the beam index is wrapped around N 1 O 1  (i.e. l 1 =0 and l 1 =N 1 O 1  corresponds to the same beam direction), the module operator is used. The interval essentially defines a size Δ 1 +Δ 2 +1 window around l 1 =2l 2  of restricted first components that impact the restriction of the second component with (sub)-index l 2 . In some such embodiments, a symmetric window is used, so that Δ 1 =Δ 2 . A good choice may be Δ 1 =Δ 2 =1, i.e. a size 3 window, due to that the beamwidth corresponding to second components is twice that of first components. In another embodiment Δ 1 =O 1  and Δ 2 =O 1 −1 so that a size 2O 1  windows is used in order to be more conservative in the restriction. 
     In a further aspect of the present disclosure, separate CBSRs are signaled for the first group and the second group. The CBSR signaling for the first group defines a restriction of the first component while the CBSR signaling for the second group defines a restriction of the second component. The CBSR signaling for the first group thus determines the CBSR for the precoders of certain ranks while the CBSR signaling for the second group determines the CBSR for the precoders of other ranks. In some embodiments, the signaling of the CBSR corresponding to the second group depends on the number of antenna ports configured. For instance, when the number of antenna ports is less than 16, the CBSR corresponding to the second group is not signaled. When the number of antenna ports is larger than or equal to 16, the CBSR corresponding to the second group is signaled. In one embodiment, the NR Type I codebook is used and the CBSR signaling comprises two bitmaps:
         one length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit is mapped to an (l 1 ,m) value which in turn indicates the restriction of the first component v l     1     ,m , and   one length (N 1 /2)N 2 O 1 O 2  bitmap b 0 b 1 , . . . b (N     1     /2)N     2     O     1     O     2     −1  where each bit is mapped to an (l 2 ,m) value which in turn indicates the restriction of the second component v l     2     ,m .       

     Furthermore, rather than receive only a first component or indication thereof in CBSR, the UE can receive a second component or indication thereof for codebook subset restriction as well. Thus, in some examples, the UE can receive CBSR from a network node, the CBSR indicating a first component for codebook restriction of a first group of codebooks. In these examples, the first component can be common to precoders of the first group of precoders. In addition, the CBSR can indicate a second component for codebook restriction of a second group of codebooks, where the second component is common to precoders of the second group of precoders. In an aspect of these example embodiments, the second component can be different than the first component. Thus, according to these components, the UE can restrict precoders selectable from a codebook in the first group of codebooks based on the first component and can restrict precoders selectable from a codebook in the second group of codebooks based on the second component. 
     In a further aspect, a UE can receive a joint indication of a combination of a rank value and a first index and/or a second index. In an aspect of these example embodiments, the first index identifies at least a first complex number that scales a two-dimensional (2D) Discrete Fourier Transform (DFT) beam and the second index identifies at least a second complex number that also scales the 2D DFT beam. The UE can also determine a number of states that the first index and/or second index can attain according to (a) the rank value and (b) at least one of a codebook configuration and a number of channel state information (CSI) reference signal ports. 
     In some embodiments, a UE  102  may implement co-phasing and rank subset restriction as a mechanism of adjusting combinations used in CSI reporting. In particular, this mechanism can include a UE  102  receiving a joint indication of combinations of a rank value and a first index and/or a second index from a network node  106 , where the first index identifies at least a first complex number φ n  that scales a 2D DFT beam, the second index identifies at least a second complex number that also scales the 2D DFT beam. Based on the joint indication, the UE  102  can determine a number of states that the first and/or second index can attain according to the rank value and a codebook configuration and/or a number of CSI-RS ports. Furthermore, the mechanism can involve the UE  102  generating a CSI report that indicates only the values of rank and the first index and/or second index that are permitted according to the joint indication. Naturally, the UE  102  can also transmit the generated CSI report to a network node  106 . 
     In an additional feature of the present embodiments, co-phasing and rank may be jointly indicated using a bitmap identifying combinations of a first and/or second index (such as i 1,3  and i 2 ) and a rank indication v. According to this optional aspect, the codebook subset restriction bitmap value b g(v-1)+C     2     i     1,3     +C     1     i     2    is associated with the precoder for v layers. Codebook index i 1,3  identifies the state of a first co-phasing parameter θ p , and index i 2  identifies the state of a second co-phasing parameter φ n . Vector c n  is a noise/interference vector indicating the results of a random process. Additionally, depending on the ordering of bits in the bitmap used for a particular embodiment, C 2 =4, and C 1 =2 or C 2 =2, and C 1 =4. The remaining factor, g(⋅), can be defined according to Table 6, below: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Value of Codebook-Config, with 
                   
