TDOA estimation for cyclostationary sources: New correlations-based bounds and estimators

We consider the problem of time difference of arrival (TDOA) estimation for cyclostationary signals in additive white Gaussian noise. Classical approaches to the problem either ignore the cyclostationarity and use ordinary cross-correlations, or exploit the cyclostationarity by using cyclic cross-correlations, or combine these approaches into a multicycle approach. Despite contradicting claims in the literature regarding the performance-ranking of these approaches, there has been almost no analytical comparative performance study. We propose to regard the estimated (ordinary or cyclic) correlations as the ldquofront-endrdquo data, and based on their asymptotically Gaussian distribution, to compute the asymptotic Cramer-Rao bounds (CRB) for the various combinations (ordinary/single-cycle/multi-cycle). Using our cyclic-correlations-based CRB (termed ldquoCRBCRBrdquo), we can bound the performance of any (unbiased) estimator which exploits a given set of correlations. Moreover, we propose an approximate maximum likelihood estimator (with respect to the correlations), and show that it attains our CRBCRB asymptotically in simulations, outperforming the competitors.