osed-loop MIMO schemes. The codebooks with ranks greater than one are used without transformation when the MS is operating in transformation codebook- based feedback mode. The transmit correlation matrix R is fed back to support transformation mode of codebook-based precoding. R is fed back periodically and one correlation matrix is valid for the entire band. As an example, the correlation matrix for eight transmit antennas has the following format: (10-52) 10.5 IEEE 802. 16m downlink MIMO schemes where the "*" denotes the conjugate operator. The diagonal entries of matrix R are positive and the non-diagonal entries are complex-valued. Due to the symmetry property of the correlation matrix, only the upper triangular elements need to be fed back following quantization. The R matrix is normalized by the maximum element amplitude, and then quantized to reduce the feedback overhead. The normalized diagonal elements are quantized by 1 bit and the normalized complex-valued elements are quantized by 4 bits. The total number of bits of feedback is 6 bits for two transmit antennas, 28 bits for four transmit antennas, and 120 bits for eight transmit antennas. The MS and the serving BS use the same transformation based on the correlation matrix fed back by the MS. Figure 10-39 illustrates the various distributions of the precoding vectors in multi-dimensional space. The differential feedback is a different approach to the enhancement of feedback accuracy. The differential feedback exploits the correlation between precoding matrixes adjacent in time or frequencies. It only feeds back the difference between the current and the previous beamforming matrixes. If the channel variation between two feedbacks is small, quantization codewords are concentrated in a small region on the Grassmannian manifold and not uniformly distributed over the entire beamforming space. For low-mobility users, differential feedback may improve the feedback accuracy without increasing the number of feedback bits. The feedback starts initially and rest