Limited feedback precoding for spatial multiplexing systems

Spatial multiplexing multiple-input multiple-output (MIMO) wireless systems are of both theoretical and practical importance because they can achieve high spectral efficiencies by demultiplexing the incoming bit stream into multiple substreams. It has been shown that sending fewer substreams than the number of transmit antennas by linear precoding can provide improved error rate performance. Methods for designing linear precoders using perfect channel knowledge have previously been proposed. In many wireless systems, the assumption of complete channel knowledge is unrealistic because of the lack of forward and reverse channel reciprocity. To overcome this difficulty, we propose a precoding scheme that does not require transmit channel knowledge. The precoder is designed at the receiver and conveyed to the transmitter using a limited number of bits. The limited feedback represents an index within a finite set, or codebook, of precoding matrices. The receiver selects one of these codebook matrices using a modified version of a previously proposed full channel knowledge precoder selection criterion. A precoder codebook design method for maximizing the average effective channel power is shown to relate to chordal distance Grassmannian subspace packing. Simulation results show this technique outperforms antenna subset selection spatial multiplexing.