Approximate likelihood ratio detectors for linear processes

Approximately optimum detectors for problems in which either the signal or noise is a linear process are developed. An approximate expression for the characteristic function of a class of linear processes is inverted to obtain a convergent series approximation for the joint probability density. From this series, a detection algorithm is designed that is optimum when applied to the series and approximately optimum when applied to the original process. This technique is applied and evaluated in several cases that model coherent or instantaneous amplitude signal detection in reverberation noise, multipath transmission, and similar problems.