1. A transmitter for use with multiple transmit antennas, comprising: a precoder unit configured to precode data for transmission using a precoding matrix selected from a codebook, corresponding to different transmission layers, wherein the codebook is derived from column subsets of multiple N by N precoding matrices, wherein N is the number of transmit antennas, wherein each of said precoding matrices is derived from the Householder transformation of a length N constant modulus vector; and a transmit unit configured to transmit the precoded data.