Applying Metropolis-Hastings-within-Gibbs algorithms for data detection in relay-based communication systems

When a Markov Chain Monte Carlo (MCMC) method is applied to solve signal-processing problems, it is commonly implemented using Gibbs sampler. The implementation of Gibbs sampler requires the availability of full conditional probability density functions (pdfs) of all the parameters of interest of a problem. For some problems, however, the full conditional pdfs of all the parameters of interest are not readily available. In such cases, Metropolis-Hastings method can be incorporated within a Gibbs sampler to draw samples from the parameters whose full conditional pdf cannot be analytically determined. This paper demonstrates the application of such an algorithm, known as Metropolis-Hastings-within Gibbs, by considering the problem of joint data detection and channel estimation of a single-hop relay-based communication system. By formulating the signal model of the transmission process in alternative ways, we develop two algorithms for the problem. Moreover, simulation results of the two algorithms are provided to illustrate their effectiveness.