Nested Codebook Design For MIMO Precoders

In multi-input, multi-output (MIMO) communication systems, significant throughput gains can be obtained by closed-loop operation, where two aspects of the transmission are adapted to channel conditions: the transmission rank (number of independent spatial layers); and the precoding matrix which maps the spatial layers to the transmit antennas. To facilitate feedback and signaling, the precoding matrix for each rank is often restricted to a finite pre-determined codebook. Prior research has studied the problem of designing the codebook independently for each rank, with the aim of maximizing throughput gains for a given codebook size. In this paper, we propose to jointly design the family of codebooks for various transmission ranks. Our nested codebooks greatly simplify both codebook design and the selection of precoding matrix for a specific channel. In addition, we prove by analysis and simulation results that the complexity reduction is obtained without sacrificing throughput gains. Due to these advantages, the proposed structured codeboook design has been accepted for use in the 3GPP Long Term Evolution (LTE) standard [9].