MIMO Detection for High Order QAM by Canonical Dual Approach

We develop a canonical dual approach for solving the MIMO problem. First, a special linear transformation is introduced to reformulate the original problem into a constrained quadratic programming problem. Then, we derive a canonical dual problem which is piecewise continuous problem with no duality gap. Under certain conditions, the canonical problem becomes a concave maximization dual problem over a convex feasible domain. By getting the stationary point of the canonical dual problem, we can find either an optimal or approximate solution of the original problem. A gradient decent algorithm is proposed to solve the MIMO problem and simulation results are provided to demonstrate the effectiveness of the method.

[1]  Zhi-Quan Luo,et al.  Performance analysis of quasi-maximum-likelihood detector based on semi-definite programming , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[2]  Joakim Jaldén,et al.  MIMO Detection by Lagrangian Dual Maximum-Likelihood Relaxation: Reinterpreting Regularized Lattice Decoding , 2014, IEEE Transactions on Signal Processing.

[3]  Giuseppe Caire,et al.  Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels , 2004, IEEE Transactions on Information Theory.

[4]  S. J. Li,et al.  On the stability of a dual weak vector variational inequality problem , 2008 .

[5]  S. Fang,et al.  Canonical dual approach to solving 0-1 quadratic programming problems , 2008 .

[6]  Layne T. Watson,et al.  Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm , 2013, Optim. Methods Softw..

[7]  Cong Ling,et al.  Decoding by embedding: Correct decoding radius and DMT optimality , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[8]  Pak-Chung Ching,et al.  A block alternating likelihood maximization approach to multiuser detection , 2004, IEEE Transactions on Signal Processing.

[9]  Cong Ling,et al.  Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding , 2010, IEEE Transactions on Information Theory.

[10]  Xiaojun Zhou,et al.  Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems , 2014, Appl. Math. Comput..

[11]  Chong-Yung Chi,et al.  The Equivalence of Semidefinite Relaxation MIMO Detectors for Higher-Order QAM , 2009, IEEE Journal of Selected Topics in Signal Processing.

[12]  Björn E. Ottersten,et al.  On the complexity of sphere decoding in digital communications , 2005, IEEE Transactions on Signal Processing.

[13]  Joakim Jaldén,et al.  Achieving a Vanishing SNR Gap to Exact Lattice Decoding at a Subexponential Complexity , 2011, IEEE Transactions on Information Theory.

[14]  Sergio Verdú,et al.  Computational complexity of optimum multiuser detection , 1989, Algorithmica.

[15]  Giuseppe Caire,et al.  On maximum-likelihood detection and the search for the closest lattice point , 2003, IEEE Trans. Inf. Theory.

[16]  Ami Wiesel,et al.  Semidefinite relaxation for detection of 16-QAM signaling in MIMO channels , 2005, IEEE Signal Processing Letters.

[17]  D. Gao.  Solutions and optimality criteria to box constrained nonconvex minimization problems , 2007 .

[18]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[19]  Dirk Wübben,et al.  Lattice Reduction , 2011, IEEE Signal Processing Magazine.

[20]  Joakim Jaldén,et al.  DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models , 2009, IEEE Transactions on Information Theory.

[21]  Vittorio Latorre,et al.  Canonical dual solutions to nonconvex radial basis neural network optimization problem , 2013, Neurocomputing.

[22]  D. Gao.  Duality Principles in Nonconvex Systems , 2000 .

[23]  P. Viswanath,et al.  Fundamentals of Wireless Communication: The wireless channel , 2005 .

[24]  Shu-Cherng Fang,et al.  Canonical dual approach to solving the maximum cut problem , 2012, J. Glob. Optim..

[25]  David Yang Gao,et al.  Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming , 2004, J. Glob. Optim..

[26]  D. Gao.  Duality Principles in Nonconvex Systems: Theory, Methods and Applications , 2000 .

[27]  Xiaofeng Wang,et al.  Semidefinite programming relaxation approach for multiuser detection of QAM signals , 2007, IEEE Transactions on Wireless Communications.

[28]  Nikos D. Sidiropoulos,et al.  A Semidefinite Relaxation Approach to MIMO Detection for High-Order QAM Constellations , 2006, IEEE Signal Processing Letters.

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

[30]  Jacob Goldberger,et al.  MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation , 2010, IEEE Transactions on Information Theory.

[31]  Shu-Cherng Fang,et al.  GLOBAL EXTREMAL CONDITIONS FOR MULTI-INTEGER QUADRATIC PROGRAMMING , 2008 .

[32]  Amir K. Khandani,et al.  On the limitations of the naive lattice decoding , 2010, IEEE Trans. Inf. Theory.