Hybrid SAG-FSO/SH-FSO/RF Transmission for Next-Generation Satellite Communication Systems

Next-Generation Satellite Communication Systems

Item Type Article

Authors Samy, Ramy;Yang, Hong Chuan;Rakia, Tamer;Alouini, Mohamed- Slim

Citation Samy, R., Yang, H.-C., Rakia, T., & Alouini, M.-S. (2023). Hybrid SAG-FSO/SH-FSO/RF Transmission for Next-Generation Satellite Communication Systems. IEEE Transactions on Vehicular

Technology, 1–13. https://doi.org/10.1109/tvt.2023.3281256 Eprint version Post-print

DOI 10.1109/tvt.2023.3281256

Publisher Institute of Electrical and Electronics Engineers (IEEE) Journal IEEE Transactions on Vehicular Technology

Rights (c) 2023 IEEE. Personal use of this material is permitted.

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Hybrid SAG-FSO/SH-FSO/RF Transmission for Next-Generation Satellite Communication Systems

Ramy Samy, Hong-Chuan Yang, Senior Member, IEEE, Tamer Rakia, and Mohamed-Slim Alouini, Fellow, IEEE

Abstract—Recent advances demonstrate satellite communica- tion (SatCom) as a potent enabler for future Terabit/s global connectivity. Existing SatCom systems, however, rely mostly on radio frequency (RF) transmission, whose limited available bandwidth is the main bottleneck for further data rate increases.

Free-space optical (FSO) communication links, with huge license- free bandwidth, have emerged as an attractive alternative.

Despite their ability to deliver high-throughput transmissions, FSO communications are weather-dependent and susceptible to atmospheric turbulence. Hybrid FSO/RF and space-air-ground (SAG) FSO transmissions are possible solutions to increase the reliability of FSO-based transmission systems. A strategically deployed unmanned-aerial vehicle, acting as a relay, can suc- cessfully mitigate the adverse effect of atmospheric turbulence, while the hybrid FSO/RF transmission can address weather- dependent effects. These solutions can also be integrated to create a system with significantly improved performance and reliability.

To evaluate the performance of the resulting integrated trans- mission system, we analyze the outage probability and average symbol error probability in this work. Asymptotic expressions are also derived to get further insight into the system behavior and calculate the overall diversity gain. Furthermore, we consider the optimal design of switching thresholds. The numerical results show that the integrated transmission system achieves about 10 dB performance gain over existing solutions for both downlink and uplink scenarios.

Index Terms—Satellite communication systems, Internet from Space, SAG integrated networks, performance analysis, hybrid FSO/RF transmission.

I. INTRODUCTION

T

HE worldwide total data transmission rate in 2022 has reached 1165 Terabit/s, up from 932 Terabit/s in 2021 [1]. This represents a 25% increase, similar to that of the previous years. However, Internet access remains unaffordable or unavailable in many regions of the world. Costly setup has created a digital divide that isolates a substantial portion of the world’s population—2.7 billion people remain offline [1].

Future wireless networks should reduce the digital divide and provide new alternatives for affordable Internet connectivity.

Copyright (c) 2015 IEEE. Personal use of this material is permitted. How- ever, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. This work was supported in part by a Discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. (Corresponding author:

Ramy Samy.)

Ramy Samy and Hong-Chuan Yang are with the Department of Electrical and Computer Engineering, University of Victoria, BC, Canada (e-mail:

{ramyzaghloul, hy}@uvic.ca); Tamer Rakia is with the Avionics Department, Military Technical College, Cairo, Egypt (e-mail: tamer_nabiel@yahoo.com);

Mohamed-Slim Alouini is with the Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Makkah Province 23955-6900, Saudi Arabia (e-mail:

slim.alouini@kaust.edu.sa)

In fact, the growing capacity demand and the need for global coverage have driven the evolution of non-terrestrial networks (NTNs), which can enable a wide range of applications, such as smart cities, industrial Internet, and vehicle-to-everything (V2X) communication [2], [3].

Satellite communication (SatCom) systems are one of the most popular NTNs, complementing terrestrial networks [4].

