Two-channel likelihood detectors for arbitrary linear channel distortion

This paper derives likelihood and generalized likelihood detection test statistics for a set of two-channel problems. This set includes additive Gaussian and non-Gaussian noise, known signals, signals with unknown deterministic parameters, signals with unknown statistical parameters, and signals completely unknown. The set also includes arbitrary linear channel distortion, which is a generalization of time delay, frequency shift, and multipath. Simple expressions are obtained for the test statistic in the weak signal limit for additive non-Gaussian noise. The ambiguity function is derived under the assumption of white Gaussian noise with the signal completely unknown. Generalizations of the ambiguity function are derived and are used to construct detection statistics for other signal problems.