Complex Amplitudes Tracking Loop for multipath channel estimation in OFDM systems under slow to moderate fading

This paper deals with multipath channel estimation for Orthogonal Frequency-Division Multiplexing systems under slow to moderate fading conditions. Most of the conventional methods exploit only the frequency-domain correlation by estimating the channel at pilot frequencies, and then interpolating the channel frequency response. More advanced algorithms exploit in addition the time-domain correlation, by employing Kalman filters based on the approximation of the time-varying channel. Adopting a parametric approach and assuming a primary acquisition of the path delays, channel estimators have to track the complex amplitudes of the paths. In this perspective, we propose a less complex algorithm than the Kalman methods, inspired by second-order Phase-Locked Loops. An error signal is created from the pilot-aided Least-Squares estimates of the complex amplitudes, and is integrated by the loop to carry out the final estimates. We derive closed-form expressions of the mean squared error of the algorithm and of the optimal loop coefficients versus the channel state, assuming a Rayleigh channel with Jakes' Doppler spectrum. The efficiency of our reduced complexity algorithm is demonstrated, with an asymptotic mean squared error lower than the first-order auto-regressive Kalman filters reported in the literature, and almost the same as a second-order Kalman-based algorithm. HighlightsAn algorithm for tracking the complex amplitudes of a multipath channel in OFDM is proposed.This reduced complexity algorithm is inspired by second-order Phase-Locked Loops (PLLs).Closed-form expressions for the optimal coefficients and the MSE of the estimator are provided.Outperforms in terms of asymptotic MSE the more complex first-order Auto-Regressive Kalman estimator of the literature under slow to moderate fading conditions.Asymptotic MSE is almost the same as a second-order model based-Kalman estimator.