Bayesian Symbol Detection in Wireless Relay Networks via Likelihood-Free Inference

This paper presents a general stochastic model developed for a class of cooperative wireless relay networks, in which imperfect knowledge of the channel state information at the destination node is assumed. The framework incorporates multiple relay nodes operating under general known nonlinear processing functions. When a nonlinear relay function is considered, the likelihood function is generally intractable resulting in the maximum likelihood and the maximum a posteriori detectors not admitting closed form solutions. We illustrate our methodology to overcome this intractability under the example of a popular optimal nonlinear relay function choice and demonstrate how our algorithms are capable of solving the previously intractable detection problem. Overcoming this intractability involves development of specialized Bayesian models. We develop three novel algorithms to perform detection for this Bayesian model, these include a Markov chain Monte Carlo approximate Bayesian computation (MCMC-ABC) approach; an auxiliary variable MCMC (MCMC-AV) approach; and a suboptimal exhaustive search zero forcing (SES-ZF) approach. Finally, numerical examples comparing the symbol error rate (SER) performance versus signal-to-noise ratio (SNR) of the three detection algorithms are studied in simulated examples.