               
               
                   
                 Number of CSI-RS ports P CSI-RS   
                 g(•) 
               
               
                   
                   
               
             
            
               
                   
                 2 with P CSI-RS  &lt; 16 
                 {0, 16, 24, 26, 28, 30, 32, 34} 
               
               
                   
                 2 with P CSI-RS  ≥ 16 
                 {0, 16, 24, 32, 40, 42, 44, 46} 
               
               
                   
                 1 with P CSI-RS  &lt; 16 
                 {0, 4, 6, 8, 10, 12, 14, 16} 
               
               
                   
                 1 with P CSI-RS  ≥ 16 
                 {0, 4, 6, 14, 22, 24, 26, 28} 
               
               
                   
                   
               
            
           
         
       
     
     The configuration Codebook-Config in Table 6 identifies the number of states used for the second index i 2  for certain values of rank, such as 1 or 2. If Codebook-Config=2, the second index i 2  identifies both a selected beam v l,m  out of a beam group of L beams in a given subband, as well as the second cophasing parameter φ n . The NR codebook design uses L=4 beams in a beam group for ranks 1 and 2 of Codebook-Config=2, consequently requiring 4 states and 2 bits, in addition to the 4 or 2 states and 2 or 1 bit required for the second cophasing parameter φ n . Therefore, Codebook-Config 2 requires 16 and 8 states for rank 1 and 2, respectively, to represent the second cophasing parameter φ n , and 4 or 3 bits for the second index i 2  in this case. 
     By contrast, Codebook-Config 1 uses L=1 beams in a beam group for all ranks, so the second index i 2  only identifies the parameter φ n  for Codebook-Config 1. Codebook-Config 1 then requires 4 and 2 states for rank 1 and 2, respectively, to represent the second cophasing parameter φ n , and 2 or 1 bit(s) for the second index i 2  in this case. The parameter θ p  requires 4 states, and so i 1,3  then uses 2 bits. Since the parameter θ p  may only be used in some conditions, such as for ranks 3 and 4, and when the number of CSI-RS ports P CSI-RS  used in the codebook is greater than or equal to 16, then the additional states or bits for θ p  are not needed in all codebook configurations. 
     The performance benefits from a larger number of states used for co-phasing parameter φ n  tends to diminish as the rank increases. Consequently, the number of states used for φ n  can be 4 for rank 1 and 2 for higher ranks, such as ranks 2 through 8. This means that above rank 4, i 2  can require only 1 bit. 
     Moreover, it can be seen that a mechanism to indicate codebook subset restriction jointly for rank, the first and second co-phasing parameters, and beam selection from a beam group can be broken down into two independent conditions: (a) whether the number of beams L in the beam group is greater than 1 (or, equivalently, if Codebook-Config=2), and (b) whether the number of CSI-RS ports used in the codebook P CSI-RS  is greater than or equal to 16 (or, equivalently, whether the number is less than 16). These conditions lead to the embodiment illustrated in Table 6, above, where the function g(⋅) is determined according to the status of these two conditions, as evidenced by each of the four permutations being indicated on one of the four rows. 
     The function g(⋅) represents the accumulation of the number of possible values of codebook indices i 1,3  and i 2  over the prior ranks v. Therefore, for Codebook-Config=2 and P CSI-RS &lt;16, since the parameter θ p  is not indicated for ranks 3 and 4, and since 16 and 8 states are required for ranks 1 and 2, respectively for i 2 , while 2 states are required for ranks greater than 2 for i 2 , g(v)=g(v−1)+Δ(v), where Δ(v)={0, 16, 8, 2, 2, 2, 2, 2} and 1&lt;v≤8, and g(v=1)=0. For Codebook-Config=2, with P CSI-RS ≥16, since the parameter θ p  is indicated for ranks 3 and 4, and since the number of states needed for ranks 1 and 2 is not influenced by the number of CSI-RS ports, in this case g(v)=g(v−1)+Δ(v), where Δ(v)={0, 16, 8, 8, 8, 2, 2, 2} and 1&lt;v≤8, and g(v=1)=0. For Codebook-Config=1, with P CSI-RS &lt;16, since the parameter θ p  is not indicated for ranks 3 and 4, and since 4 and 2 states are required for ranks 1 and 2, respectively for i 2 , while 2 states are required for ranks greater than 2 for i 2 , in this case g(v)=g(v−1)+Δ(v), where Δ(v)={0, 4, 2, 2, 2, 2, 2, 2} and 1&lt;v≤8, and g(v=1)=0. For Codebook-Config=1, with P CSI-RS ≥16, since the parameter θ p  is indicated for ranks 3 and 4, and since 4 and 2 states are required for ranks 1 and 2, respectively for i 2 , while 2 states are required for ranks greater than 2 for i 2 , in this case g(v)=g(v−1)+Δ(v), where Δ(v)={0, 4, 2, 8, 8, 2, 2, 2} and 1&lt;v≤8, and g(v=1)=0. 
