Cumulant Detector of Non-Gaussian Signals against Background of Non-Gaussian Interferences

The definition of a cumulant detector of an arbitrary order of non-Gaussian signals against the background of non-Gaussian interferences is introduced, and its sensitivity coefficient is determined. Dependencies of the sensitivity coefficient on the signal-to-interference ratio and the ratio of the cumulant coefficients of signal and interference are analyzed, and general conditions under which a cumulant detector of a given order is more sensitive than a cumulant detector of a different order are determined. In particular, the sensitivities of cumulant detectors of arbitrary orders are compared with the sensitivity of the power detector, which is the second-order cumulant detector. The validity of a cumulant detector is defined as the probability of the correct signal detection that depends on the sample size, parameters of the signal and interference distributions, and the probability of error of the first kind. The paper considers an example of the theoretical and experimental analysis of the sensitivity and reliability of the cumulant detector for the case when both the interference and the signal have Student’s distributions with different shape parameters. To experimentally verify the sensitivity and validity of the second- and fourth-order cumulant detectors, the computer simulation of the interference, signal, and their mixture was performed, and the sensitivity estimates of coefficients, the probability estimates of correct signal detection, and their relative errors were obtained.