Near-Optimal Detection in MIMO Systems Using Gibbs Sampling

In this paper we study a Markov Chain Monte Carlo (MCMC) Gibbs sampler for solving the integer leastsquares problem. In digital communication the problem is equivalent to performing Maximum Likelihood (ML) detection in Multiple-Input Multiple-Output (MIMO) systems. While the use of MCMC methods for such problems has already been proposed, our method is novel in that we optimize the "temperature" parameter so that in steady state, i.e. after the Markov chain has mixed, there is only polynomially (rather than exponentially) small probability of encountering the optimal solution. More precisely, we obtain the largest value of the temperature parameter for this to occur, since the higher the temperature, the faster the mixing. This is in contrast to simulated annealing techniques where, rather than being held fixed, the temperature parameter is tended to zero. Simulations suggest that the resulting Gibbs sampler provides a computationally efficient way of achieving approximative ML detection in MIMO systems having a huge number of transmit and receive dimensions. In fact, they further suggest that the Markov chain is rapidly mixing. Thus, it has been observed that even in cases were ML detection using, e.g. sphere decoding becomes infeasible, the Gibbs sampler can still offer a near-optimal solution using much less computations.

[1]  Babak Hassibi,et al.  On the sphere-decoding algorithm II. Generalizations, second-order statistics, and applications to communications , 2005, IEEE Transactions on Signal Processing.

[2]  Alexander Vardy,et al.  Closest point search in lattices , 2002, IEEE Trans. Inf. Theory.

[3]  Olle Häggström Finite Markov Chains and Algorithmic Applications , 2002 .

[4]  H. Vincent Poor,et al.  Wireless Communication Systems: Advanced Techniques for Signal Reception , 2003 .

[5]  Behrouz Farhang-Boroujeny,et al.  Implementation of a Markov Chain Monte Carlo Based Multiuser/MIMO Detector , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[7]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[8]  Haidong Zhu,et al.  Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems , 2006, IEEE Transactions on Signal Processing.

[9]  Babak Hassibi,et al.  On the sphere-decoding algorithm I. Expected complexity , 2005, IEEE Transactions on Signal Processing.

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

[11]  Haidong Zhu,et al.  On performance of sphere decoding and Markov chain Monte Carlo detection methods , 2005, IEEE Signal Processing Letters.

[12]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[13]  Rong Chen,et al.  Convergence analyses and comparisons of Markov chain Monte Carlo algorithms in digital communications , 2002, IEEE Trans. Signal Process..

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

[15]  Stephan ten Brink,et al.  Achieving near-capacity on a multiple-antenna channel , 2003, IEEE Trans. Commun..