## 5 Performance Evaluation  
In this section, we present the performance evaluation of the proposed algorithm for CB in WSN. We know from the work in [10] that the real experimentation of collaborative beamforming in WSN needs the support of carrier, phase, and time synchronization technique. Although various phase synchronization approaches of CB are presented in the literature [10], the synchronization is still under study. Therefore, we assume the synchronization can be performed and use the simulation experiment to evaluate the CB transmission performance of the proposed algorithm in CPSS. We first consider a WSN with 5 social sensor nodes and 25 physical sensor nodes, which are randomly deployed in a circular area with \(\mathcal{R}=2\lambda\) radius. We assume that each social sensor node has \(S=8\) locations in this area. The movement is based on the model of the social dynamic mobility. The location of each physical sensor nodes remains unchanged in the whole process. We first consider the INR threshold \(INR_{0}=4\) dB. The transmit power of each node has two levels, i.e., zero and \(P_{max}=\delta_{\omega}^{2}\xi/N\), where \(\xi\) is normalized by \(\delta_{\omega}^{2}\). The value of \(\xi\) is the same as that in [11; 23], which is set as 20 dB. The channel coefficient follows a distribution with a zero-mean and \(\sigma^{2}=0.2\). Moreover, the direction of the intended BS is \(\varphi_{0}=0^{\circ}\), and other three unintended BSs are located at \(\varphi_{1}=-130^{\circ}\), \(\varphi_{2}=-50^{\circ}\), and \(\varphi_{3}=120^{\circ}\), respectively. We first analyze the beam pattern performance. Based on the above setting, we present the beam pattern performance for 10 time slots in Figure 3. As we can see, the interference powers for all three unintended BSs are less than the required \(INR_{0}=4\) dB. The result shows the proposed algorithm can adapt to the location change of social sensor nodes. To further analyze the performance, we compare the proposed algorithm with log linear learning (LLL) method [29] and the random node selection algorithm [22]. The LLL is often used to optimize the game theoretical problem [30; 31]. The method focuses on the updating of the action selection probability based on the received utility. The random node selection is to choose \(L\) nodes to meet the requirement of transmission gain in the direction of intended BS or low interference power for the directions of the unintended BSs. The comparison result of average beampattern performance is shown in Figure 4. It can be observed that, when the \(INR_{0}\) is set as 4, the result indicates that the INR at the three unintended BSs of the proposed algorithm is much lower than that of the log-linear learning method and the random node selection algorithm. In addition, the SNR of the mainlobe of our proposed algorithm at the direction of the intended BS is much higher than that of the other algorithms. This is because the proposed algorithm considers the utility of all different position for all previous time slots based on regret matching. For the LLL method, the utilities of different actions are calculated and then the action selection probability is updated based on the current utility. Since the location of social sensor node is dynamic, the LLL method can hardly capture such location change. Figure 4: Average beam patterns of 10 time slots for different methods. The direction of intended BS is \(\varphi_{0}=0^{\circ}\), and the other three directions for unintended BSs are \(\varphi_{1}=-130^{\circ}\), \(\varphi_{2}=-50^{\circ}\), and \(\varphi_{3}=120^{\circ}\), respectively. Figure 3: Beam patterns for 10 time slots. The direction of intended BS is \(\varphi_{0}=0^{\circ}\), and the other three directions for unintended BSs are \(\varphi_{1}=-130^{\circ}\), \(\varphi_{2}=-50^{\circ}\), and \(\varphi_{3}=120^{\circ}\), respectively. Figure 5 shows the average SNR performance for different thresholds of \(INR_{0}\). It can be seen that the proposed algorithm has higher SNR performance than the other two algorithms.