They can help improve coverage and service quality, par- ticularly in areas where traditional terrestrial networks may have blind spots. Many satellite service providers are start- ing to launch constellations of satellites to deliver seamless broadband Internet access worldwide [5]–[7]. They serve as significant initial steps towards the advent of the "Internet from Space." Unmanned-aerial vehicles like balloons are also being considered as an effective solution to expand terres- trial network coverage and provide reliable connectivity to underserved or uncovered regions [8]–[11]. Unfortunately, both solutions mainly depend on licensed radio frequency (RF) bands, whose limited available bandwidth is the primary bottleneck for high data rate and affordable Internet access [12].

In this context, the SatCom community is exploring the optical spectrum in order to address the RF spectrum scarcity problem [13]–[15]. Despite its potential to provide high- throughput transmission, FSO communications are weather- dependent and sensitive to atmospheric turbulence effects [16]. FSO link quality is severely degraded by dense clouds.

Moreover, FSO links suffer from beam wandering and scin- tillation effects, which are mostly induced by atmospheric inhomogeneities over large distances due to wind, pressure, and temperature variations [17]. Pointing and acquisition are also challenging due to the relative movement of receivers and transmitters [18]. One possible solution is to benefit from the complementary nature of RF and FSO links and integrate them into one SatCom system [19]. The resulting hybrid FSO/RF transmissions enjoy better reliability in all weather conditions [20]–[23]. However, restoring the bandwidth-limited RF link decreases the overall system throughput.

Recently, a high-altitude platform (HAP) relay deployed between a satellite (SAT) and a ground station has been proposed to improve FSO’s usability, leading to space-air- ground (SAG) FSO transmission [24]–[28]. Because of the stratosphere’s unique properties, HAPs can maintain a quasi- stationary location, facilitating reliable line-of-sight (LoS) communication links. The HAP can also hover directly above the ground station to shorten the propagation distance of the optical signal in the atmosphere. Hence, beam wandering and atmospheric turbulence effects experienced by the ground-

HAP hop can be successfully reduced [29]. On the other hand, such HAP deployment results in a slightly longer propagation distance over the HAP-SAT hop by about 3%, assuming an 80^o satellite zenith angle (the worst-case scenario). Apart from propagation distance, optical signal power loss primarily depends on the atmospheric attenuation caused by aerosols.

As the concentration of aerosols is negligible at high al- titudes, the power loss is insignificant over the HAP-SAT hop [30]. Furthermore, the FSO transmission over the HAP- SAT hop experiences a weak turbulence effect and enjoys high reliability [31]. The HAP deployment is also attractive when working with low-earth orbit (LEO) satellite systems due to their limited communication sessions. LEO satellites roughly last 45 minutes per day on average with a given ground station [32]. With the HAP-based relay deployed at about 20 km above the ground station, satellite acquisition can be established much earlier, increasing the duration of each session and the downlink data volume.

The SAG-FSO transmission can be integrated with hybrid single-hop (SH) FSO/RF transmission, as shown in Fig. 1, to create a SatCom system with significantly improved perfor- mance and reliability [33]. The integrated transmission system can effectively reduce the blocking effects of flying drones and birds, which are relatively common in urban areas. It can also mitigate the atmospheric attenuation of small clouds at larger satellite zenith angles. Recently, we investigated the capacity and error rate performance of the integrated transmission system over the uplink scenario without considering beam divergence loss, free space loss, or atmospheric attenuation [33], [34]. In this work, we complement previous work by analyzing the end-to-end outage probability (OP) and average symbol error probability (ASEP) performance in a more general scenario. The primary contributions of this paper are summarized as follows:

1) OP and ASEP performance are analyzed over Gamma- Gamma (G-G) fading for FSO links in the presence of beam wandering, atmospheric turbulence, weather attenuation, pointing errors, free-space loss, and beam divergence loss for both uplink and downlink scenarios.

2) The cumulative distribution function (cdf) and probabil- ity density function (pdf) over Rician fading have been derived using the Meijer-G function, which will help to obtain the diversity gain of the RF link.

3) We derive asymptotic ASEP and OP expressions to ob- tain the overall system diversity gains. Such expressions are analytically tractable as they involve much simpler functions and require less computational load.

4) We also derive the optimum switching thresholds for the FSO links, which minimize the overall system ASEP.

The obtained expressions are verified using the numer- ical optimization technique.

5) The selected numerical results demonstrate the signifi- cant potential of the integrated transmission system over existing solutions. It can achieve a marked improvement even under severe wind effects, pointing errors, and weather attenuations. Additionally, we perform Monte Carlo simulations to verify the derived expressions.

Fig. 1. Integrated SatCom with hybrid SAG-FSO/SH-FSO/RF transmission.

