A software receiver phase lock loop analysis and design to implement adaptive phase tracking using a finite impulse response loop filter

In this paper we analyze the design of a digital Phase Lock Loop (PLL) for a Global Navigation Satellite System (GNSS) software receiver. Even if the topic of phase tracking has been widely studied, we found it useful to provide a short walkthrough for the design of a PLL in a real software receiver, avoiding to introduce the common theoretical phase-based model and aiming to the practical implementation of a system that deals with frequencies. Nonetheless, our analysis and design will grow away from the canonical approach, in the way that we will not resort to analog filter theory. The result is a PLL which is more reactive than the ones usually found in literature and that implements a simple method to make its bandwidth adaptive with respect to the noise that affects the signal