Path Selection in Parallel Multihop UVLC Systems Over Turbulence Channels

This article explores an underwater communication system using visible light, featuring multiple parallel relay paths and several decode-and-forward relays per path. In traditional multihop systems, the failure of a single relay can result in the collapse of the entire system, rendering single-path multihop systems unreliable. Therefore, the adoption of parallel paths becomes important to enhance system robustness. In pursuit of reducing hardware complexity, the primary goal is to select one path from these parallel options. However, the challenge lies in choosing the best path, given various factors such as noise affecting channel coefficient estimation and the impact of erroneous feedback channels. In light of these challenges, our investigation delves into a comprehensive evaluation of the $l\mathrm{{th}}$ best path selection in underwater environments. We consider both weak and moderate/strong turbulence conditions, with “weak” and “moderate/strong” turbulence conditions modeled by lognormal (LN) and gamma–gamma (GG) distributions, respectively. Closed-form expressions for the exact, approximate, and asymptotic probability of an outage are derived for both distributions when the $l\mathrm{{th}}$ best path is chosen for transmission. Additionally, we explore the incremental diversity order for LN turbulence channels and investigate the diversity order for GG turbulence channels. This comprehensive approach enables a more robust evaluation of the system's performance under various underwater conditions.