Second-Order Fade Statistics in Underwater Optical Wireless Communications in Air-Bubble and Turbidity-Impaired Environments
The propagation of underwater optical signals through air-bubble-impaired channels induces irradiance fluctuations and partial line-of-sight blockages that degrade the performance of underwater optical wireless communication (UOWC) systems. Although the first-order fading statistics of such channels have been extensively investigated, their second-order statistics, namely the level crossing rate (LCR) and average fade duration (AFD), remain rather unexplored. This paper presents a theoretical and experimental characterization of the LCR and AFD in bubble-impaired UOWC channels under different bubble sizes and water turbidity conditions. Two analytical approaches are developed based on Rice's formula and on the cumulative distribution function (CDF) together with the bivariate CDF of the sampled irradiance, and are validated experimentally. The results show that water turbidity has a negligible effect on fade statistics under small-bubble conditions. In contrast, for large bubbles, turbid water leads to shorter but more frequent fades than tap water, as particle-induced beam spreading reduces the likelihood of deep fades and prolonged blockage events. Finally, the derived second-order statistics are applied to evaluate the packet outage probability (POP) performance using a two-state Markov channel model, demonstrating that the higher fade rate in the turbid water case results in a larger POP despite the shorter fade durations.