The application of unmanned aerial vehicles (UAVs) to emerging communication systems has attracted a lot of research interests due to the advantages of UAVs, such as high mobility, flexible deployment, and cost-effectiveness. The UAV-carried base stations (UAV-BS) can provide on-demand service to users in temporary or emergency events. However, how to optimize the communication performance of a UAV-BS with a limited-bandwidth wireless backhaul is still a challenge. This paper focuses on improving the spectrum efficiency of a UAV-BS while guaranteeing user fairness under in-band backhaul constraint. We propose to maximize the minimum user rate among all the users served by the UAV-BS by jointly optimizing the allocation of bandwidth and transmit power, as well as the trajectory of the UAV-BS. As the formulated problem is non-convex, we propose an efficient algorithm to solve it suboptimally based on the alternating optimization and successive convex optimization methods. Computer simulation results show that the proposed algorithm achieves a significantly higher minimum user rate than the benchmark schemes.
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