Patent Publication Number: US-10312981-B2

Title: User equipment and methods for codebook subsampling for enhanced 4TX codebooks

Description:
This application is a continuation of U.S. patent application Ser. No. 14/739,815, filed Jun. 15, 2015, now issued as U.S. Pat. No. 9,553,643, which is a continuation of U.S. patent application Ser. No. 14/108,648, filed Dec. 17, 2013, now issued as U.S. Pat. No. 9,071,297, which claims priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application Ser. No. 61/829,968, filed May 31, 2013, each of which is incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     Embodiments pertain to wireless communications. Some embodiments relate to multiple-input multiple output (MIMO) codebook subsampling in cellular networks, such as E-UTRAN networks operating in accordance with one of the 3GPP standards for the Long Term Evolution (LTE) (3GPP LTE). 
     BACKGROUND 
     Closed-loop MIMO systems typically transmit channel state information from a receiver to a transmitter over a feedback path. The channel state information may be used to employ beamforming to compensate for the current channel conditions increasing signal-to-noise (SNR) levels at the receiver. In some of these conventional systems, a beamforming matrix may be generated at the receiver based on the channel conditions. The beamforming matrix may then be provided to the transmitter as feedback. This feedback consumes bandwidth that might otherwise be available for data traffic. To reduce the overhead associated with this feedback, codewords of a known codebook may be provided instead of an actual beamforming matrix. The codewords may indicate which beamforming matrix is to be used by the transmitter. 
     In MIMO systems, the size of the codebooks may increase significantly with number of transmit antennas N t  and the number of transmitted data streams N s . In some conventional systems, the size of the codebook may be based on the number of transmit antennas and the number of data streams. This results in a significant increase in feedback. 
     Thus, there are general needs for MIMO systems and methods for beamforming with reduced feedback. There are also general needs for MIMO systems and methods that make use of smaller codebooks. There are also general needs for MIMO systems and methods that provide improved performance without an increase in feedback. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a wireless network in accordance with some embodiments; and 
         FIG. 2  illustrates a functional block diagram of user equipment (UE) in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following description and the drawings sufficiently illustrate specific embodiments to enable those skilled in the art to practice them. Other embodiments may incorporate structural, logical, electrical, process, and other changes. Portions and features of some embodiments may be included in, or substituted for, those of other embodiments. Embodiments set forth in the claims encompass all available equivalents of those claims. 
       FIG. 1  illustrates a wireless network in accordance with some embodiments. Wireless network may be configured to operate in accordance with one of the 3GPP standards for the Long Term Evolution (LTE) (3GPP LTE). In these embodiments, wireless network  100  may include one or more enhanced node Bs (eNBs)  104  arranged for communicating with user equipment (UE), such as UE  102 . UE  102  may provide feedback  103  to an eNB  104  for performing MIMO beamforming, among other things, as described in more detail below. 
     In accordance with some embodiments, the UE  102  may be arranged for codebook subsampling for enhanced 4Tx codebooks in a 3GPP LIE network. In these embodiments, the UE  102  may configure a physical uplink control channel (PUCCH) for transmission of channel state information (CSI) feedback including a rank indicator (RI) and a precoding matrix (W1), may jointly encode a rank indicator (RI) and a precoding matrix (W1), and may perform codebook subsampling for the enhanced 4Tx codebook for: PUCCH report type 5 (RI/1st in PUCCH 1-1 submode 1; PUCCH report type 2c (CQI/1st PMI/2nd PMI) in PUCCH 1-1 submode 2; and PUCCH report type 1a (subband CQI/2nd PMI) in PUCCH 2-1. These embodiments are described in more detail below. 
     In some embodiments, for the PUCCH report type 5 (RI/1st PMI) in PUCCH 1-1 submode 1, when a maximum of four layers of data transmission (i.e., RI=1, 2, 3, or 4) is supported by the UE  102 , the UE  102  may jointly encode the RI and the W1 by employing codebook subsampling prior to configuring the CSI transmission (e.g., see table 2-1) at least for a rank indicator of two (RI=2). 
     In some embodiments, precoding matrix indices of 2, 4, 6, 8, 10, 12 and 14 are used for the codebook subsampling for RI=2 when a maximum of four layers of data transmission is supported (e.g., see table 2-1) to limit the PUCCH payload size for RI feedback to 5-bits. 
     In some embodiments, precoding matrix indices of 0-7 are used for the codebook subsampling for RI=2 when a maximum of four layers of data transmission is supported to limit the PUCCH payload size for RI feedback to 5-bits, (e.g., see table 2-2). 
     In some embodiments, precoding matrix indices of 0-6 and 8-14 are used for the codebook subsampling for RI=2 when a maximum of four layers of data transmission is supported to limit the PUCCH payload size for RI feedback to 5-bits. (e.g., see table 3-1). 
     In some embodiments, precoding matrix indices of 0-13 are used for the codebook subsampling for RI=2 when a maximum of four layers of data transmission is supported (e.g., see table 3-1) to limit the PUCCH payload size for RI feedback to 5-bits. 
     In some embodiments, when a maximum of two layers of data transmission (i.e., RI=1 or 2) is supported, the RI and W1 are jointly encoded. In these embodiments, the UE  102  may refrain from performing codebook sampling (see table 1). 
     In some embodiments, the UE  102  may configure PUCCH payload to be 11-bits for the CSI feedback when the CSI feedback includes a channel-quality indicator (CQI) and a precoding matrix indicator (PMI). The UE  102  may configure the PUCCH payload to be 5-bits for the CSI feedback when the CSI feedback includes the RI. In these embodiments, as long as the RI is included (even without PMI), the payload should be less or equal to 5 bits. 
     In some embodiments, for PUCCH report type 2c (CQI/1st PMI/2nd PMI) in PUCCH 1-1 submode 2, the method comprises performing codebook subsampling for RI-1 or RI-2 in accordance with either table 4-1 or table 4-2. 
     In some embodiments, for PUCCH report type 1a (subband CQI/2nd PMI) in PUCCH 2-1, the method comprises performing codebook subsampling for RI=1, RI=2, RI=3 or RI=4 in accordance with table 5, table 6 or table 7. 
     In some embodiments, a dual codebook structure may be used for enhanced 4Tx codebook. Two solutions are proposed for down selection as follows: 
     
