# Amplitude Modeling of Specular Multipath Components for Robust Indoor Localization
## 4 Analysis of the GPR-Based Channel Model
### SMC Amplitudes and SINR  
Figure 6 shows the GPR for various normalized SMC amplitudes \(|\hat{a}_{k}(\mathbf{p})d_{k}(\mathbf{p})|\) as a function of the direction angle \(\phi_{k}(\mathbf{p})\) of the propagation path. The estimated amplitudes from the data set are shown along the mean and the \(\pm 2\sigma\) interval, as well as the predicted \(\mathrm{SINR}_{k}(\phi_{k}(\mathbf{p}^{*}))\) given by (9). It is evident that there is a correlation between the SMC amplitudes and the direction angle, as described in Section 2.3, which is exploited by the GPR. The normalization does not allow for a direct comparison of the SMC amplitudes. But the comparison of the SINR-values indicates how much ranging information each of the SMCs can yield, c.f. (5). It is shown that the SINR for reflections on the EPB is high, around 40, see Figure 5(b) which is much higher than the SINR for other SMCs, see Figure 5(c)-n, except the LOS link. Please note that on the east side of the room, there are fewer obstacles which makes the SMCs more reliable than others. For the reflections on the WW, c.f. Figure 5(c), the SINR is very low, indicating low ranging information, except at a direction approximately perpendicular to the wall, where the SINR increases steadily. The result is reasonable since, near the west wall, there are quite a few obstacles, e.g., computers, measurement equipment, etc., that could produce scattering effects. For the SMC that corresponds to VA 4, shown in Figure 5(d), the reflection on the whiteboard (visible at angles \(<\)\(-\)1.5 rad) has very high SINR, much higher than reflections on the other materials, e.g., the wooden door and the plasterboard wall. From VA 6, c.f. Figure 5(e), it is shown that reflections on the NGW with metal-coated glass windows yield very significant ranging information, reaching up to an SINR of around 20. Figure 5: EC of certain SMCs vs. number of VAs visible: (**a**) first-order VAs only, (**b**) second-order VAs only, (**c**) LOS (PA) only, (**d**) all VAs and LOS (PA). The brown solid line shows the number of VAs that are visible from the corresponding trajectory point. The dashed brown line shows the number of visible VAs that are within the set of (**a**) first-order VAs or (**b**) second-order VAs. As shown in Figure 6f,g,i,k, for VA 7, 8, 11 and 13, the SINR is not as good as the first-order SMCs, but better than the other second-order SMCs shown in Figure 6h,j,l,m,n. Figure 6: _Cont._  
Implementing GPR on measurement data allows us to predict the SINR as well as the amplitude of the SMCs for each point \(\mathbf{p}^{*}\) in an environment at which an SMC is visible. Figure 7 shows this prediction result in terms of the \(\text{SINR}_{k}(\mathbf{p}^{*})\), while Figure 8 shows the predicted mean amplitude \(\mathbb{E}[\psi(\phi_{k}(\mathbf{p}^{*}))|\mathcal{D}_{k},\theta_{k}^{\text{ abs}}/\|\mathbf{a}_{k}-\mathbf{p}^{*}\|.\) It is evident that the LOS path has very high SINR compared to other SMCs, thus it yields very high range information. However, in the case that the LOS is not available, choosing a good NLOS SMC is necessary. Two parameters could be used to choose between SMCs, the SINR and the SMC amplitude.