Modeling and estimation for Doppler-shifted Gaussian random processes

We address the problems of modeling Doppler-shifted wide-band Gaussian random processes and of estimating the Doppler parameter from a finite series of discrete-time samples. Relations between the continuous-time process, the Doppler shift parameter and the discrete-time process obtained by sampling are established. Approximate rational models are proposed. Various estimators are proposed for the Doppler parameter when the second-order statistics of the original continuous-time random process are known. The Cramer-Rao bound is derived. The estimators are compared experimentally on synthetic Doppler-shifted data. We also hint at some extensions of the method to non-stationary processes and time-varying Doppler shifts.