# A GPS Phase-Locked Loop Performance Metric Based on the Phase Discriminator Output
## 1 Introduction  
This work describes a technique to evaluate the performance GPS receivers that track carrier phase and are vulnerable to wideband radio frequency interference (RFI). The approach is valid for any GPS application in which the receiver cannot tolerate cycle slips in the phase-lock loop (PLL). The method is directly applicable to ground-based reference receivers for differential GPS systems, as well as other ground-based receivers that require high continuity of service. It is also relevant to roving receivers, if the additional dynamic stresses on the PLL are also taken into account. The example application motivating this work is Ground Based Augmentation System (GBAS) reference station receivers subjected to broadband interference, for example, from nearby use of personal privacy devices (PPDs). Prior work [1; 2] has shown that PPDs most commonly emit broadband interference, and GBAS ground based reference receivers have experienced tracking discontinuities as a result [3]. These events can cause navigation service interruptions to aircraft on final approach. To ensure continuity of the navigation service, GBAS reference stations must be able to track GPS signals in the presence of wideband interference. A popular metric used to predict the lock performance of a PLL under noisy conditions is the total _phase jitter_ metric [4; 5; 6; 7]. A major advantage of the jitter metric over more rigorous/accurate performance evaluation tools, such as computing the mean time to cycle slip (MTCS), is in its analytical simplicity. A closed form expression for the MTCS has only been derived assuming a simple first-order phase-lock loop with additive white Gaussian noise (AWGN) [8]. Higher-order loops are much moredifficult to analyze, and, in such cases, the MTCS would need to be determined via time-consuming direct PLL simulation [9]. Additional considerations such as oscillator phase-noise and dynamic effects are not currently within the capability of the non-linear theory. In contrast, the phase jitter metric (using linear theory) is able to account for oscillator phase-noise and dynamics. However, the phase jitter metric is not without drawbacks. Regardless of whether a linear or non-linear model is used in theoretical analysis, simulation and/or experimental results are required in practice to validate PLL designs. Prior research [5] relying on the jitter metric has capitalized on the idea that reducing the noise-equivalent bandwidth of the phase-lock loop will reduce the impact of wideband interference. The jitter metric was used as a design tool to determine the minimum PLL bandwidth and carrier-to-noise ratio (\(C/N_{0}\)) at which a GPS PLL would track reliably. However, experimental results in [5] showed that the PLL was cycle slipping (and losing lock) at higher carrier-to-noise ratios than predicted by the phase jitter metric. In fact, results from other work [4; 6; 7] consistently state that in experiments, loss of lock occurs at \(C/N_{0}\) values that are higher than predicted by the phase jitter metric. In [6], analysis relying on the phase jitter metric led the authors to claim that increasing coherent averaging time would not improve PLL tracking capability in the presence of wideband interference. However, we will show that increasing coherent averaging time is essential for maintaining lock through interference events. Furthermore, our conclusions will be supported by theory as well as experimental results. In this work, we propose the standard deviation of _tracking error_ (defined here as the discriminator's estimate of the true phase error) be used as a PLL performance design metric and expound the advantages of this metric over the popular phase jitter metric (which is based on the true phase error) using theory, numerical simulation, and experimental results. We derive an augmented GPS phase-lock loop (PLL) linear model, which includes the effect of coherent averaging, to be used in conjunction with this proposed metric. This model is functionally similar to those in [10; 11].