Validity-Aware Reliability Analysis and Power-Margin Design for Fog-Limited Free-Space Optical Links

Reliable design of fog-limited free-space optical links requires attenuation-model evidence, optical collection, stochastic fading, and receiver sensitivity to be treated consistently. We present a validity-aware design framework that screens empirical fog laws against source-supported conditions and propagates the retained attenuation through a Gaussian-beam link and a common positive-intrinsic-negative (PIN) intensity-modulation/direct-detection (IM/DD) on–off keying (OOK) receiver model. For an unspecified fog type, the retained design set comprises Esmail and Ijaz; its maximum does not bound atmospheric attenuation outside this evidence-qualified set. The stochastic gain combines exact relative circular-aperture pointing coupling with weak-fluctuation, aperture-averaged lognormal scintillation. The aperture-averaging relation uses the plane-wave interpolation with the wave-number-dependent aperture parameter, and the scintillation index is converted to log-irradiance variance by moment matching. This plane-wave treatment is a stated surrogate for the Gaussian-beam terminal cases. At V = 0.483 km and L = 0.983 km, the retained-set required power is approximately 26.40 dBm, with a 3.22 dB model-form margin and a 0.43 dB stochastic-fading margin. At V = 0.50 km and L = 1.00 km, a near-collimated terminal reduces the retained-set required power by 4.86 dB; fixing the receiver threshold and allowing 0.5 dB RMS threshold-estimation error increase it by about 0.25 and 1.20 dB, respectively. The production 64/64 Hermite/Laguerre quadrature is checked against independent integration for representative system configurations, and other design conditions retain explicit numerical-accuracy limits. The resulting maps quantify model-conditional reliable distance, minimum power, and physical design margins.