Maximum likelihood 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 nonlinear transformed path periodograms. We have found 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 non-sparse multipath fading channels. Exploiting the sparseness of the channel impulse response is shown to significantly reduce the threshold signal-to-noise ratio (SNR) 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 realise this improvement. The assumption of a diagonal autocorrelation matrix is shown to affect the accuracy performance only at high SNRs which however can often be outside the SNRs of interest.