Abstract:
Methods and apparatus for efficiently feeding back preceding information in a multiple input multiple output (MIMO) system. A codebook including a plurality of codebook entries is constructed. A plurality of subsets of codebook entries are defined for the codebook. Each subset includes a plurality of codebook entries. A subset of codebook entries is selected for precoding data in dependence upon a channel condition, and a codebook entry is selected from the subset. Then, a subset index corresponding to the selected subset, and a codebook entry index corresponding to the selected codebook entry within the selected subset, is transmitted as feedback information.

Description:
CLAIM OF PRIORITY 
       [0001]    This application makes reference to, incorporates the same herein, and claims all benefits accruing under 35 U.S.C. §119 from a provisional application earlier filed in the U.S. Patent &amp; Trademark Office on 26 Sep. 2007 and there duly assigned Ser. No. 60/960,372. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to methods and apparatus for efficiently feeding back precoding information in a multiple input multiple output (MIMO) system. 
         [0004]    2. Description of the Related Art 
         [0005]    Orthogonal Frequency Division Multiplexing (OFDM) is a popular wireless communication technology to multiplex data in frequency domain. 
         [0006]    A multiple antenna communication system, which is often referred to as multiple input multiple output (MIMO) system, is widely used in combination with OFDM technology, in a wireless communication system to improve system performance. 
         [0007]    When the transmission channels between the transmitters and the receivers are relatively constant, it is possible to use a closed-loop MIMO scheme to further improve system performance. In a closed-loop MIMO system, the receiver first transmits information regarding the channel condition to the transmitter. The transmitter utilizes this information, together with other considerations such as scheduling priority, data and resource availability, to select a preceding unit. In the transmitter, the data streams to be transmitted are precoded, i.e., pre-multiplied by the preceding matrix, before being passed on to the multiple transmit antennas. 
         [0008]    In a contemporary closed-loop MIMO precoding scheme, when a transmitter precodes data before transmitting the data to a receiver, the transmitter informs the receiver of the precoding information such as precoding matrix index (PMI) and transmission rank. 
         [0009]    The precoding matrix indication (PMI) and rank feedback on a subband basis can result in significant feedback overhead. For example, and assuming 4-bits per subband for PMI and 2-bits per subband for rank, the total overhead for feedback on five subbands is 30 bits. For larger system bandwidths, the system needs to support a larger number of subbands, thus resulting in even larger feedback overhead. Also, for finer granularity of PMI/rank feedback in frequency, the overhead also increases. Therefore, there is a need to improve the PMI and rank feedback mechanisms that reduces the overhead. 
       SUMMARY OF THE INVENTION 
       [0010]    It is therefore an object of the present invention to provide a method and apparatus for efficiently feeding back precoding information. 
         [0011]    According to one aspect of the present invention, a codebook including a plurality of codebook entries is constructed. A plurality of subsets of codebook entries are defined for the codebook. Each subset includes a plurality of codebook entries. A subset of codebook entries is selected for precoding data in dependence upon a channel condition, and a codebook entry is selected from the subset. Then, a subset index corresponding to the selected subset, and a codebook entry index corresponding to the selected codebook entry within the selected subset, is transmitted as feedback information. 
         [0012]    At least two subsets may have no overlapping codebook entries. 
         [0013]    Alternatively, at least two subsets may have at least one overlapping codebook entry. 
         [0014]    A transmission resource block may be divided into a plurality of time units in time domain and a plurality of frequency units in frequency domain. Then, the selection of the codebook entry and the transmission of the codebook entry index may be performed for each frequency unit in the transmission resource block. 
         [0015]    Moreover, a transmission rank may be selected and a transmission rank index corresponding to the selected transmission rank may be transmitted. The selection of the transmission rank and the transmission of the transmission rank index may be performed for each frequency unit in the transmission resource block. 
         [0016]    Alternatively, the selection of the codebook entry and the transmission of the codebook entry index may be performed for each time unit in the transmission resource block. 
         [0017]    Still alternatively, the selection of the codebook entry and the transmission of the codebook entry index may be performed for each frequency unit within each time unit in the transmission resource block. 
         [0018]    According to another aspect of the present invention, a plurality of subsets may be defined for a codebook, and each subset includes a single codebook entry. A subset is selected for precoding data in dependence upon a channel condition. Then, a subset index corresponding to the selected subset is transmitted as feedback information. 
         [0019]    According to still another aspect of the present invention, a plurality of subsets may be defined for a codebook, and each subset includes a plurality of codebook entries. A bitmap may be defined for each of the subset. The bitmap consists of at least one bit-“0” and at least one bit-“1”. Each bit-“1” indicates a corresponding codebook entry in the subset. A subset of codebook entries is selected for precoding data in dependence upon a channel condition, and a codebook entry is selected from the subset. Then, a bitmap corresponding to the selected subset and a codebook entry index corresponding to the selected codebook entry within the selected subset is transmitted as the feedback information. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]    A more complete appreciation of the invention, and many of the attendant advantages thereof, will be readily apparent as the same becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings in which like reference symbols indicate the same or similar components, wherein: 
