  In multi-input-multi-output (MIMO) detection, semidefinite relaxation (SDR)
has been shown to be an efficient high-performance approach. Developed
initially for BPSK and QPSK, SDR has been found to be capable of providing
near-optimal performance (for those constellations). This has stimulated a
number of recent research endeavors that aim to apply SDR to the high-order QAM
cases. These independently developed SDRs are different in concept and
structure, and presently no serious analysis has been given to compare these
methods. This paper analyzes the relationship of three such SDR methods, namely
the polynomial-inspired SDR (PI-SDR) by Wiesel et al., the bound-constrained
SDR (BC-SDR) by Sidiropoulos and Luo, and the virtually-antipodal SDR (VA-SDR)
by Mao et al. The result that we have proven is somehow unexpected: the three
SDRs are equivalent. Simply speaking, we show that solving any one SDR is
equivalent to solving the other SDRs. This paper also discusses some
implications arising from the SDR equivalence, and provides simulation results
to verify our theoretical findings.
