andard base codebook adheres to this input distribution and thereby has a good performance. In contrast, the DFT codebook suffers from the constant modulus constraint that requires all vector entries to have the same magnitude. Although more than two codewords exist, the DFT codebook only has two valid codewords, in this case as shown by the two clusters at 45° and -45° on the semicircle. This leaves large uncovered areas in the quantization space and causes large quantization errors for input vectors around [1,0]" and [0,1]t. On the other hand, for highly correlated channels, the entry magnitudes of the input beamforming vector are close, due to the high correlation of the channel responses. The DFT codewords with constant modulus entries match to the input distribution that has close entry magnitudes and thus has a good performance. Note that there are two clusters of the DFT codewords and only one of them is used for each correlated scenario. Since the other cluster is too far away from the input vector, it is not used. This is the drawback of the DFT codebook because it only exploits rough information about the magnitude similarity. In contrast, the transformed codebook makes use of both the magnitude and phase information about the antenna correlation. The uniform codewords of the IEEE 802.16-2009 standard base codebook are dynam- ically transformed to only one cluster pointing to one direction, as shown on the right side of Figure 10-39. As the correlation diminishes, the codeword concentration of the transformed code- book decreases and the codebook becomes similar to the legacy base codebook for uncorrelated channels. The link-level performance of some closed-loop SU-MIMO rate-1 codebooks with high-correla- tion (i.e., closely-spaced antennas and small angle spread) and low-correlation have been compared and are shown in Figures 10-41 and 10-42. The channel model is the modified ITU PedB 3 km/h. There are four transmit-antennas at the BS and two receive antennas at the MS. The antenna spacing of BS transm