# Radar-Assisted Multiple Base Station Cooperative mmWave Beam Tracking
## 4 Numerical Results
### Performance for Linear Mobility Scenario
Moreover, with multi-RSU cooperation, both the performance of Distance Priority and Radar Echo Strength Priority schemes are very close to that of the RSRP Priority scheme, i.e., the upper bound of spectral efficiency. On the other hand, all three switching methods exhibit low spectral efficiency when there is no cooperation, among which the Distance Priority scheme performs worst due to the extremely inaccurate vehicle position estimation, while the Radar Echo Strength Priority scheme has a relatively large spectral efficiency owing to the consideration of received power. In addition, a deep neural network(DNN)-based beam prediction algorithm is evaluated and used as a comparison scheme. Specifically, the DNN used for training consists of one input layer, two hidden layers and one output layer, where the number of neurons in the hidden layer is set to 128 and an activation function is added between every two layers to enhance the model's nonlinear modeling capability. The input of the DNN is the signal power received by the vehicle from the different RSUs at the previous moment. The output is the index of the optimal served RSU and the optimal beamforming angle (AOD) for the next moment. The RSU and vehicle can use the predicted RSU index and AOD from the DNN model to perform beam tracking in highly dynamic scenarios. Since the predicted metrics have both continuous values such as angle and discrete values such as the RSU index, the preprocessing of the data set is divided into two categories, with mean-variance normalization for continuous values and one-hot coding for discrete values. Moreover, both MSE and cross-entropy are used as loss functions and the Adam algorithm is applied to optimize the neural network. As shown in Figure 9, the spectral efficiency of the DNN prediction-based scheme is higher than that of the no-cooperation scheme, which indicates that the DNN model is able to learn the nonlinear correlation between multiple received signal powers and optimal beam directions. However, the accuracy of DNN prediction of AOD is limited by the types of features used for training and the learning capability of the network, while the massive MIMO-based beamforming system is particularly sensitive to beam angle errors, thus the spectral efficiency of the DNN prediction scheme is lower than that of the multi-RSU cooperation scheme proposed in this paper. Figure 8: Received SNR at the vehicle side 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 10, the performance of the proposed scheme with LOS paths blocked is shown, which gives the variation of its spectral efficiency for different numbers of blocked LOS paths. Specifically, three RSUs are deployed for cooperation, and LOS paths exist between each RSU and the vehicle when there is no blocking. Since the RSU cannot accurately track the vehicle when the LOS path is blocked, which will provide a large error during the multi-RSU cooperation, therefore, it is necessary to recognize which RSU's LOS path is blocked in the existence of blocking and exclude it from the cooperation. Considering that the reflection coefficients of obstacles and vehicles are different, the radar echo strength reflected by obstacles is lower, thus the radar echo strength is used to distinguish the blocked RSUs. The evaluation results are shown in Figure 10. When the LOS paths of all 3 RSUs are not blocked, the multi-RSU cooperation exploits the sensing information provided by all RSUs and thus has the optimal performance. When 1 LOS path is blocked, there are only 2 RSUs involved in cooperation, however, the spectral efficiency only slightly decreases, which indicates that 2 RSUs can still provide a large cooperation gain. When 2 LOS paths are blocked, multi-RSU cooperation cannot be performed, so the spectral efficiency is lowest. Figure 10: Spectral efficiency for a single vehicle and 3 RSUs when LOS path is blocked, with antenna number \(N_{t}=N_{r}=64\), \(M=16\), vehicles speed \(v=50\) m/s.