On the performance of semidefinite relaxation MIMO detectors for QAM constellations

Due to their computational efficiency and strong empirical performance, semidefinite relaxation (SDR)-based algorithms have gained much attention in multiple-input multiple-output (MIMO) detection. In the case of a binary phase-shift keying (BPSK) constellation, the theoretical performance of the SDR approach is relatively well-understood. However, little is known about the case of quadrature amplitude modulation (QAM) constellations, although simulation results suggest that the SDR approach should work well in the low signal-to-noise ratio (SNR) region. In this paper we make a first step towards explaining such phenomenon by showing that in the case of QAM constellations, several commonly used SDR-based algorithms will provide a constant factor approximation to the optimal log-likelihood value in the low SNR region with exponentially high probability. Our result gives some theoretical justification for using SDR-based algorithms for the MIMO detection of QAM signals, at least in the low SNR region.