Achievable Capacity Scaling Laws of Three-Dimensional Wireless Social Networks

With the development of aeronautical telecommunication and unmanned aerial vehicles (UAVs), wireless networks will be extended to three-dimensional (3-D) space. Besides, 3-D wireless networks have been widely deployed in battlefields, which consist of aircraft, UAVs, ground troops, and fleets. When nodes in thesewireless networks form swarm and cooperate with each other, there will be social behavior among them and 3-D wireless social networks emerge. Although the study of wireless social networks has been initiated, the capacity of 3-D wireless social networks is unknown. In this paper, we derive the achievable capacity of 3-D wireless social networks. It shows that the capacity is a function of the pathloss exponent, the number of nodes, the social group concentration, the contact concentration, and the size of social group. When the social group concentration or the contact concentration exceeds a threshold, the wireless social network is scalable and the capacity of wireless social network is much larger than that of the wireless network without social behavior. Besides, we discover the existence of a singular point for social group concentration and contact concentration, where the network capacity skips to a larger value than the neighborhood. The results reveal the interplay between wireless communication and social connection in 3-D space, which brings an insight into the design of 3-D wireless networks.