Detection Of A Non-gaussian Signal In Gaussian Noise Using High-order Spectral Analysis

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Abstract
The most general solution to the classical problem of detecting a random signal in additive noise is known to be achieved by performing a likelihood ratio test (LRT) on the received data. When the signal and noise processes are both (stationary) Gaussian, the LRT processor is the simple, well-known, power spectrum based detector. With a non-Gaussian signal, however, the LRT processor becomes extremely complex and therefore is rarely considered to be a practical solution. In this paper we propose the use of higher-order spectra (HOS) for improving (relative to the power spectrum detector) the detection performance in the general non-Gaussian case. The idea is to alw 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 would clearly indicate that a signal is present. The resulting processor corrs;sts 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 all detectors outputs. The new method is demonstrated using the third-order spectra (called bispectrum), aMrough 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 also have a significantly better performance. 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.

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