  In this paper, we consider a fundamental problem in modern digital
communications known as multi-input multi-output (MIMO) detection, which can be
formulated as a complex quadratic programming problem subject to unit-modulus
and discrete argument constraints. Various semidefinite relaxation (SDR) based
algorithms have been proposed to solve the problem in the literature. In this
paper, we first show that the conventional SDR is generally not tight for the
problem. Then, we propose a new and enhanced SDR and show its tightness under
an easily checkable condition, which essentially requires the level of the
noise to be below a certain threshold. The above results have answered an open
question posed by So in [35]. Numerical simulation results show that our
proposed SDR significantly outperforms the conventional SDR in terms of the
relaxation gap.