The remaining part of this paper is organized as follows:

Section II introduces the system and channel models. The exact performance analysis of the integrated transmission system is carried out in Section III, while in Section IV, we present the asymptotic results. Section V studies the switching threshold optimization. Finally, Sections VI and VII present the numerical results and the conclusion, respectively.

Throughout this paper, 𝐺^{𝑚, 𝑛}_{𝑝 , 𝑞}(·) is the Meijer-G function [35, eq. (9.301)], Γ(·) denotes the Gamma function [35, eq.

(8.310)], erfc(·)represents the complementary error function, 𝐼_𝑛(·)indicates the modified Bessel function [35, eq. (8.406)], andE{·} denotes statistical expectation.

II. SYSTEM ANDCHANNELMODELS

Here, we consider an integrated transmission system, where the ground station can communicate with the SAT through FSO or RF channels, as illustrated in Fig. 1. We prioritize the FSO transmission through the HAP and use it whenever its link quality is acceptable, i.e., it satisfies a target quality- of-service (QoS) requirement [34]. If the SAG-FSO link is no longer acceptable, the system will first check the SH-FSO transmission before restoring the RF transmission. We use the hard-switching scheme due to its practical relevance. The SH- FSO transmission serves as an additional backup to increase the system’s reliability during unfavorable channel conditions.

Even though the SH-FSO transmission is more susceptible to atmospheric turbulence effects, it can transmit at a significantly higher data rate than the RF link [33]. We prefer a direct RF link to the satellite to minimize HAP’s power consumption and hardware complexity, as HAP is a resource-limited system.

Note that the FSO links may undergo correlated fading effects if the distance between FSO transmitters is less than the coherence diameter of the atmosphere [36]. For uncorrelated fading, the current system configuration requires a distance of approximately 20cm [36, eq. (8)].

A. Signalling Model

We adopt phase shift keying (PSK) modulation for RF and FSO transmissions. The transmitted signal is given by

𝑥(𝑡)=∑︁

𝑘

𝑔(𝑡−𝑘 𝑇_s)cos(2𝜋 𝑓_s𝑡+𝜑

𝑘), (1)

where𝑇_s represents the symbol duration,𝑔(𝑡) is the shaping pulse with 0 ≤ 𝑡 ≤𝑇_s, 𝜑

𝑘 ∈ [0, . . . ,2𝜋(𝑀 −1)/𝑀] denotes the modulated symbol’s phase, 𝑀 is the modulation order, and 𝑓_s denotes the carrier frequency. We also adopt intensity modulation and direct detection (IM/DD) or heterodyne detec- tion (HD) at the optical receiver. In this work, we apply FSO transmission over the HAP-SAT (HS), ground-HAP (GH), and ground-SAT (GS) hops. For the ground-HAP hop, the baseband signal received at the HAP is given by [24, eq. (2)]

𝑦GH[𝑘]=

𝜂GH 𝑃

GH 𝐺

GH 𝐼

GH

^𝑏₂

𝑥[𝑘] +𝑛

GH[𝑘], (2) where 𝑏 depends on the detection scheme used (𝑏 = 2 for IM/DD scheme and 𝑏 = 1 for HD scheme), 𝜂

GH indicates the optical-to-electrical conversion efficiency of the receiver (Rx) at the relay, 𝑃

GH is the transmit (Tx) power over the ground-HAP hop, 𝑥[𝑘] denotes the modulated symbol, and 𝑛GH[𝑘] denotes the additive white Gaussian noise (AWGN) with E{𝑛

GH[𝑘]𝑛^∗

GH[𝑘]}= 𝜎²

𝑛GH [37]. The gain of the ground- HAP hop,𝐺

GH, equals

𝐺^tx

f 𝐺^rx

f

FSL_GH , where𝐺^tx

f,𝐺^rx

f , andFSL_GH are the Tx gain, Rx gain, and free-space loss, respectively. Here, the free-space loss is defined as ^{4𝜋 𝐿}_𝜆^GH

f

, where𝜆

f indicates the optical wavelength and 𝐿_GH = ℎ_H−ℎ_G

sec(𝜃_GH) denotes the slant range, where ℎ_G, ℎ_H, and 𝜃_GH are the aperture height of the ground station, HAP altitude, and HAP zenith angle, respectively. Besides, the aggregated channel irradiance, 𝐼

