On the Linear Precoder Design for MIMO Channels with Finite-Alphabet Inputs and Statistical CSI

TL;DR

This paper develops a novel linear precoder design for MIMO channels with finite-alphabet inputs and statistical CSI, providing a lower bound, optimal structure, and an iterative algorithm that significantly improves performance.

Contribution

It derives a closed-form lower bound for average mutual information, reveals the optimal precoder structure, and proposes an effective iterative algorithm for design.

Findings

The lower bound achieves asymptotic optimality at low and high SNRs.

The proposed algorithm converges reliably and improves performance.

The new precoding method outperforms conventional approaches.

Abstract

This paper investigates the linear precoder design that maximizes the average mutual information of multiple-input multiple-output channels with finite-alphabet inputs and statistical channel state information known at the transmitter. This linear precoder design is an important open problem and is extremely difficult to solve: First, average mutual information lacks closed-form expression and involves complicated computations; Second, the optimization problem over precoder is nonconcave. This study explores the solution to this problem and provides the following contributions: 1) A closed-form lower bound of average mutual information is derived. It achieves asymptotic optimality at low and high signal-to-noise ratio regions and, with a constant shift, offers an accurate approximation to the average mutual information; 2) The optimal structure of the precoder is revealed, and a unified two-step iterative algorithm is proposed to solve this problem. Numerical examples show the convergence and the efficacy of the proposed algorithm. Compared to its conventional counterparts, the proposed linear precoding method provides a significant performance gain.