On the problem of optimal signal detection in discrete-time, correlated, non-Gaussian noise

Abstract : Recent results of the detection of signals in discrete-time correlated, non-Gaussian noise in which the univariate statistics and a general covariance structure of the noise are known have been obtained. the results are predicted on the assumption that a solution to the signal detection problem based on knowledge of univariate statistics and a convariance structure is 'reasonable,' even though it is known that in general a non-Gaussian noise process is not completely specified by such information. to examine this issue of 'reasonableness,' we present two general non-Gaussian noise models that are equivalent in these assumed attributes and yet lead to fundamentally different detection structures. This difference in the detection structures indicate the signal detection problem is not adequately formulated without additional knowledge of the structure of the non-Gaussian noise process. We further present a specific radar example to quantify the difference in the detection structures.

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