Optimal Memory Size Formula for Moving-Average Digital Phase-Locked Loop

This letter proposes a new moving-average form of digital phase-locked loop (DPLL) that uses the average value of measurements on a memory horizon and the correction term to estimate phase information. This ensures the desired unbiasedness property for the phase information. A new formula for the optimal memory size of the proposed DPLL with minimization of the expected squared phase error is established. A numerical example is given to show that the developed DPLL has superior robustness against quantization and incorrect noise compared to the existing DPLLs.