GH, can be expressed as [24]

𝐼GH=𝐼^𝑙

GH𝐼

𝑎

GH𝐼

𝑝

GH, (3)

where 𝐼^𝑙

GH is the attenuation factor, 𝐼

𝑎

GH is the atmospheric turbulence, and 𝐼

𝑝

GH represents the pointing errors. The atten- uation factor 𝐼^𝑙

GH primarily depends on beam divergence loss and atmospheric attenuation due to FSO weather-dependent effects, which is given by [38, eq. (4)]

𝐼^𝑙

GH=

𝜋 𝐷²

H

4(𝜙

𝐺𝐿

GH)² 𝐼^w

GH, (4)

where𝜙

G,𝐷

H, and 𝐼^w

GH denote the Tx beam divergence angle, Rx aperture diameter at the relay, and the weather-dependent attenuation factor, respectively. Following the Beer-Lambert law, the FSO weather-dependent attenuation can be expressed as 𝐼^𝑤

GH = exp(−𝜑

f𝑑_w) [16], where 𝜑

f is the attenuation coefficient (in dB/km) due to fog or clouds between the ground station and HAP, and𝑑_𝑤 indicates the distance over which the weather impact takes place, i.e., the thickness of considered clouds [39, Sec. (3)]. Similarly, the signalling model for the direct ground-SAT hop can be obtained but omitted for conciseness.

At the HAP-based relay, a decode-and-forward (DF) scheme is used to avoid noise forwarding [24], [26], [40]. The received

information is first decoded at the HAP-based relay to obtain ˆx[k]. Then, ˆx[k] is forwarded to the satellite. The received signal at the satellite is described as

𝑦HS[𝑘]=

𝜂HS 𝑃

HS 𝐺

HS 𝐼

HS

^𝑏₂ ˆ 𝑥[𝑘] +𝑛

HS[𝑘], (5) where𝐺

HS indicates the gain of the HAP-SAT hop and is ob- tained as𝐺_GHabove. As HAPs are typically stationed at cloud- free altitudes, the weather attenuation will be almost equal to unity. Consequently,𝐼^𝑙

HS can be simplified to ^{𝜋 𝐷}

2 S 4(^𝜙_H^𝐿_HS)². For the direct RF link to the satellite, the baseband signal at the receiver is represented by [41, eq. (6)]

𝑦_𝑟[𝑘]=√︁

𝑃_𝑟

√︁

𝐺_𝑟 ℎ_𝑟 𝑥[𝑘] +𝑛_𝑟[𝑘], (6) where ℎ_r is the fading channel gain that follows the Rician fading model, 𝑃_𝑟 indicates the transmit power, and 𝑛_𝑟[𝑘] denotes the AWGN with E{𝑛_𝑟[𝑘]𝑛^∗

𝑟[𝑘]} = 𝜎²

𝑛_𝑟. The noise variance𝜎_𝑛²

𝑟 is given by𝜎_𝑛²

𝑟 =𝑃_n𝑁_𝑟, where𝑃_nand𝑁_𝑟 denote the noise power and the noise figure, respectively. The path gain, 𝐺_𝑟, can be expressed as [25, eq. (10)]

𝐺_𝑟 = 𝐺^tx

𝑟 𝐺^rx

𝑟

FSL𝑟 𝐿_A 𝐿_w

, (7)

where𝐺^tx_𝑟 denotes the Tx antenna gain,𝐺^rx_𝑟 denotes the Rx antenna gain, FSLr = ₄𝜋 𝐿

GS 𝜆_𝑟

2

, 𝐿

GS = ℎ

S−ℎ

G

sec(𝜃

GS) denotes the slant range to satellite, where ℎ

G, ℎ

S, and 𝜃

GS

represent the aperture height of the ground station, SAT altitude, and SAT zenith angle, respectively. 𝐿_A denotes the gaseous atmosphere loss due to water vapor and oxygen, while the loss due to weather effects is represented by 𝐿_w. In [42], the international telecommunication union (ITU) recommends clouds and fog attenuation model for frequencies up to 200 GHz, which is given by

𝐿_w=𝜑_𝑟 𝑑_w, (8)

where 𝜑_𝑟 represents the RF weather-dependent attenuation coefficient (in dB/km).

B. Channel Model

For FSO transmissions, we adopt the well-known G-G fading model with weather impairments and pointing errors.

