Reliability of Spectrum-Efficient Mixed Satellite-Underwater Systems

The combination of radio-frequency (RF) communication and underwater optical wireless communication (UOWC) plays a vital role in the underwater Internet of Things (UIoT). This correspondence proposes a dual-hop hybrid satellite underwater system that exploits non-orthogonal multiple access (NOMA) as a spectrum-efficient access technique. The RF link from the satellite to the relay on an oil platform is presumptively subject to a Shadowed-Rician (SR) fading, while the UOWC channels from the relay to the underwater destinations are suggested to follow Exponential-Generalized Gamma (EGG) distributions. The reliability of the system is characterized in terms of both underwater destinations and system outage probabilities (OPs). We derive new closed-form expressions for the OPs under imperfect successive interference cancellation (SIC) conditions. Furthermore, the asymptotic OP and the diversity order (DO) are obtained to learn more about the system’s performance. The results are verified through an extensive representative Monte-Carlo simulation. Also, we investigate the performance against the turbulence of the salty water, air bubbles level (BL), temperature gradients (TG), shadowing parameters, and satellite pointing errors due to satellite motion, even if the beam is pointed at the center of the directive antenna relay, the beam will randomly oscillate. Finally, we contrast our approach with the conventional orthogonal multiple access (OMA) scheme to demonstrate its superiority.

conductivity of the water does. Additionally, RF is costly and only has very limited communication ranges [3]. In the literature, efforts have been devoted to characterizing the UOWC model systems and analyzing the performance. In [4], [5] the UOWC model has been proposed over mixed Exponential-Generalized Gamma (EGG), including the effect of turbulence for both fresh and saltwater, with temperature gradient and air bubbles.
In [6], authors investigated the effectiveness of multipleinput multiple-output (MIMO) UOWC systems using on-off keying (OOK) modulation in the presence of turbulence, absorption, and scattering of optical waves. Further, the UOWC can be linked to the terrestrial communication system via RF links with dual-hop cooperative protocols, which enables the underwater real-time monitoring systems. It has been indicated in [7] that the relaying node is necessary for extending the communication range for UOWC systems. In [5], [8], authors have studied the effectiveness of the amplify-and-forward (AF) relaying protocol with a dual-hop UWOC system.
Satellite networks provide wide coverage and rapid deployment of terrestrial wireless communication systems [9]. Hence, integrating underwater with satellite communications will further extend the applications of space-underwater integration. In [10], authors have proposed an asymmetric satellite-UOWC system based on a decode-and-forward (DF) relay for oceanic monitoring purposes, where the UWOC was based on cascaded independent non-identically distributed Gamma-Gamma channel coefficients and the satellite link was a Shadowed-Rician distribution. A hybrid satellite-underwater acoustic was presented in [11]. The authors in [12], have evaluated the average bit error rate's closed-form expression for a satellite-UOWC system that used EGG distribution for the UWOC link. The performance of a hybrid satellite-UWOC system's secrecy has been investigated in [13], where an Unmanned Aerial Vehicle (UAV) was considered as an eavesdropper for the satellite link.
Non-orthogonal multiple access (NOMA) has been investigated for improving the spectral efficiency of UOWC systems [14], [15], [16]. NOMA improves performance over the standard orthogonal multiple access (OMA) approaches by allowing several users to share the same frequency/time resource while exploiting the power domain by multiplexing the signals of several users at various power levels [17], [18], [19], [20], [21], [22]. As a result, users with better channel gains decode and exclude messages meant for other users before decoding their own messages using the successive interference cancellation (SIC) technique. However, practical SIC techniques are not perfect which may lead to error propagation and decoding errors [23]. Satellite communications are crucial for oil operations since oil activities frequently take place in the most remote areas where there is no terrestrial network infrastructure. Many works have studied merging satellites with oil platforms as monitoring oil pollution to ensure environmental safety to avoid the risk of spill accidents by using underwater sensors for monitoring any unusual actions and taking necessary precautions [24], [25]. So this motivated us to build a system connecting the satellite and underwater sensors through a relay placed on an oil platform for monitoring and data exchanging applications.
As far as the authors' knowledge goes, the research on hybrid satellite-UOWC based on the NOMA scheme with imperfect SIC is still not investigated. Inspired by the aforementioned observation, we propose a hybrid satellite-UOWC based on the NOMA scheme with imperfect SIC. The contribution of this paper is to (1) derive a new closed-form expression of OP assuming that the RF channel distribution undergoes Shadowed-Rician and the UOWC channel has EGG fading. (2) Obtain an asymptotic expression of the OP and hence the diversity order of the proposed system.
(3) Verify our analysis via an extensive Monte-Carlo simulation while changing various parameters including shadowing conditions and different pointing error angles for the RF link, as well as temperature gradients and air bubbles at different water levels for the underwater link. (4) Finally, compare the proposed system with a benchmark OMA-based system. This paper's remaining sections are organised as follows: in Section II, the suggested system and channel models are explained, while in Section III, analytical formulations of the exact and asymptotic OPs and the diversity order are produced. Illustrative numerical outcomes are shown in Section IV. The concluding statements are defined in Section V.

