Detection of a non-Gaussian signal in Gaussian noise using high-order spectral analysis

The use of higher-order spectra (HOS) is proposed for improving (relative to the power spectrum detector) the detection performance in the general non-Gaussian case. The idea is to detect the high-order spectral content of the received signal (HOS domain detection). Under the assumption that the additive noise is Gaussian, the presence of such high HOS content clearly indicates that a signal is present. The resulting processor consists of the HOS domain detector in parallel with the conventional power spectrum detector. The final decision whether the signal is present or not is based on the outputs of all the detectors. The method is demonstrated using the third-order spectra (called bispectrum), although it can be extended to higher-order analysis (e.g., trispectrum, etc.). The performance of the above processor is analyzed, and it is shown that it always performs at least as well as the conventional power spectrum detector. Under certain conditions on the signal, it can perform significantly better. The resulting performance improvement is most impressive in detecting non-Gaussian weak signals in a heavy noise environment. Such improvement is analytically demonstrated for a spectrally and bispectrally flat bandlimited signal.