The pdf of the irradiances 𝐼_ij, ij ∈ {GS,HS,GH}, can be expressed as [43, eq. (1)]

𝑓𝐼ij(𝐼)= 𝜉²

ij 𝐼⁻¹

Γ(𝛼

ij)Γ(𝛽

ij)𝐺³

,0 1,3 𝛼_ij𝛽_ij

𝐼 𝐼^𝑙

ij

𝜉²

ij+1

𝜉²

ij, 𝛼

ij, 𝛽

ij

! , (9) where 𝜉_ij is the pointing error coefficient and 𝛽_ij and 𝛼_ij indicate the small-scale and large-scale fading parameters related to atmospheric turbulence effects. Their calculations are given in the Appendix.

The instantaneous and average received SNRs can be ex- pressed as [24, eq. (6, 9)]

𝛾ij, 𝑏 = (𝜂

ij 𝑃

ij 𝐺

ij 𝐼

ij)^𝑏 𝜎_𝑛²

ij

, (10)

¯

𝛾ij, 𝑏 =

(𝜂

ij 𝑃

ij 𝐺

ij 𝑘

ij 𝐼^𝑙

ij)^𝑏 𝜎_𝑛²

ij

, (11)

respectively, where 𝑘

ij=𝜉²

ij/(𝜉²

ij +1). With the application of (9), (10), and the power transformation of random variables, the unified pdf of the instantaneous SNR forIM/DDandHD is obtained after some algebraic manipulations, as [44, eq. (2)]

𝑓_𝛾

ij(𝛾)=

𝜉²

ij 𝛾⁻¹

𝑏 Γ(𝛼

ij)Γ(𝛽

ij)

×𝐺^3,0

1,3 𝛼

ij𝛽

ij𝑘

ij

𝛾 𝜇ij, 𝑏

𝑏¹

𝜉²

ij+1

𝜉²

ij, 𝛼

ij, 𝛽

ij

! , (12) where 𝜇

ij, 𝑏 represents the average electrical SNR, which is

linked to 𝛾¯

ij, 𝑏 as

𝜇ij,1 = 𝛾¯

ij,1, and

𝜇ij,2 =

𝛼ij𝛽

ij𝜉²

ij(𝜉²

ij+2)

(𝛼

ij+1) (𝛽

ij+1) (𝜉²

ij +1)² 𝛾¯

ij,2.

With the application of (12) and [45, eq. (07.34.21.0084.01)], the cdf of 𝛾

ij is obtained after some algebraic manipulations, as

𝐹_𝛾

ij(𝛾)=X_ij 𝐺 ^{3𝑏 , 1}

𝑏+1,3𝑏+1

E_ij 𝛾

𝜇ij, 𝑏

1 , B_ij¹ B_ij² , 0

, (13) where X_ij =

𝑏 𝛼ij+𝛽ij−2

𝜉² ij

(2𝜋)^𝑏−1 Γ(𝛼_ij)Γ(𝛽_ij), E_ij = 𝛼 ij𝛽

ij𝑘 ij 𝑏²

^𝑏 , B_ij¹ = {

𝜉² ij+1

𝑏 , . . . ,

𝜉² ij+𝑏

𝑏 } comprises of 𝑏 terms, and B_ij² = {

𝜉² ij 𝑏, . . . ,

𝜉²

ij+𝑏−1

𝑏 ,

𝛼ij 𝑏 , . . . ,

𝛼ij+𝑏−1

𝑏 ,

𝛽ij 𝑏, . . . ,

𝛽ij+𝑏−1

𝑏 } comprises of 3𝑏 terms.

The instantaneous SNR at the RF receiver is represented by [38, eq. (6)]

𝛾_𝑟=𝛾¯_𝑟 ℎ²_𝑟, (14) where

¯

𝛾_𝑟 = 𝑃_𝑟 𝐺_𝑟 𝜎_𝑛²

𝑟

(15) represents the average SNR of the RF link [46, eq. (5.34)].

