Vector Precoding for Wireless MIMO Systems: A Replica Analysis

TL;DR

This paper uses the replica method to analyze vector precoding in wireless MIMO systems, revealing its advantages over traditional methods and proposing a new nonlinear precoding technique with polynomial complexity.

Contribution

It introduces a replica analysis framework for vector precoding applicable to general channel matrices and proposes a new nonlinear precoding method outperforming existing NP-hard solutions.

Findings

Vector precoding performs better with complex alphabets.

The proposed nonlinear precoding outperforms NP-hard Tomlinson-Harashima precoding.

Performance improves when transmit antennas are slightly more than twice the receive antennas.

Abstract

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.