Novel constrained algorithm for delay estimation in the presence of mulitpath transmissions

A delayed version of a bandlimited signal can be represented by convolving a sinc function and the signal itself. By using this property, a novel constrained LMS algorithm that estimates the difference in arrival times of signal at two spatially separated receivers with multipath propagations is developed. The new model consists of two adaptive FIR filters to compensate the multipath effect in each channel and a third adaptive FIR filter to act as a delay estimator. With constraints, all filter coefficients are expressed in terms of the derived time delay as well as the multipath parameters. The error surface is multimodal and proper initialization is required to give good estimation of the system variables. Derivation of the proposed algorithm is given and simulations are included to demonstrate the effectiveness and validity of the algorithm.