     Therefore, in an embodiment, a mechanism of adjusting combinations used in CSI reporting in a UE  102  is provided. For example, such a mechanism may include a UE  102  receiving a joint indication of combinations of a rank value and a first index and/or a second index. In an aspect, this first index identifies (at least) a first complex number φ n  that scales a 2D DFT beam, while the second index identifies (at least) a second complex number that also scales the 2D DFT beam. The mechanism can also include the UE  102  determining the number of states that the first and/or second index can attain according to the rank value and at least one of a codebook configuration and a number of CSI-RS ports. Furthermore, the UE  102  can generate a CSI report that only indicates values of rank and the first index and/or second index that are permitted according to the joint indication. Finally, the UE  102  can round out the mechanism by transmitting the CSI report to a network node  106 . 
     In view of the details presented above, example methods will now be presented in reference to the figures.  FIGS. 7A-7E  show flow diagrams of five example methods that may, in some examples, be performed by the UE  102  to carry out the techniques discussed above. In addition.  FIGS. 8A-8C  show flow diagrams of three non-limiting methods that may be performed by the network node  106  in some examples. 
     Specifically,  FIG. 7A  illustrates an example method  300  for carrying out the above-described aspects at UE  102 . As illustrated, at block  302 , the UE  102  can receive CBSR signaling for a first component  128  common to precoders in a first group of codebooks  118 . As discussed at length above, a restriction of the first component  128  maps or can map to a restriction of a second component. As also described above, the second component  130  is common to precoders in a second group of codebooks  120 . In addition, at block  304 , the UE  102  can restrict precoders selectable from a codebook in the second group of codebooks  120  based on the second component  130 . For purposes of the present disclosure, the term “restrict” or “restricting” can mean “defining a restriction of a component or components.” 
     Turning to  FIG. 7B , another example method  306  for codebook subset restriction at a UE  102  is provided. As shown, at block  308 , method  306  can include receiving, from a network node  106 , CBSR signaling for a first component  128  common to precoders in a first group of codebooks  118 . In further aspects, the first component  128  maps to a second component  130  and the second component  130  is common to precoders in a second group of codebooks  120 . In addition, at block  310 , method  306  can include restricting precoders selectable from a codebook in the second group of codebooks  120  based on the second component  130 . 
     A further example embodiment of a method  312  for codebook subset restriction at a UE is shown in  FIG. 7C . In method  312 , at block  314 , the UE  102  can receive, from a network node  106 , CBSR signaling that indicates a first component  128  common to precoders in a first group of codebooks  118 . In addition, at block  316 , the UE  102  can map the first component  128  to a second component  130  that is different than the first component  128  and that is common to precoders in a second group of codebooks  120 . Furthermore, at block  318 , method  312  includes restricting precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the second component  130 . 
     In another example embodiment shown in  FIG. 7D , method  320  can include, at block  322 , receiving codebook subset restriction CBSR signaling from a network node  106  that indicates a restriction for a first component  128  common to precoders  124  in a first group of codebooks  118 . The method may also include, at block  324 , mapping the restriction for the first component  128  to a restriction for a second component  130 . Again, the second component  130  can be different than the first component  128  and can be common to precoders  126  in a second group of codebooks  120 . Additionally, method  320  can include, at block  326 , restricting precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the restriction for the second component  130 . 
       FIG. 7E  presents yet another example method  328  for codebook selection restriction at a user equipment UE  102 . As shown in the flowchart, at block  330 , the method  328  can include receiving codebook subset restriction CBSR signaling from a network node  106 , the CBSR signaling indicating a first component  128  for codebook restriction of a first group of codebooks  118 . The CBSR signaling can indicate a second component  130  for codebook restriction of a second group of codebooks  120 , the second component  130  being different than the first component  128 . In addition, at block  332 , method  328  can include restricting precoders selectable from a codebook in the first group of codebooks  118  based on the first component  128  as well as restricting precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the second component  130 . 
