Patent Publication Number: US-2023155642-A1

Title: Method and apparatus for selection of linear combination coefficients for precoding in frequency-selective channels

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is based on and claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No. 63/279,865, which was filed in the U.S. Patent and Trademark Office on Nov. 16, 2021, the entire content of which is incorporated herein by reference. 
    
    
     FIELD 
     The disclosure relates generally to precoding matrix indicator (PMI) selection, and more particularly, to linear combination coefficient (LCC) matrix selection that is compliant with an eType-II codebook. 
     BACKGROUND 
     In the downlink (DL) of multiple-input multiple-output (MIMO) wireless communication systems such as long term evolution (LTE) or 5 th  generation (5G) new radio (NR), when operating in a frequency division duplexing (FDD) mode, precoding at a base station (or a “gNB” in NR), which may align transmitted data streams to dominant channel eigen-modes, is made possible by channel state information (CSI) feedback from a user equipment (UE). More specifically, precoder selection by the base station for the precoding relies on implicit CSI feedback sent by the UE to the base station. Implicit CSI feedback occurs when the UE, instead of reporting an entire channel matrix, reports an index of a preferred precoding matrix selected from a predefined codebook, known at both the base station and the UE. In NR, such an index is referred to as a PMI. 
     It is up to UE implementation as to how to determine the best PMI for current channel conditions. The disclosure provides methods for a UE to determine a PMI. 
     Specifically, the disclosure considers a PMI codebook structure such as an eType-II codebook defined in NR Rel-16 (hereinafter, “an NR-compliant codebook”), where the precoding matrix consists of the product of three components:
         a beam selection matrix,   an LCC matrix, and   a frequency decompression matrix.       

     The beam selection matrix is wideband, i.e., the selected beams are common to all sub-bands (denoted by N 3 , i.e., the number of sub-bands). The LCCs, on the other hand, vary for different sub-bands. However, instead of selecting a specific LCC matrix for each individual sub-band (which may result in excessive overhead), the LCC matrix contains M&lt;N 3  frequency components (or discrete Fourier transform (DFT) components), which are mapped to the N 3  sub-bands by the frequency decompression matrix. 
     Conventionally, the LCC selection is performed as follows. 
     Initially, individual LCC matrices are determined for each of the N 3  sub-bands. Thereafter, compression to M&lt;N 3  frequency components is determined by choosing the M DFT components that capture the most energy out of the N 3  original LCCs. Herein, this procedure will be referred to as a “sub-band (SB) LCC selection”. 
     Based on further analysis, however, it has been determined that this procedure is not optimal. For example, in highly frequency selective channels (such as extended vehicular A (EVA) or extended typical urban (ETU) channel profiles), because the compression from N 3  to M components incurs significant losses, the compressed LCCs do not accurately reflect the frequency variations of the channel in each of the N 3  sub-bands. 
     SUMMARY 
     Accordingly, this disclosure is provided to address at least the problems and/or disadvantages described above and to provide at least some of the advantages described below. 
     An aspect of the disclosure is to provide a new LCC selection methods that, instead of computing the LCCs individually for each sub-band and then compressing them, computes a single LCC matrix for an entire band (herein, referred to as “wideband (WB) LCC selection”) or for groups of sub-bands (herein, referred to as “sub-band grouping (SBG) LCC selection”). The derivation is based on maximizing an upper bound of the channel capacity. 
     The resulting PMI is fully compliant with the eType-II PMI feedback structure. In other words, the WB LCC or SBG LCC matrices can be mapped to an NR-compliant codebook, in a transparent manner for the base station. As such, the disclosure does not require changes in the existing NR Rel-16 Specifications. 
     Another aspect of the disclosure is to provide an adaptive LCC selection method that automatically switches between legacy, WB, and SBG LCC selection depending on a metric that measures LCC energy captured by DFT compression. As a result, if the gNB configures eType-II codebook under unfavorable channel conditions for LCC compression, the UE can recast (transparently to the gNB) its LCC feedback to be WB or SBG. 
     In accordance with an aspect of the disclosure, a method is provided for a UE. The method includes determining a PMI selection decision metric; selecting one of an SB LCC selection method, a WB LCC selection method, or an SBG LCC selection method, based on the determined PMI selection decision metric; determining, using the selected LCC selection method, PMI indices based on sub-bands configured by a base station; and transmitting the determined PMI indices to the base station. 
     In accordance with another aspect of the disclosure, a UE is provided, which includes a transceiver; and a processor configured to determine a PMI selection decision metric, select one of an SB LCC selection method, a WB LCC selection method, or an SBG LCC selection method, based on the determined PMI selection decision metric, determine, using the selected LCC selection method, PMI indices based on sub-bands configured by a base station, and transmit, via the transceiver, the determined PMI indices to the base station. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features, and advantages of certain embodiments of the present disclosure will be more apparent from the following detailed description, taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    illustrates an SB LCC selection method; 
         FIG.  2    illustrates a WB LCC selection method, according to an embodiment; 
         FIG.  3    is flowchart illustrating a method of selecting an LCC method, according to an embodiment; 
         FIG.  4    is flowchart illustrating a method of selecting an LCC method based on first decision metric, according to an embodiment; 
         FIG.  5    is flowchart illustrating a method of selecting an LCC method based on a second decision metric, according to an embodiment; and 
         FIG.  6    illustrates an electronic device in a network environment, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments of the present disclosure are described in detail with reference to the accompanying drawings. It should be noted that the same elements will be designated by the same reference numerals although they are shown in different drawings. In the following description, specific details such as detailed configurations and components are merely provided to assist with the overall understanding of the embodiments of the present disclosure. Therefore, it should be apparent to those skilled in the art that various changes and modifications of the embodiments described herein may be made without departing from the scope of the present disclosure. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness. The terms described below are terms defined in consideration of the functions in the present disclosure, and may be different according to users, intentions of the users, or customs. Therefore, the definitions of the terms should be determined based on the contents throughout this specification. 
     The present disclosure may have various modifications and various embodiments, among which embodiments are described below in detail with reference to the accompanying drawings. However, it should be understood that the present disclosure is not limited to the embodiments, but includes all modifications, equivalents, and alternatives within the scope of the present disclosure. 
     Although the terms including an ordinal number such as first, second, etc. may be used for describing various elements, the structural elements are not restricted by the terms. The terms are only used to distinguish one element from another element. For example, without departing from the scope of the present disclosure, a first structural element may be referred to as a second structural element. Similarly, the second structural element may also be referred to as the first structural element. As used herein, the term “and/or” includes any and all combinations of one or more associated items. 
     The terms used herein are merely used to describe various embodiments of the present disclosure but are not intended to limit the present disclosure. Singular forms are intended to include plural forms unless the context clearly indicates otherwise. In the present disclosure, it should be understood that the terms “include” or “have” indicate existence of a feature, a number, a step, an operation, a structural element, parts, or a combination thereof, and do not exclude the existence or probability of the addition of one or more other features, numerals, steps, operations, structural elements, parts, or combinations thereof. 
     Unless defined differently, all terms used herein have the same meanings as those understood by a person skilled in the art to which the present disclosure belongs. Terms such as those defined in a generally used dictionary are to be interpreted to have the same meanings as the contextual meanings in the relevant field of art, and are not to be interpreted to have ideal or excessively formal meanings unless clearly defined in the present disclosure. 
     The electronic device according to one embodiment may be one of various types of electronic devices. The electronic devices may include, for example, a portable communication device (e.g., a smart phone), a computer, a portable multimedia device, a portable medical device, a camera, a wearable device, or a home appliance. According to one embodiment of the disclosure, an electronic device is not limited to those described above. 
     The terms used in the present disclosure are not intended to limit the present disclosure but are intended to include various changes, equivalents, or replacements for a corresponding embodiment. With regard to the descriptions of the accompanying drawings, similar reference numerals may be used to refer to similar or related elements. A singular form of a noun corresponding to an item may include one or more of the things, unless the relevant context clearly indicates otherwise. As used herein, each of such phrases as “A or B,” “at least one of A and B,” “at least one of A or B,” “A, B, or C,” “at least one of A, B, and C,” and “at least one of A, B, or C,” may include all possible combinations of the items enumerated together in a corresponding one of the phrases. As used herein, terms such as “1st,” “2nd,” “first,” and “second” may be used to distinguish a corresponding component from another component, but are not intended to limit the components in other aspects (e.g., importance or order). It is intended that if an element (e.g., a first element) is referred to, with or without the term “operatively” or “communicatively”, as “coupled with,” “coupled to,” “connected with,” or “connected to” another element (e.g., a second element), it indicates that the element may be coupled with the other element directly (e.g., wired), wirelessly, or via a third element. 
     As used herein, the term “module” may include a unit implemented in hardware, software, or firmware, and may interchangeably be used with other terms, for example, “logic,” “logic block,” “part,” and “circuitry.” A module may be a single integral component, or a minimum unit or part thereof, adapted to perform one or more functions. For example, according to one embodiment, a module may be implemented in a form of an application-specific integrated circuit (ASIC). 
     Hereinafter, the following selection procedures are described:
         1. WB LCC selection: a single LCC matrix is computed for the entire band and mapped to NR-compliant (e.g., eType-II codebook) PMI indices.   2. SBG LCC selection: a set of N g  LCC matrices are computed for N g ≤M sub-band groups, and mapped to the NR-compliant PMI indices.   3. Adaptive LCC selection: a method for automatically choosing the LCC selection mode (legacy, WB, or SBG) according to proposed metrics that measures the LCC energy captured by DFT compression or based on capacity comparisons.       

