On the asymptotic performance of time-delay and Doppler estimation with a carrier modulated by a band-limited signal

Time-delay and Doppler estimation is crucial in various engineering fields, being the estimation of these parameters one of the key initial step in the receiver's operational sequence. Due to its importance, several expressions of the CRB and MLE have been derived over the years. However, in all these previous works, it is assumed the wave transmission process introduces an unknown phase which prevents from estimating both time-delay and transmission phase component. In this contribution we revisit this problem under the condition that there are certain practical problems where the transmission phase can be estimated apart, adding this additional measure to the observation model. Then, we rederive a novel MLE under this condition and we provide closed-form expression of the achievable MSE of time-delay and Doppler estimation in the asymptotic region under the band-limited signal condition. Both expression are validated via Monte Carlo simulations. This analysis uncovers five operational regions, refining existing knowledge and providing valuable insights into time-delay estimation theory