The role of third order spectrum in maximum likelihood time delay estimation of a random multi-tone signal in noise

The authors present the maximum-likelihood (ML) time-delay estimator (TDE) for a special class of non-Gaussian signals, when the radiated signal is a harmonically related random multitone signal. For this case they show that when the signal has a nonzero bispectrum (i.e. in the case of phase coupling), the ML TDE consists of the noncoherent estimator plus an extra processor that is, at least for low SNR, directly related to the signal bispectrum. The performance of the TDE is analyzed by using the Cramer-Rao lower bound, and it is shown that the improved processor is superior