A Near-Maximum-Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In multiple-input multiple-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an <emphasis><formula formulatype="inline"><tex>N</tex></formula></emphasis>-dimensional complex space. In general, this problem is known to be NP-hard. In this paper, a quasi-ML algorithm based on semi-definite programming (SDP) is proposed. We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems. </para>