Design of Bayesian signal detectors using Gaussian-mixture models

Addressed is the problem of Bayesian detector design for a signal with unknown parameters when the prior distribution of the parameters is non-Gaussian, and, possibly, the noise is non-Gaussian. An optimal detector for a Gaussian-mixture model of the parameter prior distribution is derived. A general technique for design of suboptimal Bayesian detectors with arbitrary prior distributions of the unknown parameter by means of Gaussian-mixture approximations is proposed. The technique is illustrated over an example with Rayleigh prior distribution, and the performance of the designed detector is evaluated by Monte Carlo simulation.