     Further aspects not explicitly shown in one or more of  FIGS. 7A, 7B, 7C, 7D , and  7 E may also be realized by the UE  102  in further embodiments, including those that include the following features. For example, in some embodiments, the first component is a vector from a first set of vectors, and the precoders in the first group of codebooks include one or more vectors from the first set of vectors. In some examples, the second component is a vector from a second set of vectors, where the precoders in the second group of codebooks include one or more vectors from the second set of vectors. In some instances, the second component constitutes a vector of a different size than that of the first component, such as where vectors in the second set of vectors are half the size of the vectors in the first set of vectors 
     Furthermore, in some instances, the CBSR signaling can include a bitmap that contains a plurality of bits, where each bit of the plurality of bits indicates a vector from the first set of vectors. Some examples can include determining whether the second component is restricted based on a bit indicating that the first component is restricted, for instance. In some examples, the first component can be utilized to restrict precoders selectable from a codebook in the first group of codebooks based on the first component. In an aspect, as described above, the first component may be a length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit constitutes an (l 1 ,m) value indicating, at least in part, a first two-dimensional restriction vector v l     1     ,m . 
     In addition, the methods of any of  FIGS. 7A, 7B, 7C, 7D, and 7E  can involve selecting a precoder from the precoders selectable from the codebook in the second group of codebooks. In a further aspect, the methods can include generating a CSI report indicating the selected precoder, and optionally also transmitting the CSI report to ta network node. 
     Furthermore, some implementations can include determining whether the second component is restricted based on a plurality of bits indicating whether the first component is restricted for at least one of (or for each of) v 2l+1,m , v 2l−1,m , and v 2l,m . In some examples, the first component has an associated index l 1  and the second component has an associated index l 2 , and l 1  and l 2  have a relation r such that l 1 =rl 2 . In these instances, the method can also include monitoring a size Δ 1 +Δ 2 +1 window around any restricted first component with l 1 =rl 2  that impacts the restriction of its related second components. In some implementations, Δ 1 =Δ 2  and the window size is three. 
     In a further example feature, the first group of codebooks can include rank 1, rank 2, rank 5, rank 6, rank 7, and/or rank 8 codebooks, and/or the second group of codebooks can include rank 3 and/or rank 4 codebooks. 
     Turning to the network node methods in  FIG. 8A , the figure illustrates a method  400  performed by a network node  106  for codebook subset restriction, which includes generating  402  codebook subset restriction CBSR signaling that indicates a first component  128  common to precoders  124  in a first group of codebooks  118 , where the first component  128  maps to a second component  130  common to precoders  126  in a second group of codebooks  120 . Furthermore, the CBSR signaling is configured to cause a UE  102  to restrict precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the second component  130 . In addition, at block  404 , method  400  includes transmitting the CBSR signaling to the UE. 
       FIG. 8B  presents another network node  106  method  406  that includes determining a first component  128  that is common to precoders  124  in a first group of codebooks  118  at block  408 . Again, the first component  128  maps to a second component  130  that is different than the first component  128  and is common to precoders  126  in a second group of codebooks  120 . At block  410 , the method  406  includes generating CBSR signaling that restricts precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the second component  130 . This includes the network node  106  generating the CBSR signaling to indicate the first component  128  that maps to the second component  130 . Then, at block  412 , method  406  can include transmitting the CBSR signaling at block  412 . 
     In another example method  414  for codebook selection restriction at network node  106  presented in  FIG. 8C , the network node  106  can generate, at block  416 , codebook subset restriction CBSR signaling. In an aspect, the CBSR signaling indicates a first component  128  for codebook restriction of a first group of codebooks  118  and a second component  130  for codebook restriction of a second group of codebooks  120 . Furthermore, the CBSR signaling causes the UE  102  to restrict precoders selectable from a codebook  119  in the first group of codebooks  118  based on the first component  128  and to restrict precoders  126  selectable from a codebook  121  in the second group of codebooks  120  based on the second component  130 . In addition, at block  418 , the network node  106  transmits the CBSR signaling to the UE  102 . 
