Resolution of overlapping Doppler shifted echoes

This paper considers the problem of estimating the time delays and Doppler shifts of a known waveform received via several distinct paths by an array of antennas. The general maximum likelihood estimator is presented, and is shown to require a 2d-dimensional non-linear minimization, where d is the number of received signal reflections. Two alternative solutions based on signal and noise subspace fitting are proposed, requiring only a d-dimensional minimization. In particular, we show how to decouple the required search into a two-step procedure, where the delays are estimated and the Dopplers solved for explicitly. Initial conditions for the time delay search can be obtained by applying generalizations of the MUSIC and ESPRIT algorithms