Detection of non-Gaussian signals using integrated polyspectrum

We consider the problem of detecting an unknown, random, stationary, non-Gaussian signal in Gaussian noise of unknown correlation structure. The same framework applies if one desires to determine whether the given random signal is non-Gaussian. The most commonly used method for detection of random signals is the so-called energy detector, which cannot distinguish between Gaussian and non-Gaussian signals and requires the knowledge of the noise power. Recently, the use of bispectrum and/or trispectrum of the signal has been suggested for detection of non-Gaussian signals. The higher order spectra-based detectors do not require the knowledge of the noise statistics if the noise is Gaussian. In this paper, we suggest the use of an integrated polyspectrum (bispectrum of trispectrum) to improve computational efficiency of the detectors based on polyspectrum and to possibly further enhance their detection performance. We investigate conditions under which use of the integrated polyspectrum is appropriate. The detector structure is derived, acid its performance is evaluated via simulations and comparisons with several other existing approaches