Hierarchical Deep Learning for Joint Turbulence and PE Estimation in Multi-Aperture FSO Systems

Accurate characterization of free-space optical (FSO) channels requires joint estimation of transmitter pointing errors, receiver angle-of-arrival (AoA) fluctuations, and turbulence-induced fading. However, prior work treats these impairments separately because their multiplicative coupling in the received signal limits conventional estimators and hinders simultaneous recovery. We propose a multi-aperture FSO receiver that exploits spatial diversity across a lens array to decouple these effects. Based on this architecture, a hierarchical deep learning framework sequentially estimates AoA, transmitter pointing error, and turbulence coefficients, reducing learning complexity and enabling robust inference under strong atmospheric fading. Simulations show near-MAP accuracy with orders-of-magnitude lower complexity and clear gains over end-to-end learning baselines in both estimation accuracy and generalization. To our knowledge, this is the first practical joint estimation of all three parameters, enabling reliable, turbulence-resilient multi-aperture FSO systems.