           [0021]      FIG. 1  schematically illustrates an Orthogonal Frequency Division Multiplexing (OFDM) transceiver chain; 
           [0022]      FIG. 2  schematically illustrates a Multiple Input Multiple Output (MIMO) transceiver chain; 
           [0023]      FIG. 3  schematically illustrates a single codeword MIMO transmission scheme; 
           [0024]      FIG. 4  schematically illustrates a multiple codeword MIMO transmission scheme; 
           [0025]      FIG. 5  schematically illustrates a feedback-based MIMO preceding and decoding system; 
           [0026]      FIG. 6  schematically illustrates an example of MIMO preceding on different subbands; 
           [0027]      FIG. 7  schematically illustrates an example of MIMO rank on different subbands; 
           [0028]      FIG. 8  schematically illustrates four subsets of a codebook as an embodiment according to the principles of the present invention; 
           [0029]      FIG. 9  schematically illustrates a MIMO PMI and rank feedback as an embodiment according to the principles of the present invention; 
           [0030]      FIG. 10  schematically illustrates four subsets of a codebook as another embodiment according to the principles of the present invention; 
           [0031]      FIG. 11  schematically illustrates a MIMO PMI and rank feedback as another embodiment according to the principles of the present invention; 
           [0032]      FIG. 12  schematically illustrates four subsets of a codebook as still another embodiment according to the principles of the present invention; 
           [0033]      FIG. 13  schematically illustrates a MIMO PMI and rank feedback as still another embodiment according to the principles of the present invention; 
           [0034]      FIG. 14  schematically illustrates a MIMO PMI and rank feedback as still another embodiment according to the principles of the present invention; 
           [0035]      FIG. 15  schematically illustrates a MIMO PMI and rank feedback assuming a wideband-PMI plus delta-PMI on a subband basis as an embodiment according to the principles of the present invention; 
           [0036]      FIG. 16  schematically illustrates a wideband-PMI and delta-PMI set as an embodiment according to the principles of the present invention; 
           [0037]      FIG. 17  schematically illustrates a wideband-PMI and delta-PMI set as another embodiment according to the principles of the present invention; 
           [0038]      FIG. 18  schematically illustrates a MIMO PMI and rank feedback assuming a wideband-PMI plus delta-PMI on a subband basis as another embodiment according to the principles of the present invention; 
           [0039]      FIG. 19  schematically illustrates a bitmap of a subset of a codebook as still another embodiment according to the principles of the present invention; and 
           [0040]      FIG. 20  schematically illustrates a MIMO PMI and rank feedback as still another embodiment according to the principles of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0041]      FIG. 1  illustrates an Orthogonal Frequency Division Multiplexing (OFDM) transceiver chain. In a communication system using OFDM technology, at transmitter chain  110 , control signals or data  111  is modulated by modulator  112  and is serial-to-parallel converted by Serial/Parallel (S/P) converter  113 . Inverse Fast Fourier Transform (IFFT) unit  114  is used to transfer the signal from frequency domain to time domain. Cyclic prefix (CP) or zero prefix (ZP) is added to each OFDM symbol by CP insertion unit  116  to avoid or mitigate the impact due to multipath fading. Consequently, the signal is transmitted by transmitter (Tx) front end processing unit  117 , such as an antenna (not shown), or alternatively, by fixed wire or cable. At receiver chain  120 , assuming perfect time and frequency synchronization are achieved, the signal received by receiver (Rx) front end processing unit  121  is processed by CP removal unit  122 . Fast Fourier Transform (FFT) unit  124  transfers the received signal from time domain to frequency domain for further processing. 
         [0042]    The total bandwidth in an OFDM system is divided into narrowband frequency units called subcarriers. The number of subcarriers is equal to the FFT/IFFT size N used in the system. In general, the number of subcarriers used for data is less than N because some subcarriers at the edge of the frequency spectrum are reserved as guard subcarriers. In general, no information is transmitted on guard subcarriers. 
         [0043]    Multiple Input Multiple Output (MIMO) schemes use multiple transmission antennas and multiple receive antennas to improve the capacity and reliability of a wireless communication channel. A MIMO system promises linear increase in capacity with K where K is the minimum of number of transmit (M) and receive antennas (N), i.e. K=min(M,N). A simplified example of a 4×4 MIMO system is shown in  FIG. 2 . In this example, four different data streams are transmitted separately from four transmission antennas. The transmitted signals are received at four receive antennas. Some form of spatial signal processing is performed on the received signals in order to recover the four data streams. An example of spatial signal processing is vertical Bell Laboratories Layered Space-Time (V-BLAST) which uses the successive interference cancellation principle to recover the transmitted data streams. Other variants of MIMO schemes include schemes that perform some kind of space-time coding across the transmission antennas (e.g., diagonal Bell Laboratories Layered Space-Time (D-BLAST)) and also beamforming schemes such as Spatial Division multiple Access (SDMA). 
         [0044]    The MIMO channel estimation consists of estimating the channel gain and phase information for links from each of the transmission antennas to each of the receive antennas. Therefore, the channel for M×N MIMO system consists of an N×M matrix: 
         [0000]    
       