     As will be described below, these selection procedures can improve eType-II PMI selection performance under frequency selective channels (e.g., EVA, ETU, etc.). 
     Additionally, to avoid degradation over channels with low frequency selectivity (e.g., EPA), the adaptive LCC selection may selectively apply WB/SBG methods when beneficial, while switching back to legacy methods in other cases. 
     Although embodiments of the disclosure are described below utilizing DFT-based compression, the disclosure is not limited thereto, and other compression techniques are possible. 
     Conventional SB LCC Selection Method 
     Let L be the number of beams, v the number of layers, N T =2N 1 N 2  the number of CSI-RS ports (where N 1  and N 2  are the numbers of horizontal and vertical antennas, respectively, and the number 2 accounts for cross-polarized antennas), N 3  the number of PMI sub-bands before compression, and M the number of frequency domain (FD) components after compression. 
     For a certain layer l∈{1, . . . , v}, the eType-II precoder is given by Equation (1). 
         W   l   (lay)   =W   1   {tilde over (W)}   2,l   W   f,l   H   (1)
 
     In Equation (1), W 1 ∈  is a wideband and layer-common beam selection matrix, {tilde over (W)} 2,l  ∈  is a matrix of compressed LCCs, and W f,l ∈  is a DFT compression matrix. 
     From this, Equation (2) can be written. 
         W   f   ,l=F (:, M   init +[0 m   l ])  (2)
 
     In Equation (2), F is a full N 3 ×N 3  DFT matrix, out of which M columns identified by M init  (common to all layers) and by vector m l  ∈  (layer-specific) can be selected. 
     In Equation (1), W l   (lay)  ∈  represents the precoder a single layer and for all sub-bad. 
     The eType-II precoder can also be expressed for all layers and for a given sub-band k, by defining a matrix W k   (SB) ∈ . This expression may be more useful for the formulation of a capacity optimization problem for which Equation (3) can be written. 
         W   k   (SB)   =W   1 [ {tilde over (W)}   2,1   W   f,1   H (:, k ) . . .  {tilde over (W)}   2,v   W   f,v   H (:, k )]  (3)
 
     Now, Equations (4) and (5) can be defined: 
     
       
         
           
             
               
                 
                   
                     
                       W 
                       ~ 
                     
                     2 
                   
                   
                     = 
                     def 
                   
                   
                     
                       [ 
                       
                         
                           
                             W 
                             ~ 
                           
                           
                             2 
                             , 
                             1 
                           
                         
                         ⁢ 
                         … 
                         ⁢ 
                             
                         
                           
                             W 
                             ~ 
                           
                           
                             2 
                             , 
                             v 
                           
                         
                       
                       ] 
                     
                     ∈ 
                     
                       ℂ 
                       
                         2 
                         ⁢ 
                         L 
                         × 
                         Mv 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     D 
                     k 
                   
                   
                     = 
                     def 
                   
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 f 
                                 k 
                               
                               ( 
                               
                                 
                                   M 
                                   init 
                                 
                                 , 
                                 
                                   m 
                                   1 
                                 
                               
                               ) 
                             
                           
                           
                               
                           
                           
                               
                           
                         
                         
                           
                               
                           
                           
                             ⋱ 
                           
                           
                               
                           
                         
                         
                           
                               
                           
                           
                               
                           
                           
                             
                               
                                 f 
                                 k 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     M 
                                     init 
                                   
                                   , 
                                   
                                     m 
                                     v 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                     ∈ 
                     
                       ℂ 
                       
                         Mv 
                         × 
                         v 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In Equation (5), 
         f   k ( M   nit   ,m   l ) ( F ( k,M   init +[0 m   l ])) H ∈   (6)
 
     With this new notation, Equation (3) can be rewritten as Equation (7). 
         W   k   (SB)   =W   1   {tilde over (W)}   2   D   k   (7)
 
       FIG.  1    is a block diagram of SB LCC selection method. 
     Referring to  FIG.  1   , a UE receives a configuration of a plurality of sub-bands (1, 2, . . . , N 3 ) and performs singular value decomposition (SVD) on each of the N 3  sub-bands. Thereafter, the UE must perform compression for each sub-band to arrive at the M FD components, which are reported to the base station for decompression and identification of the LCC matrices W 2,k . 
     More specifically, the SB LCC selection method proceeds as follows. 
     Step 1. The per-SB capacity optimization problem is formulated for each k∈1, . . . , N 3  as shown in Equation (8), where E k    H k W 1 . 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       k 
                     
