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Unmanned aerial vehicles (UAVs) can be used as aerial wireless base stations when cellular networks go down. Prior studies on UAV-based wireless coverage typically consider downlink scenarios from an aerial base station to ground users. In this paper, we consider an uplink scenario under disaster situations (such as earthquakes or floods), when cellular networks are down. We formulate the placement problem of UAVs, where the objective is to determine the locations of a set of UAVs that maximize the time duration of uplink transmission until the first wireless device runs out of energy. We prove that this problem is NP-complete. Due to its intractability, we start by restricting the number of UAVs to be one. We show that under this special case the problem can be formulated as a convex optimization problem under a restriction on the coverage angle of the ground users. After that, we propose a gradient projection-based algorithm to find the optimal location of the UAV. Based on this, we then develop an efficient algorithm for the general case of multiple UAVs. The proposed algorithm starts by clustering the wireless devices into several clusters where each cluster being served by one UAV. After it finishes clustering the wireless devices, it applies the gradient projection-based algorithm in each cluster. We also formulate the problem of minimizing the number of UAVs required to serve the ground users such that the time duration of uplink transmission of each wireless device is greater than or equal to a threshold value. We prove that this problem is NP-complete and propose to use two efficient methods to determine the minimum number of UAVs required to serve the wireless devices. We validate the analysis by simulations and demonstrate the effectiveness of the proposed algorithms under different cases.

UAVs to the Rescue: Prolonging the Lifetime of Wireless Devices Under Disaster Situations