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Discrete-time detection in \epsilon -mixing noise

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2 Author(s)

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.

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Information Theory, IEEE Transactions on  (Volume:26 ,  Issue: 2 )