Performance analysis and design of the optimal frequency-assisted phase tracking loop

The frequency-assisted phase tracking (FAPT) is investigated extensively in comparison with the phase tracking (PT) in a Kalman filter (KF) frame to explore the role the augmented frequency measurement plays in FAPT. It is found that the FLL-assisted PLL is suboptimal in structure, while the FAPT is optimal in the minimum variance sense. Hence, the KF frame provides not only a rational method to compare the FAPT with the PT but also an insight into the effects of frequency and phase measurements on PT. The impact of the two typical discriminators, ATAN and ATAN2, on the phase tracking performance in the FAPT and the PT is studied by Monte Carlo simulations and covariance analysis. The results show that the pull-in range affects the lock-in threshold, and the linear region determines the performance under high dynamic environments. In addition, the measurement variance dominates the tracking accuracy under weak signal conditions. The phase discriminator governs the performance of the FAPT. In terms of both the tracking accuracy and the lock-in threshold, the augmented frequency measurement in the FAPT filters is very helpful in tracking the high dynamic signal, but it contributes little to the weak signal tracking.