Analysis of semidefinite programming relaxation approach for m aximum likelihood MIMO detection

Many signal processing applications reduce to solving integer least square problems, e.g., Maximum Likelihood (ML) detection, which is NP-hard. Recently semidefinite programming (SDP) approach has been shown to be promising approach to combinatorial problems. SDP methods have been applied to the communications problem, e.g., [1], [2], [3]. But so far no theoretical analysis of the algorithm is shown and the evaluation of the SDP approach for detection is based only on simulation results. In this paper, we theoretically evaluate bounds for the SDP approach. We also establish relationship between the exact maximum/minimum value of the objective function to the SDP relaxed (approximate) maximum/minimum value of the objective function.