Cooperative Terrestrial-Underwater Wireless Optical Links by Using an Amplify-and-Forward Strategy +
Footnote †: This paper is an extended version of conference paper: Converging Underwater and FSO Ground Communication Links. In Proceedings of the 2019 Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 3-7 March 2019. [PERSON]  
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scintillation, which involves random fades of the received optical signal intensity. To model this randomly fading characteristic of the atmospheric channel under variable turbulence conditions, extensive research has been performed by the scientific community. Accordingly, different mathematical models for the probability density function of the received irradiance have been proposed so far [22; 23; 24; 25; 26]. In the case of underwater FSO systems, the turbulent medium is the marine underwater environment but the effects over the optical signal are mainly the same, although originating from different physical phenomena. For example, the ocean dynamics that defines the turbulent process in the marine environment is mainly caused by ocean currents describing the motion of water within the oceans. Such currents induce temperature and pressure differences and, therefore, random fluctuations in its refractive index [27]. Factors such as turbidity [28] or salinity [29] of water are, in addition, completely related to refractive index variations, affecting the performance in these systems. In this respect, in order to characterize underwater optical turbulence-induced fading, underwater optical turbulence-induced fading can be described with different stochastic models such as the log-normal distribution [30], appropriated for weak fluctuation regime; the double Gamma model [29], accurately consistent with turbid seawater such as coastal and harbor water; or the Weibull function model, recently proposed in [18] to characterize the fading induced by either salinity or temperature in underwater optical channels. The aim of this work is to extend the scope of optical wireless communications from the terrestrial to the underwater environment, thus inducing heterogeneous infrastructure that includes not only communication links in the atmospheric environment but also their extension to the underwater medium, by means of a cooperative terrestrial-underwater FSO (TU-FSO) system. Thus, the use of cooperative communications is naturally proposed as a consequence of enabling optical technologies in different media, both atmospheric and oceanic. In addition, cooperative transmission can significantly improve performance by increasing diversity order by using the most favorable relays from among the different nodes available in the communication network. This is a well-known technique in radio-frequency systems, where more attention has been directed to the concept of user cooperation as a new form of diversity for future wireless communication systems [31; 32; 33]. In the FSO communications context, cooperative links can be considered by assuming different techniques, such as parallel transmission schemes as well as serial transmission, evaluating bit error rate, outage probability and ergodic capacity when considering amplify-and-forward (AF) retransmission and decode-and-forward (DF) retransmission [34; 35; 36; 37; 38; 39]. Among the different cooperative communication strategies, an AF link with variable gain is adopted in this work, allowing the evaluation of performance in terms of error rate when different block signaling schemes are assumed. Among the statistical distributions defined in the bibliography to model the scintillation effect induced by the medium turbulence, the Malaga or \(\mathcal{M}\)[26] distribution has been adopted here for the terrestrial FSO link, whereas the Weibull distribution [18] has been selected to model the intensity fluctuations produced in the underwater FSO segment.