Due to the strong LoS in the SatCom environment, the Rician fading can accurately model the RF link [26], [27]. Using (14), [47, eq. (2.15)], and the power transformation of random variables, the pdf of the instantaneous SNR can be described as [47, eq. (2.16)]

𝑓_𝛾

𝑟(𝛾)= 𝐾+1

¯ 𝛾_𝑟 exp

−(𝐾+1) 𝛾

¯ 𝛾_𝑟

−𝐾

×𝐼₀

2

√︂

𝐾(𝐾+1) 𝛾

¯ 𝛾_𝑟

, (16) where 𝐾 is the Rician factor. With the application of series expansion to the Bessel function [35, eq. (8.447.1)] and rewriting the exponential function using the Meijer-G function [48, eq. (11)], the pdf in (16) can be written as

𝑓_𝛾

𝑟(𝛾)=H₁ 𝛾^𝑢 𝐺^1,0

0,1

F 𝛾

− 0

, (17)

whereH₁ =F exp(−𝐾) Í∞ 𝑢=0

(𝐾F )^𝑢

(𝑢!)² denotes the summation operation and F = ^𝐾_𝛾¯⁺¹

𝑟 . With the application of [45, eq.

(07.34.21.0084.01)], the corresponding cdf is given by 𝐹_𝛾

𝑟(𝛾)=H₁ 𝛾^𝑢+1 𝐺^1,1

1,2

F 𝛾

−𝑢 0 ,−𝑢−1

. (18) III. EXACTANALYSIS

Now, we analyze the OP and ASEP of the integrated trans- mission system, taking into account beam wandering, beam divergence, pointing errors, atmospheric turbulence, free-space loss, and weather effects.

A. Outage Analysis

The OP is defined as the probability that the instantaneous received SNR will fall below a particular 𝛾

th threshold. The threshold is chosen to meet a predefined QoS requirement, typically in terms of target SEP. The OP of the proposed SatCom can be written as

𝑃

SatCom out =𝑃

SAG out 𝑃

SH out 𝑃

RF

out , (19)

where 𝑃

RF out = 𝐹_𝛾

𝑟(𝛾

th) denotes the OP of the direct RF link to the satellite calculated using the cdf of 𝛾_𝑟 defined in (18).

𝑃

SH

out represents the OP of the SH-FSO transmission given by (13) with the corresponding 𝜇

GS, 𝑏, 𝜉

GS, 𝛽

GS, and 𝛼

GS values.

𝑃

SAG

out represents the OP of the SAG-FSO transmission, which is calculated as

𝑃

SAG out =1−

1−𝑃

HS

out 1−𝑃

GH out

, (20)

where𝑃

HS out and𝑃

GH

outare the OP of the HAP-SAT and ground- HAP hops, respectively, defined by (13) using the correspond- ing 𝜇

ij, 𝑏,𝜉

ij, 𝛽

ij, and𝛼

ij values.

B. Error Rate Analysis

Assuming MPSK signalling, the SEP conditioned on the instantaneous SNR can be described as [49, eq. (11)]

𝑃(𝑒|𝛾)= 𝐴 2erfc√

𝛾sin 𝜋 𝑀

, (21)

where

𝐴=

(1, 𝑀=2;

2, 𝑀 >2.

(22) Note that the expression in (21) is exact when 𝑀 =2 and an upper bound when𝑀 >2[47, eq. (8.25)]. With the application of [45, eq. (07.34.03.0619.01)], (21) is written as

𝑃(𝑒|𝛾)= 𝐴 2√ 𝜋

𝐺^2,0

1,2

𝛾

sin 𝜋

𝑀 2

1 0,¹

2

. (23) Applying the Maclaurin series [35, eq. (3.321)], (21) can also be rewritten as

𝑃(𝑒|𝛾)= 𝐴 2 − 𝐴

√ 𝜋

H₂ 𝛾^𝑣+

1

2 , (24)

whereH₂ =Í∞ 𝑣=0

( −1)^𝑣 (sin_𝑀^𝜋)^2𝑣+1

𝑣! (2𝑣+1) .

According to the system operation, the SAG-FSO transmis- sion acts as the main link, while the SH-FSO/RF transmission acts as the backup. Therefore, the overall system ASEP is given by

¯ 𝑃

SatCom

𝑒 =𝑃¯

SAG

𝑒 + 𝑃

SAG out 𝑃¯

SH−h

𝑒 , (25)

where 𝑃¯

SAG

𝑒 represents the ASEP of the SAG-FSO link when 𝛾GH and 𝛾

HS are greater than a predefined threshold 𝛾

th,𝑃

SAG out

is calculated in (20), and 𝑃¯

SH−h

𝑒 denotes the ASEP of the SH- FSO/RF transmission.

Considering DF relaying scheme, 𝑃¯

SAG

𝑒 is given by [50, eq.