     Further aspects not explicitly shown in one or more of  FIGS. 8A, 8B, and 8E  may also be realized by the UE  102  in further embodiments, including those that include the following features. For example, in some embodiments of these methods, the first component is a vector from a first set of vectors, and the precoders in the first group of codebooks include one or more vectors from the first set of vectors. In some examples, the second component is a vector from a second set of vectors, where the precoders in the second group of codebooks include one or more vectors from the second set of vectors. In some instances, the second component constitutes a vector of a different size than that of the first component, such as where vectors in the second set of vectors are half the size of the vectors in the first set of vectors. Furthermore, some embodiments can include the network node receiving  106 , from the UE  102 , CSI report indicating permitted codebook subsets corresponding to restricted codebook subsets. In an aspect of some example embodiments, as described above, the first component may be a length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit constitutes an (l 1 ,m) value indicating, at least in part, a first two-dimensional restriction vector v l     1     ,m . 
       FIG. 9A  illustrates additional details of an example UE  102  of a wireless communication system  100  according to one or more embodiments. The UE  102  is configured, e.g., via functional means or units (also may be referred to as modules or components herein), to implement processing to perform certain aspects described above in reference to at least methods presented in  FIGS. 7A, 7B, 7C, 7D, and 7E . As shown in  FIG. 9B , the UE  102  in some embodiments for example includes means, modules, components, or units  530 ,  540 , and  550  (among other possible means, modules, components, or units not shown explicitly in  FIG. 5B ) for performing aspects of these methods. In some examples, these means, modules, components, or units can be realized in processing circuitry  500 . Specifically, the functional means or units of the UE  102  may include a receiving unit/module  530  configured to receive one or more wireless communications from a network node, such as CBSR signaling in blocks  302 ,  308 ,  314 ,  322 , and  330  of  FIGS. 7A, 7B, 7C, 7D, and 7E . In addition, the UE can include a mapping unit/module  540  to perform mapping of a first component (and/or restriction thereof) to a second component as described above and performed, for example, blocks  316  and  324  of  FIGS. 7 and 7D , above. In addition, UE  102  may include a restrict unit/module for restricting precoders selectable from a codebook as a result of the mapping, for instance in block  332 . 
     In at least some embodiments, the UE  102  comprises one or more processing circuitry/circuits  500  configured to implement processing of the methods presented in  FIGS. 7A, 7B, 7C, 7D, and 7E  and certain associated processing of the features described in relation to other figures, such as by implementing functional means or units above. In one embodiment, for example, the processing circuit(s)  500  implements functional means or units as respective circuits. The circuits in this regard may comprise circuits dedicated to performing certain functional processing and/or one or more microprocessors in conjunction with memory  520 . In embodiments that employ memory  520 , which may comprise one or several types of memory such as read-only memory (ROM), random-access memory, cache memory, flash memory devices, optical storage devices, etc., the memory  520  stores program code that, when executed by the one or more for carrying out one or more microprocessors, carries out the techniques described herein. 
     In one or more embodiments, the UE  102  also comprises communication circuitry  510 . The communication circuitry  510  includes various components (e.g., antennas) for sending and receiving data and control signals. More particularly, the circuitry  510  includes a transmitter that is configured to use known signal processing techniques, typically according to one or more standards, and is configured to condition a signal for transmission (e.g., over the air via one or more antennas). Similarly, the communication circuitry includes a receiver that is configured to convert signals received (e.g., via the antenna(s)) into digital samples for processing by the one or more processing circuits. 