         
           
             
               
                 
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                             h 
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                     ] 
                   
                 
               
               
                 
                   ( 
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         [0000]    where h ij  represents the channel gain from transmission antenna j to receive antenna i. In order to enable the estimations of the elements of the MIMO channel matrix, separate pilots are transmitted from each of the transmission antennas. 
         [0045]    An example of single-code word MIMO scheme is given in  FIG. 3 . In case of single-code word MIMO transmission, a cyclic redundancy check (CRC) is added to a single information block and then coding, for example, using turbo codes and low-density parity check (LDPC) code, and modulation, for example, by quadrature phase-shift keying (QPSK) modulation scheme, are performed. The coded and modulated symbols are then demultiplexed for transmission over multiple antennas. 
         [0046]    In case of multiple codeword MIMO transmission, shown in  FIG. 4 , the information block is de-multiplexed into smaller information blocks. Individual CRCs are attached to these smaller information blocks and then separate coding and modulation is performed on these smaller blocks. After modulation, these smaller blocks are respectively demultiplexed into even smaller blocks and then transmitted through corresponding antennas. It should be noted that in case of multi-code word MIMO transmissions, different modulation and coding can be used on each of the individual streams, and thus resulting in a so-called Per Antenna Rate Control (PARC) scheme. Also, multi-code word transmission allows for more efficient post-decoding interference cancellation because a CRC check can be performed on each of the code words before the code word is cancelled from the overall signal. In this way, only correctly received code words are cancelled, and thus avoiding any interference propagation in the cancellation process. 
         [0047]    In a closed-loop MIMO preceding system, for each transmission antenna size we construct a set of precoding matrices (i.e., codewords) and let this set be known at both the Node-B (i.e., the base station) and the user equipment (UE). We call this set of matrices as the “codebook” and denote it P={P 1 , . . . , P L }. Here L=2 q  denotes the size of the codebook and q is the number of (feedback) bits needed to index the codebook. In a limited feedback precoding MIMO system illustrated in  FIG. 5 , once the codebook is specified for a MIMO system, the receiver observes a channel realization, selects the best preceding matrix (i.e., codeword) to be used at the moment, and feeds back the index of the codeword to the transmitter. 
         [0048]    An example of precoding is DFT-based or Fourier precoding. A Fourier matrix is a N×N square matrix with entries given by: 
         [0000]        P   mn   =e   j2πmn/N    (2) 
         [0000]    For example, a 2×2 Fourier matrix can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
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                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   3 
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         [0000]    Similarly, a 4×4 Fourier matrix can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
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                   ( 
                   4 
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         [0049]    Other forms of precoding include matrices obtained using Householder (HH) equation. An N×N Householder matrix is defined as follows: 
         [0000]        W=I   N −2 uu   H   , ∥u∥= 2,   (5) 
         [0000]    where I N  is an N×N identity matrix, u is a unit vector. The Householder matrix represents a reflection on the unit vector u in an N-dimensional complex space, which is a unitary operation. The u is also referred to as the generating vector. Assuming a generating vector u 0   T =[1 −1 −1 −1], the 4×4 Householder matrix is given as below: 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     0 
                   
