Discrete-time detection inepsilon-mixing noise

The design of detectors for known signals in non-Gaussianφ-mixing noise is considered. The class ofφ-mixing processes considered is seen to be quite general and allows flexible modeling of a variety of dependent noises. Applying the criterion of asymptotic relative efficiency, the design of the optimal memoryless detector is specified and is seen to depend only on second-order statistical knowledge of the noise. It is then shown that in many cases this design reduces to approximating the noise process with anm-dependent process, finding the corresponding nonlinearity as a solution to a Fredholm integral equation of the second kind, and obtaining the optimal nonlinearity through a limiting process. In addition, conditions are given for the existence of a unique optimal nonlinearity. A bound on the performance of the optimalφ-mixing detector relative to that of the detector designed under anm-dependent assumption is given. Extensions to the ease of detectors with memory are considered.