       FIG. 10A  illustrates additional details of an example network node  106  of a wireless communication system  10  according to one or more embodiments. As shown in  FIG. 10B , the network node  106  is configured, e.g., via functional means, components, modules, or units to implement processing to perform certain aspects described above in reference to at least methods presented in  FIGS. 8A, 8B, and 8C . In some examples, these means, modules, components, or units may be realized via processing circuitry  600  of  FIG. 10A . 
     In at least some embodiments, the network node  106  comprises one or more processing circuits  600  configured to implement processing of the methods of  FIGS. 8A, 8B, and 8C , such as by implementing functional means or units above. In one embodiment, for example, the one or more processing circuits (or processing circuitry)  600  implements functional means or units as respective circuits. The circuits in this regard may comprise circuits dedicated to performing certain functional processing and/or one or more microprocessors in conjunction with memory  1020 . In embodiments that employ memory  1020 , which may comprise one or several types of memory such as read-only memory (ROM), random-access memory, cache memory, flash memory devices, optical storage devices, etc., the memory  1020  stores program code that, when executed by the one or more for carrying out one or more microprocessors, carries out the techniques described herein. 
     In one or more embodiments, the network node  106  also comprises communication circuitry  601 . The communication circuitry  601  includes various components (e.g., antennas) for sending and receiving data and control signals. More particularly, the circuitry  601  includes a transmitter that is configured to use known signal processing techniques, typically according to one or more standards, and is configured to condition a signal for transmission (e.g., over the air via one or more antennas). Similarly, the communication circuitry includes a receiver that is configured to convert signals received (e.g., via the antenna(s)) into digital samples for processing by the one or more processing circuits. 
     Those skilled in the art will also appreciate that embodiments herein further include corresponding computer programs. A computer program comprises instructions which, when executed on at least one processor of the network node  106  or UE  102 , cause these devices to carry out any of the respective processing described above. Furthermore, the processing or functionality of network node  106  or UE  102  may be considered as being performed by a single instance or device or may be divided across a plurality of instances of network node  106  or UE  102  that may be present in a given system such that together the device instances perform all disclosed functionality. 
     In an aspect, the user equipment  102  may correspond to any mobile (or even stationary) device that is configured to receive/consume user data from a network-side infrastructure, including laptops, phones, tablets, IoT devices, etc. The network node  106  may be any network device, such as a base station, eNB, gNB, access point, or any other similar device. 
     Embodiments further include a carrier containing such a computer program. This carrier may comprise one of an electronic signal, optical signal, radio signal, or computer readable storage medium. A computer program in this regard may comprise one or more code modules corresponding to the means or units described above. 
     The present embodiments may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the disclosed subject matter. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein. Below is a set of exemplary enumerated embodiments of what has been described herein. 
     ENUMERATED EMBODIMENTS 
     1. A method for codebook subset restriction at a user equipment (UE), comprising: 
     receiving from a network node codebook subset restriction signaling (CBSR) that indicates a first component common to precoders in a first group of codebooks; 
     mapping the first component to a second component that is different than the first component and that is common to precoders in a second group of codebooks; and 
     restricting precoders selectable from a codebook in the second group of codebooks based on the second component. 
     2. The method of embodiment 1, further comprising restricting precoders selectable from a codebook in the first group of codebooks based on the first component. 
     3. The method of either of embodiment 1 or 2, wherein the first component comprises a length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit constitutes an (l 1 ,m) value indicating, at least in part, a first two-dimensional restriction vector v l     1     ,m . 
     4. The method of embodiment 3, wherein mapping the first component to the second component comprises forming a second two-dimensional vector {tilde over (v)} l     2     ,m  of a different size than that of v l     1     ,m . 
