Efficient Implementation of Quasi- Maximum-Likelihood Detection Based on Semidefinite Relaxation

In this paper we develop two quasi-maximum likelihood (ML) channel detectors for multiuser detection: semidefinite relaxation (SDR) detector and phase-shift-keying (PSK) detector. These detectors can deliver near-ML bit error rate (BER) performance with a polynomial worst-case complexity. The SDR detector for binary-phase-shift-keying (BPSK) constellation is based on a convex SDR, whereas the PSK detector for $M$-PSK constellations is based on a nonconvex low-rank SDR. The SDR detector is implemented using a dual-scaling interior-point method, while the PSK detector is based on a coordinate descent strategy on a feasible region homotopy. We use dynamic dimension reduction and warm start techniques to achieve signal-to-noise ratio (SNR)-sensitive improvements for both detectors. Numerical simulations of BER performance and running time indicate the effectiveness of the two quasi-ML detectors when compared to the conventional sphere decoder and its variants.