# Car Bumper Effects in ADAS Sensors at Automotive Radar Frequencies
## 5 Results and Discussion
The power received at a distance reduced in \(\mathrm{R^{\prime}}\) would be,  
\[\mathrm{P_{r}}=\frac{\mathrm{P_{t}G^{2}\lambda^{2}\sigma}}{(4\pi)^{3}\big{(} \mathrm{R-R^{\prime}}\big{)}^{4}} \tag{3}\]  
Then,  
\[\frac{\mathrm{P^{\prime}}_{r}}{\mathrm{P_{r}}}=\frac{\mathrm{R^{4}}}{\big{(} \mathrm{R-R^{\prime}}\big{)}^{4}} \tag{4}\]  
As in our case the power is reduced by 2.5 dB,  
\[10\mathrm{log}_{10}\frac{\mathrm{R^{4}}}{\big{(}\mathrm{R-R^{\prime}}\big{)}^{ 4}}=2.5 \tag{5}\]  
\[\mathrm{R^{\prime}}=\mathrm{R}\ \Big{(}1-10^{\frac{-2.5}{40}}\Big{)} \tag{6}\]  
Then, the detection distance is reduced by 33.5 m for radars configured to work at distances of 250 m. In the same way, those configured to 50 m and 100 m would suffer a decrease of 6.7 m and 13.4 m in their range, respectively. However, as reported in Section 2, commercial radars achieving detection distances of 300 m, or even more, have enough transmission power to compensate for the attenuation caused by the bumpers, keeping the range within requirements. There are several factors that affect the attenuation of the car bumper, such as the material and the thickness of the coating, and so on. In this work, the analysis of all of them should be limited to the available samples; they come from real-world automotive elements, not from a chemical company that could build samples with varied and specific compositions, thickness and coatings. Taking into account these contour conditions, and as shown in Figure 7, we can observe these factors affecting the attenuation. Thus, bumper samples B.1 and C.2 show quite similar values. However, sample B.1 has two layers of base and sample C.2 only has one, so the base thickness does not seem to clarify the attenuation effect. This idea is reinforced by the performance of sample A.2, which is not painted and shows similar or even higher attenuation values than those of the two samples mentionedearlier. This also occurs in the simulation results in [40], where the losses due to a non-painted bumper can be higher than those of painted pieces. In that work, we can also see values in the order of the ones we have measured. Reference [41] describes that the metallic paint permittivity shows an imaginary part higher than that of the pearlescent paint, and that both have higher values than solid paint. Hence, the paint composition could explain why the attenuation of sample C.2 is almost the same as that of sample B.1, despite having only one layer of base. The slightly thicker varnish layer of bumper samples D.2 and E could explain the higher attenuation than the others. Sample E has a similar behavior compared to sample D.2 at lower frequencies, but it presents higher attenuation values in the upper part of the analyzed frequency band. Bumper sample number E has a composition of 10% talc. According to [42], the real part of the permittivity increases with the concentration of talc in the substrate. However, the paint composition of sample E seems to compensate for this effect and still presents the highest attenuation among the samples. To validate the accuracy of the results obtained,  
The uncertainty of the measurements is defined in terms of the experimental standard deviation, s, by (7). Figure 5:0  
where N is the number of measurements performed, \(\mathrm{M_{i}}\) is each individual measurement result and \(\mathrm{M_{mean}}\) is the mean of the 10 results. If we apply a coverage factor of 1.96 (95% of the values falling in the interval [\(-1.96\) s, \(1.96\) s]), we obtain the values shown in Figure 5:1  
If we calculate the relative uncertainty, i.e., normalized by the mean value (Figure 10), we can observe that, in general, it is more difficult to measure the attenuation with precision as the frequency grows. Figure 5:2 Uncertainty in % derived from measurements of sample D.2, with a 95% coverage interval. Figure 5:3 Uncertainty in dB derived from measurements of sample D.2, with a 95% coverage interval. These values of uncertainty agree with those reported in [44] for shielding effectiveness measurements in textiles.