Simple carrier frequency rate-of-change estimators

This paper is concerned with the estimation of the rate-of-change of the instantaneous frequency of an unmodulated carrier. Such an issue arises, for instance, in satellite communication systems based on a low-Earth-orbit constellation, wherein the speed of each satellite relative to earth is rapidly time-varying, and consequently, the received carrier is affected by nonnegligible Doppler shift and Doppler rate. First, we present simple yet efficient estimators of the Doppler rate derived from maximum-likelihood estimation theory. Next, we investigate their performance in terms of bias and estimation error variance. Finally, we compare our variance results with the relevant modified Cramer-Rao bound