Lm. Garth et Y. Bresler, A COMPARISON OF OPTIMIZED HIGHER-ORDER SPECTRAL DETECTION TECHNIQUES FOR NON-GAUSSIAN SIGNALS, IEEE transactions on signal processing, 44(5), 1996, pp. 1198-1213
Using the Gaussian noise rejection property of higher order spectra (H
OS), HOS-based detectors have been proposed that outperform convention
al second-order techniques in certain scenarios. Based on statistical
tests proposed by Subba Rao and Gabr, as well as Hinich, recently, Kle
tter and Messer, and Hinich and Wilson, have developed similar bifrequ
ency-domain detectors that are dependent on bispectral estimates of th
e observation process. Formalizing the estimate consistency requiremen
ts and the asymptotics for these detectors, we derive a new F-test sta
tistic. We consider the detrimental effects of using spectral estimate
s in the denominator of Hinich's test. We determine refined conditiona
l distributions for third- and fourth-order versions of his detector.
We also modify his test for colored scenarios, Extending the bispectra
l detectors to their kth-order counterparts, we calculate the optimal
smoothing bandwidth to use in constructing the HOS estimates, producin
g the best detection performances for both our F-test and Hinich's tes
t with our refined distributions. These new bandwidths yield significa
nt improvements in detector performance over previous results. For the
finite sample case, our calculations characterize the tradeoff betwee
n the two detectors and demonstrate that a larger smoothing bandwidth
than the one suggested by previous researchers should be used. Our cal
culations are verified using simulations for both white and colored ca
ses.