Maximum likelihood estimates of the time and frequency differences of arrival of weak cyclostationary digital communications signals

Algorithms for the asymptotic weak-signal maximum-likelihood estimates (MLE) of the time and frequency differences of arrival of digital communications signals are presented. Results from Monte Carlo simulations with BPSK signals indicate the new algorithms outperform traditional techniques like the generalized cross correlation function and the complex ambiguity function when the signal-to-interference-and-noise ratio falls significantly below 0 dB. The performance of the MLEs exceeds the Cramer-Rao lower bounds on the variance of these estimates for stationary signal models in some instances as well