                     = 
                     
                       
                         argmax 
                         
                           W 
                           
                             2 
                             , 
                             k 
                           
                         
                       
                       ⁢ 
                          
                       log 
                       ⁢ 
                          
                       det 
                       ⁢ 
                       
                         ( 
                         
                           I 
                           + 
                           
                             
                               ρ 
                               ⁡ 
                               ( 
                               
                                 
                                   E 
                                   k 
                                 
                                 ⁢ 
                                 
                                   W 
                                   
                                     2 
                                     , 
                                     k 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     E 
                                     k 
                                   
                                   ⁢ 
                                   
                                     W 
                                     
                                       2 
                                       , 
                                       k 
                                     
                                   
                                 
                                 ) 
                               
                               H 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     which has a closed-form solution, given by S k  ∈  equal to the first v right singular vectors of E k . 
     Step 2. For each layer l, define 
         S   l   lay   [ S   1 (:, l ) . . .  S   N     3   (:, l )]∈   (9)
 
     The M compression vectors w f,l,1 , . . . , w f,l,M , i.e., the columns of matrix W f,l  in Equation (2), are selected by w f,l,j =f i,     l,j    for j∈{1, . . . , M}, with 
     
       
         
           
             
               
                 
                   
                     
                       { 
                       
                         
                           i 
                           
                             l 
                             , 
                             1 
                           
                         
                           
                         , 
                         … 
                             
                         , 
                           
                         
                           i 
                           
                             l 
                             , 
                             
                               N 
                               3 
                             
                           
                         
                       
                       } 
                     
                     = 
                     
                       
                         sort 
                         
                           i 
                           ∈ 
                           
                             { 
                             
                               1 
                               , 
                               … 
                                   
                               , 
                               
                                 N 
                                 3 
                               
                             
                             } 
                           
                         
                       
                       ⁢ 
                       
                         
                            
                           
                             
                               s 
                               l 
                               lay 
                             
                             ⁢ 
                             
                               f 
                               i 
                             
                           
                            
                         
                         2 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where f 1 , . . . , f N     SB    are columns of the DFT matrix F in Equation (2), and sort i (x i ) returns the indices of the arguments x i  ∈  sorted in decreasing order. Then, given the vectors w f,l,j  and S l   lay  the compressed LCCs {tilde over (W)} 2,l  are obtained by: 
         {tilde over (W)}   2,l   =S   l   lay   W   f,l   (11)
 
     Further, the above-described SB LCC selection method is intrinsically suboptimal because it decouples the problem in two steps. Performance of the SB LCC selection method tends to degrade as the frequency selectivity increases, and as M&lt;&lt;N 3  (which is typically the case in NR Rel-16). For example, under frequency selective channels, the optimal per-SB coefficients vary across SBs. Therefore, the compression of 2LN 3 v coefficients to 2LMv (ratio: N 3 /M) is necessarily lossy, regardless of the chosen compression basis. 
     To address the above and other issues present in the conventional SB LCC selection method, the following selection methods are provided. 
     WB LCC Selection Method 
     In the WB LCC selection method, a single LCC matrix is computed for the entire band and mapped to NR-compliant (e.g., eType-II codebook) PMI indices. 
     Instead of solving the optimization problem for each SB, i.e., finding the best {tilde over (W)} 2  and D k  for each sub-band k, it is assumed that W 2 ={tilde over (W)} 2 D k  is wideband (common to all sub-bands, i.e., does not depend on k). With this assumption, a capacity optimization problem can be formulated as in Equation (12). 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       argmax 
                       
                         W 
                         2 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         
                           N 
                           3 
                         
                       
                       
                         log 
                         ⁢ 
                            
                         det 
                         ⁢ 
                            
                         
                           ( 
                           
                             I 
                             + 
                             
                               
                                 ρ 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     E 
                                     k 
                                   
                                   ⁢ 
                                   
                                     W 
                                     2 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     
                                       E 
                                       k 
                                     
                                     ⁢ 
                                     
                                       W 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 H 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     An approximate solution is proposed to the WB capacity optimization problem in Equation (8) by applying an upper bound. Then, using the Weinstein-Aronszajn identity, Equation (12) can be rewritten as Equations (13) and (14). 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       argmax 
                       
                         W 
                         2 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         
                           N 
                           3 
                         
                       
                       
                         log 
                         ⁢ 
                            
                         det 
                         ⁢ 
                         
                           ( 
                           
                             I 
                             + 
                             
                               ρ 
                               ⁢ 
                               
                                 
                                   ( 
                                   
                                     
                                       E 
                                       k 
                                     
                                     ⁢ 
                                     
                                       W 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 H 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     E 
                                     k 
                                   
                                   ⁢ 
                                   
                                     W 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   = 
                   
                     
                       argmax 
                       
                         W 
                         2 
                       
                     
                     ⁢ 
                     
                       1 
                       
                         N 
                         3 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         
                           N 
                           3 
                         
                       
                       
                         log 
                         ⁢ 
                            
                         det 
                         ⁢ 
                         
                           ( 
                           
                             I 
                             + 
                             
                               ρ 
                               ⁢ 
                               
                                 W 
                                 2 
                                 H 
                               
                               ⁢ 
                               
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                                 k 
                                 H 
                               
                               ⁢ 
                               
                                 E 
                                 k 
                               
                               ⁢ 
                               
                                 W 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Because of the concavity of log det(X), Equations (15) and (16) are as follows. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         N 
                         3 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         
                           N 
                           3 
                         
                       
                       
                         log 
                         ⁢ 
                            
                         
                           det 
                           ⁡ 
                           ( 
                           
                             I 
                             + 
                             
                               ρ 
                               ⁢ 
                               
                                 W 
                                 2 
                                 H 
                               
                               ⁢ 
                               
                                 E 
                                 k 
                                 H 
                               
                               ⁢ 
                               
                                 E 
                                 k 
                               
                               ⁢ 
                               
                                 W 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   ≤ 
                   
                     log 
                     ⁢ 
                        
                     det 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           1 
                           
                             N 
                             3 
                           
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             
                               N 
                               3 
                             
                           
                           
                             ( 
                             
                               I 
                               + 
                               
                                 ρ 
                                 ⁢ 
                                 
                                   W 
                                   2 
                                   H 
                                 
                                 ⁢ 
                                 
                                   E 
                                   k 
                                   H 
                                 
                                 ⁢ 
                                 
                                   E 
                                   k 
                                 
                                 ⁢ 
                                 
                                   W 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                                    
                   
                     = 
                     
                       log 
                       ⁢ 
                          
                       det 
                       ⁢ 
                          
                       
                         ( 
                         
                           I 
                           + 
                           
                             ρ 
                             ⁢ 
                             
                               
                                 W 
                                 2 
                                 H 
                               
                               ( 
                               
                                 
                                   1 
                                   
                                     N 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       1 
                                     
                                     
                                       N 
                                       3 
                                     
                                   
                                   
