  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.
