Vector Precoding for Wireless MIMO Systems: A Replica Analysis

We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We find that vector precoding performs much better for complex than for real alphabets. As a byproduct, we find a nonlinear precoding method with polynomial complexity that outperforms NP-hard Tomlinson-Harashima precoding for binary modulation on complex channels if the number of transmit antennas is slightly larger than twice the number of receive antennas. Index Terms Multiple-antenna wireless, multiple-input multiple-output (MIMO), spatial equalization, Tomlinson-Harashima precoding, replica method, random matrices, R-transform.