Tightness of a new and enhanced semidefinite relaxation for MIMO detection

TL;DR

This paper introduces an enhanced semidefinite relaxation for MIMO detection, demonstrating its tightness under certain noise conditions and outperforming conventional methods in reducing the relaxation gap.

Contribution

The paper proposes a new enhanced SDR for MIMO detection and proves its tightness under specific noise thresholds, addressing an open question in the field.

Findings

Enhanced SDR is tight under low noise levels.

Proposed SDR outperforms conventional SDR in relaxation gap.

Addresses an open problem in MIMO detection theory.

Abstract

In this paper, we consider a fundamental problem in modern digital communications known as multi-input multi-output (MIMO) detection, which can be formulated as a complex quadratic programming problem subject to unit-modulus and discrete argument constraints. Various semidefinite relaxation (SDR) based algorithms have been proposed to solve the problem in the literature. In this paper, we first show that the conventional SDR is generally not tight for the problem. Then, we propose a new and enhanced SDR and show its tightness under an easily checkable condition, which essentially requires the level of the noise to be below a certain threshold. The above results have answered an open question posed by So in [35]. Numerical simulation results show that our proposed SDR significantly outperforms the conventional SDR in terms of the relaxation gap.