Separating multipaths by global optimization of a multidimensional matched filter

A transmitted signal can arrive at a receiver via several refracted Fermat paths. If the paths are independent in the Fresnel sense, then the received signal can be modeled as the sum of amplitude scaled and time shifted copies of a predetermined replica plus white noise. We present an algorithm that uses the replica to determine the time shifts and amplitudes for each path. It is referred to as an n-dimensional matched filter algorithm by analogy with the well-known matched filter algorithm. The cross correlation between the received signal and the replica oscillates near the center frequency of the transmitted signal. This causes the n-dimensional matched filter output to have many local maxima that are not globally optimal. The time shifts and amplitude scalings for the Fermat paths are determined by maximizing the output of the n-dimensional matched filter. The algorithm is more robust and efficient than others currently available. Simulated realizations of received signals were generated with multipath and noise characteristics similar to an ocean acoustic transmission case. These realizations were then separated into arrival times and corresponding amplitudes by the algorithm. The results of these tests and the general limitations of the algorithm are discussed.