Optimization of the second order autoregressive model AR(2) for Rayleigh-Jakes flat fading channel estimation with Kalman filter

This paper deals with the estimation of the flat fading Rayleigh channel with Jakes' Doppler spectrum (model due to R.H. Clarke in 1968) and slow fading variations. A common method in literature consists in approximating the variations of the channel using an auto-regressive model of order p (AR(p)), whose parameters are adjusted according to the “correlation matching” (CM) criterion and then estimated by a Kalman filter (KF). Recent studies based on first order AR(1) showed that the performance is far from the Bayesian Cramer-Rao bound for slow to moderate channel variations, which is the case for many applications. The same studies on first order model have shown the importance of replacing the CM criterion with a MAV criterion (Minimization of Asymptotic Variance). Moreover, it has been shown in literature that increasing the order of the model by passing from AR(1) to AR(2) did not improve the performance when the CM criterion is considered. In order to obtain an improvement in performance, it is essential to consider the MAV criterion with second order autoregressive model AR(2), as shown in this article. By imposing a linear relation between one of the parameters and the Doppler frequency, we derive analytic formulas for suboptimal adjustment of the parameters of AR(2) as a function of the noise level and the Doppler frequency of the channel. Theoretical assumptions are validated via simulation.