Markov chain Monte Carlo algorithms for CDMA and MIMO communication systems

In this paper, we develop novel Bayesian detection methods that are applicable to both synchronous code-division multiple-access and multiple-input multiple-output communication systems. Markov chain Monte Carlo (MCMC) simulation techniques are used to obtain Bayesian estimates (soft information) of the transmitted symbols. Unlike previous reports that widely use statistical inference to estimate a posteriori probability (APP) values, we present alternative statistical methods that are developed by viewing the underlying problem as a multidimensional Monte Carlo integration. We show that this approach leads to results that are similar to those that would be obtained through a proper Rao-Blackwellization technique and thus conclude that our proposed methods are superior to those reported in the literature. We also note that when the channel signal-to-noise ratio is high, MCMC simulator experiences some very slow modes of convergence. Thus accurate estimation of APP values requires simulations of very long Markov chains, which may be infeasible in practice. We propose two solutions to this problem using the theory of importance sampling. Extensive computer simulations show that both solutions improve the system performance greatly. We also compare the proposed MCMC detection algorithms with the sphere decoding and minimum mean square error turbo detectors and show that the MCMC detectors have superior performance.