                                     
                                       E 
                                       k 
                                       H 
                                     
                                     ⁢ 
                                     
                                       E 
                                       k 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               W 
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Equation (12) is an upper bound of the original capacity function. The upper bound of Equation (12) is maximized with respect to W 2  by the eigenvectors of 
     
       
         
           
             
               
                 1 
                 
                   N 
                   3 
                 
               
               ⁢ 
               
                 
                   ∑ 
                   
                     k 
                     = 
                     1 
                   
                   
                     N 
                     3 
                   
                 
                 
                   
                     E 
                     k 
                     H 
                   
                   ⁢ 
                   
                     E 
                     k 
                   
                 
               
             
             = 
             
               
                 
                   W 
                   1 
                   H 
                 
                 ( 
                 
                   
                     1 
                     
                       N 
                       3 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       
                         N 
                         3 
                       
                     
                     
                       
                         H 
                         k 
                         H 
                       
                       ⁢ 
                       
                         H 
                         k 
                       
                     
                   
                 
                 ) 
               
               ⁢ 
               
                 
                   W 
                   1 
                 
                 . 
               
             
           
         
       
     
     The approximate solution to Equation (12) is shown in Equation (17). 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     E 
                     ⁢ 
                     V 
                     ⁢ 
                     
                       D 
                       ⁡ 
                       ( 
                       
                         
                           
                             W 
                             1 
                             H 
                           
                           ( 
                           
                             
                               1 
                               
                                 N 
                                 3 
                               
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   1 
                                 
                                 
                                   N 
                                   3 
                                 
                               
                               
                                 
                                   H 
                                   k 
                                   H 
                                 
                                 ⁢ 
                                 
                                   H 
                                   k 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           W 
                           1 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     In Equation (13), EVD(X), which represents eigenvalue decomposition, is a function that returns a 2L×v matrix whose columns are the v dominant eigenvectors of X. 
     Though simulation, it has been verified that the upper bound of the WB capacity in Equation (16) is tight. Therefore, the solution of Equation (17) is sufficiently accurate. However, it is possible to further refine the solution by gradient descent. 
     Exploiting the fact that log det(X) is differentiable, i.e., as shown in Equation (18): 
       ∇ log det( X )=( X   −1 ) T ,  (18)
 
     the gradient can be computed in Equation (19): 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     
                       W 
                       2 
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         N 
                         3 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           
                             κ 
                             ˙ 
                           
                           = 
                           1 
                         
                         
                           N 
                           3 
                         
                       
                       
                         log 
                         ⁢ 
                            
                         det 
                         ⁢ 
                         
                           ( 
                           
                             I 
                             + 
                             
                               ρ 
                               ⁢ 
                               
                                 W 
                                 2 
                                 H 
                               
                               ⁢ 
                               
                                 E 
                                 k 
                                 H 
                               
                               ⁢ 
                               
                                 E 
                                 k 
                               
                               ⁢ 
                               
                                 W 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     with respect to W 2 , starting from W 2 =V, and iteratively optimize W 2  by gradient descent. 
     Below, it is shown that the solution V∈  to the wideband capacity optimization problem of Equation (17) can be mapped one-to-one to NR-compliant eType-II LCC ({tilde over (W)} 2,l W f,l   H ). 
     As a preliminary step, per-layer phase rotation is applied as shown in Equation (20). 
     
       
         
           
             
               
                 
                   
                     V 
                     ′ 
                   
                   = 
                   
                     V 
                     · 
                     
                       [ 
                       
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                   ϕ 
                                   1 
                                 
                               
                             
                           
                           
                               
                           
                           
                               
                           
                         
                         
                           
                               
                           
                           
                             ⋱ 
                           
                           
                               
                           
                         
                         
                           
                               
                           
                           
                               
                           
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                   ϕ 
                                   v 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     In Equation (16), ϕ j =∠V(1,j). 
     Thereafter, mapping of V′ to {tilde over (W)} 2,l W f,l   H  is done as follows:
         For each layer l, set {tilde over (W)} 2,l =[V′(:, l) 0 2L×(M-1) ].   Set M init =1, so that, for all layers l,       

     
       
         
           
             
               
                 
                   W 
                   
                     f 
                     , 
                     l 
                   
                 
                 ( 
                 
                   : 
                   
                     , 
                     1 
                   
                 
                 ) 
               
               = 
               
                 
                   1 
                   
                     
                       N 
                       3 
                     
                   
                 
                 ⁢ 
                 1 
               
             
             ; 
           
         
       
     
     in order words, 
     
       
         
           
             
               W 
               
                 f 
                 , 
                 l 
               
               H 
             
             = 
             
               
                 1 
                 
                   
                     N 
                     3 
                   
                 
               
               ⁢ 
               
                 
                   exp 
                   ⁡ 
                   ( 
                   
                     
                       
                         j 
                         ⁢ 
                         2 
                         ⁢ 
                         π 
                       
                       
                         N 
                         3 
                       
                     
                     [ 
                     
                       
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           X 
                         
                         
                           X 
                         
                       
                       
                         
                           0 
                         
                         
                           X 
                         
                         
                           X 
                         
                       
                     
                     ] 
                   
                   ) 
                 
                 . 
               
             
           
         
       
         
         
           
             The choice of {m l } l=1   v  does not matter as long as M init =1. Without loss of generality, m l =[2, . . . , M] is set. 
           
         
       
    
     With these steps, the resulting precoder (before quantization) for each sub-band k may be determined using Equation (21). 
         W=W   1 [ {tilde over (W)}   2,1   W   f   H (:, k ) . . .  {tilde over (W)}   2,v   W   f   H (:, k )]= W   1   V′∈         (21)
 
     As shown above, for all sub-bands, the LCC matrix is equal to the desired EVD-based precoder V′. That is, WB LCC may be applied to eType-II PMIs in a transparent manner (i.e., the PMI maintains the same formal structure as the NR-compliant eType-II codebook with FD compression). 
     Up to this point, there is no compression loss from V′ to {tilde over (W)} 2,l W f,l   H  in Equation (21). In contrast, in the legacy eType-II method, there is a compression loss when mapping the 2L×N 3 ×v coefficients V k  to 2L×M×v compressed coefficients, with M&lt;N 3 . 
     As required by the NR standard Specification, amplitude and phase quantization are applied to the elements of {tilde over (W)} 2,j  and report K 0 =β2LM non-zero coefficients. Note that 2L(M−1) coefficients in {tilde over (W)} 2,l  are already zero, so if 
     
       
         
           
             β 
             ≥ 
             
               1 
               M 
             
           
         
