Fractional Hamilton-Jacobi-Bellman Optimization for Robust Power Control in 6G SAGINs Non-Gaussian Wireless Channels

The sixth-generation (6 G) space-air-ground integrated networks (SAGINs) face critical challenges in establishing accurate analytical channel models and addressing nonstationary, non-Gaussian noise and interference, driven by ultrahigh mobility (e.g., unmanned aerial vehicles (UAVs) and highspeed trains) and heterogeneous propagation environments. To address these issues, this paper proposes a novel wireless channel model using symmetric $\alpha$-stable ($\mathbf{S} \alpha \mathbf{S}$) Lévy processes to accurately characterize non-Gaussian fading behaviors. Based on this model, a fractional Hamilton-Jacobi-Bellman (HJB) equation incorporating generalized Riesz fractional operators is derived to optimize power control under non-stationary interference conditions. Numerical simulations are conducted in a same-frequency, multi-base-station, multi-user downlink scenario, demonstrating the proposed framework’s effectiveness in adaptively adjusting base station transmit power.