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

[1]  Jon Feldman,et al.  Decoding turbo-like codes via linear programming , 2004, J. Comput. Syst. Sci..

[2]  Xiaodong Li,et al.  Effects of iterative detection and decoding on the performance of BLAST , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[3]  C. Tellambura,et al.  An efficient generalized sphere decoder for rank-deficient MIMO systems , 2004 .

[4]  Emmanuel J. Candès,et al.  Error correction via linear programming , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[5]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[6]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[7]  Emanuele Viterbo,et al.  A universal lattice code decoder for fading channels , 1999, IEEE Trans. Inf. Theory.

[8]  Alan A. Bertossi,et al.  A VLSI Implementation of the Simplex Algorithm , 1987, IEEE Transactions on Computers.

[9]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[10]  Tracey Ho,et al.  Polynomial Moment Relaxation for MIMO Detection , 2006, 2006 IEEE International Conference on Communications.

[11]  Chintha Tellambura,et al.  An efficient generalized sphere decoder for rank-deficient MIMO systems , 2004, IEEE 60th Vehicular Technology Conference, 2004. VTC2004-Fall. 2004.

[12]  Martin J. Wainwright,et al.  Using linear programming to Decode Binary linear codes , 2005, IEEE Transactions on Information Theory.

[13]  Wolfgang Fichtner,et al.  Performance tradeoffs in the VLSI implementation of the sphere decoding algorithm , 2004 .

[14]  B. Schutz,et al.  A VLSI-chip for a hardware-accelerator for the simplex-method , 1992, [1992] Proceedings. Fifth Annual IEEE International ASIC Conference and Exhibit.

[15]  Reinaldo A. Valenzuela,et al.  Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture , 1999 .

[16]  Bernd Sch,et al.  A Vlsi-chip-set for a Hardware-accelerator for the Simplex-method , 1992 .

[17]  Wu Li,et al.  The Linear l1 Estimator and the Huber M-Estimator , 1998, SIAM J. Optim..