Linear Programming Detection and Decoding for MIMO Systems

We develop an efficient linear programming detector (LPD) for multiple-input multiple-output (MIMO) systems. Instead of using the usual l₂ norm, our proposed LPD uses the l₁ norm as the detection metric, resulting in a mixed-integer linear program (MILP). Two branch-and-bound algorithms are proposed to solve the MILP. The solution of the MILP achieves the same full diversity order as the maximum likelihood detector. The MILP is further relaxed to a linear program (LP), which can be readily solved using the standard simplex method. We show that in some cases the solution of the LP is guaranteed to be that of the MILP. The LPD is also extended to the joint detection and decoding of linear block coded MIMO systems. Our LPD can be immediately implemented using mature circuits design for the simplex algorithm