     5. The method of embodiment 4, wherein {tilde over (v)} l     2     ,m  is half the size of v l     1     ,m . 
     6. The method of any of the previous embodiments, further comprising: 
     selecting a precoder from the restricted precoders selectable from the codebook in the second group of codebooks; 
     generating a channel state information (CSI) report indicating the selected precoder; and 
     transmitting the CSI report to the network node. 
     7. A method for codebook selection restriction at a user equipment (UE), comprising: 
     receiving codebook subset restriction signaling (CBSR) from a network node, the CBSR indicating a first component for codebook restriction of a first group of codebooks, the first component being common to precoders of the first group of precoders, and the CBSR indicating a second component for codebook restriction of a second group of codebooks, the second component being common to precoders of the second group of precoders, the second component being different than the first component; and 
     restricting precoders selectable from a codebook in the first group of codebooks based on the first component and restricting precoders selectable from a codebook in the second group of codebooks based on the second component. 
     8. The method of embodiment 7, wherein the first component comprises a first bitmap of length N 1 N 2 O 1 O 2  having values of a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1 , where each bit of the first bitmap is mapped to an (l 1 ,m) value which in turn indicates the restriction of the first component v l     1     ,m , and wherein the second component comprises a second bitmap of length (N 1 /2)N 2 O 1 O 2  having values of b 0 b 1  . . . b (N     1     /2)N     2     O     1     O     2     −1  where each bit of the second bitmap is mapped to an (l 2 ,m) value which in turn indicates the restriction of the second component v l     2     ,m . 
     9. The method of either of embodiments 7 or 8, further comprising: 
     selecting a precoder from the restricted precoders selectable from the codebook in the second group of codebooks; 
     generating a channel state information (CSI) report indicating the selected precoder; and 
     transmitting the CSI report to the network node. 
     10. A method performed by a user equipment (UE) for identifying combinations used in CSI reporting, the method comprising: 
     receiving a joint indication of a combination of a rank value and at least one of a first index and a second index, wherein the first index at least identifies a first complex number that scales a two-dimensional (2D) Discrete Fourier Transform (DFT) beam, the second index at least identifies a second complex number that also scales the 2D DFT beam; and 
     determining a number of states that the at least one of the first index and second index can attain according to the rank value and at least one of a codebook configuration and a number of channel state information (CSI) reference signal ports. 
     11. A user equipment (UE) in a wireless communication network, the UE comprising at least a processor and a memory, the memory containing instructions executable by the processor to perform the aspects of any of embodiments 1-10. 
     12. A user equipment (UE) in a wireless communication network, the UE configured to perform the aspects of any of embodiments 1-10. 
     13. A computer program comprising instructions which, when executed by at least one processor of a user equipment, causes the user equipment to perform the aspects of any of embodiments 1-10. 
     14. A carrier containing the computer program of embodiment 13, wherein the carrier is one of an electric signal, optical signal, radio signal, or computer readable storage medium. 
     15. A method performed by a network node for codebook subset restriction, comprising: 
     generating codebook subset restriction signaling (CBSR) that indicates a first component common to precoders in a first group of codebooks, the CBSR configured to cause a user equipment (UE) to map the first component to a second component that is different than the first component and that is common to precoders in a second group of codebooks, and to restrict precoders selectable from a codebook in the second group of codebooks based on the second component; and 
     transmitting the CBSR to the UE. 
     16. The method of embodiment 15, wherein the CBSR is further configured to cause the UE to restrict the precoders selectable from a codebook in the first group of codebooks based on the first component. 
     17. The method of either of embodiment 15 or 16, wherein the first component comprises a length N 1 N 2 O 1 O 2  bitmap a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1  where each bit constitutes an (l 1 ,m) value indicating, at least in part, a first two-dimensional restriction vector b l     1     ,m . 