       
         
           
             
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     Similar with 8Tx dual codebook, codebook subsampling should be applied for periodic CSI feedback to meet the PUCCH feedback channel capacity. This disclosure proposes the codebook subsampling schemes for enhanced 4Tx codebook in periodic CSI feedback. 
     In accordance with embodiments, in order to achieve reliable CSI feedback, the PUCCH payload should be no more than:
         11 bits if current CSI feedback instance includes CQI/PMI feedback;   5 bits if current CSI feedback instance includes RI feedback.       

     Then codebook subsampling may be applied for: PUCCH report type 5 (RI/1 st  PMI) in PUCCH 1-1 submode 1; PUCCH report type 2c (CQI/2 st  PMI/2 nd  PMI) in PUCCH 1-1 submode 2; PUCCH report type 1a (subband CQI/2 nd  PMI) in PUCCH 2-1; for the enhanced 4Tx codebook. 
     Codebook subsample for PUCCH 1-1 submode 1: 
     Since the enhanced 4Tx codebook reuse Rel. 8 codebook for rank 3˜4 and W1 is an identity matrix, subsampling of W1 (1 st  PMI) only needs to take rank1˜2 into consideration. In order to limit the payload size of PUCCH report type 5 within 5 bits, the following scheme could be used: 
     Alt 1) If the UE supports maximum 2 layer transmission, no subsampling is needed. RI and W1 could be jointly encoded following table 1. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 W1 index after 
                 No. W1 
               
               
                 RI 
                 sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0~15 
                 16 
               
               
                 2 
                 0~15 
                 16 
               
            
           
           
               
               
            
               
                 Total no. W1 + RI hypotheses across ranks 1-2 
                 32 (5 bits) 
               
               
                 (max. layers = 2) 
               
               
                   
               
            
           
         
       
     
     If the UE supported maximum layer is 4, RI and W1 could jointly encoded following table 2-1 or table 2-2. 
     The principle for rank 1 is to keep as many W1 as possible. For rank 2, table 2-1 is optimized to equally subsample W1 of rank 2 for solution 2a; table 2-2 is optimized for solution 2b to avoid duplicated codewords. 
     Note that table 2-1 and table 2-2 could also be used as a unified solution even if UE supports maximum 2 layer transmission. 
     
