Drone base station (DBS) is a promising technique to extend wireless connections for uncovered users of terrestrial radio access networks (RAN). To improve user fairness and network performance, in this paper, we design 3D trajectories of multiple DBSs in the drone assisted radio access networks (DA-RAN) where DBSs fly over associated areas of interests (AoIs) and relay communications between the base station (BS) and users in AoIs. We formulate the multi-DBS 3D trajectory planning and scheduling as a mixed integer non-linear programming (MINLP) problem with the objective of minimizing the average DBS-to-user (D2U) pathloss. The 3D trajectory variations in both horizontal and vertical directions, as well as the state-of-the-art DBS-related channel models are considered in the formulation. To address the non-convexity and NP-hardness of the MINLP problem, we first decouple it into multiple integer linear programming (ILP) and quasi-convex sub-problems in which AoI association, D2U communication scheduling, horizontal trajectories and flying heights of DBSs are respectively optimized. Then, we design a multi-DBS 3D trajectory planning and scheduling algorithm to solve the sub-problems iteratively based on the block coordinate descent (BCD) method. A k-means-based initial trajectory generation and a search-based start slot scheduling are considered in the proposed algorithm to improve trajectory design performance and ensure inter-DBS distance constraint, respectively. Extensive simulations are conducted to investigate the impacts of DBS quantity, horizontal speed and initial trajectory on the trajectory planning results. Compared with the static DBS deployment, the proposed trajectory planning can achieve 10-15 dB reduction on average D2U pathloss, and reduce the D2U pathloss standard deviation by 68%, which indicate the improvements of network performance and user fairness.
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