Abstract-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 CramerRao 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.

Second-order autoregressive modelbased Kalman filter for the estimation of a slow fading channel described by the Clarke model: Optimal tuning and interpretation. Digital Signal Processing, Elsevier, 2019, 90, pp. AbstractThis paper treats the estimation of a flat fading Rayleigh channel with Jakes' Doppler spectrum model and slow fading variations. A common method is to use a Kalman filter (KF) based on an auto-regressive model of order p (AR(p)). The parameters of the AR model can be simply tuned by using the correlation matching (CM) criterion. However, the major drawback of this method is that high orders are required to approach the Bayesian Cramer-Rao lower bound. The choice of p together with the tuning of the model parameters is thus critical, and a tradeoff must be found between the numerical complexity and the performance. The reasonable tradeoff arising from setting p = 2 has received much attention in the literature. However, the methods proposed for tuning the model parameters are either based on an extensive grid-search analysis or experimental results, which limits their ap-$ plicability. A general solution for any scenario is simply missing for p = 2 and this paper aims at filling this gap. We propose using a Minimization of Asymptotic Variance (MAV) criterion, for which a general closed-form formula has been derived for the optimal tuning of the model and the mean square error. This provides deeper insight into the behaviour of the KF with respect to the channel state (Doppler frequency and signal to noise ratio).Moreover, the paper interprets the proposed solution, especially the dependence of the shape of the optimal AR(2) spectrum on the channel state.Analytic and numerical comparisons with first-and second-order algorithms in the literature are also performed. Simulation results show that the proposed AR(2)-MAV model performs better than the literature and similarly to AR(p)-CM models with p ≥ 15.