Suboptimal Detection of Non-Gaussian Signals by Third-Order Spectral Analysis

The most common method for detecting an unknown random stationary signal in Gaussian noise is to perform a likelihood ratio test on the spectrum of the received signal (energy detection). If the signal happens to be Gaussian, this method is optimal. For a non-Gaussian signal, however, this method is only suboptimal, having poor performance when the signal-to-noise ratio (SNR) is small. In this paper we suggest the use of higher order spectra (HOS) for improving detection performance in the non-Gaussian case. The new method is composed of two stages. First, the higher order spectra of the received signal is estimated using conventional spectral estimation techniques; then, a (maximum) likelihood ratio test (LRT) is performed in the higher order spectra domain. It is shown that, under certain low SNR conditions, the HOS-based method performs much better than the conventional energy one. The required processor is derived and its performance is analyzed. The new method is demonstrated using the third-order spectrum (called bispectrum), although it can easily be extended to higher order analysis (e.g., trispectrum, etc.).