                   = 
                   
                     
                       
                         I 
                         4 
                       
                       - 
                       
                         2 
                          
                         
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                           0 
                         
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                             0 
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                           / 
                           
                             
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                               1 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    More generally, 
         [0000]        W   n   =I   4 −2 u   n   u   n   H   /∥u   n ∥ 2    (7) 
         [0050]    An example of Householder (HH) four transmission (4-Tx) antennas MIMO preceding codebook used in the 3GPP LTE system is given in Table 1 below. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Codebook for transmission on antenna ports {0, 1, 2, 3}. 
               
             
          
           
               
                 Codebook 
                   
                 Number of layers υ 
               
             
          
           
               
                 index 
                 u n   
                 1 
                 2 
                 3 
                 4 
               
               
                   
               
             
          
           
               
                 0 
                 u 0  = [1 −1 −1 −1] T   
                 W 0   {1}   
                 W 0   {14} /{square root over (2)} 
                 W 0   {124} {square root over (3)} 
                 W 1   {1234} {square root over (2)} 
               
               
                 1 
                 u 1  = [1 −j 1 j] T   
                 W 1   {1}   
                 W 1   {12} /{square root over (2)} 
                 W 1   {123} {square root over (3)} 
                 W 1   {1234} {square root over (2)} 
               
               
                 2 
                 u 2  = [1 1 −1 1] T   
                 W 2   {1}   
                 W 2   {12} /{square root over (2)} 
                 W 2   {123} {square root over (3)} 
                 W 2   {3214} {square root over (2)} 
               
               
                 3 
                 u 3  = [1 j 1 −j] T   
                 W 3   {1}   
                 W 3   {12} /{square root over (2)} 
                 W 3   {123} {square root over (3)} 
                 W 3   {3214} {square root over (2)} 
               
               
                 4 
                 u 4  = [1 (−1−j)/{square root over (2)} −j (1−j)/{square root over (2)}] T   
                 W 4   {1}   
                 W 4   {14} /{square root over (2)} 
                 W 4   {123} {square root over (3)} 
                 W 4   {1234} {square root over (2)} 
               
               
                 5 
                 u 5  = [1 (1−j)/{square root over (2)} j (−1−j)/{square root over (2)}] T   
                 W 5   {1}   
                 W 5   {14} /{square root over (2)} 
                 W 5   {124} {square root over (3)} 
                 W 5   {1234} {square root over (2)} 
               
               
                 6 
                 u 6  = [1 (1+j)/{square root over (2)} −j (−1+j)/{square root over (2)}] T   
                 W 6   {1}   
                 W 6   {13} /{square root over (2)} 
                 W 6   {134} {square root over (3)} 
                 W 6   {1324} {square root over (2)} 
               
               
                 7 
                 u 7  = [1 (−1+j)/{square root over (2)} j (1+j)/{square root over (2)}] T   
                 W 7   {1}   
                 W 7   {13} /{square root over (2)} 
                 W 7   {134} {square root over (3)} 
                 W 7   {1324} {square root over (2)} 
               
