Particular codebook entries used for a MIMO system of a lower dimension (i.e., having a relatively low number of antennas) can be used to generate a codebook for a MIMO system of a higher dimension (i.e., having a relatively high number of antennas). The entries in rank 1 of the codebook related to the MIMO system having four transmit antennas are used to newly construct entries for rank 1 through rank 8 of two base matrices for a MIMO base codebook related to eight transmit antennas.