Large System Analysis of Box-Relaxation in Correlated Massive MIMO Systems Under Imperfect CSI (Extended Version)

TL;DR

This paper analyzes the performance of box-relaxation decoding in massive MIMO systems with imperfect CSI and correlated channels, providing asymptotic approximations for MSE and BER and proposing optimal power allocation schemes.

Contribution

It offers the first large-system analysis of box-relaxation in correlated massive MIMO with imperfect CSI, including asymptotic performance metrics and power optimization.

Findings

Asymptotic MSE and BER approximations are accurate for small system sizes.

Optimal power allocation schemes improve performance.

Box constraint mitigates double descent phenomenon.

Abstract

In this paper, we study the mean square error (MSE) and the bit error rate (BER) performance of the box-relaxation decoder in massive multiple-input-multiple-output (MIMO) systems under the assumptions of imperfect channel state information (CSI) and receive-side channel correlation. Our analysis assumes that the number of transmit and receive antennas ($n$,and $m$) grow simultaneously large while their ratio remains fixed. For simplicity of the analysis, we consider binary phase shift keying (BPSK) modulated signals. The asymptotic approximations of the MSE and BER enable us to derive the optimal power allocation scheme under MSE/BER minimization. Numerical simulations suggest that the asymptotic approximations are accurate even for small $n$ and $m$. They also show the important role of the box constraint in mitigating the so called double descent phenomenon.