# Radar-Assisted Multiple Base Station Cooperative mmWave Beam Tracking
## 4 Numerical Results
### Performance for Linear Mobility Scenario  
In linear mobility scenario, the vehicle moves in a straight line at a nearly constant speed. We first evaluate the sensing and communication performances of the proposed multi-RSU cooperation technique for a single vehicle, i.e., 3 RSUs cooperate with each other to track a vehicle. For the kinematic state evolution noises, we set \(\sigma_{\theta}=0.4\), \(\sigma_{d}=1\) m, \(\sigma_{v}=1\) m/s and \(\sigma_{\theta}=0.4\). To evaluate the beamforming performance, we investigate the tracking of AOD during vehicle motion of the V2I network by EKF. Figure 6 presents the tracking performance of AOD per RSU versus the sampling point, both cooperative and non-cooperative. It is shown that the prediction accuracy of AOD can be improved by multi-RSU cooperation, which is closer to the real physical angle. Multi-RSU cooperation integrates the prediction of RSUs with different sensing performances and improves the vehicle location prediction accuracy through distributed sensing, which in turn can improve the AOD tracking effect. As a comparison, the single RSU is easily affected by channel variations and noise. The predicted AOD is likely to deviate from the real AOD when the vehicle is close to the RSU, i.e., in the interval where the AOD changes rapidly. Correspondingly, in Figure 7, we demonstrate the results for radar sense in terms of root mean squared error (RMSE) for both cooperative and non-cooperative AOD tracking. Simulation results show that the angular error predicted by the EKF without multi-RSU cooperation is particularly large and fails to correctly sense the real-time vehicle position. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Carrier frequency & 60 GHz \\ Channel model & eSV (9 paths) \\ Rice factor & 2 \\ Complex RCS & 25 + 25i \\ Bandwidth & 200 MHz \\ Downlink transmit power & 20 dBm \\ Noise power spectral density & \(-174\) dBm/Hz \\ \(\Delta T\) & 0.018 s \\ \(a_{1}\) & 1 \\ \(a_{2}\) & \(6.7\times 10^{-7}\) \\ \(a_{3}\) & \(2\times 10^{4}\) \\ G & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default settings in simulations. Figure 5: The simulated radar-assisted multi-RSU cooperation V2I networks. (**a**) denotes linear scenario. (**b**) denotes curvilinear scenario. To evaluate the communication performance, Figure 8 presents the received SNR at the vehicle side versus the sampling point. Simulation results show that the variation of the received SNR of the vehicle with multi-RSU cooperation is stable, while that of the vehicle without cooperation is fluctuating drastically. The SNR is very related to the direction of the transmitted and received beams, and a higher SNR can only be achieved when both the RSU and the vehicle accurately direct their narrow beams toward each other's direction. Therefore, beamforming based on accurate AOD tracking is a guarantee for higher received SNR. Moreover, in the linear mobility scenario, we assume that the AOD and AOA are equal, so the precision of AOD tracking affects both the transmit and receive beams, which in turn influences the received SNR even more. Figure 6: AOD tracking performance for a single vehicle and 3 RSUs, with antenna number \(N_{t}=N_{r}=64\), \(M=16\), vehicle speed \(v=50\) m/s. Figure 7: AOD prediction RMSE variation for a single vehicle and 3 RSUs, with antenna number \(N_{t}=N_{r}=64\), \(M=16\), vehicle speed \(v=50\) m/s. In Figure 9, the spectral efficiency of different RSU switching methods versus the downlink transmit power is shown. Simulation results show that spectral efficiency is significantly improved when multi-RSU cooperation is employed. Specifically, the proposed multiple base station cooperation improves the spectral efficiency by at least 34% over the non-cooperative scheme when the vehicle is in linear mobility, at a transmit power of 20 dBm, regardless of the RSU switching method.