On Performance Analysis of Cooperative Horizontal and Vertical Underwater VLC Systems with Best Relay Selection  
[PERSON]  
1 Institute of Technology, Nirma University, Ahmedabad 382481, Gujar  
seasons for the Pacific Ocean is studied in [13]. Due to the absorption and dispersion of visible light photons, UWVLC experiences path loss. The transmitted signal is severely attenuated by path loss, resulting in a lower signal-to-noise ratio (SNR) at the receiver and further performance degradation. The analytical expression for the path loss in the UWVLC channel is given in [17], which incorporates geometrical loss along with the losses due to absorption and scattering. In the recent literature, three different communication models of UWVLC, including horizontal, vertical, and slant models, have been proposed [18; 19; 20; 21; 22; 23; 24]. The authors in [24] presented a concatenated multilayered vertical system model considering the optical turbulence only and ignoring the effect of path loss. The authors in [20] presented vertical transmission utilizing log-normal and gamma-gamma channel models for weak and strong oceanic turbulence, respectively; however, the impact of path loss is not incorporated in [20]. The impact of constant undersea blue optical turbulence at a given depth has been considered in [25] to illustrate horizontal communication; however, the authors did not consider the effect of path loss. Spatial diversity and cooperative relaying are widely used techniques to combat fading in wireless communication systems and enhance the performance. Recently, these techniques have been investigated in the context of UWVLC systems [25; 26; 27; 28; 19; 29; 30; 31]. In [25; 26; 27; 28], the performance of the UWVLC system is analyzed for a weak turbulence scenario, in which the fading is modeled using the log-normal probability density function (PDF). The authors in [30] explored diversity for a vertical UWVLC link and derived the bit error rate expression by incorporating pointing errors. The authors in [19] exploited the advantages of cooperative communication by setting up serial relays for horizontal links. The performance improvement when using multiple relays is demonstrated in terms of a reduced bit error rate (BER). The path loss is disregarded, and only the effect of turbulence-induced fading is taken into account. The authors in [31] investigated the performance of vertical links considering the effects of both optical turbulence and path loss using multi-hop serial transmission. To the best of the authors' knowledge, none of the UWVLC cooperative models in the literature address the problem of the line of sight (LOS) channel between the source and destination being fully obstructed by any marine organisms or huge moving objects. Consequently, it is highly necessary to study a system model that may overcome this difficulty by offering many parallel paths from the source to the destination. In this paper, for the first time in the literature, we propose to overcome these issues by using multiple parallel relays and best relay selection. In this paper, we consider a best relay selection-based multi-relay decode-and-forward (DF) cooperative UWVLC system for both horizontal and vertical communication. Best relay selection is a widely used technique in radio-frequency (RF) and optical wireless communication systems employing multiple parallel relays [32; 33; 34]. In best relay selection, the link with the highest SNR is chosen to communicate with the destination node. We consider two horizontal links at a depth of 10 m and 50 m, respectively. The vertical link is modeled as an inhomogeneous cascaded layered link having different turbulence strengths. The transmission distance is assumed to be 60 m in all three considered systems. All the channels are modeled using independent and non-identically distributed log-normal random variables for weak turbulence [19]. We derive novel closed-form analytical expressions for the outage probability and ergodic capacity.