# Beyond Gaussian Assumptions: A General Fractional HJB Control Framework for L'evy-Driven Heavy-Tailed Channels in 6G

arXiv: https://arxiv.org/abs/2511.07167 · HTML: https://mlsanity.com/paper/2511.07167/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [On Privacy-Preserving Image Transmission in Low-Altitude Networks: A Swin Transformer-Based Framework with Federated Learning](https://mlsanity.com/paper/2605.12566/) (2026)

## Abstract (arXiv)

Emerging 6G wireless systems suffer severe performance degradation in challenging environments like high-speed trains traversing dense urban corridors and Unmanned Aerial Vehicles (UAVs) links over mountainous terrain. These scenarios exhibit non-Gaussian, non-stationary channels with heavy-tailed fading and abrupt signal fluctuations. To address these challenges, this paper proposes a novel wireless channel model based on symmetric α-stable L'evy processes, thereby enabling continuous-time state-space characterization of both long-term and short-term fading. Building on this model, a generalized optimal control framework is developed via a fractional Hamilton-Jacobi-Bellman (HJB) equation that incorporates the Riesz fractional operator to capture non-local spatial effects and memory-dependent dynamics. The existence and uniqueness of viscosity solutions to the fractional HJB equation are rigorously established, thus ensuring the theoretical validity of the proposed control formulation. Numerical simulations conducted in a multi-cell, multi-user downlink setting demonstrate the effectiveness of the fractional HJB-based strategy in optimizing transmission power under heavy-tailed co-channel and multi-user interference.