Design and Deployment Guidelines for UAV-Mounted RIS Under Position Uncertainty

UAV-mounted reconfigurable intelligent surfaces (RIS) are a promising enabler for 6G networks, offering dynamic control of wireless propagation for coverage enhancement, integrated sensing and communication (ISAC), and localization. By exploiting UAV mobility, RIS can maintain favorable line-of-sight links, improving channel quality in dynamic environments. However, UAV positioning uncertainties introduce channel distortions that degrade RIS phase alignment and coherent combining. This work develops a GUM-based uncertainty propagation framework for UAV-mounted RIS channels, mapping UAV position uncertainty through the geometric Tx-RIS-Rx model into the complex cascaded channel. We derive a closed-form stochastic propagation model capturing nonlinear phase uncertainty effects and quantify their impact on channel coherence. The results show that phase uncertainty induces exponential coherence loss, dominating performance degradation. To characterize this transition, we introduce a performance-driven coherence threshold (PCT) that defines the boundary where incoherent combining results in a predetermined performance loss. Results based on analytical scaling laws and Monte Carlo simulations confirm the tightness of the PCT in accurately capturing the coherence transition. This validated threshold is then leveraged to derive optimal UAV-mounted RIS placement, revealing that realistic positioning conditions significantly deviate from the conventional RIS intuition, which typically favors placement close to either the transmitter or receiver.