In this paper we study a Markov Chain Monte Carlo (MCMC) Gibbs sampler for
solving the integer least-squares 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.Comment: To appear in Globecom 200