High Diversity Detection Using Semidefinite Relaxation

Receiver diversity is an important measure of a receivers robustness towards fading in wireless communications. For the detection of binary symbols transmitted over a general MIMO channel, the semidefinite relaxation (SDR) detector is a computationally attractive alternative to exact ML detection. In the SDR detector, the hard combinatorial optimization problem arising in the ML detector is relaxed into a simple convex optimization problem followed by component wise threshold decisions. In this work, we argue that the SDR detector will provide an increase in diversity over simpler decoder structures such as the ZF and MMSE detectors. Specifically, for the case of uncoded V-BLAST transmission over a MIMO channel with real valued i.i.d. Gaussian channel coefficients we present an analytic result stating that the SDR detector achieves the maximum possible receiver diversity.