Convergence dynamics of an adaptive time delay estimator in multipath channel

An adaptive infinite-duration impulse response (IIR) filter for continuous tracking of multipath delay is analyzed. Although the adaptive algorithm is originally designed to eliminate a replica whose interpath delay is an integral multiple of the sampling period, it can be modified for estimating any real-valued multipath delay. Using a least mean square (LMS)-style method, the multipath gain and delay estimate are adapted explicitly and simultaneously, and the updating equations are computationally efficient. Convergence dynamics of the system parameters are given and effects of additive noise are investigated. It is proved that this technique can achieve the Cramer-Rao lower bound (CRLB) for high signal-to-noise ratio (SNR) conditions. The performance of the proposed system is evaluated by computer simulations which show that both static and nonstationary delays can be tracked satisfactorily.