## 3 Demonstration of the Proposed Approach
### Fabrication and Measurement
Figure 12a shows a photograph of the measurement setup for the IFA mounted on the ground with a conducting wall. The position of the wall is adjusted with an interval of 10 mm to calculate the \(\rho_{PDC}\) variation, as presented in Figure 12b. This setup gives quantitative changes in the pattern distortions for a single-antenna system affected by platform effects, which is the sole benefit of the proposed approach compared to other conventional FoMs. In the tested range of distance, the simulated \(\rho_{PDC}\) varies between 0.39 and 0.85 and the measured \(\rho_{PDC}\) varies from 0.63 to 0.84, with the same increasing trend as that shown in the simulation. However, we must admit that the measured and simulated \(\rho_{PDC}\) are more deviated at a closer distance to the wall. Such disagreement is due to strong platform effects that cause wave blockage, reflection, and scattering, which generates more fluctuations in radiation patterns. Nevertheless, the proposed coefficient \(\rho_{PDC}\) can provide straightforward and quantitative evaluation on the pattern distortion even for a single antenna system, which cannot be observed from \(\mid\)S\({}_{11}\). Figure 13 presents comparisons of the unaffected and affected patterns for different values of \(\rho_{PDC}\) at 10 mm, 40 mm, and 110 mm. The blue and red lines specify simulated and measured results, and the solid and dashed lines indicate unaffected and affected patterns, respectively. As can be seen, although the conducting wall produces an enormous amount of the pattern distortions, the maximum pattern deviation gradually reduces from 23.9 dB to 15.2 dB to 11.2 dB as the distance becomes greater. This tendency can also be found in the trend of \(\rho_{PDC}\), which corresponds to the values of \(\rho_{PDC}\) = 0.63, \(\rho_{PDC}\) = 0.71, and \(\rho_{PDC}\) = 0.84, respectively. Figure 11: Simulated and measured normalized patterns of the patch antenna in the \(yz\) plane at 6 GHz: (**a**) unaffected radiation patterns with distance = 10 mm (solid lines) and 110 mm (dashed lines), (**b**) affected radiation pattern at distance = 10 mm, and (**c**) affected radiation pattern at distance = 110 mm. In our experiments, there are some discrepancies between the simulated and measured results, especially when stronger mutual coupling or platform effects exist, although the measured \(\rho_{PDC}\) shows a similar tendency as the simulation. The possible causes for this issue are as follows: first, because the proposed coefficient uses the phase information of the radiation pattern, its calculation is sensitively affected by the information of a phase center in the multi-antenna system. In the measurement, the fabricated platform in the anechoic chamber is displaced whenever the phase center changes to a different distance to the antenna or the wall, which might have caused some error in the phase information of the patterns. Second, the antennas might also have geometric error in fabrication because they were fabricated in a laboratory environment. This geometric error results in unwanted shifts in resonant frequency, which deviates both the amplitude and phase of the radiation patterns. Third, the measured \(\rho_{PDC}\) was calculated by using radiation patterns measured with an angular interval of \(5^{\circ}\), while the simulation was based on an angular interval of \(1^{\circ}\). Because stronger mutual coupling and platform effects produce more fluctuations in radiation patterns, the antenna needs to be measured with narrower angular steps for a more accurate estimation of \(\rho_{PDC}\). Figure 12: Photograph of the measurement set-up and measured results. (**a**) Measurement of \(\rho_{PDC}\) for the fabricated IFA in an anechoic chamber. (**b**) Simulated and measured \(\rho_{PDC}\) according to distance. Figure 13: Simulated and measured normalized radiation of the IFA in the \(yz\) plane at 1.5 GHz: patterns at distances (**a**) 10 mm, (**b**) 40 mm, and (**c**) 110 mm.