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This work considers the placement of unmanned aerial vehicle base stations (UAV-BSs) with criterion of minimum UAV-recall-frequency (UAV-RF), indicating the energy efficiency of mobile UAVs networks. Several different power consumptions, including signal transmit power, on-board circuit power and the power for UAVs mobility, and the ground user density are taken into account. Instead of conventional empirical stochastic models, this paper utilizes a pattern formation system to track the instable and non-ergodic time-varying nature of user density. We show that for a single time-slot, the optimal placement is achieved when the transmit power of UAV-BSs equals their on-board circuit power. Then, for multiple time-slot duration, we prove that the optimal placement updating problem is a nonlinear dynamic programming coupled with an integer linear programming. Since the original problem is NP-hard and can not be solved with conventional recursive methods, we propose a sequential-Markovgreedy-decision method to achieve near minimal UAV-RF in polynomial time. Further, we prove that the increment of UAV-RF caused by inaccurate predicted user density is proportional to the generalization error of learned patterns. Here, in regions with large area, high-rise buildings or low user density, large sample sets are required for effective pattern formation.

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Properly 3D placement of unmanned aerial vehicle mounted base stations (UAV-BSs) can effectively prolong the life-time of the mobile ad hoc network, since UAVs are usually powered by batteries. This paper involves the on-board circuit consumption power and considers the optimal placement that minimizes the UAV-recall-frequency (UAV-RF), which is defined to characterize the life-time of this kind of network. Theoretical results show that the optimal vertical and horizontal dimensions of UAV can be decoupled. That is, the optimal hovering altitude is proportional to the coverage radius of UAVs, and the slope is only determined by environment. Dense scattering environment may greatly enlarge the needed hovering altitude. Also, the optimal coverage radius is achieved when the transmit power equals to on-board circuit power, and hence limiting on-board circuit power can effectively enlarge life-time of system. In addition, our proposed 3D placement method only require the statistics of mobile users density and environment parameters, and hence it's a typical on-line method and can be easily implemented. Also, it can be utilized in scenarios with varying users' density.