               
                 8 
                 u 8  = [1 −1 1 1] T   
                 W 8   {1}   
                 W 8   {12} /{square root over (2)} 
                 W 8   {124} {square root over (3)} 
                 W 8   {1234} {square root over (2)} 
               
               
                 9 
                 u 9  = [1 −j −1 −j] T   
                 W 9   {1}   
                 W 9   {14} /{square root over (2)} 
                 W 9   {134} {square root over (3)} 
                 W 9   {1234} {square root over (2)} 
               
               
                 10 
                 u 10  = [1 1 1 −1] T   
                     W 10   {1}   
                     W 10   {13} /{square root over (2)} 
                     W 10   {123} {square root over (3)} 
                     W 10   {1324} {square root over (2)} 
               
               
                 11 
                 u 11  = [1 j −1 j] T   
                     W 11   {1}   
                     W 11   {13} /{square root over (2)} 
                     W 11   {134} {square root over (3)} 
                     W 11   {1324} {square root over (2)} 
               
               
                 12 
                 u 12  = [1 −1 −1 1] T   
                     W 12   {1}   
                     W 12   {12} /{square root over (2)} 
                     W 12   {123 }{square root over (3)} 
                     W 12   {1234} {square root over (2)} 
               
               
                 13 
                 u 13  = [1 −1 1 −1] T   
                     W 13   {1}   
                     W 13   {13} /{square root over (2)} 
                     W 13   {123 }{square root over (3)} 
                     W 13   {1324} {square root over (2)} 
               
               
                 14 
                 u 14  = [1 1 −1 −1] T   
                     W 14   {1}   
                     W 14   {13} /{square root over (2)} 
                     W 14   {123 }{square root over (3)} 
                     W 14   {3214} {square root over (2)} 
               
               
                 15 
                 u 15  = [1 1 1 1] T   
                     W 15   {1}   
                     W 15   {12} /{square root over (2)} 
                     W 15   {123} {square root over (3)} 
                     W 15   {1234} {square root over (2)} 
               
               
                   
               
             
          
         
       
     
