Robust Doppler Spread Estimation in the Presence of a Residual Carrier Frequency Offset

In high data-rate transmission systems, accurate Doppler spread estimation is a critical task for not only mobile velocity estimation, but also for optimal adaptive processing. It is known that the residual carrier frequency offset (CFO) which is inherent to the asynchrony between the communicating ends in a wireless link has a detrimental effect on the Doppler spread estimation. In this correspondence, we propose a new simple and accurate approach that copes with this issue by explicitly taking the CFO into account when estimating the Doppler spread. This new approach stems from the fact that the cross-correlation of the channel is a weighted summation of monochromatic plane waves (or an inverse Fourier transform of its power spectral density). It turns out that these plane waves are locally (as compared to the sampling rate) distributed around a main frequency which is nothing but the CFO. Using this property, we base our analysis on Taylor series expansions in addition to an observation temporal aperture to develop a two-ray spectrum approximate model for the Doppler spread estimation. We find that the Doppler spread is half of the frequency spacing between both rays which are located symmetrically around the CFO. Finally, we deduce new closed-form estimators for the Doppler spread and also for the CFO. These estimators are accurate and practical in environments with isotropic scattering where the channel power spectrum density (PSD) is symmetric. Simulations are provided to illustrate the advantages of the proposed method and its robustness to the CFO.