Trajectory Optimization for Cellular-Connected UAV in Complex Environment with Partial CKM

Cellular-connected unmanned aerial vehicles (UAVs) are expected to play an increasingly important role in future wireless networks. To facilitate the reliable navigation for cellular-connected UAVs, channel knowledge map (CKM) is considered a promising approach capable of tackling the non-negligible co-channel interference resulting from the high line-of-sight (LoS) probability of air-ground (AG) channels. Nevertheless, due to measurement constraints and the aging of information, CKM is usually incomplete and needs to be regularly updated to capture the dynamic nature of complex environments. In this paper, we propose a novel trajectory design strategy in which UAV navigation and CKM completion are incorporated into a common framework, enabling mutual benefits for both tasks. Specifically, a cellular-connected UAV deployed in an urban environment measures the radio information during its flight and completes the CKM with Kriging interpolation. Based on the method of grid discretization and spherical approximation, a mixed-integer multi-objective optimization problem is formulated. The problem falls into the category of combinatorial mathematics and is essentially equivalent to determining an optimum sequence of grid points to traverse. Through proper mathematical manipulation, the problem is reformulated as variants of two classic models in graph theory, namely the shortest-path problem (SPP) and the traveling salesman problem (TSP). Two navigation strategies based on the two different models are proposed and thoroughly compared based on numerical results to provide implementable methods for engineering practice and reveal the trade-offs between UAV navigation and CKM completion. Simulation results reveal that the proposed navigation strategies can quickly expand the Pareto boundary of the problem and approach the performance of fully-known CKM.