Asymptotic receiver structures for joint maximum likelihood time delay estimation and channel identification using Gaussian signals

The problem of jointly estimating the relative time delay and the impulse response linking two received discrete-time Gaussian signals is addressed. Using two different methods, possible structures for the joint maximum-likelihood (ML) estimator are proposed, when the observation interval is long compared to both the delay to estimate and the correlation time, of the various random processes involved. These structures generalize the cross-correlation method with prefiltering that implements the ML estimation of pure time delays