## 4 Characterization and Performance Analysis
### SQM Variation Profiles  
Figures 2 and 3 show the SQM variation profiles for Ratio and Delta metrics defined in Table 1. To extract these profiles, a single reflection is considered. Then the relative delay of the reflected signal is swept through a range of values to evaluate SQM metric outputs for in-phase (blue lines) and out-of-phase (red lines) multipath components for two signal-to-multipath ratio (SMR) values. It is observed that the SQM variation envelopes reach their maximum values around 0.5 chips where the late monitoring correlator is affected by the peak of the reflected correlation curve. Afterwards, whilst the multipath correlation curve passes the late monitoring correlator, the SQM variation envelopes decrease until multipath signal delay (\(\tau\)) becomes greater than 1.5 chips and the multipath correlation curve no longer overlaps with tracking and monitoring correlators. For BOC(1,1) this reduction in variation envelopes shows a different behavior between 0.5 and 1 chips due to the different shape of the BOC(1,1) correlation curve. In all cases, a lower SMR results in higher SQM variations due to the higher level of multipath relative power. Nominal Standard Deviations (SD) of the metrics are also shown in Figures 2 and 3 for different C/N\({}_{0}\) values. These values will now be used to evaluate the sensitivity of the SQM metrics in multipath detection. Based on a desired false alarm probability, a detection threshold is usually defined as a multiple of SD (for example three or five times) with clean data set. Therefore, for a given multipath scenario, if the SQM envelopes exceed the detection threshold, the SQM approach is considered sensitive, otherwise the multipath effect cannot be detected. As shown in the figures, for a given level of SMR, a higher C/N\({}_{0}\) increases SQM sensitivity by reducing the nominal SD of the SQM metrics and thus lowering possible detection thresholds. Figure 1: Multipath range error envelopes for (**a**) Narrow Correlator (NC) tracking strategy, BPSK(1) and BOC(1,1) signaling schemes; (**b**) High Resolution Correlator (HRC) tracking strategy, BPSK(1) and BOC(1,1) signaling schemes. Figure 2: _Cont_. Figure 3: \(Cont\). Figure 2: SQM variation envelopes of (single-sided) Ratio metric for **(a)** Narrow Correlator (NC) tracking strategy and BPSK(1) signaling; **(b)** Narrow Correlator (NC) tracking strategy and BOC(1,1) signaling; **(c)** High Resolution Correlator (HRC) tracking strategy and BPSK(1) signaling; **(d)** High Resolution Correlator (HRC) tracking strategy and BOC(1,1) signaling. For the Double-Delta SQM metric, the SQM envelopes are similar to those of the Delta metric (as the difference of monitoring correlators normalized by prompt) under the NC strategy. As discussed in Section 3, this is because the NC DLL discriminator keeps the tracking early-minus-late value around zero. However, under the HRC strategy, the corresponding envelopes are slightly different since HRC exploits different combinations of tracking correlators (see Equations (5) and (6)). Figure 4 shows the SQM variation envelopes for the Double-Delta metric for the HRC tracking strategy. Figure 3: SQM variation envelopes of Delta metric for (**a**) Narrow Correlator (NC) tracking strategy and BPSK(1) signaling; (**b**) Narrow Correlator (NC) tracking strategy and BOC(1,1) signaling; (**c**) High Resolution Correlator (HRC) strategy and BPSK(1) signaling; (**d**) High Resolution Correlator (HRC) strategy and BOC(1,1) signaling. Inspection of the Delta and Double-Delta SQM envelopes in Figures 3 and 4 shows that SQM outputs are zero (or below the nominal SDs) for some intervals of short-delay multipath. This multipath period induces range errors that are not detectable by SQM metrics. To elaborate on this phenomenon, consider Figure 5 which shows a BPSK(1) correlation function affected by multipath and divided into different regions.