# Analysis of Dual-Band Direction of Arrival Estimation in Multipath Scenarios
## 5 Validation of the Simulation Environment  
The validation of the approach introduced in the previous paragraph is the goal of the present section. Virtual scenarios implemented by means of the aforementioned proposed techniques and subsequent investigations, performed to reach the highlighted objective, make use of the following parameters: the actual azimuthal DoA is set equal to \(0^{\circ}\) while the distance \(D\) ranges from \(0.5\,\mathrm{m}\) to \(3\,\mathrm{m}\). For each study case, the Image antenna (I) is kept \(2\,\mathrm{m}\) away from the Target (T), to explore a wide range of direction of interference signal. These parameters define a set of virtual scenarios compatible with the implementation of corresponding physical experiment. The first validation step consisted of evaluating the simulated power distribution for one of the 8 antennas (the one pointing toward \(\theta=0^{\circ}\)) within the entire range of angles and distances considered and under the assumption that the Image antenna is inactive. The resulting power distribution is illustrated in Figure 7 where the shape of the pattern at the two frequencies is clearly highlighted. The latter maintains the shape of the power pattern along the distance of test. The second step was implemented by running the same simulation, but considering the Image antenna activated. In this case, the latter is fed with \(\chi=1\,\mathrm{dB}\) with respect to the Target antenna, meaning a very severe multi-path. The effects of undesired signals recombination are clearly visible in Figure 8 that shows areas where the recombination is extremely destructive for both frequencies. To further investigate the performance of the proposed simulation environment in terms of multi-path effects prediction, the calculated RSSI data from the two frequencies are synthesized, at three different distances \(D_{1}=2\,\mathrm{m}\), \(D_{2}=2.5\,\mathrm{m}\) and \(D_{3}=3\,\mathrm{m}\). The data, virtually collected from both T and I antennas, are evaluated considering a variation  
Figure 8: Power distribution relative to antenna #1 in the case of a severe interference from the image antenna, at 2.45 GHz (**top**) and 5.2 GHz (**bottom**). almost always more accurate than the single one, or at least equivalent. This is true even if one of the two frequencies is severely impaired by multi-path. Given the fact that a reduced number of positive results can be fortuitous, the same analysis has been performed considering all five available distances for measurement results, cumulatively. The data obtained from this simulation are presented in Figures 15 and 16. These graphs have the same meaning of those already presented in previous figures. This comparison shows how it is not always the same frequency that performs worse than the other. In particular, the \(2.45\,\mathrm{GHz}\) signal has poorer performance  
Figure 14: 90-th percentile DoA estimation error for \(D=3\,\mathrm{m}\). Figure 12: 90-th percentile DoA estimation error for \(D=2\,\mathrm{m}\). Figure 13: 90-th percentile DoA estimation error for \(D=2.5\,\mathrm{m}\). up to around \(\chi=5\) dB, then we have an inversion and is 5.2 GHz that decays in quality. From the experiments we can infer that the wireless channel becomes much more sensitive to multi-path effects at lower frequency than to the higher one. This is not surprising because losses due to the pathloss at higher frequencies make the bounced signal weaker than the direct one. In addition, the antenna element adopted in the reference system exhibits a higher directivity at 5.2 GHz as shown in Figure 3. All these contribute to reduce multi-path impairments at higher frequency, and thus avoid the peak reported in Figures 11 and 13-16. Consequently, the selection strategy between the two frequencies is carried out by the final identification procedure that weights for each set of simulated data the response at both the frequencies by their variance: this led to the extinction of the peak from the combined results.