Predictive Importance Sampling Based Coverage Verification for Multi-UAV Trajectory Planning

Abstract: Unmanned aerial vehicle (UAV) networks are emerging as a promising solution for ultra-reliable low-latency communication (URLLC) in next-generation wireless systems. A key challenge in millimeter wave UAV networks is maintaining continuous line of sight (LoS) coverage for mobile users, as existing snapshot-based trajectory planning methods fail to account for user mobility within decision intervals, leading to catastrophic coverage gaps. Standard uniform sampling for continuous coverage verification is computationally prohibitive, requiring huge number of samples to estimate rare failure events with latencies incompatible with real-time requirements. In this work, we propose a predictive importance sampling (PIS) framework that drastically reduces sample complexity by concentrating verification efforts on predicted failure regions. Specifically, we develop a long short-term memory mixture density network (LSTM-MDN) architecture to capture multimodal user trajectory distributions and combine it with defensive mixture sampling for robustness against prediction errors. We prove that PIS provides unbiased failure probability estimates with lower variance than uniform sampling. We then integrate PIS with multi-agent deep deterministic policy gradient (MADDPG) for coordinated multi-UAV trajectory planning using an adaptive multi-objective reward function balancing throughput, coverage, fairness, and energy consumption. Lastly, the simulation results show how our suggested method outperforms three other state-of-the-art methods in terms of coverage rate, throughput, and verification latency, making proactive coverage management for URLLC-aware UAV networks feasible.