       
     
     (which is typically the case), all coefficients are reported. Therefore, only quantization plays a role here. 
       FIG.  2    illustrates a WB LCC selection method, according to an embodiment. 
     Referring to  FIG.  2   , instead of solving the optimization problem for each of the N 3  SBs as illustrated in  FIG.  1   , an average of the N 3  SBs is determined and then the UE performs EVD on the determined average, which returns a 2L×v matrix whose columns are the v dominant eigenvectors of X (e.g., see Equation (17) above). 
     Thereafter, the UE performs per-layer phase rotation and one-to-one maps the phase rotated values an NR-compliant PMI indices, which are then reported to the base station. 
     SBG LCC Selection Method 
     In SBG LCC selection, a set of N g  LCC matrices may be computed for N g ≤M sub-band groups, and mapped to the NR-compliant PMI indices. 
     To simplify the notation, denote by w∈  single row of W 2  and by {tilde over (w)}∈  a row of {tilde over (W)} 2 . In addition, the layer index l may be omitted, to provide: 
         w={tilde over (w)}W   f   H   (22)
 
     In Equation (22), W f =F N     3   (:, b)∈  contains M chosen DFT bases indexed by vector b∈{0, . . . , N 3 −1} M , and F N ∈  is a full DFT matrix of size N. 
     As an example, let N 3 =8 and M=4. 
     Suppose a precoder w target  with sub-band grouping is desired, e.g., 
         w   target =[ a b c d a b c d ]  (23)
 
       or 
         w   target =[ a a b b c c d d ]  (24)
 
     In order to set {tilde over (w)} and b such that w=w target , and to determine the conditions for w=w target  to be achievable, the following procedure may be used. 
     The DFT of w target  may be computed by Equation (25). 
         {tilde over (w)}   N     3     =w   target   F   N     3   .  (25)
 
     Denote by [i 1 , . . . , i M     NZ   ] the indices of the non-zero elements of {tilde over (w)} N     3   . If M NZ ≤M, then the desired precoder can be achieved using Equation (26): 
         w=w   target   (26)
 
       by setting 
         b (1:  M   NZ )=[ i   1   , . . . ,i   M     NZ   ]  (27)
 
       and 
         {tilde over (w)} =[ {tilde over (w)}   N     3   (:,[ i   1   , . . . ,i   M     NZ   ])0 1×(M-M     NZ     ) ]=[ w   target   F   N     3   (:,[ i   1   , . . . i   M     NZ   ])0 1×(M-M     NZ     ) ].  (28)
 
     The coefficients of b(M NZ +1:M) may be arbitrarily set, because these DFT bases are multiplied by zeros. By plugging Equations (27) and (28) into Equation (22), it can be verified that Equation (26) is satisfied. This condition is referred to herein as “lossless compression,” because w (length N 3 ) may be fully recovered from the compressed vector {tilde over (w)} (length M). 
     As can be seen from Equation (27), lossless compression cannot be achieved if M NZ &gt;M, because b has length M. Therefore, a condition for w=w target  to be achievable is M NZ ≤M. 
     Let N g  be the number of sub-band groups, i.e., the number of different values in w target . For example, in Equations (23) and (24), N g =4. Then:
         “Non-contiguous” SBG of the form w target =[α 1 α 2  . . . α N     g   , . . . α 1 α 2 α N     g   ], such as in Equation (23), can be achieved with lossless compression if N 3  is an integer multiple of N g (which implies M NZ =N g ) and by choosing M≥N g .   “Contiguous” SBG of the form w target =[α 1  . . . α 1 α 2  . . . α 2  . . . α N     g    . . . a N     g   ] with N g ≥2, such as in Equation (24), cannot be achieved with lossless compression by any       

     
       
         
           
             M 
             ≤ 
             
               
                 N 
                 3 
               
               2 
             
           
         
       
     
     (note that 
     
       
         
           
             M 
             &gt; 
             
               
                 N 
                 3 
               
               2 
             
           
         
       
     
     is not allowed by the current NR specification) because, for any 
     
       
         
           
             
               
                 N 
                 g 
               
               ≥ 
               2 
             
             , 
             
               
                 M 
                 
                   N 
                   ⁢ 
                   Z 
                 
               
               &gt; 
               
                 
                   
                     N 
                     3 
                   
                   2 
                 
                 . 
               
             
           
         
       
     
     Based on the results above, non-contiguous SBG may be the preferred option as it results in lossless compression (if the aforementioned conditions are satisfied). Contiguous SBG is also possible, but may result in lossy compression. 
     To implement SBG LCC selection, a similar approach is followed as the one applied to WB LCC selection, except that separate eigenvectors V i ∈  are estimated for each of the groups i∈{1, . . . , N g }. Specifically, let 
     
       
         
           
             
               
                 
                   
                     V 
                     i 
                   
                   = 
                   
                     
                       EVD 
                       ⁡ 
                       ( 
                       
                         
                           
                             W 
                             1 
                             H 
                           
                           ( 
                           
                             
                               
                                 N 
                                 g 
                               
                               
                                 N 
                                 3 
                               
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   1 
                                 
                                 
                                   
                                     N 
                                     3 
                                   
                                   
                                     N 
                                     g 
                                   
                                 
                               
                                 
                               
                                 
                                   H 
                                   
                                     i 
                                     + 
                                     
                                       
                                         N 
                                         g 
                                       
                                       ( 
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                   H 
                                 
                                 ⁢ 
                                 
                                   H 
                                   
                                     i 
                                     + 
                                     
                                       
                                         N 
                                         g 
                                       
                                       ( 
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           W 
                           1 
                         
                       
                       ) 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     Let V′ i  be a phase-rotated version of V i , similar to Equation (20), i.e., 
     
       
         
           
             
               
                 
                   
                     V 
                     i 
                     ′ 
                   
                   = 
                   
                     
                       V 
                       i 
                     
                     · 
                     
                       
                         [ 
                         
                           
                             
                               
                                 e 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                     ϕ 
                                     
                                       i 
                                       , 
                                       1 
                                     
                                   
                                 
                               
                             
                             
                                 
                             
                             
                                 
                             
                           
                           
                             
                                 
                             
                             
                               ⋱ 
                             
                             
                                 
                             
                           
                           
                             
                                 
                             
                             
                                 
                             
                             
                               
                                 e 
                                 
                                   
                                     - 
                                     j 
                                   
                                   ⁢ 
                                   
                                     ϕ 
                                     
                                       i 
                                       , 
                                       v 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     In Equation (30), ϕ i,j =∠V(1,j). 
     Then, for each layer l∈{1, . . . , v}, 
         W   target,l =[ V′   1 (:, l ) . . .  V′   N     g   (:, l ) . . .  V′   1 (:, l ) . . .  V′   N     g   (:, l )]∈   (31)
 
     W target,l  is mapped to {tilde over (W)} 2,l W f,l   H  in the same way as in legacy eType-II, i.e., by selecting the M largest elements of ∥W target,l F N     3   ∥, subject to the NR specification restrictions. 
     Adaptive LCC Selection Method 
     From simulation results, it can be observed that in certain scenarios (e.g., with highly frequency selective channels and high rank), WB and/or SBG LCC selection outperforms legacy eType-II LCC selection (i.e., SB LCC selection). However, in other scenarios (e.g., an EPA channel), SB LCC selection may perform better. Therefore, in accordance with an embodiment, a method is provided for determining when to apply SB LCC selection, WB LCC selection, or SBG LCC selection. 
     According to an embodiment, a ratio between LCC energy after FD compression and total LCC energy before FD compression may be used as a PMI selection decision metric for such a determination. Mathematically, this may be expressed by Equation (32). 
     
