A comparison of optimized higher order spectral detection techniques for non-Gaussian signals

Using the Gaussian noise rejection property of higher order spectra (HOS), HOS-based detectors have been proposed that outperform conventional second-order techniques in certain scenarios. Based on statistical tests proposed by Suhha Rao and Gabr (1980), as well as Hinich (1982), Kletter and Messer (1990), and Hinich and Wilson (1990), have developed similar bifrequency-domain detectors that are dependent on bispectral estimates of the observation process. Formalizing the estimate consistency requirements and the asymptotics for these detectors, we derive a new F-test statistic. We consider the detrimental effects of using spectral estimates in the denominator of Hinich´s test. We determine refined conditional distributions for third- and fourth-order versions of his detector. We also modify his test for colored scenarios. Extending the bispectral detectors to their kth-order counterparts, we calculate the optimal smoothing bandwidth to use in constructing the HOS estimates, producing the best detection performances for both our F-test and Hinich´s test with our refined distributions. These new bandwidths yield significant improvements in detector performance over previous results. For the finite sample case, our calculations characterize the tradeoff between the two detectors and demonstrate that a larger smoothing bandwidth than the one suggested by previous researchers should be used. Our calculations are verified using simulations for both white and colored cases