An Insight to the Outage Performance of Multi-Hop Mixed RF/FSO/UWOC System

: In this paper, we investigate the outage performance of the three-hop mixed system integrating radio frequency (RF), free space optics (FSO), and under water optical communication (UWOC) system. The closed-form analytical expressions for the outage probability of the system are derived. In the considered system, the RF channel follows the Nakagami-m distribution, the FSO channel observes the Gamma-Gamma fading statistics, and the UWOC link experiences a mixture Exponential Generalized Gamma (EGG) fading distribution. To verify the derived analytical expressions, numerical simulations are also carried out, and we present the inﬂuence of the various link parameters such as path loss, atmospheric turbulence, pointing errors, angle-of-arrival ﬂuctuations, water salinity, and scintillation on the performance of the decode and forward (DF) relayed multi-hop communication system.


Introduction
The free space optical (FSO) network has become a competent point-to-point wireless transmission solution because of the availability of its high bandwidth in the unregulated spectrum [1]. When the FSO networks are compared with their counterpart radio frequency (RF) systems, they offer much higher bandwidth and capacity. In wireless communication systems, the FSO provides a favorable solution for last mile connectivity issues. It is suitable for a wide range of applications like the back-haul of cellular systems, enterprise/building connectivity, disaster recovery redundant backup links, etc. [2]. The FSO systems need a direct line-of-sight (LOS) path and their transmission is tremendously controlled by the atmospheric turbulence and the pointing error; hence, these factors affect the performance of FSO systems [3][4][5][6][7]. To combine the benefits of both lines, mixed networks that include both RF and FSO links have been recommended. While the RF link is a great complement bution under the influence of pointing errors, and Exponential Generalized Gamma (EGG) distribution, respectively. The first relay node receives information from the source node located at a distance via RF link. The first intermediate DF relay node then transmits the signal towards the second intermediate DF relay node via FSO link. Furthermore, the second relay node decodes and forwards the received signal towards the destination receiver on the UWOC link. To investigate the performance of the proposed three-hop mixed system model, the SNR statistics of the considered multi-hop system are derived in terms of the cumulative distribution function (CDF) of the end-to-end instantaneous signal-to-noise ratio (SNR) of the system. Later, these statistics are utilized to derive the closed-form analytical expression for the system outage probability. The proposed mixed system's behavior under high-SNR conditions is monitored. Additionally, numerical simulation is used to confirm the mathematical analysis of the suggested model while taking into account the influence of different link factors, such as the effect of path loss, atmospheric turbulence, pointing errors, angle-of-arrival (AOA) fluctuations, multipath fading parameter, water salinity, scintillation caused by air bubbles, and temperature gradient.
The proposed three-hop communication system model and channel models of RF, FSO, and UWOC links are presented in Section 2. The outage probability analysis of the proposed system and asymptotic outage analysis are carried out in Sections 3 and 4, respectively. The simulation results and numerical results are demonstrated in Section 5, and lastly, the paper is concluded in Section 6. For ease of reference a list of abbreviations and symbols utilized in the paper are given in Table 1 and Table 2, respectively.

System Modeling
The system model demonstrated in Figure 1 presents a three-hop mixed RF/FSO/UWOC system employing DF relaying protocol. In the proposed model, the source node shown by S sends the information signal towards the destination node denoted as D.
We assume that no direct communication is feasible between the source and the destination nodes due to different environmental obstacles and long distance; hence, communication between these two takes place with the help of two DF relays, termed R 1 and R 2 . The source S is situated at the distant location and sends the signaling information towards the destination node D, such as ocean divers. The S in the first hop sends the information signal towards the first relay R 1 , which is mounted on the lighthouse. This link (SR 1 ) is assumed to be an RF link. The received information signal at R 1 is decoded and converted into the FSO signal and forwarded towards the second relay, R 2 , which is mounted on a floating vehicle (FV) over the sea surface, such as a boat used by the ocean divers. The second relay, R 2 , decodes the received FSO signal, converts it to a visible light signal, and forwards the optical signal to the divers under the sea surface via UWOC link. Here, the Doppler effect is ignored and the UWOC link is assumed to be static. For the presented three-hop mixed system, the RF link is assumed to be modeled by Nakagami-m distribution, the FSO channel is modeled by the Gamma-Gamma fading statistics considering the impact of pointing errors, atmospheric turbulence, and angleof-arrival (AOA) fluctuations, denoted as θ FOV , and the UWOC link is assumed to be modeled by EGG distribution, respectively. It has been assumed that the optical signal transmission underwater is remarkably influenced by absorption and scattering, rather than the turbulence caused by the temperature gradient and air bubbles under the water.

