  We present a flexible stochastic model for a class of cooperative wireless
relay networks, in which the relay processing functionality is not known at the
destination. In addressing this problem we develop efficient algorithms to
perform relay identification in a wireless relay network. We first construct a
statistical model based on a representation of the system using Gaussian
Processes in a non-standard manner due to the way we treat the imperfect
channel state information. We then formulate the estimation problem to perform
system identification, taking into account complexity and computational
efficiency. Next we develop a set of three algorithms to solve the
identification problem each of decreasing complexity, trading-off the
estimation bias for computational efficiency. The joint optimisation problem is
tackled via a Bayesian framework using the Iterated Conditioning on the Modes
methodology. We develop a lower bound and several sub-optimal computationally
efficient solutions to the identification problem, for comparison. We
illustrate the estimation performance of our methodology for a range of widely
used relay functionalities. The relative total error attained by our algorithm
when compared to the lower bound is found to be at worst 9% for low SNR values
under all functions considered. The effect of the relay functional estimation
error is also studied via BER simulations and is shown to be less than 2dB
worse than the lower bound.
