Semidefinite relaxation (SDR) is a suboptimal but computationally e±cient approach to maximum-likelihood (ML) MIMO detection, the latter of which is computationally very
hard especially for large problem sizes. SDR was first developed for the BPSK and QPSK cases, in which simulations have indicated that SDR can yield near-optimal performance.
Recently, a number of research endeavors have focused on extending SDR to the case of higher-order QAM. This paper reports some useful results on this problem. First, we show that three of the existing SDR methods, known as polynomial-inspired SDR (PI-SDR), bound-constrained SDR (BC-SDR), and virtually-antipodal SDR (VA-SDR), are equivalent for 16-QAM, then extend the result to higher-order QAM constellations. Second, we investigate the relationship between Mobasher's SDRs and tightened bound-constrained SDR (TBC-SDR) for 16-QAM constellation. Finally, we develop a specialized interior-point algorithm for the implementation of BC-SDR. The proposed algorithm is computationally efficient exploiting the BC-SDR structures, and enables us to handle larger problem sizes in practice.

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