Improving the tuning of first-order autoregressive model for the estimation of amplify and forward relay channel

This paper deals with the estimation of the Amplify-and-Forward channel. Considering two widely accepted Rayleigh links with Jakes´ spectrum, a first-order autoregressive model AR(1) is used to approximate the cascade of both links. A standard estimation algorithm is the Kalman filter. In this paper, we keep the choice of the AR(1)-Kalman filter, but we show that the method usually exploited in the literature to calculate the AR(1)-model parameter presents some disappointing results. We propose other values of the AR(1)-model parameter to improve the channel estimation, based on an off-line minimization of the asymptotic mean square error MSE for a given Doppler and signal to noise ratio. The simulation results show a considerable gain in terms of MSE of the well-tuned Kalman-based channel estimator, especially for the most common scenario of slow-fading channel.