The Equivalence of Semidefinite Relaxation MIMO Detectors for Higher-Order QAM

TL;DR

This paper proves that three different semidefinite relaxation methods for MIMO detection with higher-order QAM are mathematically equivalent, unifying their theoretical understanding and implications.

Contribution

It establishes the equivalence of three distinct SDR methods for high-order QAM MIMO detection, clarifying their relationship and simplifying future research.

Findings

The three SDR methods are mathematically equivalent.

Solving any one SDR yields solutions for all three methods.

Simulation results confirm the theoretical equivalence.

Abstract

In multi-input-multi-output (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient high-performance approach. Developed initially for BPSK and QPSK, SDR has been found to be capable of providing near-optimal performance (for those constellations). This has stimulated a number of recent research endeavors that aim to apply SDR to the high-order QAM cases. These independently developed SDRs are different in concept and structure, and presently no serious analysis has been given to compare these methods. This paper analyzes the relationship of three such SDR methods, namely the polynomial-inspired SDR (PI-SDR) by Wiesel et al., the bound-constrained SDR (BC-SDR) by Sidiropoulos and Luo, and the virtually-antipodal SDR (VA-SDR) by Mao et al. The result that we have proven is somehow unexpected: the three SDRs are equivalent. Simply speaking, we show that solving any one SDR is equivalent to solving the other SDRs. This paper also discusses some implications arising from the SDR equivalence, and provides simulation results to verify our theoretical findings.