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. Part of this work was presented in the conference ISCCSP 2010 [1]. This paper is an improved version of the on-line (unpublished) Gipsa-lab research report [2] L. Ros is with GIPSA-lab, Image and Signal Department, BP 46 38402 Saint Martin d’Hères FRANCE (e-mail corresponding author: [email protected]). H. Hijazi is with Lebanese International University (LIU), Beirut, LEBANON ([email protected]). E.P. Simon is with IEMN lab, TELICE group, 59655 Villeneuve d’Ascq, University of Lille, FRANCE ([email protected]) Preprint submitted to Elsevier November 21, 2013 KeywordsOFDM, Channel estimation, Rayleigh multipath channel with Jakes’ Doppler spectrum, Phase-Locked Loop (PLL), Kalman filter (KF), second-order model.