The use of the unmanned aerial vehicle (UAV) has been foreseen as a promising technology for the next generation communication networks. Since there are no regulations for UAVs deployment yet, most likely they form a network in coexistence with an already existed network. In this work, we consider a transmission mechanism that aims to improve the data rate between a terrestrial base station (BS) and user equipment (UE) through deploying multiple UAVs relaying the desired data flow. Considering the coexistence of this network with other established communication networks, we take into account the effect of interference, which is incurred by the existing nodes. Our primary goal is to optimize the three-dimensional (3D) trajectories and power allocation for the relaying UAVs to maximize the data flow while keeping the interference to existing nodes below a predefined threshold. An alternating-maximization strategy is proposed to solve the joint 3D trajectory design and power allocation for the relaying UAVs. To this end, we handle the information exchange within the network by resorting to spectral graph theory and subsequently address the power allocation through convex optimization techniques. Simulation results show that our approach can considerably improve the information flow while the interference threshold constraint is met.
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