## 1 Introduction  
Cyber-physical-social system (CPSS) is attracting increasing attention through the integration of social system and cyber-physical system (CPS). The CPSS as a novel paradigm enables the deep interaction of social space and CPS or Internet of Things (IoT), which brings significant changes for improving the service and management of complex physical systems. Architectures, methods and schemes of CPSS for different application areas have been proposed [1; 2; 3; 4; 5; 6; 7; 8; 9]. The wireless sensor network (WSN) as the sensing network is one of the most important parts. Importantly, compared with CPS or IoT, the CPSS contains a large number of social sensors, such as smart phones and tablets. The social sensors have a great impact on data collection, transmission, and processing. The novel WSN composed of social and physical sensors undertakes the collection task of sensing information and plays an important role in CPSS. Since the sensor nodes are battery-powered and the battery capacities are limited, improving energy-efficiency of transmission for the novel WSN in CPSS is still one of the most important research topics. In recent years, the emerging collaborative beamforming (CB) technique provides a novel solution for improving energy efficiency of information transmission in traditional WSN. However, due to the characteristic of dynamic social mobility for social sensors, the related studies of CB in traditional WSN composed of physical sensors are not applicable for the CPSS. Our objective was to integrate the social dynamic model with collaborative beamforming technique to solve the problem of coordinated transmission of WSN with social and physical sensors for the CPSS. In CPS, the traditional WSN only considering fixed physical sensors is widely used to sense or collect the large-scale information due to the characteristics of low cost, lower power and the small devices. The energy efficient schemes for the traditional WSN have been paid great attention in the past few decades. In recent years, the emerging of collaborative beamforming (CB) technique brings a novel solution for improving the energy efficiency of WSNs [10]. The CB technique requires that all fixed sensor nodes in WSN divide into different clusters. All fixed sensor nodes in a cluster transmit collaboratively the sensing information to the intended base station (BS). In process of transmission, the phase synchronization is achieved by the existing synchronization methods. The CB can enhance the transmission gain in intended direction and reduce the interference power at other directions. In other words, these fixed sensor nodes in CB can obtain the beampattern with stable mainlobe and low sidelobe by the cooperative way. Since the sensor nodes are randomly deployed in the given areas, the random distribution of sensor nodes cause that the amplitude of sidelobe in beampattern presents the unpredictability [11; 12; 13]. It means that the node locations have an important impact for the amplitude of sidelobe [14]. However, the high sidelobe level can lead to the strong interference for the others unintended BSs. Therefore, achieving the required sidelobe level can effectively improve the service performance of CPS. On the other hand, the existing CB optimization methods for sidelobe control in WSN mainly consider the fixed and static sensor nodes. These methods generally include transmission coefficient optimization [15; 16; 17; 18; 19; 20] and sensor node selection [21; 22; 23]. These methods integrate the coefficient optimization into node selection. They first use the intelligence algorithm to optimize the peak sidelobe level and then select an optimal sensor node set based on the regular antenna array. However, these research works have not presented the analysis of the computational complexity and the implementation scheme of information transmission.