Performance analysis of a second order FLL assisted third order PLL for tracking doppler rates

The comprehensive analysis of the Spread Spectrum Responder (SSR) carrier tracking loops is presented. A mathematical model of a second-order FLL assisted third-order PLL is illustrated to study the performance in dynamics and noise. A fixed point method is used in the work to analyze the stable regions for the FLL, PLL and FLL assisted PLL. The Chapman-Kolmogorov (C-K) equation is utilized to express the steady-state Probability Density Function (PDF) of these three loops. The steady-state mean and variance are also be derived. At last, we discuss the optimizations for the combined loop due to the fact that the assisted tracking loop can be considered as an equivalent third-order PLL. This work will play an important role in designing the high dynamic carrier tracking.