Cramer-Rao lower bound for frequency estimation in multipath Rayleigh fading channels

This paper concerns the estimation of the frequency offset of a known (pilot) signal propagated through a slowly fading multipath channel, such that channel parameters are considered to be constant over the observation interval. We derive a Cramer-Rao lower bound (CRLB) and maximum likelihood (ML) frequency estimation algorithm for additive Gaussian noise and path amplitudes having complex zero-mean Gaussian distribution when covariance matrices of the fading and noise are known. In particular, we consider the scenarios with white noise, independent fading of path amplitudes and pilot signals with a diagonal correlation matrix. We compare simulation results for the ML estimator with the CRLB. We also show that the results obtained can be extended to scenarios with fast fading channels.