       
         
           
             
               
                 
                   r 
                   
                     = 
                     def 
                   
                   
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           1 
                         
                         v 
                       
                       
                         
                            
                           
                             
                               V 
                               
                                 ( 
                                 l 
                                 ) 
                               
                             
                             ⁢ 
                             
                               W 
                               
                                 f 
                                 , 
                                 l 
                               
                             
                           
                            
                         
                         F 
                         2 
                       
                     
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           1 
                         
                         v 
                       
                       
                         
                            
                           
                             V 
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                         
                         F 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     In Equation (32), V k ∈  is the SVD-based precoder for sub-band k, and V (l) =[V 1 (:, l) . . . V N     3   (:,l)]∈   
     This metric indicates how much energy is captured by FD compression. Therefore, the higher the metric, the better SB LCC selection is expected to perform. However, if the metric is low, SB LCC selection suffers from larger FD compression loss, which suggests that WB or SBG LCC selection may perform better. Accordingly, a switching criterion between SB LCC selection and WB or SBG LCC selection may be expressed by:
         If r&gt;γ→ apply SB LCC selection. N 3      If r≤γ→ apply WB or SBG LCC selection.       

     The value of γ can be optimized by simulations under different channels, or chosen adaptively based on estimated delay spread and/or Doppler frequency, or updated online. 
     Further, for deciding between WB and SBG, it can be observed that:
         When N 3  is even and N 3 &lt;19 (i.e., when SB grouping achieves lossless compression), SBG outperforms WB by up to 0.5 dB or at least it is not worse than WB.   When N 3  is odd or N 3 &gt;19 (i.e., when lossless compression cannot be achieved by SB grouping), WB outperforms SBG by up to 1.2 dB.       

     Therefore, when r≤γ, a decision rule between WB or SBG selection is:
         When N 3  is even and N 3 &lt;N MAX , apply SBG LCC selection.   Otherwise, apply WB LCC selection.       

     Note that the specific value of N MAX  (e.g., 19) depends on codebook restrictions in NR Rel-16 Spec, and may change if aspect of the disclosure are applied to future versions of NR or to communication systems that follow different standards. Accordingly, while 19 is provided as an example for N MAX  herein, the disclosure is not limited to this value. 
     According to another embodiment, an average capacity difference (ΔC avg ) may be used as a PMI selection decision metric for such a determination. Mathematically, this may be expressed by Equation (33): 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       C 
                       avg 
                     
                   
                   
                     = 
                     def 
                   
                   
                     
                       1 
                       
                         N 
                         
                           S 
                           ⁢ 
                           B 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           s 
                           = 
                           1 
                         
                         
                           N 
                           SB 
                         
                       
                       
                         ( 
                         
                           
                             C 
                             
                               
                                 SB 
                                 - 
                                 FDC 
                               
                               , 
                               s 
                             
                           
                           - 
                           
                             C 
                             
                               WB 
                               , 
                               s 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     Equation (33), C SB-FDC,s    Σ i∈SB s  log det (I+ρ(H i W SB-FDC,s )(H i W SB-FDC,s ) H ) and C WB,s    Σ i∈SB s  log det(I+ρ(H i W WB )(H i W WB ) H ).
         If ΔC avg &gt;0→ apply SB LCC selection.   If ΔC avg ≤0→ apply WB or SBG LCC selection.       

     Similar to using a ratio between LCC energy after FD compression and total LCC energy before compression may be used as a PMI selection decision metric, the determination of whether to use the WB or SBG LCC selection may be based on conditions for lossless compression being verified. That is, a decision rule between WB or SBG selection is:
         When N 3  is even and N 3 &lt;N MAX , apply SBG LCC selection.   Otherwise, apply WB LCC selection.       

