An MCMC-MIMO Detector as a Stochastic Linear System Solver Using Successive Overrelexation

In this paper, we consider a Markov chain Monte Carlo (MCMC) algorithm using Gibbs sampling for signal detection in multiple input multiple output (MIMO) or code division multiple access (CDMA) systems. It is shown that the MCMC detector can be seen as a stochastic linear system solver. Based on this point of view, we generalize the MCMC detector using a relaxation factor that can improve the convergence rate. For the MCMC detector, since a faster convergence rate implies a lower computational complexity, it is important to have a faster convergence rate especially for large MIMO systems, which can also be achieved by optimizing the temperature parameter. While the optimal temperature parameter heavily depends on the signal-to-noise ratio (SNR), it is shown that a good relaxation factor can be found for wide range of the SNR and other parameters.