h open-loop SU-MIMO and open-loop MU-MIMO modes. For non-adaptive precoding on a given sub-carrier k, the matrix Wk is selected from a predefined base codebook or from a subset of the base codebook for a given rank. There are three types of codebooks and their associated feedback modes for adaptive precoding, defined in the IEEE 802.16m, as follows: 1. The base codebook mode where the PMI feedback from an MS is indicative of an entry in the base codebook that is used by the serving BS to determine a new precoder. 2. The transformation codebook mode where the PMI feedback from an MS represents an entry in the transformed base codebook according to long-term channel information. 3. The differential codebook mode where the PMI feedback from an MS provides an entry in the differential codebook or an entry in the base codebook on PMI reset time. The feedback from an MS provides a differential knowledge of the short-term channel information. This feedback represents information that is used along with other feedback information known at the BS for determining a new precoder. The base codebook for two transmit antennas comprises either a 3-bit codebook for adaptive precoding or a codebook subset for non-adaptive precoding. For four transmit antennas, the base codebook consists of either a 6-bit codebook or a 4-bit codebook which is a subset of the 6-bit codebook when using adaptive precoding, and a codebook subset when non-adaptive precoding is used. The base codebook for eight transmit antennas is formed from either a 4-bit codebook for adaptive precoding or a codebook subset for non-adaptive precoding. The mobile stations are required to support the base and transformation modes and may optionally support the differential mode. The transformation and differential feedback modes are applied to the base codebook or to a subset of the base codebook. In order to provide additional spatial diversity, the precoding coefficients Wk change every uP SC sub- carriers and every V sub-frames where the values of and V depend on th