Second-order autoregressive model-based Kalman filter for the estimation of a slow fading channel described by the Clarke model: Optimal tuning and interpretation

Abstract

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.

Interference Analysis for Multi-Carrier Systems Over Fast-Fading Multipath Channels

“…• providing a generalized system model that is valid for multi-carrier communication over doubly-dispersive channels and deriving the theoretical expected received power at each time-frequency slot, • analyzing the generalized multi-carrier system's performance in doubly-dispersive channels using the derived theoretical values of ISI and ICI versus normalized Doppler spread assuming Rayleigh channel with Jakes' Doppler spectrum (Clarke model [8], [9]). This is done for pulse shapes using different optimization criteria, • analyzing the time-frequency localization of interference (ISI and ICI) by using the derived theoretical expression versus the offset relative to the index of the desired timefrequency slot, • and providing Monte-Carlo simulation results that validate the provided theoretical interference formulas.…”

Kalman Filter Channel Estimation in 2 × 2 and 4 × 4 STBC MIMO-OFDM Systems

“…In paper [14]- [19], the time-varying channel is modeled as a first order autoregressive (AR1) model. KF channel estimation with second order autoregressive (AR2) model was proposed in [20] and [21]. It uses the minimum asymptotic variance criterion to tune the parameters of the AR2 model and gives the theoretical analysis for the first time.…”