Detection of Unknown Signals Under Complex Elliptically Symmetric Distributions

Detection of unknown signals is considered under complex elliptically symmetric (CES) distributions, a wide family that includes several well-known distributions as special cases. We study the detection problem for unknown deterministic signals and random CES signals, both corrupted by CES noise. For detection of unknown deterministic signals, we form the generalized likelihood ratio test and reduce it to a sufficient test statistic, which is either the norm of the received vector or a function of it. Performance analysis is provided under both known and estimated noise scatter matrix. For detection of random CES signals, we form the likelihood ratio test, provide performance analysis, and establish conditions under which the sufficient test statistic is given by the norm of the received vector. Interestingly, this norm test statistic is proven to be the uniformly most powerful test for the detection of all CES distributed signals.

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