Multipath time-of-arrival estimation via modified projection onto convex sets

A low complexity algorithm is proposed for estimating the multipath time-of-arrival (TOA) and attenuation factors from a noisy received signal consisting of multiple overlapped echoes. Different from the conventional projection onto convex sets (POCS) method, the proposed approach harnesses the sparse property of multipath channel and the ℓ₁-norm is adopted as the measurement of sparsity. The TOA estimation problem is solved by a series of projection onto convex sets, including hypersphere and hyper-polyhedra. The computational complexity of the modified POCS algorithm is O(N log N) per iteration with N being the length of the received signal. Simulation results confirm that the proposed approach provides better performance in terms of temporal resolution and robustness to noise compared with the matched filtering and the conventional POCS method.