         [0051]    The four antenna ports codebook given in Table 1 uses a total of sixteen (16) generating vectors {u 0 , u 1 , . . . u 15 }. These sixteen generating vectors result in sixteen 4×4 Householder matrices {W 0 , W 1 , . . . , W 15 }, which form the precoders for rank4 transmissions. The precoders for lower ranks are obtained by column subset selection from the rank4 precoders. The rank1 precoders always consist of the first column of the matrix. This codebook also exhibits a nested property, that is, lower rank precoders are a subset of the higher rank precoder for the same generating vector. For example for the first rank 4 precoder w 0   {1234} /2 consisting of W 0 , the rank 1, 2 and 3 precoders w 0   {1} , w 0   {14} /√{square root over (2)}, w 0   {124} /√{square root over (3)} consists of column  1 , columns ( 1 , 4 ) and columns ( 1 , 2 , 4 ) of W 0  respectively. 
         [0052]    The precoding used for MIMO transmission needs to be feedback by the User Equipment (UE) to the base station, i.e., Node-B. The preceding feedback information consists of precoding-matrix or column identity. Moreover, due to frequency-selective fading in an OFDM system, the optimal preceding over different subbands can be different as shown in  FIG. 6 . Therefore, the preceding information can be sent on a subband basis. In the example of  FIG. 6 , the three hundred used subcarriers are divided into five subbands of sixty subcarriers each. We assume rank-1 transmission over all the subbands. The precoders used for rank-1 transmission in SB 1 ,  2 ,  3 ,  4  and  5  are W 4   {1} , W 1   {1} , W 1 { 1 }, W 9   {1}  and W 15   {1} , respectively. 
         [0053]    It is well known that even when a system can support 4×4 MIMO, rank-4 (4 MIMO layers) transmissions are not always desirable. The MIMO channel experienced by the UE generally limits the maximum rank that can be used for transmission. In general for weak users in the system, a lower rank transmission is preferred over a high rank transmission from throughput perspective. Moreover due to frequency-selective fading optimal rank may be different on different subbands. Therefore, for optimal performance, UE need to feedback the rank information on a subband basis as shown in  FIG. 7 . In the example of FIG.  7 ., the transmissions on SB 1 ,  2 ,  3 ,  4  and  5  use rank 1, 2, 2, 1 and 3 respectively. 
         [0054]    The precoding matrix indication (PMI) and rank feedback on a subband basis can result in significant feedback overhead. For example, assuming 4-bits per subband for feeding back PMI and 2-bits per-subband for feeding back rank, then the total overhead for feedback on 5 subbands is 30 bits. For larger system bandwidths, the system needs to support a larger number of subbands resulting in even larger feedback overhead. Also, for finer granularity of PMI/rank feedback in frequency, the overhead also increases. Therefore, there is a need to improve the PMI and rank feedback mechanisms that reduces the overhead. 
         [0055]    In a first embodiment according to the principles of the present invention, a subset of the total precoding codebooks are selected and fed back to the transmitter at a given time. For example, the codebook of Table 1 can be divided into four subsets as shown in  FIG. 8 . For feedback at a given time, the UE can select either of subset  1 , subset  2 , subset  3  or subset  4 . Each subset includes four codebook entries, and each codebook entry includes four precoders, with each precoder corresponding to a transmission rank. The PMI feedback is then provided as an codebook entry index within the selected subset. 
         [0056]    An example of MIMO PMI feedback assuming feedback using codebook subset  2  is shown in  FIG. 9 . The subset  2  consists of four codebook entries having indices  4 - 7 . Also, in this example, we assumed that the UE selects rank-2 transmission over all the subbands. As the transmission rank in a 4×4 MIMO system can be either 1, 2, 3 or 4, we use 2-bits for rank indication feedback. Also, 2-bits are used to indicate one of the selected codebook subsets from a total of four subsets. As the codebook subset consists of four codebook entries, 2-bits are used for PMI indication per subband. For the case of five subbands considered in this example, the scheme results in a total of 14-bits overhead. 
         [0057]    In a second embodiment according to the principles of the present invention, the subsets have overlapping elements. As shown in  FIG. 10 , the codebook is divided into four subsets, and each subset has eight codebook entries (elements). For example, subset  1  has codebook entries having indices  0 - 7 , and subset  2  has codebook entries having indices  4 - 11 . Subset  1  and subset  2  have overlapping codebook entries  4 - 7 . 
         [0058]    In a third embodiment according to the principles of the present invention as shown in  FIG. 11 , the MIMO rank can be different in different subbands. For the case of four codebook subsets, this requires 4-bits feedback overhead per subband for PMI and rank indication. Also, 2-bits are used to indicate the codebook subset selection. This results in a total overhead of 22-bits for the case of five subbands. 
         [0059]    In a fourth embodiment according to the principles of the present invention, the codebook of Table 1 is divided into eight subsets as shown in  FIG. 12 . Each subset includes two codebook entries. For feedback at a given time, the UE can select one subset. The PMI feedback is then provided as the codebook entry index within the selected subset. 
