  The multiple-input multiple-output (MIMO) detection problem is a fundamental
problem in modern digital communications. Semidefinite relaxation (SDR) based
algorithms are a popular class of approaches to solving the problem because the
algorithms have a polynomial-time worst-case complexity and generally can
achieve a good detection error rate performance. In spite of the existence of
various different SDRs for the MIMO detection problem in the literature, very
little is known about the relationship between these SDRs. This paper aims to
fill this theoretical gap. In particular, this paper shows that two existing
SDRs for the MIMO detection problem, which take quite different forms and are
proposed by using different techniques, are equivalent. As a byproduct of the
equivalence result, the tightness of one of the above two SDRs under a
sufficient condition can be obtained.
