Carrier phase tracking performance of a digital PLL under low SNR conditions for spread spectrum TT&C links

Abstract

This paper presents the analysis of the carrier phase tracking performance of a third-order digital phase-locked loop (DPLL) in low signal-to-noise ratio (SNR) spread spectrum telemetry, tracking, and command (TT&C) systems. A signal model is established in the post-despreading period, and the steady-state phase error variance is obtained as the inverse of the loop SNR. A quantification of the tracking threshold is obtained when the loop SNR is 10dB, and the loss of lock is modeled using cycle slip analysis. A unified criterion for the combination of thermal noise and dynamic stress is presented to find the optimal bandwidth of the loop, which is around 10Hz. Simulation results verify the theoretical analysis with relative errors less than 5%. A sensitivity analysis across five representative mission scenarios demonstrates that the optimal bandwidth ranges from 6.5 to 13.1Hz depending on the Doppler dynamics, confirming the robustness of the design methodology. Parameter design guidelines for low-SNR spread spectrum TT&C receivers are presented.