A Unified Channel Model and Performance Evaluation for Underwater-to-Air Optical Links

This paper develops a conditional statistical framework for nominally normal underwater-to-air optical links. It combines bulk attenuation, normalized log-normal atmospheric and Weibull underwater fluctuations, and entrance-pupil collection with surface-tilt-dependent Fresnel transmission. Conditioning transmission and beam displacement on a common tilt preserves their dependence. Product distributions with explicit support and Jacobians yield integrals valid for arbitrary positive Weibull shape. Average uncoded OOK bit error rate (BER) and outage are evaluated using consistent power, noise and SNR definitions. Independent component-wise Monte Carlo verifies the full conditional model at six reference configurations; targeted importance sampling checks selected BER values down to approximately 6 x 10^-9. A circular-pupil Gaussian integral reveals parameter-dependent errors in the equivalent-beam collection approximation, including a 36.9% BER underestimate at one tested operating point. Conditional power and distance studies therefore use the circular-pupil reference and distinguish low-error short-air-segment conditions from collection-limited conditions. Source-anchored spectral and water-type contrasts, together with illumination and receiver checks, identify the dependence of these results on the prescribed operating conditions. The framework supplies reproducible error and outage calculations within a single-patch scalar model; physical operating ranges additionally depend on the surface, propagation and receiver assumptions.