Channel Knowledge Map (CKM)-Assisted Multi-UAV Wireless Network: CKM Construction and UAV Placement

Channel knowledge map (CKM) has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle (UAV) communications, by exploiting the site- and location-specific radio propagation information. This paper investigates a CKM-assisted multi-UAV wireless network, by focusing on the construction and utilization of CKMs for multi-UAV placement optimization. First, we consider the CKM construction problem when data measurements for only a limited number of points are available. Towards this end, we exploit a data-driven interpolation technique, namely the Kriging method, to construct CKMs to characterize the signal propagation environments. Next, we study the multi-UAV placement optimization problem by utilizing the constructed CKMs, in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations (GBSs). However, the weighted sum rate function based on the CKMs is generally non-differentiable, which renders the conventional optimization techniques relying on function derivatives inapplicable. To tackle this issue, we propose a novel iterative algorithm based on derivative-free optimization, in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions, and accordingly, the UAVs' placement locations are updated by maximizing the approximate function subject to a trust region constraint. Finally, numerical results are presented to validate the performance of the proposed designs. It is shown that the Kriging method can construct accurate CKMs for UAVs. Furthermore, the proposed derivative-free placement optimization design based on the Kriging-constructed CKMs achieves a weighted sum rate that is close to the optimal exhaustive search design based on ground-truth CKMs, but with much lower implementation complexity. In addition, the proposed design is shown to significantly outperform other benchmark schemes.