Effects of multiple CW interferers on carrier synchronization

In this paper the modeling and analysis of the effects of multiple CW interferers on phase locked loop performance is conducted such that the operating vulnerability to jamming, interference or multipath can be accessed. First, in the absence of additive noise and presence of interference within the loop passband, a statistical model is developed which demonstrates the effect of multiple CW interferers on the phase error process. The steady state phase error is characterized statistically through its probability density function and moments. The conditions for keeping locked and the probability that the loop stays locked to the desired carrier frequency are derived for arbitrary loop filter characteristics. A novel outage criterion is established for the satisfactory operation of the loop and outage probabilities are presented for certain operating scenarios. Second, assuming the presence of additive white Gaussian noise, a Fokker Planck analysis is conducted in order to obtain the probability density function, moments and cycle slip rates of the phase error process.