A. SYSTEM MODEL
In this paper, we take into consideration a hybrid downlink satellite-UOWC based on the NOMA scheme with imperfect SIC. The system model consisting of a low earth orbit (LEO) Iridium satellite (S) with L-band, decode and forward (DF) Relay (R) on the surface of an oil platform, and two underwater destinations (D i ), i ∈ {f , n}, i.e., D f and D n are considered to be a far destination and a near destination, respectively, as shown in Fig. 1. We assume that under the half-duplex communication mode, each node has a single antenna. Thus, the satellite transmits data to the two destinations in two time slots. S transmits a superimposed signal x s = √ a f p s x f + √ a n p s x n over RF channel to DF R during the first time slot, where x f and x n are the signals for D f and D n , respectively, a f and a n are the NOMA power allocation factors for D f and D n at S, respectively, p s is the total power transmitted at S.
The received signal y R at R from S can be written as y R = h s √ Qx s +n s where h s denotes the channel fading coefficient of the RF channel from S to R with gain expectation E[|h s | 2 ] = 1, the additive white Gaussian noise (AWGN) is represented by n s ∼ CN (0, σ 2 s ), which has a variance of σ 2 s and a mean of 0. Q represents the link budget from satellite to relay and can be given by is the beam gain and can be calculated as [27] are the firstkind Bessel function with order one and three, respectively, u = 2.07123 d r , r denotes the radius of the beam, and the distance between the beam's boresight and the relay is denoted by d, G s is the maximum antenna gain of the satellite, G R is the receiver antenna gain, L p and L f represent the depointing loss and free-space loss, respectively. L p can be formulated in dB as [28, (5. The relay first decodes x f , assuming that the NOMA power allocation factors a f > a n and a f + a n = 1, then uses SIC to decode x n , based on NOMA method. Hence, the signalto-interference-plus-noise ratios (SINRs) of decoding x f and x n at R can be respectively expressed as respectively assuming imperfect SIC conditions where ρ s = p s /σ s 2 denotes the transmit signal-tonoise ratio (SNR) at S, and η denotes the residual interference signal cancellation factor (0 ≤ η ≤ 1).
In the second time slot, R decodes and retransmits a received superimposed signal x R = b f p R x f + √ b n p R x n over UOWC channels to the two destinations, where b f and b n are the NOMA power allocation factors for D f and D n at R, respectively, p R is the total power transmitted at R. Hence, the received signals at the far and near destinations are respectively expressed as y Df = ε f |h f | 2 x R + n u and y Dn = ε n |h n | 2 x R + n u , where n u denotes AWGN with zero mean and variance σ 2 u , ε f and ε n represent photodetectors responsivity (i.e., ε f = ε n ∼ = 1), and h f and h n are the channel for R-D f and R-D n links respectively. According to NOMA technique, D f decodes the received signal to extract its own signal, as we assume that b f > b n and b f + b n = 1. The first decodes x f then uses SIC to extract x n . Consequently, the SINRs to decode x f and x n at D n are respectively

