Embodiments of the present disclosure provide a transmitter, a receiver and methods of operating a transmitter and a receiver. In one embodiment, the transmitter is for use with NT transmit antennas and includes a precoder unit configured to precode data for transmission using a preceding matrix selected from a nested codebook, wherein the nested codebook provides codebooks corresponding to different transmission layers that are derived from column subsets of multiple NT×NT preceding matrices. The transmitter also includes a transmit unit configured to transmit the precoded data. In another embodiment, the receiver includes a receive unit configured to receive preceded data. The receiver also includes a precoder selection unit configured to select a preceding matrix from a nested codebook for the preceded data, wherein the nested codebook provides codebooks corresponding to different transmission layers that are derived from column subsets of multiple NT×NT preceding matrices.