On detection with a class of matched filters and higher-order statistics

The authors of an earlier paper (G.B. Giannakis and M.K. Tsatsanis, IEEE Trans. Acoust. Speech Signal Process, vol.38, no.7, p.1284-1990). Propose examining the zero-th lag of the higher-order (>2) cumulant of the output of a matched filter for detection. This approach exploits the desirable properties of cumulants including their insensitivity to additive colored Gaussian noise of unknown covariance. A binary hypothesis test is formulated which chooses between two Gaussian distributions which arise from the asymptotic cumulant estimator's behavior. The detection results of the earlier paper are extended to a class of filters which include the matched filter, phase-only matched filters, and inverse filters.<>