B. CHANNEL STATISTICS
The UOWC channels, h i , between R and D i are assumed to follow EGG distribution, in which the cumulative distribution function (CDF) is expressed as [4], [29] where λ is the parameter for the exponential distribution, a, b, and c are the parameters used to characterize the generalized Gamma distribution, 0 < w < 1 is the mixture coefficient between the two distributions, and the average electrical SNR is calculated based on the kind of receiver detection, such as heterodyne detection (r = 1) or intensity modulation/direct detection (IM/DD) (r = 2) such that where x is the average SNR of the UOWC links. On the other side, the RF channel, h s , the link between S and R is assumed to experience Shadowed-Rician distribution, in which the CDF is given by [30] where SR distribution's parameters are α, β, and δ, ψ(k) = , and the severity parameter is m.

III. OUTAGE PROBABILITY ANALYSIS
Outage probability is considered as one of the important metrics to evaluate the performance of communication systems and to determine if the receiver can effectively decode its own information. So in this section, we evaluate the reliability of the proposed system in terms of OPs of both destinations nodes and the overall system. We also estimate the asymptotic OP and the diversity order.

A. OP OF D F
The outage at the far destination happens when the R or the D f fail to decode the signal x f such that the received SINR falls below the target threshold value [31]. Hence the outage probability of the far destination denoted by OP f can be formulated as where γ f = 2 R f − 1 is the threshold SNR relating to the target data rate R f at the D f to detect x f , τ 1 = γ f a f −a n γ f with a f > a n γ f , and ν 1 = (1) and (3) and substituting in (4), the closed-form expression of OP f can be obtained as (5), shown at the bottom of the page.

B. OP OF D N
The outage at the near destination happens when the R or the D n fail to decode the signal x f or x n , as detecting x n at D n needs first to detect x f then use SIC to remove x f based on NOMA. Hence the outage probability at near destination denoted by OP n can be formulated as where γ n = 2 R n − 1 is the threshold SNR relating to the target data rate R n at the D n to detect x n , τ = max(τ 1 , τ 2 ), τ 2 = γ n a n −ηa f γ n with a n > ηa f γ n , ν = max(ν 1 , ν 2 ), and ν 2 = γ n b n −ηb f γ n with b n > ηb f γ n . By substituting (1) and (3) in (6), the closed-form expression of OP n can be written as in (7), shown at the bottom of the page.

C. OP OF THE SYSTEM
The probability that one of the receiver nodes in the proposed system, or all of the receiver nodes, which are the relay, near and far destinations, experiences an outage denotes the system outage probability OP sys , which can be written as The final expression of the OP sys can be given as in (9), shown at the bottom of the page. after substituting the CDFs (1) and (3) into (8).

D. ASYMPTOTIC OP AND DIVERSITY ORDER
The asymptotic behaviors of OP for D f , D n , and overall system with imperfect SIC at high SNR region is written as Q , and the asymptotic of F ∞ |h i | 2 can be given as [4], [32] The diversity order (DO) is known as the slope of the asymptotic outage curves and can be calculated as DO = − lim ρ→∞ (log(OP)/log(ρ)). After a thorough examination, one can deduce from (10) that the system diversity order (DO) is Since ac 1 and argmin(l) = 0, thus DO = 1 r . Therefore, we can observe that the diversity order of the system depends on the used detection techniques as confirmed in Fig. 2.