       
         
           
               
               
               
             
               
                 TABLE 2-1 
               
               
                   
               
               
                   
                 W1 index after 
                 No. W1 
               
               
                 RI 
                 sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0~15 
                 16 
               
               
                 2 
                 0, 2, 4, 6, 8, 10, 12, 14 
                 8 
               
               
                 3 
                 0 
                 1 
               
               
                 4 
                 0 
                 1 
               
            
           
           
               
               
            
               
                 Total no. W1 + RI hypotheses across ranks 1-4 
                 26 (5 bits) 
               
               
                 (max. layers = 4) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 2-2 
               
               
                   
               
               
                   
                 W1 index after 
                 No. W1 
               
               
                 RI 
                 sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0~15 
                 16 
               
               
                 2 
                 0~7  
                 8 
               
               
                 3 
                 0 
                 1 
               
               
                 4 
                 0 
                 1 
               
            
           
           
               
               
            
               
                 Total no. W1 + RI hypotheses across ranks 1-4 
                 26 (5 bits) 
               
               
                 (max. layers = 4) 
               
               
                   
               
            
           
         
       
     
     Alt 2) Another alternative is the same as alt 1) except table 2-1 and table 2-2 are changed to table 3-1 and table 3-2 respectively to effectively use the 32 W1 hypotheses that could be indicated with 5 bits. 
     
       
         
           
               
               
               
             
               
                 TABLE 3-1 
               
               
                   
               
               
                   
                 W1 index after 
                 No. W1 
               
               
                 RI 
                 sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0~15 
                 16 
               
               
                 2 
                 0~6, 8~14 
                 14 
               
               
                 3 
                 0 
                 1 
               
               
                 4 
                 0 
                 1 
               
            
           
           
               
               
            
               
                 Total no. W1 + RI hypotheses across ranks 1-4 
                 32 (5 bits) 
               
               
                 (max. layers = 4) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 3-2 
               
               
                   
               
               
                   
                 W1 index after 
                 No. W1 
               
               
                 RI 
                 sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0~15 
                 16 
               
               
                 2 
                 0~13 
                 14 
               
               
                 3 
                 0 
                 1 
               
               
                 4 
                 0 
                 1 
               
            
           
           
               
               
            
               
                 Total no. W1 + RI hypotheses across ranks 1-4 
                 32 (5 bits) 
               
               
                 (max. layers = 4) 
               
               
                   
               
            
           
         
       
     
     Codebook subsample for PUCCH 1-1 submode 2: 
     Since the enhanced 4Tx codebook of rank 3˜4 reuse Rel. 8 codebook and W1 is an identity matrix, W2 could be indicated by 4 bits for rank 3˜4. Then no subsampling is needed for PUCCH 1-1 submode 2 in rank 3˜4. 
     For rank 1˜2, the table 4-1 or table 4-2 could be used for codebook subsampling. The principle of subsampling for rank 1 is to equally distribute the DFT precoding vector within the AoD (angle of departure) range of eNB. The principle of subsampling for rank 2 is to keep all of the 2 possible co-phasing while covering eNB&#39;s AoD range with W1 as much as possible. 
     The definition of e i  is the same, i.e. e i  is a 4×1 vector with the ith component equals to 1 and the other components are zero. e.g. e1=[1 0 0 0]′; 
     
       
         
           
               
               
               
             
               
                 TABLE 4-1 
               
               
                   
               
               
                   
                   
                 No. W1 + W2 
               
               
                 RI 
                 W1 + W2 index after sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                 1 
                 W1: 0, 2, 4, 6, 8, 10, 12, 14 or 1, 3, 5, 7, 9, 11, 
                 128 (7 bits) 
               
