## 2 Related Work
Then, a collaborative node set is selected from the candidate nodes based on a circular antenna array. Similarly, the authors in [20] utilized the genetic algorithm (GA) to minimize the peak sidelobe amplitude. Furthermore, several coefficient optimization methods are proposed to extend network lifetime. A multi-objective beampattern optimization problem is formulated in [18], and a metaheuristic method is proposed to calculate the transmission coefficient. This method can ensure low peak sidelobe level and energy consumption, in comparison with the existing heuristic algorithms. In [19], a beampattern optimization method based on non-dominated sorting genetic algorithm II (NSGA II) is proposed to prolong network lifetime for CB in WSN, which effectively reduces the energy consumption and improves the performance ofthe peak sidelobe. The optimization objectives involve the peak sidelobe and beampattern directivity. Since the transmission coefficient is characterized as a continuous variable, these intelligent algorithms generally have high computational complexity and cause redundant energy consumption. In addition, the corresponding implementation schemes are not introduced in details. To provide another solution, the situation that the transmitter of each node only has two power levels (i.e., zero and maximum power) is considered. The optimization objective is mainly to minimize the interference power at direction of the other unintended BS by determining the nodes states in terms of active or sleep states. The beampattern optimization problem is typically regarded as a node selection problem. As the problem is a non-convex and combinatory in nature, it is difficult to be solved in polynomial time. Heuristic and combinatory optimization methods are utilized to minimize the sidelobe level. In [22], the authors proposed a random node selection method. This method randomly selects \(L\) nodes from \(N\) nodes and evaluates whether the sidelobe level of the \(N\) nodes meets the given requirement in the direction of unintended BS. Then, it needs to repeat the above process until the requirement is met. However, the computational complexity of this method is very high which may significantly increase the energy consumption of sensor nodes. To reduce the computational complexity, a node selection algorithm based on cross-entropy optimization (CEO) is proposed in [23]. The evaluation results show that the CEO algorithm has better sidelobe performance and lower computational complexity than the method proposed in [22]. However, it only considers static physical sensor nodes and can hardly be extended to mobile networks including the CPSS. In summary, most of the above-mentioned related works tend to use intelligence algorithms to solve the CB optimization problems for WSN in CPS. These methods assume that the physical sensors in WSN are fixed. However, the social sensors have the property of social dynamic mobility, which significantly affect the performance of CPSS. Therefore, in this work, we focus on the integration of social and physical sensors and propose a corresponding CB optimization method to improve the transmission performance in CPSS.