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Noise performance of Frequency-Locked Loop based on pilot signal

In contrast with Phase-Locked Loop (PLL), Frequency Locked Loop (FLL) has better dynamic performance. There were papers dealing with noise performance of FLL. However, under the circumstance of CW input, there were large gap between simulation results and theory results which were obtained from published papers. This paper analysis the reason of the gap and proposes an improved calculation method in the condition of four-quadrant arctangent and cross product discriminator. Results show that the improved calculation method fits the simulation result very well.