               
                   
                 13,15 
                   
               
               
                   
                 W2: 0~15 
                   
               
               
                 2 
                 W1: 0, 2, 4, 6, 8, 10, 12, 14 or 1, 3, 5, 7, 9, 11, 
                 8 × 2 = 16 
               
               
                   
                 13, 15 
                 (4 bits) 
               
               
                   
                 W2: for each W1, choose only 
                   
               
               
                   
                 (Y1, Y2) = (e1, e1) with all 2 possible 
                   
               
               
                   
                 co-phasing, i.e. 
                   
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           
                             W 
                             
                               2 
                               , 
                               n 
                             
                           
                           ∈ 
                           
                             { 
                             
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               , 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           j 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             - 
                                             j 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                         
                         , 
                         
                           
                             with 
                             ⁢ 
                             
                               
 
                             
                             ( 
                             
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                           = 
                           
                             ( 
                             
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 4-2 
               
               
                   
               
               
                   
                   
                 No. W1 + W2 
               
               
                 RI 
                 W1 + W2 index after sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                 1 
                 W1: 0, 2, 4, 6, 8, 10, 12, 14 or 1, 3, 5, 7, 9, 11 
                 128 (7 bits) 
               
               
                   
                 13, 15 
                   
               
               
                   
                 W2: 0~15 
                   
               
               
                 2 
                 W1: 0, 4, 8, 12 or 1, 5, 9, 13 or 2, 6, 10, 14 or 
                 4 × 
               
               
                   
                 3, 7, 11, 15 
                 (2 + 1 + 1) =  
               
               
                   
                 W2: for each W1, choose (Y1, Y2) = (e1, e1) 
                 16 (4 bits) 
               
               
                   
                 with all 2 possible co-phasing, i.e. 
                   
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           
                             W 
                             
                               2 
                               , 
                               n 
                             
                           
                           ∈ 
                           
                             { 
                             
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               , 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           j 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             - 
                                             j 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                         
                         , 
                         
                           
                             
                               with 
                               ⁢ 
                               
                                 
 
                               
                               ( 
                               
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ) 
                             
                             = 
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ) 
                             
                           
                           ; 
                         
                       
                     
                   
                   
                     
                       
                         
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             choose 
                             ⁢ 
                             
                               
                                   
                               
                               ⁢ 
                               
                                   
                               
                             
                             ( 
                             
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                               , 
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 4 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           with 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             W 
                             
                               2 
                               , 
                               n 
                             
                           
                           = 
                           
                             { 
                             
                               
                                 1 
                                 2 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         Y 
                                         1 
                                       
                                     
                                     
                                       
                                         Y 
                                         2 
                                       
                                     
                                   
                                   
                                     
                                       
                                         Y 
                                         1 
                                       
                                     
                                     
                                       
                                         Y 
                                         2 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                             } 
                           
                         
                         ; 
                       
                     
                   
                   
                     
                       
                         
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           chose 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 e 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           with 
                         
                       
                     
                   
                   
                     
                       
                         
                           W 
                           
                             2 
                             , 
                             n 
                           
                         
                         ∈ 
                         
                           { 
                           
                             
                               1 
                               2 
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     
                                       Y 
                                       1 
                                     
                                   
                                   
                                     
                                       Y 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     
                                       Y 
                                       2 
                                     
                                   
                                   
                                     
                                       - 
                                       
                                         Y 
                                         1 
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                           } 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     Codebook subsample for PUCCH 2-1: 
     Regarding PUCCH reporting type 1a, i.e. subband CQI/second PMI reporting, the codebook subsampling of table 5 or table 6 or table 7 could be applied. 
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                   
                 No. W2 
               
               
                 RI 
                 W2 index after sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                 1 
                 0~15 
                 16 (4 bits) 
               
               
                 2 
                 W2: for each W1, choose (Y1, Y2) ∈ {(e1, e1), 
                 2 × 2 = 4 
               
               
                   
