Model-based deep unfolding for robust and efficient free-space optical channel estimation under turbulence and impulsive jamming

Abstract

Abstract Atmospheric turbulence makes free-space optical (FSO) channels fluctuate, and a receiver that does not track them pays in bit errors. As a controlled simulation study, we address pilot-aided channel estimation for an on–off keying direct-detection link with temporally correlated Gamma–Gamma fading and an on–off jammer that makes the additive noise heavy-tailed. We propose URMNet, a compact interpretable network that unrolls a robust maximum-a-posteriori iteration: each layer reweights pilots to suppress jammer outliers and then applies a learned denoiser between them. Unlike the black-box deep estimators used in FSO, every layer is a step of the underlying estimator. URMNet, with 8,989 parameters, is compared against classical estimators and six learned baselines, including Kolmogorov–Arnold and Mamba architectures. Across eight seeds, with confidence intervals and paired significance tests, it is significantly the most accurate under Gaussian noise, within 1.4 dB of a Bayesian Cramer–Rao bound, and under jamming it matches the strongest architectures using 2.4 to 4.4 times fewer parameters; the efficiency is in model size, not arithmetic or speed: weight-tied unrolling gives it the highest FLOP count and mid-pack inference time. We report plainly the regimes where a classical robust estimator still wins, and validate the statistical channel against a wave-optics propagation.