IV. RESULTS AND DISCUSSIONS
In this section, we confirm the validity of our analysis of the hybrid satellite-UOWC NOMA-based system under imperfect SIC by providing representative numerical simulations and showing the impact of various parameters on the performance of the system. The simulation results are performed over 10 6 iterations by implementing the Monte-Carlo simulation. The link between S and R is subject to Shadowed-Rician fading with variable shadowing levels where Table 1 [33] provides the channel parameters. The simulation parameters employed in this section are summarized in Table 2. We set η = 0.1 and the power allocation factors for far and near destinations to a f = b f = 0.7, a n = b n = 0.3, respectively. The target rates of the far and near destinations are R f = 0.5, R n = 0.75 bps/Hz, respectively. We assume that the total transmit power at satellite and relay are equal such that ρ s = ρ R = ρ. For various air bubble scenarios in thermally uniform and temperature gradient (TG)-based UOWC channels, the values of (w, λ, a, b, c) are achieved practically in [4, Tables 1, 2]. Fig. 2 shows the OPs variations against ρ for both IM/DD and heterodyne detection methods with BL= 2.4 L/min at a uniform temperature water. As can be shown, the heterodyne outperforms IM/DD detection technique in terms of OPs at both destinations and the overall system. The figure shows that the analytical curves excellently agree with the Monte-Carlo simulation, which confirms the correctness of our derivations. Furthermore, Fig. 2 shows at high SNR values the asymptotic lines of the OPs gotten by using (10). It can be observed that in the high SNR regime, the OP's asymptotic results perfectly match the analytical results, which validates the derived asymptotic equations. According to the diversity analysis, for heterodyne and IM/DD receivers, respectively, we anticipate a diversity order of 1 and 0.5, which is consistent with the findings in Fig. 2. Fig. 3 plots the OPs versus ρ at different air BLs with a uniform temperature. It is shown from the figure that higher air BL leads to degradation of the OPs spanning the entire range of ρ attributable to a rise in water turbulence. Also, it is clear from this figure that the system performance is enhanced based on NOMA with imperfect SIC compared with the OMA scheme as the NOMA technique utilizes the spectrum more efficiently. Fig. 4 depicts the effect of different shadowing scenarios given in Table 1 for the S-R link on the OPs for the entire range of ρ at BL = 2.4 L/min and uniform temperature. It is observed that shadowing has a considerable impact on system performance. As increased shadowing severity corresponds to worse propagation conditions, FHS results in the worst outage performance, while ILS represents the best scenario. Fig. 5 demonstrates the OP versus the pointing error angle between the beam center and the relay with different TG. As the pointing angle increases, the outage behaviors of  both destinations and the overall system become significantly worse. For example, at θ e = 12 • , the system suffers from a full outage. This is because, as the angle increases, the relay becomes closer to the edge of the received beam from the satellite. So, the satellite's beam should be adjusted to target the relay to improve system performance. Additionally, this figure demonstrates that an increase in TG from 0.05 to 0.15 • C/cm leads to a degradation in OP, for fixed BL = 2.4 L/min and ρ = 35 dB.
In Fig. 6, the graph for the OPs versus power allocation factor of D f at fixed ρ = 35 dB is illustrated at BL = 2.4 L/min and 4.7 L/min with a uniform temperature. It is shown from the figure that with increasing power allocation factor assigned to the far destination such that a f = b f , the more power transmitted to D f , OP f improves while OP n enhances in the first scene then degrades because of increase in the interference level in SINR at D n . Additionally, it can be seen that the OPs deteriorate with a rise in BL, as the higher the BL, the higher the water turbulence.

V. CONCLUSION
In this paper, we have investigated the outage performance of the downlink NOMA-based hybrid satellite UOWC with the aid of DF relay in the case of imperfect SIC. The outage probabilities expressions of the exact and asymptotic at the two NOMA destinations and the system have been derived. We also have illustrated the effect of atmospheric conditions including shadowing, path loss, and depointing loss, as well as different underwater scenarios for salty water such as air bubbles level under uniform and temperature gradients. The results showed that an increase in water turbulence like air bubbles and temperature gradients causes degradation in outage behavior. Furthermore, an increase in atmospheric conditions like shadowing, and pointing error angle leads to a declination in outage performance. Finally, the NOMA-based outage behaviors of the proposed system with imperfect SIC outperform those of the OMA scheme.