     18. The method of embodiment 17, wherein causing the UE to map the first component to the second component comprises causing the UE to form a second two-dimensional vector {tilde over (v)} l     2     ,m  of a different size than that of v l     1     ,m . 
     19. The method of embodiment 18, wherein v l     2     ,m  is half the size of v l     1     ,m . 
     20. A method for codebook selection restriction at network node, comprising: 
     generating codebook subset restriction signaling (CBSR), the CBSR indicating a first component for codebook restriction of a first group of codebooks, the first component being common to precoders of the first group of precoders, and the CBSR indicating a second component for codebook restriction of a second group of codebooks, the second component being common to precoders of the second group of precoders, the second component being different than the first component, the CBSR causing a user equipment (UE) to restrict precoders selectable from a codebook in the first group of codebooks based on the first component and to restrict precoders selectable from a codebook in the second group of codebooks based on the second component; and 
     transmitting the CBSR to the UE. 
     21. The method of embodiment 20, wherein the first component comprises a first bitmap of length N 1 N 2 O 1 O 2  having values of a 0 a 1  . . . a N     1     N     2     O     1     O     2     −1 , where each bit of the first bitmap is mapped by the UE to an (l 1 ,m) value which in turn indicates the restriction of the first component v l     1     ,m , and wherein the second component comprises a second bitmap of length (N 1 /2)N 2 O 1 O 2  having values of b 0 b 1  . . . b (N     1     /2)N     2     O     1     O     2     −1  where each bit of the second bitmap is mapped by the UE to an (l 2 ,m) value which in turn indicates the restriction of the second component v l     2     ,m . 
     22. The method of either of embodiments 20 or 21, further comprising receiving a channel state information (CSI) report indicating permitted codebook subsets corresponding to the restricted codebook subsets from the UE. 
     23. A method performed by a network node, comprising: 
     generating a joint indication of combinations of a rank value and at least one of a first index and a second index, wherein the first index at least identifies a first complex number that scales a two-dimensional (2D) Discrete Fourier Transform (DFT) beam, the second index at least identifies a second complex number that also scales the 2D DFT beam, the joint combination causing a user equipment (UE) to determine a number of states that the at least one of the first index and second index can attain according to the rank value and at least one of a codebook configuration and a number of channel state information (CSI) reference signal ports; 
     transmitting the joint indication to the UE. 
     24. A network node in a wireless communication network, the network node comprising at least a processor and a memory, the memory containing instructions executable by the processor to perform the aspects of any of embodiments 15-23. 
     25. A network node in a wireless communication network, the network node configured to perform the aspects of any of embodiments 15-23. 
     26. A computer program comprising instructions which, when executed by at least one processor of a network node, causes the network node to perform the aspects of any of embodiments 15-23. 
     27. A carrier containing the computer program of embodiment 26, wherein the carrier is one of an electric signal, optical signal, radio signal, or computer readable storage medium. 
     28. A method performed by a network node for codebook subset restriction, comprising:
         determining a first component that is common to precoders in a first group of codebooks, wherein the first component maps to a second component that is different than the first component and that is common to precoders in a second group of codebooks;   generating codebook subset restriction signaling (CBSR) that restricts precoders selectable from a codebook in the second group based on the second component, by generating the CBSR to indicate the first component that maps to the second component; and   transmitting the CBSR.       

     29. A network node in a wireless communication network, the network node comprising at least a processor and a memory, the memory containing instructions executable by the processor to perform the aspects of embodiment 28. 
     30. A network node in a wireless communication network, the network node configured to perform the aspects of embodiment 28. 
     31. A computer program comprising instructions which, when executed by at least one processor of a network node, causes the network node to perform the aspects of embodiment 28. 
     32. A carrier containing the computer program of embodiment 26, wherein the carrier is one of an electric signal, optical signal, radio signal, or computer readable storage medium.