                 (e2, e2)} with all 2 possible co-phasing, i.e. 
                 (2 bits) 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           
                             
                               W 
                               
                                 2 
                                 , 
                                 n 
                               
                             
                             ∈ 
                             
                               { 
                               
                                 
                                   
                                     1 
                                     2 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             Y 
                                             1 
                                           
                                         
                                         
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             Y 
                                             1 
                                           
                                         
                                         
                                           
                                             - 
                                             
                                               Y 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                                 , 
                                 
                                   
                                     1 
                                     2 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             Y 
                                             1 
                                           
                                         
                                         
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                       
                                         
                                           
                                             j 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               Y 
                                               1 
                                             
                                           
                                         
                                         
                                           
                                             
                                               - 
                                               j 
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               Y 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                               } 
                             
                           
                           , 
                           
                             
                               with 
                               ⁢ 
                               
                                 
 
                               
                               ( 
                               
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ) 
                             
                             ∈ 
                             
                               { 
                               
                                 
                                   ( 
                                   
                                     
                                       e 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     , 
                                     e1 
                                   
                                   ) 
                                 
                                 , 
                                 
                                   ( 
                                   
                                     
                                       e 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       3 
                                     
                                     , 
                                     
                                       e 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                               } 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                     
                   
                 
                   
               
               
                   
               
               
                 3 
                 0, 4, 8, 12 or 1, 5, 9, 13 or 2, 6, 10, 14 or 3, 7, 
                 4 (2 bits) 
               
               
                   
                 11, 15 or 0, 1, 2, 3 
                   
               
               
                 4 
                 0, 4, 8, 12 or 1, 5, 9, 13 or 2, 6, 10, 14 or 3, 7, 
                 4 (2 bits) 
               
               
                   
                 11, 15 or 0, 1, 2, 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                   
                   
                 No. W2 
               
               
                 RI 
                 W2 index after sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                 1 
                 0~15 
                 16 (4 bits) 
               
               
                 2 
                 W2: for each W1, choose 
                 4 × 1 = 4 
               
               
                   
                 (Y1, Y2) ∈ {(e1, e1), (e2, e2), (e3, e3), 
                 (2 bits) 
               
               
                   
                 (e4, e4)} with only 1 co-phasing, i.e. 
                   
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           W 
                           
                             2 
                             , 
                             n 
                           
                         
                         ∈ 
                         
                           
                             { 
                             
                               
                                 1 
                                 2 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         Y 
                                         1 
                                       
                                     
                                     
                                       
                                         Y 
                                         2 
                                       
                                     
                                   
                                   
                                     
                                       
                                         Y 
                                         1 
                                       
                                     
                                     
                                       
                                         - 
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                             } 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             with 
                             ⁢ 
                             
                               
 
                             
                             ( 
                             
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               , 
                               
                                 Y 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                         ∈ 
                         
                           { 
                           
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 e1 
                               
                               ) 
                             
                             , 
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 , 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ) 
                             
                             , 
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   3 
                                 
                                 , 
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   3 
                                 
                               
                               ) 
                             
                             , 
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   4 
                                 
                                 , 
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   4 
                                 
                               
                               ) 
                             
                           
                           } 
                         
                       
                     
                   
                 
                   
               
               
                   
               
               
                 3 
                 0, 4, 8, 12 or 1, 5, 9, 13 or 2, 6, 10, 14 or 3, 
                 4 (2 bits) 
               
               
                   
                 7, 11, 15 or 0, 1, 2, 3 
                   
               
               
                 4 
                 0, 4, 8, 12 or 1, 5, 9, 13 or 2, 6, 10, 14 or 3, 
                 4 (2 bits) 
               
               
                   
                 7, 11, 15 or 0, 1, 2, 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                   
                   
                 No. W2 
               
               
                 RI 
                 W2 index after sub-sampling 
                 hypotheses 
               
               
                   
               
             
            
               
                 1 
                 0~15 
                 16 (4 bits) 
               
               
                 2 
                 W2: for each W1, choose (Y1, Y2) = (e1, e1) 
                 2 + 1 + 1 = 4 
               
               
                   
                 with all 2 possible co-phasing, i.e. 
                 (2 bits) 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           
                             W 
                             
