## 5 Decoupled Criteria for GNSS Code Tracking Evaluation  
### Anti-Interference Rate  
The unmatched code tracking evaluation criterion Equation (21) is coupled with numerous factors. In order to study the influence of one factor, it needs a hypothetical assumption of other factors. While in the signal design, it is not enough to consider merely one hypothetical assumption, but as many as possible to reflect the actual case. However, traversing all the possible value of factors exaggerates the calculation, as well as making the useful information overwhelmed by the influence of numerous factors. Therefore, a concise evaluation criterion considering only essential factors is necessary.  
To study the effect of interference in the theoretical evaluation, a criterion with similar physical meaning to the quality factor, or Q factor is needed [18]. For this purpose, part of the coefficients of the signal to interference ratio (SIR) is obtained from the variance of ranging error Equation (21), and its root square is shown in Equation (24) with the unit of Hz\({}^{-1}\), defined as the _anti-interference rate_:  
\[\
u=\sqrt{\frac{\mathcal{X}_{s\delta}}{\varpi^{2}\beta_{s}^{2}}} \tag{24}\]  
where:  
\[\varpi=\frac{\int_{-\beta_{s}/2}^{\beta_{s}/2}f^{2}\mathcal{X}_{s,\delta}(f)df }{\sqrt{\int_{-\beta_{s}/2}^{\beta_{s}/2}f^{2}G_{s}(f)df}} \tag{25}\]\[\beta_{\delta}=\sqrt{\int_{-\beta_{\gamma}/2}^{\beta_{\gamma}/2}f^{2}G_{\delta}(f)df} \tag{26}\]  
\[\mathcal{X}_{\delta}=\int_{-\beta_{\gamma}/2}^{\beta_{\gamma}/2}f^{2}G_{\epsilon }(f)G_{\delta}(f)df \tag{27}\]  
The anti-interference rate Equation (24) represents the derivative of the interference strength, in other words, it represents the signal's ability to resist a certain kind of interference. Except for the interference, other essential influencing factors of receiving bandwidth, local despreading waveform, are also necessary to be considered in the criterion. Meanwhile, some external factors represent less of the ability of signal to resist interference, such as interference strength, WGN strength, and other receiver implementation parameters, are not included in the criterion. Thus, the anti-interference rate is a decoupled criterion, which can better represent the inherent performance of the received signal under interference. It also supports the unmatched receiving.  
It should be noted that, although Equation (24) seems like the normalization of the previous defined code tracking spectral separation coefficient (CT-SSC) [11], provided as Equation (27), further study shows that the anti-interference rate has substantial distinction from the code tracking SSC. First, the anti-interference rate Equation (24) considers the effect of unmatched receiving, which is not representing in the traditional CT-SSC [11] itself. Second, from the physical meaning aspect, the traditional CT-SSC itself depicts the spectral separation between the interference and received signal, while the anti-interference rate is influenced by the spectrum of interference, received signal and also local despreading signal, thus representing an overall effects of interference on the code tracking. From this point of view, it should also be distinguished with an evaluation criterion named effective \(C/N_{0}\), which is also defined in [11]. Effective \(C/N_{0}\) reflects the effect of interference on the correlator output SNIR, thereby it is a useful criterion for evaluation of acquisition performance.  
Moreover, the intermediate results Equation (25), Equation (26) have specific meaning and are available for tracking performance evaluation.