Semidefinite Programming Relaxation Based Virtually Antipodal Detection for Gray Coded 16-QAM MIMO Signalling

An efficient semidefinite programming relaxation (SDPR) based virtually antipodal (VA) detection approach is proposed for Gray coded 16-QAM signalling over multiple-input--multiple-output (MIMO) channels. The existing index-bit-based VA-SDPR (IVA-SDPR) method is incapable of making direct binary decisions concerning the individual information bits without making symbol decisions first, except for the linear natural-mapping aided rectangular QAM constellations. By contrast, our new method is capable of directly deciding on the information bits of the ubiquitous Gray-mapping aided 16-QAM by employing a strikingly simple linear matrix representation (LMR) of 4-QAM. As an appealing benefit, the conventional "signal-to-symbol-to-bits\´\´ decision process is substituted by a simpler "signal-to-bits\´\´ decision process for the classic Gray-mapping aided rectangular 16-QAM. Furthermore, when combined with low-complexity bit-flipping based "hill climbing\´\´, the proposed direct-bit-based VA-SDPR (DVA-SDPR) detector achieves the best bit-error-ratio (BER) performance among the known SDPR-based MIMO detectors in the context considered, while still maintaining a worst-case complexity order as low as O[(4N_T+1)^3.5].