Third-order complex amplitudes tracking loop for slow fading channel estimation

This paper deals with channel estimation over a flat fading Rayleigh channel with Jakes' Doppler Spectrum. Many estimation algorithms exploit the time-domain correlation of the channel by employing a Kalman filter based on a first-order (or sometimes second-order) approximation of the time-varying channel. In the low-variation channel scenario, generally speaking, a well-chosen higher order estimator can perform better than a lower order one (Ros et al., [1] [2]). Based on this fact, we propose a third-order tracking loop estimator inspired by the principle of the phase-locked loop (PLL). The proposed estimator has a less complex structure compared to the Kalman-based estimators. In addition, the mean-squared-error (MSE) of the proposed estimator is studied, as well as the parameter optimization with the aim of minimizing the MSE. The closed form expression of the optimal MSE is given and validates the interest of our approach.