Multipath delay estimation using the magnitude spectrum

Four methods are presented by which the relative delay structure of a multipath signal can be estimated from the Fourier magnitude spectrum of the observation. The phase of the underlying source signal may be completely unknown. While the signal autocorrelation function could be used to estimate relative delay from uniform samples of the received magnitude spectrum, the novelty of the proposed methods lies in the fact that the magnitude spectrum samples are not assumed to be uniformly spaced. This makes these methods appropriate for use in frequency-hopped and collaborative sensing systems. Four methods, including a least-squares (LS), maximum likelihood (ML), maximum a posteriori (MAP), and entropy-based approach are presented. Simulation and laboratory experiments indicate that the MAP and ML algorithms provide the best performance