Performance analysis of rectangular quadrature amplitude modulation for multiple-input multiple-output dual-hop cooperative underwater visible light communication system

This paper investigates a multiple-input multiple-output dual-hop underwater visible light communication (UWVLC) system with decode and forward (DF) relay, considering turbulence-induced fading and path loss. Our research aims to analyze the performance of this system under weak oceanic turbulence, featuring M laser sources at the transmitter and N detectors at the destination. We model the UWVLC channel using a log-normal distribution and employ one laser diode and one photodetector at the relay. By selecting the optimal laser source and photodetector based on maximum instantaneous signal-to-noise ratio (SNR), we derive the cumulative distribution function (CDF) of the end-to-end SNR. Utilizing this CDF expression, we provide closed-form expressions for outage probability and average symbol error probability (ASEP) using Gauss–Hermite quadrature techniques for the rectangular quadrature amplitude modulation scheme. We analyze ASEP for different constellation points with M sources and N photodetectors and present simulation results demonstrating ASEP versus average SNR, as well as outage probability versus average SNR, showcasing close agreement with analytical predictions. Moreover, we offer insights for system designers by presenting a trade-off between constellation points and the number of lasers, along with the number of photodetectors, to optimize system performance.