 NB). The base codebook of SU-MIMO with two transmit antennas consists of rank-1 codebook C(2,1,3) and rank-2 codebook C(2,2,3). Example rank-1 and rank-2 base codebooks and their subset codebooks are shown in Table 10-27. The base codebook for MU-MIMO is the same as the rank-1 base codebook for SU-MIMO. The base codebooks and their rank-1 subsets for SU-MIMO and MU-MIMO can be transformed as a function of the BS transmit correlation matrix. The N X N transmit correlation matrix R = E{H#Hij} is quantized and fed back to the serving BS with longer period than PMI, where Hij denotes the correlated channel matrix corresponding to the ith OFDM symbol and the jth sub-carrier. The transmit correlation matrix R contains the averaged directions for beamforming. The transform codebook improves the performance in highly correlated channels, with non-calibrated antenna arrays, and with cross-polarized antennas. For the transformation mode, the PMI feedback from a mobile station represents an entry of the transformed base codebook according to long-term channel infor- mation. In transformation mode, both the BS and MS transform the rank-1 base codebook to a rank-1 transformed codebook using the correlation matrix. The transformation for codewords of rank-1 codebook is defined as follows: (10-51) Where Vi and Ui are the ith codeword of the base and the transformed codebook, respectively. Once the transformed codebook is calculated, both the MS and the serving BS use the transformed codebook for CHAPTER 10 The IEEE 802. 16m Physical Layer (Part II) Table 10-27 Example Base Code and Subset Codebooks [2] C(2,1,3,m) [C1,C2] Base Codebook Codebook Index C(2,1,3) 0.7071 -0.7071 0.7071 -0.5000 -0.5000i 0.7071 -0.7071i 0.7071 0.5000 -0.5000i 0.7071 0.7071 0.7071 0.5000 +0.5000i 0.7071 0.7071i 0.7071 -0.5000 +0.5000i C(2,2,3) C(2,2,3,m) = 0.7071 -0.7071 0.7071 0.7071 0.7071 -0.5000 -0.5000i 0.7071 0.5000 + 0.5000i 0.7071 -0.7071i 0.7071 0.7071i 0.7071 0.5000 -0.5000i 0.7071 -0.5000 + 0.5000i 100~111 feedback and precoding of rank-1 cl