Frequency estimation in multipath Rayleigh-sparse-fading channels

Maximum-likelihood (ML) data-aided frequency estimation in multipath Rayleigh-fading channels with sparse impulse responses is investigated. We solve this problem under the assumption that the autocorrelation matrix of the pilot signal can be approximated by a diagonal matrix, the fading of different path amplitudes are independent from each other, and the additive noise is white and Gaussian. The ML frequency estimator is shown to be based on combining nonlinearly transformed path periodograms. We have derived the nonlinear function for the two cases: known and unknown fading variances. The new frequency estimators lead, in particular cases, to known ML frequency estimators for nonsparse multipath fading channels. The use of a priori information about the mean number of paths in the channel allows a significant improvement of the accuracy performance. Exploiting the sparseness of the channel impulse response is shown to significantly reduce the threshold signal-to-noise ratio at which the frequency error departs from the Cramer-Rao lower bound. However, precise knowledge of the channel sparseness is not required in order to realize this improvement.