RF Link Modeling
The Nakagami-m channel model is a generalized model and mathematically tractable [20]. Here in this section, we deal with the detailed description of the RF link modeling. At R 1 , the CDF of the instantaneous SNR, F γRF (γ), is given by Equation (2), as in [27], as whereγ RF represents the average SNR, γ is the instantaneous SNR of the RF link, Γ(., .) stands for the upper incomplete Gamma function, L RF is the RF channel path loss given as L RF = Ad α RF , where α represents the path loss exponent, A is assumed to be a constant related to the transmission environment and frequency of the information signal, and d RF represents the distance between S and R 1 . The parameter m denotes the Nakagami-m fading parameter and it can be calculated as m ≈ (K+1) 2 2K+1 ; K here stands for the Rician factor [28].

FSO Link
The FSO link follows the Gamma-Gamma fading statistics with the impact of the angle-of-arrival of the FSO beam. The Gamma-Gamma fading model is a general and mathematically tractable composite FSO model [4]. The probability density function (PDF) of instantaneous electrical SNR, f γFSO (γ), is given, as in [29,30], as , ρ is optical-to-electrical efficiency, P t 1 is source-transmitted optical power, σ n 1 is the standard deviation of Gaussian noise, σ 2 θ is the variance of T x − R x misalignment orientations, and pointing error ζ = w e 2σ s ; here σ s stands for the standard deviation of the pointing error displacement, and w e is the equivalent beam width at the receiver. α f and β f represent the atmospheric turbulence parameters associated with the atmospheric conditions and Γ(·) stands for the standard Gamma function. A 0 =er f 2 (v), where er f (.) denotes the error function and h l stands for atmospheric path loss, given as in [31]. Now integrating (2) using ([Equation (07.34.21.0084.01) [32]), we derive the closed-form expression for the CDF of instantaneous SNR for the FSO link given as (3)

UWOC Link Modeling
This section deals with UWOC link modeling. It has been assumed that the optical signal transmission underwater is remarkably influenced by absorption and scattering, rather than the turbulence caused by the temperature gradient and air bubbles under the water. The combined effect of the fading can be appropriately characterized by the Exponential Generalized Gamma distribution with different water salinity. The CDF of the instantaneous SNR, F γUW (γ), of the UWOC link is given by Equation (21) in [33] as where w, λ, a, b, c are the parameters associated with the EGG distribution, r is set to 2, which specifies the intensity modulation and direct detection (IM/DD) scheme, and µ r is the average SNR of the UWOC link. The parameters employed for different water salinity and the temperature gradient for varying bubble levels are taken from [33].

