Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO

TL;DR

This paper analyzes the symbol error rate of the Box-relaxation optimization decoder in massive MIMO systems, providing exact asymptotic formulas and insights into its performance relative to bounds and other decoders.

Contribution

It derives exact asymptotic SER expressions for the BRO decoder in massive MIMO, revealing its near-optimal performance and independence of errors.

Findings

BRO achieves SER within 3dB of the matched-filter bound.

SER approaches the MFB as antennas increase.

Error events for fixed symbols are asymptotically independent.

Abstract

The maximum-likelihood (ML) decoder for symbol detection in large multiple-input multiple-output wireless communication systems is typically computationally prohibitive. In this paper, we study a popular and practical alternative, namely the Box-relaxation optimization (BRO) decoder, which is a natural convex relaxation of the ML. For iid real Gaussian channels with additive Gaussian noise, we obtain exact asymptotic expressions for the symbol error rate (SER) of the BRO. The formulas are particularly simple, they yield useful insights, and they allow accurate comparisons to the matched-filter bound (MFB) and to the zero-forcing decoder. For BPSK signals the SER performance of the BRO is within 3dB of the MFB for square systems, and it approaches the MFB as the number of receive antennas grows large compared to the number of transmit antennas. Our analysis further characterizes the empirical density function of the solution of the BRO, and shows that error events for any fixed number of symbols are asymptotically independent. The fundamental tool behind the analysis is the convex Gaussian min-max theorem.