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

TL;DR

This paper introduces Bayesian inference methods for symbol detection in wireless relay networks with intractable likelihood functions, demonstrating improved detection algorithms through simulation.

Contribution

The paper develops three novel Bayesian algorithms to address intractable likelihoods in non-linear relay network detection, advancing the state-of-the-art in wireless communication inference.

Findings

MCMC-ABC achieves accurate detection performance.

MCMC-AV provides a computationally efficient alternative.

SES-ZF offers a suboptimal but fast detection method.

Abstract

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 non-linear processing functions. When a non-linear 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 non-linear relay function choice and demonstrate how our algorithms are capable of solving the previously intractable detection problem. Overcoming this intractability involves development of specialised 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.