Detection of non-Gaussian signals by frequency domain Kurtosis estimation

The detection of signals by power spectrum density (PSD) estimation is a well known and often employed method. The PSD estimate is essentially a second order measure which is not sensitive to the statistical nature of the signals. For non-Gaussian signals, a frequency domain Kurtosis (FDK) estimate supplements the PSD estimate and in some cases of practical importance is superior as a detection statistic. Non-Gaussian signals occur in underwater acoustics due to multipath and frequency modulation effects. Specifically, we have considered sinusoidal and narrowband Gaussian signals which, when propagated through fading or multipath environments, are received as non-Gaussian in terms of a frequency domain Kurtosis estimate. The environment is modeled by introducing amplitude probability density distributions which are due to the fading or multipath conditions. Several distributions were considered previously which included Rayleigh and log-normal, both of which have been experimentally verified to exist in the ocean. The asymptotic probability of detection for a randomly occurring signal is derived for the PSD and FDK. A simulation comparing the probability of detection for the FDK and PSD is also included.