Complex amplitudes tracking loop for multi-path channel estimation in OFDM systems: Synthesis and extension

This study deals with pilot-aided multi-path channel estimation for orthogonal frequency division multiplexing (OFDM) systems under slow to moderate fading conditions. Some algorithms exploit the channel time-domain correlation by using Kalman filters (KFs) to track the channel multi-path complex amplitudes (CAs), assuming a primary acquisition of the delays. Recently, it was shown that less complex algorithms, based on a second-order Complex Amplitude Tracking Loop (CATL) structure and a Least-Square (LS) pilot-aided error signal, can also reach near optimal asymptotic mean-squared error (MSE) performance. The LS-CATL-based algorithms are inspired by digital Phase-Locked Loops (PLL), as well as by the “prediction-correction” principle of the KF (in steady-state mode). This paper sums up and extends our previous results for the tuning and steady-state performance of the LS-CATL algorithm: analytic formulae are given for the first-, second-, and third-order loops, usable here for the multi-path multi-carrier scenario, and adaptable to any Doppler spectrum model of wide-sense stationary channels.