# Car Bumper Effects in ADAS Sensors at Automotive Radar Frequencies
## 5 Results and Discussion  
The first measurements were taken with the samples as provided by the company, i.e., with the actual curvature they had. Although they tried to provide the flatter samples they could, it was almost impossible to find a perfectly flat section in a real-world modern car bumper. For each type of composition (A, B, etc. ), two samples were measured (A.1 and A.2, B.1 and B.2, etc. ), except for sample E, as only one piece was available. The measured attenuation for each bumper sample is depicted in Figure 6. The horizontal axis represents the frequency, and the vertical axis represents the attenuation in dB. Each colored line depicts the results for a specific sample type. The same color but different line styles (solid or dotted) were used for samples with the same composition. From the figure, we can observe that samples of the same material present more differences in their attenuation compared to others with different compositions. This could be associated with the air gaps between the sample and the holder caused by the curvature that changes among  
Figure 5: Sample holder, (**a**) receiving side, and (**b**) transmitting side. the samples depending on how they are positioned. This seems to cause variability that compromises the accuracy of the measurements. With the aim of isolating both effects, the curvature and the composition itself, we flattened one sample of each bumper type and then repeated the measurements. The measurement outcomes for the flat samples are shown in Figure 7. The results show a decreasing trend of the attenuation with the frequency, with reductions between 0.55 dB and 0.86 dB when comparing the end frequencies in the radar band. This result agrees with the transmission measurements for painted polycarbonate samples described in [38] for the same frequency band. Figure 6: Measured attenuation as a function of the frequency for the different bumper samples. Figure 7: Measured attenuation as a function of the frequency for flat bumper samples. If we compare the results of the curved and flat samples, despite the differences, the trend and order of magnitude are the same. Thus, the rest of the analysis focuses on the flat samples. The maximum attenuation observed in the flat samples is 1.25 dB. Thus, the propagated radar signal would suffer an additional attenuation lower than 2.50 dB when passing through the bumpers (considering the out and back paths in the monostatic radar configuration typical for these car devices). This is translated into a needed increase in the transmitted power (by means of higher gain amplifiers and/or antennas) to maintain the same detection range, or into a reduction in the detection range when maintaining the same antennas and amplifiers. The reduction in detection distance can be calculated using the radar range equation, which relates the power delivered to the receiver with the transmitted power within a radar system. Its simplest form for a monostatic radar is [39],  
\[\mathrm{P_{r}}=\frac{\mathrm{P_{t}G^{2}\lambda^{2}\sigma}}{(4\pi)^{3}\mathrm{R ^{4}}} \tag{2}\]  
where  
* \(\mathrm{P_{r}}\) is the received power;
* \(\mathrm{P_{t}}\) is the transmitted power;
* \(\mathrm{G}\) is the gain of the antenna (transmitting and receiving antenna is the same);
* \(\lambda\) is the wavelength;
* \(\sigma\) is the radar cross-section of the target;
* \(\mathrm{R}\) is the distance between the radar and the target.