Deconvolution in the presence of Doppler with application to specular multipath parameter estimation

High-resolution multipath parameter estimates can be obtained through various deconvolution procedures, all of which-in the limit-rely on some form of inverse filtering. Although deconvolution in a multipath environment free from Doppler is well understood and well documented, this is not true for the case when motion of the multipath components relative to the receiver imposes a Doppler shift on the transmitted probing signal. This paper describes the effect of Doppler on a broad class of deconvolution methods by studying the effect of Doppler on the output of an inverse filter. It is shown that in the presence of Doppler, the deconvolution outputs are comprised chiefly of two signal-related functions, one of which may be designed in such a way as to be free from the range-Doppler coupling effects inherent in correlation processing. Knowledge of these two functions provides insight into the signal design issues relevant to deconvolution-based multipath parameter estimation systems and is useful in designing appropriate constraints and post-processing algorithms that may lead to an accurate extraction of the Doppler and delay parameters of the multipath channel. These results are applied to two known deconvolution methods: the method of projection onto convex sets (POCS) and the method of least squares (LS)