     A determination as to which PMI selection decision metric to be used may be performed in various ways, e.g., preset during UR manufacturing, signaled by the base station, determined by the UE based on system parameters and/or requirements, and the disclosure is not limited to a particular method. 
       FIG.  3    is flowchart illustrating a method of selecting an LCC method, according to an embodiment. 
     Referring to  FIG.  3   , an apparatus that is wirelessly connected to a base station, e.g., a UE, determines a PMI selection decision metric in step  301 . 
     In step  302 , the UE selects one of an SB LCC selection method, a WB LCC selection method, or an SBG LCC selection method, based on the determined PMI selection decision metric. 
     In step  303 , the UE determines PMI indices based on the configured sub-bands using the selected LCC selection method, e.g., as illustrated in  FIG.  2   , when the WB LCC selection method is selected. 
     In step  304 , the UE transmits the determined PMI indices to the base station. 
       FIG.  4    is flowchart illustrating a method of selecting an LCC method based on first decision metric, according to an embodiment. Specifically,  FIG.  4    illustrate a method of selecting an LCC method based on a ratio between LCC energy after FD compression and total LCC energy before FD compression. 
     Referring to  FIG.  4   , in step  401 , the UE determines the PMI selection decision metric as the ratio between LCC energy after FD compression and total LCC energy before FD compression (r), e.g., as shown above in Equation (28). 
     In step  402 , the UE compares the ration with a threshold (γ), which can be optimized by simulations under different channels, chosen adaptively based on estimated delay spread and/or Doppler frequency, updated online, etc. 
     If the ratio is greater than the threshold (r&gt;γ) in step  402 , then the UE selects the SB LCC selection method in step  403 . However, if the ratio is not greater than the threshold (r≤γ) in step  402 , then the UE selects the WB LCC selection method or the SBG LCC selection method in steps  404  to  406 . 
     More specifically, in step  404 , the UE determines if N 3  is even and N 3 &lt;N MAX . As described above, when N 3  is even and N 3 &lt;N MAX , an SB grouping achieves lossless compression, and SBG LCC selection may outperform WB LCC selection by up to 0.5 dB or is at least no worse than WB LCC selection. 
     Accordingly, if N 3  is even and N 3 &lt;N MAX  in step  404 , then the UE selects the SBG LCC selection method in step  405 . However, if N 3  is odd or N 3 ≥N MAX  in step  404 , then the UE selects the WB LCC selection method in step  406 . 
       FIG.  5    is flowchart illustrating a method of selecting an LCC method based on a second decision metric, according to an embodiment. Specifically,  FIG.  5    illustrate a method of selecting an LCC method based on an average capacity difference (ΔC avg ). 
     Referring to  FIG.  5   , in step  501 , the UE determines the PMI selection decision metric as ΔC avg  e.g., as shown above in Equation (33). 
     In step  502 , the UE determines whether the ΔC avg &gt;0. 
     If ΔC avg &gt;0 in step  502 , then the UE selects the SB LCC selection method in step  503 . However, if t ΔC avg ≤0 in step  502 , then the UE selects the WB selection method or the SBG LCC selection method in steps  504  to  506 . 
     More specifically, in step  504 , the UE determines if N 3  is even and N 3 &lt;N MAX . 
     If N 3  is even and N 3 &lt;N MAX  in step  504 , then the UE selects the SBG LCC selection method in step  505 . However, if N 3  is odd or N 3 ≥N MAX  in step  504 , then the UE selects the WB LCC selection method in step  506 . 
       FIG.  6    illustrates an electronic device in a network environment, according to an embodiment. For example, the election device in  FIG.  6    may perform the UE operations as described above with reference to  FIGS.  1 - 5   . 
     Referring to  FIG.  6   , the electronic device  601 , e.g., a UE or mobile terminal including GPS functionality, in the network environment  600  may communicate with an electronic device  602  via a first network  698  (e.g., a short-range wireless communication network), or an electronic device  604  or a server  608  via a second network  699  (e.g., a long-range wireless communication network). The electronic device  601  may communicate with the electronic device  604  via the server  608 . The electronic device  601  may include a processor  620 , a memory  630 , an input device  650 , a sound output device  655 , a display device  660 , an audio module  670 , a sensor module  676 , an interface  677 , a haptic module  679 , a camera module  680 , a power management module  688 , a battery  689 , a communication module  690 , a subscriber identification module (SIM)  696 , or an antenna module  697  including a GNSS antenna. In one embodiment, at least one (e.g., the display device  660  or the camera module  680 ) of the components may be omitted from the electronic device  601 , or one or more other components may be added to the electronic device  601 . In one embodiment, some of the components may be implemented as a single integrated circuit (IC). For example, the sensor module  676  (e.g., a fingerprint sensor, an iris sensor, or an illuminance sensor) may be embedded in the display device  660  (e.g., a display). 
     The processor  620  may execute, for example, software (e.g., a program  640 ) to control at least one other component (e.g., a hardware or a software component) of the electronic device  601  coupled with the processor  620 , and may perform various data processing or computations. As at least part of the data processing or computations, the processor  620  may load a command or data received from another component (e.g., the sensor module  676  or the communication module  690 ) in volatile memory  632 , process the command or the data stored in the volatile memory  632 , and store resulting data in non-volatile memory  634 . The processor  620  may include a main processor  621  (e.g., a central processing unit (CPU) or an application processor, and an auxiliary processor  623  (e.g., a graphics processing unit (GPU), an image signal processor (ISP), a sensor hub processor, or a communication processor (CP)) that is operable independently from, or in conjunction with, the main processor  621 . Additionally or alternatively, the auxiliary processor  623  may be adapted to consume less power than the main processor  621 , or execute a particular function. The auxiliary processor  623  may be implemented as being separate from, or a part of, the main processor  621 . 
     The auxiliary processor  623  may control at least some of the functions or states related to at least one component (e.g., the display device  660 , the sensor module  676 , or the communication module  690 ) among the components of the electronic device  601 , instead of the main processor  621  while the main processor  621  is in an inactive (e.g., sleep) state, or together with the main processor  621  while the main processor  621  is in an active state (e.g., executing an application). According to one embodiment, the auxiliary processor  623  (e.g., an image signal processor or a communication processor) may be implemented as part of another component (e.g., the camera module  680  or the communication module  690 ) functionally related to the auxiliary processor  623 . 
     The memory  630  may store various data used by at least one component (e.g., the processor  620  or the sensor module  676 ) of the electronic device  601 . The various data may include, for example, software (e.g., the program  640 ) and input data or output data for a command related thereto. The memory  630  may include the volatile memory  632  or the non-volatile memory  634 . 
     The program  640  may be stored in the memory  630  as software, and may include, for example, an operating system (OS)  642 , middleware  644 , or an application  646 . 
     The input device  650  may receive a command or data to be used by other component (e.g., the processor  620 ) of the electronic device  601 , from the outside (e.g., a user) of the electronic device  601 . The input device  650  may include, for example, a microphone, a mouse, or a keyboard. 
     The sound output device  655  may output sound signals to the outside of the electronic device  601 . The sound output device  655  may include, for example, a speaker or a receiver. The speaker may be used for general purposes, such as playing multimedia or recording, and the receiver may be used for receiving an incoming call. According to one embodiment, the receiver may be implemented as being separate from, or a part of, the speaker. 
     The display device  660  may visually provide information to the outside (e.g., a user) of the electronic device  601 . The display device  660  may include, for example, a display, a hologram device, or a projector and control circuitry to control a corresponding one of the display, hologram device, and projector. According to one embodiment, the display device  660  may include touch circuitry adapted to detect a touch, or sensor circuitry (e.g., a pressure sensor) adapted to measure the intensity of force incurred by the touch. 
     The audio module  670  may convert a sound into an electrical signal and vice versa. According to one embodiment, the audio module  670  may obtain the sound via the input device  650 , or output the sound via the sound output device  655  or a headphone of an external electronic device  602  directly (e.g., wiredly) or wirelessly coupled with the electronic device  601 . 
     The sensor module  676  may detect an operational state (e.g., power or temperature) of the electronic device  601  or an environmental state (e.g., a state of a user) external to the electronic device  601 , and then generate an electrical signal or data value corresponding to the detected state. The sensor module  676  may include, for example, a gesture sensor, a gyro sensor, an atmospheric pressure sensor, a magnetic sensor, an acceleration sensor, a grip sensor, a proximity sensor, a color sensor, an infrared (IR) sensor, a biometric sensor, a temperature sensor, a humidity sensor, or an illuminance sensor. 