                               2 
                               , 
                               n 
                             
                           
                           ∈ 
                           
                             { 
                             
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                               , 
                               
                                 
                                   1 
                                   2 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           Y 
                                           1 
                                         
                                       
                                       
                                         
                                           Y 
                                           2 
                                         
                                       
                                     
                                     
                                       
                                         
                                           j 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             1 
                                           
                                         
                                       
                                       
                                         
                                           
                                             - 
                                             j 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             Y 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                         
                         , 
                         
                           
                             
                               with 
                               ⁢ 
                               
                                 
 
                               
                               ( 
                               
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 
                                   Y 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ) 
                             
                             = 
                             
                               ( 
                               
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 , 
                                 
                                   e 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
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       FIG. 2  illustrates a functional block diagram of a UE in accordance with some embodiments. UE  200  may be suitable for use as UE  102  ( FIG. 1 ). The UE  200  may include physical layer circuitry  202  for transmitting and receiving signals to and from eNBs  104  ( FIG. 1 ) using one or more antennas  201 . UE  200  may also include medium access control layer (MAC) circuitry  204  for controlling access to the wireless medium. UE  200  may also include processing circuitry  206  and memory  208  arranged to perform the operations described herein. 
     In some embodiments, the UE  200  may be part of a portable wireless communication device, such as a personal digital assistant (PDA), a laptop or portable computer with wireless communication capability, a web tablet, a wireless telephone, a smartphone, a wireless headset, a pager, an instant messaging device, a digital camera, an access point, a television, a medical device (e.g., a heart rate monitor, a blood pressure monitor, etc.), or other device that may receive and/or transmit information wirelessly. In some embodiments, the UE  200  may include one or more of a keyboard, a display, a non-volatile memory port, multiple antennas, a graphics processor, an application processor, speakers, and other mobile device elements. The display may be an LCD screen including a touch screen. 
     The one or more antennas  201  utilized by the UE  200  may comprise one or more directional or omnidirectional antennas, including, for example, dipole antennas, monopole antennas, patch antennas, loop antennas, microstrip antennas or other types of antennas suitable for transmission of RF signals. In some embodiments, instead of two or more antennas, a single antenna with multiple apertures may be used. In some multiple-input multiple-output (MIMO) embodiments, the antennas may be effectively separated to take advantage of spatial diversity and the different channel characteristics that may result between each of antennas and the antennas of a transmitting station. In some MIMO embodiments, the antennas may be separated by up to 1/10 of a wavelength or more. 
     Although the UE  200  is illustrated as having several separate functional elements, one or more of the functional elements may be combined and may be implemented by combinations of software-configured elements, such as processing elements including digital signal processors (DSPs), and/or other hardware elements. For example, some elements may comprise one or more microprocessors, DSPs, application specific integrated circuits (ASICs), radio-frequency integrated circuits (RFICs) and combinations of various hardware and logic circuitry for performing at least the functions described herein. In some embodiments, the functional elements may refer to one or more processes operating on one or more processing elements. 
