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

This study deals with channel estimation in tracking mode over a flat Rayleigh fading 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 model of the time-varying channel. However, the nature of the approximation model itself degrades the estimation performance for slow to moderate varying channel scenarios. Furthermore, the Kalman-based algorithms exhibit a certain complexity. Hence, a different model and approach has been investigated in this study to tackle all of these issues. A novel phase-locked-loop-structured third-order tracking loop estimator with a low complexity is proposed. The connection between a steady-state Kalman filter based on a random walk approximation model and the proposed estimator is first established. Then, a suboptimal mean-squared-error (MSE) is given in a closed-form expression as a function of the tracking loop parameters. The parameters that minimise this suboptimal MSE are also given in a closed-form expression. The asymptotic MSE and bit-error-ratio simulation results demonstrate that the proposed estimator outperforms the first- and second-order Kalman-based filters reported in literature. The robustness of the proposed estimator is also verified by a mismatch simulation.