Discrete-time detection inepsilon-mixing noise

The design of detectors for known signals in non-Gaussian
\phi
-mixing noise is considered. The class of
\phi
-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 an
m
-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 optimal
\phi
-mixing detector relative to that of the detector designed under an
m
-dependent assumption is given. Extensions to the ease of detectors with memory are considered.