On the use of first-order autoregressive modeling for Rayleigh flat fading channel estimation with Kalman filter

This letter deals with the estimation of a flat fading Rayleigh channel with Jakes's spectrum. The channel is approximated by a first-order autoregressive (AR(1)) model and tracked by a Kalman filter (KF). The common method used in the literature to estimate the parameter of the AR(1) model is based on a correlation matching (CM) criterion. However, for slow fading variations, another criterion based on the minimization of the asymptotic variance (MAV) of the KF is more appropriate, as already observed in few works (Barbieri et al., 2009 [1]). This letter gives analytic justification by providing approximated closed-form expressions of the estimation variance for the CM and MAV criteria, and of the optimal AR(1) parameter.

► We want to estimate a flat fading Rayleigh channel with Jakes' spectrum.
► The channel is approximated with an AR(1)-model and tracked by a Kalman filter.
► We provide a theoretical analysis of the estimation error.
► The minimum asymptotic error variance is fixed as criterion.
► Closed form expressions of optimal AR(1)-coefficient and correspondent MSE are given.