# Experimental Evaluation of a MIMO Radar Performance for ADAS Application
## 3 Results
### Mean Error in Range  
Each of the pedestrians in the first scene was also followed separately, calculating the average error of the position of the echoes that, with high probability, are coming from the target under study. As explained, the echoes that come from the target (or pedestrian) under test have to be selected manually, and the position of those echoes must be compared with the corresponding points on the estimated instantaneous trajectory of each target. In Figure 6, the obtained mean error in range is shown for the three pedestrians. The basic limit of the system's spatial resolution is given by the known expression  
\[\Delta r=\frac{c}{2 ST_{c}}, \tag{2}\]  
\(S\) is the slope of the frequency-temporal variation, \(c\) is the speed of light, and \(T_{c}\) is the duration of a chirp. In our case, we have \(S=20\;\mathrm{MHz}/\upmu\mathrm{s}\) and \(T_{c}=N_{pc}/f_{s}=21.33\;\upmu\mathrm{s}\). And it results \(\Delta r=0.35\;\mathrm{m}\). As it can be seen in Figure 7, the mean error in the localization of the targets does not depend critically on the selected value for the \(PFA_{range}\), although it is clearly better for low values. This behavior comes from the fact that the targets have been detected correctly most of the time. However, on some occasions, echoes affected by noise or false targets have been considered good. This can be seen in Figure 8, where the error in the localization of one of the pedestrians has been represented as a function of the distance to the radar in two cases. There are two appreciable differences between the two cases shown in the figure. For the higher value of \(PFA_{range}\) a quite large number of echoes have been accepted by the system/observer as coming from the target, including some of them with an important error (-2.5 m). For the low value of that parameter, however, the number of valid echoes is much lower, as is the maximum error (<1 m). It must be remembered, however, that the selection of the 'correct' echoes has been carried out visually, considering what the temporal processing of the signals was showing on the screen. This adds a point of arbitrariness that, on the other hand, cannot be avoided. Nor if the task is performed by an algorithm or an  
Figure 6: Effective probability of false alarm in the three scenes, obtained as a function of the PFA parameter chosen for the detection of targets at a distance. For the selection of velocities, the value \(PFA_{vel}=0.2\;\) was used in all cases. artificial intelligence application, because the system does not know previously the number, nature, trajectory, or speed of the targets. The evaluation of errors has also been made for the two paths of the motorbike in scenario 2, as shown in Figure 9. As the motorbike has an important horizontal dimension, the position mean error is higher than in the case of pedestrians, although, on the other hand, in this particular experiment, the radar never has a complete vision of that horizontal dimension of the vehicle due to the angle of the paths with respect to the radar position (see Figure 4). Figure 8: Range error committed along the tracking of one of the targets in scenario 1, for two values of the \(\mathit{PFA}_{\mathit{range}}\) parameter. Figure 7: Mean error in distance obtained for individual targets in the first scenario. To end this section, in Figure 10, the range error measured during the evolution of the motorbike in scenario 3 is shown. Actually, the trajectory with which the position of the echoes is being compared has been deduced from the echo map itself, averaging the position of the echoes as they appear in time in order to obtain a smooth and continuous path. It could be seen that important errors are reported in some specific positions of the motorbike, which correspond to the moments when the motorcycle is traveling perpendicular to the line of sight of the radar (see Figure 5).