     Embodiments may be implemented in one or a combination of hardware, firmware and software. Embodiments may also be implemented as instructions stored on a computer-readable storage medium, which may be read and executed by at least one processor to perform the operations described herein. A computer-readable storage medium may include any non-transitory mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a computer-readable storage medium may include read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash-memory devices, and other storage devices and media. In these embodiments, one or more processors may be configured with the instructions to perform the operations described herein. 
     In some embodiments, the UE  200  may be configured to receive OFDM communication signals over a multicarrier communication channel in accordance with an OFDMA communication technique. The OFDM signals may comprise a plurality of orthogonal subcarriers. In some broadband multicarrier embodiments, eNBs (including macro eNB  104  and pico eNBs) may be part of a broadband wireless access (BWA) network communication network, such as a Worldwide Interoperability for Microwave Access (WiMAX) communication network or a 3rd Generation Partnership Project (3GPP) Universal Terrestrial Radio Access Network (UTRAN) Long-Term-Evolution (LTE) or a Long-Term-Evolution (LTE) communication network, although the scope of the invention is not limited in this respect. In these broadband multicarrier embodiments, the UE  200  and the eNBs may be configured to communicate in accordance with an orthogonal frequency division multiple access (OFDMA) technique. 
     In some LTE embodiments, the basic unit of the wireless resource is the Physical Resource Block (PRB). The PRB may comprise 12 sub-carriers in the frequency domain×0.5 ms in the time domain. The PRBs may be allocated in pairs (in the time domain). In these embodiments, the PRB may comprise a plurality of resource elements (REs). A RE may comprise one sub-carrier x one symbol. 
     Two types of reference signals may be transmitted by an eNB including demodulation reference signals (DM-RS), channel state information reference signals (CIS-RS) and/or a common reference signal (CRS). The DM-RS may be used by the UE for data demodulation. The reference signals may be transmitted in predetermined PRBs. 
     In some embodiments, the OFDMA technique may be either a frequency domain duplexing (FDD) technique that uses different uplink and downlink spectrum or a time-domain duplexing (TDD) technique that uses the same spectrum for uplink and downlink. 
     In some other embodiments, the UE  200  and the eNBs may be configured to communicate signals that were transmitted using one or more other modulation techniques such as spread spectrum modulation (e.g., direct sequence code division multiple access (DS-CDMA) and/or frequency hopping code division multiple access (FH-CDMA)), time-division multiplexing (TDM) modulation, and/or frequency-division multiplexing (FDM) modulation, although the scope of the embodiments is not limited in this respect. 
     In some LTE embodiments, the UE  200  may calculate several different feedback values which may be used to perform channel adaption for closed-loop spatial multiplexing transmission mode. These feedback values may include a channel-quality indicator (CQI), a rank indicator (RI) and a precoding matrix indicator (PMI). By the CQI, the transmitter selects one of several modulation alphabets and code rate combinations. The RI informs the transmitter about the number of useful transmission layers for the current MIMO channel, and the PMI indicates the codebook index of the precoding matrix (depending on the number of transmit antennas) that is applied at the transmitter. The code rate used by the eNB may be based on the CQI. The PMI may be a vector that is calculated by the UE and reported to the eNB. In some embodiments, the UE may transmit a physical uplink control channel (PUCCH) of format 2, 2a or 2b containing the CQI/PMI or RI. 
     In these embodiments, the CQI may be an indication of the downlink mobile radio channel quality as experienced by the UE  200 . The CQI allows the UE  200  to propose to an eNB an optimum modulation scheme and coding rate to use for a given radio link quality so that the resulting transport block error rate would not exceed a certain value, such as 10%. In some embodiments, the UE may report a wideband CQI value which refers to the channel quality of the system bandwidth. The UE may also report a sub-band CQI value per sub-band of a certain number of resource blocks which may be configured by higher layers. The full set of sub-bands may cover the system bandwidth. In case of spatial multiplexing, a CQI per code word may be reported. 
     In some embodiments, the PMI may indicate an optimum precoding matrix to be used by the eNB for a given radio condition. The PMI value refers to the codebook table. The network configures the number of resource blocks that are represented by a PMI report. In some embodiments, to cover the system bandwidth, multiple PMI reports may be provided. PMI reports may also be provided for closed loop spatial multiplexing, multi-user MIMO and closed-loop rank 1 precoding MIMO modes. 
     In some cooperating multipoint (CoMP) embodiments, the network may be configured for joint transmissions to a UE in which two or more cooperating/coordinating points, such as remote-radio heads (RRHs) transmit jointly. In these embodiments, the joint transmissions may be MIMO transmissions and the cooperating points are configured to perform joint beamforming. 
     The Abstract is provided to comply with 37 C.F.R. Section 1.72(b) requiring an abstract that will allow the reader to ascertain the nature and gist of the technical disclosure. It is submitted with the understanding that it will not be used to limit or interpret the scope or meaning of the claims. The following claims are hereby incorporated into the detailed description, with each claim standing on its own as a separate embodiment.