Outage Probability Analysis
The outage probability performance of the proposed mixed multihop communication system is investigated in this section. For the proposed system, the end-to-end instantaneous SNR of the received signal at node D, γ DF , is given as [34] where, γ FSO , γ RF , γ UW represent the instantaneous SNRs of FSO, RF, and UWOC links, respectively. Using (5), the equivalent CDF of the γ DF can be written, as given in [35], as Further, the probability of the outage can be an important tool in evaluating the reliability of the communication systems. It can be defined as the probability when γ DF is lower than the specific value of the threshold, γ th such that the system performance is considered as insufficient. Accordingly, the P DF out may be evaluated from (6) by substituting γ by γ th , that is, P DF out (γ th ) = F γDF (γ th ). Therefore, substituting F γRF (γ), F γFSO (γ), and F γUW (γ) from (1), (3), and (4), respectively, and putting γ th in place of γ, we obtain the closed-form expression for the probability of outage of the proposed mixed RF/FSO/UWOC system, shown as

Asymptotic Analysis
The analytical expression for the outage probability of the considered system model is quite complex. Therefore, asymptotic outage probability provides more understanding on the impact of the system's channel parameters on the system's outage probability. By assuming an independent and identically distributed case, that is,γ RF =γ FSO =γ UW , the overall asymptotic outage probability can be written as the sum of the individual asymptotic CDF of the each channel SNR. In the high-SNR region, the overall asymptotic outage performance of the triple-hop mixed communication system can be approximated as where F ∞ γRF (γ th ), F ∞ γFSO (γ th ), and F ∞ γUW (γ th ) are CDF's of S → R 1 , R 1 → R 2 , and R 2 → D links at high-SNR regimes, respectively.
The coding gain and the diversity order can be defined as (G xy Cγ ) −G xy D , where xy ∈ {SR 1 , R 1 R 2 , R 1 D}, G xy C is the coding gain and G xy D is the diversity order of the link [36]. We need to find out F ∞ γRF (γ th ), F ∞ γFSO (γ th ), and F ∞ γUW (γ th ) one by one as shown below.

RF Link (S → R 1 )
At high-SNR regime, the CDF of the first hop, i.e., the RF link given in (1), can be re-written according to the form given in [37], as

FSO Link
At high-SNR regime, the CDF of the FSO link, as given in (3), can be written asymptotically using identity ( [38], Equation (6.2.2)) [36], as where a j = a p (j), for j = 1 to 3,

UWOC Link (R 2 → D)
The asymptotic expression of the CDF of the third hop, i.e., the UWOC link, given in (4), can be expressed as in [39], as Further, substituting (9), (10), and (11) in (8) and re-arranging terms, the asymptotic expression at high-SNR regime for the end-to-end outage probability of the system can be given as Now, coding gain and diversity gain are simply evaluated from the asymptotic outage probability of the system mentioned in (12). It can be clearly seen that the system performance is dominated by the parameters of the worst link among the three links. Hence, the diversity gain of the system is min( b k 2 , m, ac). Based on G D , there can be three cases to examine the system's overall outage performance, as shown below.

1.
Case 1: Among three links, when only one link is dominating, the coding gain can be written as 2. Case 2: When two links are dominating out of three links, the coding gain can be written as 3. Case 3: When all three links are dominating, then the coding gain can be written as

