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, existing literature addresses these impairments in isolation, since their multiplicative coupling in the received signal severely limits conventional estimators and prevents simultaneous recovery. In this paper, we introduce a novel multi-aperture FSO receiver architecture that leverages spatial diversity across a lens array to decouple these intertwined effects. Building on this hardware design, we propose a hierarchical deep learning framework that sequentially estimates AoA, transmitter pointing error, and turbulence coefficients. This decomposition significantly reduces learning complexity and enables robust inference even under strong atmospheric fading. Simulation results demonstrate that the proposed method achieves near-MAP accuracy with orders-of-magnitude lower computational cost, and substantially outperforms end-to-end learning baselines in terms of estimation accuracy and generalization. To the best of our knowledge, this is the first work to demonstrate practical joint estimation of these three key parameters, paving the way for reliable, turbulence-resilient multi-aperture FSO systems.

💡 Research Summary

This paper presents a groundbreaking approach to a critical challenge in Free-Space Optical (FSO) communication: the joint estimation of atmospheric turbulence, transmitter pointing errors (PE), and receiver angle-of-arrival (AoA) fluctuations. Traditionally, these impairments have been studied in isolation, but in practice, they multiplicatively couple in the received signal, making simultaneous estimation with conventional methods extremely difficult and limiting system performance.

The proposed solution is two-fold, combining innovative hardware design with a sophisticated machine learning strategy. First, the authors introduce a multi-aperture FSO receiver architecture. Instead of a single large lens, an array of smaller lenses is employed, each focusing the incident beam onto its own quad photodetector (PD). This design provides spatial diversity and, crucially, enables precise measurement of focal-spot displacement on each quad PD caused by AoA variations. The paper establishes a comprehensive system model that integrates the pointing gain (modeled via a deviated Gaussian beam), the AoA-induced gains on the quad PD (derived in closed-form using Gaussian PSF and normal CDFs), and Gamma-Gamma distributed turbulence fading per aperture.

Building upon this hardware model, the core intellectual contribution is a hierarchical deep learning framework for sequential parameter estimation. Recognizing the complexity of end-to-end joint estimation, the framework decomposes the problem into three cascaded stages inspired by the physical signal structure:

1. Stage 1 (AoA Estimation): A neural network takes the normalized ratios of the four PD outputs from each lens (e.g., (A-B)/(A+B)) as input. These ratios are designed to cancel out common multiplicative scaling factors (like PE and turbulence), allowing the network to focus solely on recovering the AoA.
2. Stage 2 (PE Estimation): Using the AoA estimates from Stage 1, the raw measurements are compensated for the AoA effect. Another network then analyzes the pattern of AoA-compensated aggregate power across all lenses in the array to estimate the transmitter pointing error.
3. Stage 3 (Turbulence & Rx Jitter Estimation): The receiver jitter is simply calculated as the difference between the estimated AoA and PE. Finally, the per-aperture turbulence coefficients are recovered from the residual signal variations after removing the estimated pointing gain component.

This “divide-and-conquer” strategy offers significant advantages: it drastically reduces learning complexity, mitigates overfitting, lowers inference latency, and improves generalization by dedicating specialized networks to simpler sub-tasks. Extensive simulation results validate the framework’s effectiveness. The proposed hierarchical method achieves estimation accuracy very close to the optimal but computationally prohibitive Maximum A Posteriori (MAP) estimator, while requiring orders-of-magnitude lower computational cost. It substantially outperforms a monolithic end-to-end deep learning baseline, particularly in AoA estimation accuracy and data efficiency. The work also provides practical insights, such as guidelines for choosing the lens array size based on turbulence strength. By successfully demonstrating the first practical scheme for joint estimation of these three key parameters in a multi-aperture FSO system, this research paves the way for more reliable, adaptive, and turbulence-resilient optical wireless links for next-generation communication networks.