     The interface  677  may support one or more specified protocols to be used for the electronic device  601  to be coupled with the external electronic device  602  directly (e.g., wiredly) or wirelessly. According to one embodiment, the interface  677  may include, for example, a high definition multimedia interface (HDMI), a universal serial bus (USB) interface, a secure digital (SD) card interface, or an audio interface. 
     A connecting terminal  678  may include a connector via which the electronic device  601  may be physically connected with the external electronic device  602 . According to one embodiment, the connecting terminal  678  may include, for example, an HDMI connector, a USB connector, an SD card connector, or an audio connector (e.g., a headphone connector). 
     The haptic module  679  may convert an electrical signal into a mechanical stimulus (e.g., a vibration or a movement) or an electrical stimulus which may be recognized by a user via tactile sensation or kinesthetic sensation. According to one embodiment, the haptic module  679  may include, for example, a motor, a piezoelectric element, or an electrical stimulator. 
     The camera module  680  may capture a still image or moving images. According to one embodiment, the camera module  680  may include one or more lenses, image sensors, image signal processors, or flashes. 
     The power management module  688  may manage power supplied to the electronic device  601 . The power management module  688  may be implemented as at least part of, for example, a power management integrated circuit (PMIC). 
     The battery  689  may supply power to at least one component of the electronic device  601 . According to one embodiment, the battery  689  may include, for example, a primary cell which is not rechargeable, a secondary cell which is rechargeable, or a fuel cell. 
     The communication module  690  may support establishing a direct (e.g., wired) communication channel or a wireless communication channel between the electronic device  601  and the external electronic device (e.g., the electronic device  602 , the electronic device  604 , or the server  608 ) and performing communication via the established communication channel. The communication module  690  may include one or more communication processors that are operable independently from the processor  620  (e.g., the application processor) and supports a direct (e.g., wired) communication or a wireless communication. According to one embodiment, the communication module  690  may include a wireless communication module  692  (e.g., a cellular communication module, a short-range wireless communication module, or a global navigation satellite system (GNSS) communication module) or a wired communication module  694  (e.g., a local area network (LAN) communication module or a power line communication (PLC) module). A corresponding one of these communication modules may communicate with the external electronic device via the first network  698  (e.g., a short-range communication network, such as Bluetooth™, wireless-fidelity (Wi-Fi) direct, or a standard of the Infrared Data Association (IrDA)) or the second network  699  (e.g., a long-range communication network, such as a cellular network, the Internet, or a computer network (e.g., LAN or wide area network (WAN)). These various types of communication modules may be implemented as a single component (e.g., a single IC), or may be implemented as multiple components (e.g., multiple ICs) that are separate from each other. The wireless communication module  692  may identify and authenticate the electronic device  601  in a communication network, such as the first network  698  or the second network  699 , using subscriber information (e.g., international mobile subscriber identity (IMSI)) stored in the subscriber identification module  696 . 
     The antenna module  697  may transmit or receive a signal or power to or from the outside (e.g., the external electronic device) of the electronic device  601 . According to one embodiment, the antenna module  697  may include one or more antennas, and, therefrom, at least one antenna appropriate for a communication scheme used in the communication network, such as the first network  698  or the second network  699 , may be selected, for example, by the communication module  690  (e.g., the wireless communication module  692 ). The signal or the power may then be transmitted or received between the communication module  690  and the external electronic device via the selected at least one antenna. 
     At least some of the above-described components may be mutually coupled and communicate signals (e.g., commands or data) therebetween via an inter-peripheral communication scheme (e.g., a bus, a general purpose input and output (GPIO), a serial peripheral interface (SPI), or a mobile industry processor interface (MIPI)). 
     According to one embodiment, commands or data may be transmitted or received between the electronic device  601  and the external electronic device  604  via the server  608  coupled with the second network  699 . Each of the electronic devices  602  and  604  may be a device of a same type as, or a different type, from the electronic device  601 . All or some of operations to be executed at the electronic device  601  may be executed at one or more of the external electronic devices  602 ,  604 , or  608 . For example, if the electronic device  601  should perform a function or a service automatically, or in response to a request from a user or another device, the electronic device  601 , instead of, or in addition to, executing the function or the service, may request the one or more external electronic devices to perform at least part of the function or the service. The one or more external electronic devices receiving the request may perform the at least part of the function or the service requested, or an additional function or an additional service related to the request, and transfer an outcome of the performing to the electronic device  601 . The electronic device  601  may provide the outcome, with or without further processing of the outcome, as at least part of a reply to the request. To that end, a cloud computing, distributed computing, or client-server computing technology may be used, for example. 
     One embodiment may be implemented as software (e.g., the program  640 ) including one or more instructions that are stored in a storage medium (e.g., internal memory  636  or external memory  638 ) that is readable by a machine (e.g., the electronic device  601 ). For example, a processor of the electronic device  601  may invoke at least one of the one or more instructions stored in the storage medium, and execute it, with or without using one or more other components under the control of the processor. Thus, a machine may be operated to perform at least one function according to the at least one instruction invoked. The one or more instructions may include code generated by a complier or code executable by an interpreter. A machine-readable storage medium may be provided in the form of a non-transitory storage medium. The term “non-transitory” indicates that the storage medium is a tangible device, and does not include a signal (e.g., an electromagnetic wave), but this term does not differentiate between where data is semi-permanently stored in the storage medium and where the data is temporarily stored in the storage medium. 
     According to one embodiment, a method of the disclosure may be included and provided in a computer program product. The computer program product may be traded as a product between a seller and a buyer. The computer program product may be distributed in the form of a machine-readable storage medium (e.g., a compact disc read only memory (CD-ROM)), or be distributed (e.g., downloaded or uploaded) online via an application store (e.g., Play Store™), or between two user devices (e.g., smart phones) directly. If distributed online, at least part of the computer program product may be temporarily generated or at least temporarily stored in the machine-readable storage medium, such as memory of the manufacturer&#39;s server, a server of the application store, or a relay server. 
     According to one embodiment, each component (e.g., a module or a program) of the above-described components may include a single entity or multiple entities. One or more of the above-described components may be omitted, or one or more other components may be added. Alternatively or additionally, a plurality of components (e.g., modules or programs) may be integrated into a single component. In this case, the integrated component may still perform one or more functions of each of the plurality of components in the same or similar manner as they are performed by a corresponding one of the plurality of components before the integration. Operations performed by the module, the program, or another component may be carried out sequentially, in parallel, repeatedly, or heuristically, or one or more of the operations may be executed in a different order or omitted, or one or more other operations may be added. 
     As presented in the above-described embodiments, an SB LCC selection method is not always the best approach for dealing with frequency-selective channels. Therefore, alternative approaches are provided (i.e., WB or SBG LCC selection), based on WB capacity maximization, which outperform SB LCC selection methods under medium/high-selectivity channel conditions. The WB and SBG methods are fully compatible with existing frequency domain compression (FDC) framework (e.g., the eType-II codebook of NR Rel-16), and therefore, do not require any specification change or additional signaling. 
     Additionally, adaptive methods are also provided that dynamically switch between SB LCC selection method, WB, and SBG methods depending on the instantaneous channel, thereby providing consistent performance improvements. For example, simulation results using WB or SBG LCC selection show that the proposed methods achieve gains up to 2.5 dB over legacy eType-II PMI selection. 
     Although certain embodiments of the present disclosure have been described in the detailed description of the present disclosure, the present disclosure may be modified in various forms without departing from the scope of the present disclosure. Thus, the scope of the present disclosure shall not be determined merely based on the described embodiments, but rather determined based on the accompanying claims and equivalents thereto.