Numerical Results
For the proposed model, the numerical results are plotted for the outage probability at low-and high-SNR regimes for fresh water and salty water in the presence of air bubbles and temperature gradient. We are considering the intensity modulation and direct deduction technique; thus, r = 2. The threshold SNR (γ th ) is set at 5 dB. The FSO link parameters such as atmospheric attenuation, h l = 0.9, length of the turbulent FSO link, d FSO = 1 km, beam radius of the turbulent link, w d 1 = 2.5 m, the jitter, σ s = 30 cm, and turbulence parameters, α f and β f , for the FSO link are assumed to be 5.42 and 3.8. Further, the FOV angle of the FSO transceiver at R 2 is 7 mrad and the standard deviation of AOA fluctuations is considered to be σ θ = 7 mrad . The values of considered UWOC link parameters i.e., bubble levels, temperature gradient, w, λ, a, b, c have been adopted from [33]. Figure 2 presents the outage performance of the proposed system under the influence of the AOA fluctuations. It has been demonstrated that the outage performance of the system is not good for the low values of the AoA. However, the outage performance of the system improves significantly with increase in the AOA, θ FOV . For example, at SNR = 25 dB and θ FOV = 4 mrad, the P DF out is equal to 2.499 × 10 −3 , and at SNR = 25 dB and θ FOV = 8 mrad, the P DF out is equal to 6.238 × 10 −8 . Moreover, it is also noticed that after a certain value of average SNR, the other impairments dominate over AOA fluctuations, and the effect of the AOA fluctuations becomes negligible. Figure 3 shows the outage performance of the proposed system under varying pointing errors assuming moderately turbulent conditions. It is observed from the plots that the outage probability of the considered system decreases as the value of ζ increases; hence, the system performance increases as pointing errors, parameter ζ, increase. It can be said that the system's performance improves with the decreasing impact of the pointing errors in the FSO channel. The pointing errors result from misalignment between the transmitter and receiver or turbulence. Figure 4 presents the outage probability of the system w.r.t. the Nakagami fading factor, m with varying average SNR (dB) for the salty water type. It is observed that the system shows high values of outage probability at low values of m (severity is high). The severity decreases as the value of m increases. Further, it is also observed that after a certain value, i.e., m = 5, the outage performance of the system becomes stable as the impact of fading due to the RF link becomes negligible. Further, the impact of the fading in the RF link also reduces with an increase in the average SNR of the system. For example, at m = 5, SNR = 5 dB, the outage probability is equal to 7.401 × 10 −4 and at m = 5, SNR = 20 dB, the outage probability is equal to 3.756 × 10 −6 .    The plot in Figure 5 demonstrates the outage probability of the mixed system under the impact of turbulent water conditions in both water types, i.e., fresh water and salty water types. As expected, the outage performance of the system improves with the decrease in temperature gradient and air bubbles. For example, for fresh water with average SNR at 8 dB and bubble level 4.7 L/min, the P DF out is 2.8836 × 10 −6 , and with bubble level 16.5 L/min, the P DF out is 3.4207 × 10 −4 . Also, for salty water with average SNR at 8 dB and bubble level 4.7 L/min, the P DF out is 2.2815 × 10 −6 , and with bubble level 16.5 L/min, the P DF out is 2.0146 × 10 −3 . Figure 6 shows the outage performance of the system at low-SNR and high-SNR regimes. The graph is plotted for the salty water type and lower bubble level and temperature gradient with pointing error = 2, for moderately turbulent atmospheric conditions with AOA fluctuation = 7 mrad. It is observed that in the simulation results, the asymptotic outage plots are in perfect agreement with the theoretical analysis and the Monte Carlo simulation, hence validating the analytical modeling of the three-hop mixed RF/FSO/UWOC system. Figure 7 shows the influence of atmospheric turbulence on the outage probability of the system w.r.t. the average SNR in dB at the destination node. We assume direct detection at the receiver with γ th at 0 dB. The outage probability of the system is analyzed in different atmospheric turbulence conditions for ξ = 2. The outage probability in highly turbulent conditions is more and it decreases from moderately to weakly turbulent conditions. From the figure it can be seen that the outage probability of the three-hop system reduces as the atmospheric turbulence changes from high-to low-turbulence scenarios. However, for the proposed model, the changes in the outage performance are not significant, and hence the system also slightly outperforms in highly turbulent conditions.

Conclusions
In this paper, a UAV-based relay-assisted hybrid mixed RF/FSO/UWOC system has been proposed to maintain communication between two distant nodes, one above the terrestrial building and the other underwater. The analytical exact closed-form expressions for the outage probability of the system have been obtained using the CDF of the end-to-end SNR of the system. The outage performance of the system has also been analyzed at the high-SNR regime to gain insight into the system's performance. The derived theoretical expressions are verified using the simulation results, showing the effect of various system parameters such as atmospheric loss, pointing error, atmospheric turbulence, and link interruption due to angle of arrival and underwater turbulent parameters of the proposed system model's performance.

Conflicts of Interest:
The authors declare no conflict of interest.