Second-order modeling for Rayleigh flat fading channel estimation with Kalman Filter

This paper deals with channel estimation over flat fading Rayleigh channel with Jakes´ Doppler spectrum. Many estimation algorithms exploit the time-domain correlation of the channel by employing Kalman Filter based on an approximation of the time-varying channel. A common method used in the literature is based on a first-order auto-regressive (AR1) model for the channel approximation, combined with a Correlation Matching (CM) criterion to fix the value of the AR1-parameter. In this paper, we propose first to replace the AR1 model by a specific second-order (Or2) model (as the one used for the phase estimation in presence of frequency offset), which is more appropriate for slow fading variations. Secondly, we propose a criterion based on the Minimization of the Asymptotic Variance (MAV) of the Kalman estimator to fix the parameter of the Or2-model. Closed-form expressions of the optimum Or2-parameter and of the corresponding Mean Square Error (MSE) are derived for a given channel state (Doppler spread, SNR). MSE theoretical analysis and simulation results prove a significant improvement with the Or2-MAV approach compared to more conventional AR1-CM approach (or even AR1-MAV optimized approach) in terms of MSE, especially for slow fading variations.