Digital Phase-Locked Loop Behavior with Clock and Sampler Quantization

This paper deals with the analysis of digital phase-locked loop (DPLL) models that take into account the discrete nature of the analog-to-digital converter (ADC) and the numerical controlled oscillator (NCO). The models are general enough to allow for different kinds of noise distributions and nonuniform qnantization. Weak assumptions on the nature of the loop parameters reduce the models to finite Markov chain problems. It is shown that the resulting probability transition matrices are "lumpable," which translates into convenient Computational savings. In this manner, an exact statistical analysis is possible not only for first-order but also for second-order loops. Numerical results give evidence that for appropriate ADC and NCO characteristics, few quantization levels are needed to match the performance of models that ignore qnantization. However, when the values of these characteristics are not proper, a substantial change in performance can occur. This change in the loop behavior cannot be analyzed or predicted by those models that neglect the quantization effects. It is also found that the use of a nonlinear ADC improves the loop behavior when the noise density distribution is heavy-tailed, e.g., atmospheric noise.