## 2 Related Work  
In recent years, cyber-physical-social system (CPSS) attracts a great amount of attention because it considers the integration of the human activity with CPS or IoT. Many applications based on CPSS have been developed, such as intelligent transportation [2] and smart city [3]. The corresponding architecture, methodology, control, and command schemes are also proposed [1; 4; 5]. In particular, the sensing network architecture based on WSN as an important part of CPSS plays a significant role for sensing, transmitting and collecting information. Since the WSN architecture composed of social and physical sensor nodes is significantly different from that of traditional WSN, the related research works on traditional WSN are not applicable for CPSS due to the characteristics of dynamic social mobility for social sensors. Therefore, some novel methods are proposed to solve the emerging problems in CPSS. For example, a moving centroid based routing protocol is presented to deal with the incompletely predictable cyber devices in cyber-physical-social distributed systems [6]. In [7], the authors studied a fusion scheme of cellular network and wireless sensor for CPSS. To prolong the lifetime of the IoT, a novel rendezvous data routing scheme based on lower sensors is proposed to achieve the data transmission for scalable CPS networking infrastructure [8]. In addition, a new sensor trajectory planning method is proposed to solve the trajectory planning problem for robotic CPSS [9]. However, all the above-mentioned methods have not considered the improvement of transmission efficiency of the novel WSN in CPSS. In [24], the authors presented a framework and infrastructure of collaborative CPS to improve the management efficiency of the increasing number of devices. The importance of collaboration among components is considered. On the other hand, the collaborative beamforming technique has been studied extensively in recent years, as it can increase the transmission range and improve the energy efficiency. The related research works on CB transmission in WSN can be divide into three classes, with respect to beampattern analysis, sidelobe level optimization, and synchronization scheme. The analysis of beampattern mainly focuses on the performance of mainlobe, sidelobe, and directivity for different sensor node distributions [10]. The sensor nodes distributions mainly include uniform distribution [11], Gaussian distribution [12], and arbitrary distribution [13]. Based on the analysis of beampattern for different nodes distributions, results are obtained for the performance characteristics of different node distributions and the feasibility of the CB technique in WSN. However, for WSN with small-size nodes, the beampattern performance with random node distribution can hardly meet the transmission requirement in practical applications. To address this problem, the researchers mainly focus on the minimization of peak sidelobe level and the sidelobe control at the unintended receiver directions. The two optimization objectives can be achieved by transmission coefficient optimization and sensor node selection. The two classes of methods can be differential according to the characteristic of transmission coefficient. When the transmission coefficient is continuous, the corresponding methods mainly focus on the optimization of transmission power coefficient. If each sensor node in WSN has only two states, i.e., active on or active off, node selection is generally considered to solve the optimization problem. For transmission coefficient optimization, intelligent algorithms are often used to solve the minimum peak sidelobe or maximum energy efficiency problem for CB in WSN. Due to the non-convex characteristics of this optimization problem, intelligence heuristic algorithms are often employed. For example, the authors in [17; 21] utilized particle swarm optimization (PSO) and the firefly algorithm (FA) to optimize the amplitude coefficient of each collaborative node, respectively.