         [0060]    An example of MIMO PMI feedback assuming feedback using codebook subset  4  from a total of eight subsets is shown in  FIG. 13 . The subset  4  consists of codebook indices  6 - 7 . Also, in this example, we assume that the UE selects rank-2 transmission over all the subbands. As the rank in a 4×4 MIMO system can be either 1, 2, 3 or 3, we use 2-bits for rank indication feedback. Also, 3-bits are used to indicate one of the selected codebook subsets from a total of 8 subsets. As each codebook subset has two codebook entries (i.e., precoders) for a fixed rank, 1-bit are used for PMI indication per subband. For the case of five subbands considered in this example, the scheme results in a total of 10-bits overhead. 
         [0061]    In a fifth embodiment according to the principles of the present invention as shown in  FIG. 14 , the codebook subset consists of a single codebook entry. This results in a total of 16-subsets. In this case, 2-bits are used for rank indication and 4-bits for codebook subset indication resulting in a total of 6-bits overhead. This is assuming that a single rank is selected for all the subbands. Note that since the subset size is just one index, there is no additional information needed to be fed back on a per subband basis. In the example of  FIG. 14 , a transmission rank of 2 and codebook subset  8  consisting of a codebook entry from the codebook with index  7  is selected for feedback. 
         [0062]    In a six embodiment according to the principles of the present invention as shown in  FIG. 15 , a wideband-PMI that is valid or good for all of the subbands plus a delta-PMI on a subband basis is provided as feedback to the transmitter. The wideband-PMI indicates the codebook entry index within the entire codebook. For each codebook entry, a set of codebook entries are defined. The relative delta-PMI indicates the PMI, i.e., the index of the codebook entry, relative to the defined set. An example of Wideband-PMI and relative delta-PMI set is shown in  FIG. 16 . In this case, for a codebook entry having a wideband-PMI index of  7 , three delta-PMI codebook entries having codebook indices of  2 ,  11  and  15  are defined. This represents a set of four codebook entries including the wideband-PMI codebook entry having an index of  7  and the three codebook entries having indices of  2 ,  11  and  15 , respectively. Then, 2-bits are required for indicating delta-PMI per subband. As shown in  FIG. 16 , four combinations can indicate one of the four elements in the set to represent delta-PMI per subband. In the example of in  FIG. 15 , SB 1 ,  2 ,  3 ,  4  and  5  use index  11 ,  7 ,  2 ,  15  and  7 , respectively. We require 2-bits for rank indication, 4-bits for wideband-PMI and 2-bits for delta-PMI per subband. This results in a total feedback overhead of 16-bits. 
         [0063]    In a seventh embodiment according to the principles of the present invention as shown in  FIG. 18 , the wideband-PMI plus delta-PMI index set is of size  2  as shown in  FIG. 17 . In this case, for a codebook entry having a wideband-PMI index of  7 , a subset consisting of a codebook entry having an index of  2  is defined. This represents a total subset size of  2  and 1-bit is required for delta-PMI per subband. In the example of  FIG. 18 , SB 1 ,  2 ,  3 ,  4  and  5  use index  7 ,  7 ,  2 ,  2  and  7  respectively. We require 2-bits for rank indication, 4-bits for wideband-PMI and 1-bit for delta-PMI per subband. This results in a total feedback overhead of 11-bits. 
         [0064]    In an eighth embodiment according to the principles of the present invention, the selected subset is indicated by a bitmap. In case of a total of 16 precoders, a bitmap having 16-bits is used as shown in  FIG. 19 . Starting from the left end of the bitmap, each bit corresponds to a precoder (i.e., a codebook entry). The bits of ‘1’ in the bitmap indicate that the corresponding precoder is part of the subset. In the example of  FIG. 19 , a subset consisting of precoders with index  2 ,  6 ,  10  and  13  is selected. The precoding feedback is then provided by picking precoders from this subset. Note that the bit map approach in this embodiment allows dynamically constructing a subset by picking any precoders for the subset. The bitmap only indicates the subset. And, separate signaling for the selected codebook entry is needed. 
         [0065]    The embodiments of the current invention are described by considering precoding feedback in the frequency-domain. The same principles can be applied for efficient precoding feedback in the time-domain as shown in  FIG. 20 . A subset is selected and delta-PMI feedback is provided for different sub frames. The principles of the current invention can further be extended to the case where delta-PMI is provided both in the frequency and time domain simultaneously. In the example of  FIG. 20 , the subset is selected from the four subsets in  FIG. 8 . 
         [0066]    In other embodiments of the current invention, the feedback granularity in the time or frequency domain, for example the subband size for PMI feedback is configured by the base station. Also, it is possible to tradeoff feedback granularity and preceding granularity. For example, preceding can be provided for a larger number of subbands with coarse precoding granularity (smaller subset size). In another example, precoding can be provided for a fewer subbands with finer preceding granularity (larger subset size). 
         [0067]    While the forgoing explanation of the principles of the present invention have been shown and described in detail in connection with the preferred embodiments, it will be apparent to those skilled in the art that modifications and variations can be made without departing from the spirit and scope of the invention as defined by the appended claims.