(22)]

¯ 𝑃

SAG 𝑒 =𝑃¯

HS 𝑒 + 𝑃¯

GH 𝑒 − 𝑃¯

HS 𝑒 𝑃¯

GH

𝑒 , (26)

where 𝑃¯

HS 𝑒 and 𝑃¯

GH

𝑒 denote the ASEP of the HAP-SAT and ground-HAP hops, respectively, when𝛾

HS≥𝛾

thand𝛾

GH ≥𝛾

th. The analytical expression of 𝑃¯

GH

𝑒 can be derived as

¯ 𝑃

GH

𝑒 =

∫ ∞ 𝛾th

𝑃(𝑒|𝛾) 𝑓_𝛾

GH(𝛾) 𝑑 𝛾

=

∫ ∞ 0

𝑃(𝑒|𝛾) 𝑓_𝛾

GH(𝛾) 𝑑 𝛾

| {z }

𝐼₁

−

∫ 𝛾_th 0

𝑃(𝑒|𝛾) 𝑓_𝛾

GH(𝛾) 𝑑 𝛾

| {z }

𝐼₂

.

(27) The expression of 𝑃¯

GH

𝑒 is now split into two terms, 𝐼₁ and𝐼₂. The analytical expression of 𝐼₁ can be calculated using (12), (23), and [45, eq. (07.34.21.0013.01)] as

𝐼₁= 𝐴 X_GH 2√

𝜋

𝐺 ^{3𝑏 , 2}

𝑏+2, 3𝑏+1

E_GH sin_𝑀^𝜋2

𝜇_{GH, 𝑏}

1,¹

2,B_GH¹ B²

GH,0

! . (28) After applying (24), 𝐼₂ is obtained by

𝐼₂=

∫ ^𝛾th 0

𝐴 2 𝑓_𝛾

GH(𝛾) 𝑑 𝛾 −

∫ ^𝛾_th

0

√𝐴 𝜋

H₂ 𝛾

𝑣+1 2

𝑓_𝛾

GH(𝛾) 𝑑 𝛾 . (29) Using [45, eq. (07.34.21.0084.01)], 𝐼₂ can be analytically expressed as

𝐼₂ =X_GH 𝐴

2 𝐺 ^{3𝑏 , 1}

𝑏+1,3𝑏+1

E_GH 𝛾

th

𝜇_{GH, 𝑏}

1 , B_GH¹ B²

GH , 0

− X_GH 𝐴

√ 𝜋

H₂ 𝛾

𝑣+1 2 th

×𝐺 ^{3𝑏 , 1}

𝑏+1,3𝑏+1

E_GH 𝛾

th

𝜇_{GH, 𝑏}

1−𝑣−¹₂,B_GH¹ B_GH² ,−𝑣−¹₂

. (30) Similar to (27), the analytical expression of 𝑃¯

HS

𝑒 is obtained, replacing 𝜇_{GH, 𝑏}, 𝜉_GH, 𝛼_GH, and 𝛽_GH with 𝜇_{HS, 𝑏}, 𝜉_HS, 𝛼_HS, and 𝛽HS. Consequently, the ASEP of the FSO transmission through the HAP in (26) can be obtained.

The ASEP of the SH-FSO/RF transmission in (25) is calculated as [24, eq. (27)]

¯ 𝑃

SH−h 𝑒 =𝑃¯

SH

𝑒 + 𝑃

SH out 𝑃¯

RF

𝑒 , (31)

where𝑃

SH

outcan be calculated using (13) with the corresponding parameters 𝜇

GS, 𝑏,𝜉

GS, 𝛽

GS, and𝛼

GS,𝑃¯

SH

𝑒 denotes the ASEP of the SH-FSO transmission when 𝛾

GS ≥ 𝛾

th and is calculated

using (28) and (30) with the corresponding 𝜇

GS, 𝑏, 𝜉

GS, 𝛽

GS, and 𝛼

GS values, and 𝑃¯

RF

𝑒 indicates the ASEP of the RF link, which is represented by

¯ 𝑃

RF 𝑒 =

∫ ∞ 0

𝑃(𝑒|𝛾) 𝑓_𝛾

𝑟(𝛾) 𝑑 𝛾 . (32) With the application of (17), (23), and [45, eq.

(07.34.21.0013.01)], 𝑃¯

RF

𝑒 can be analytically expressed as

¯ 𝑃

RF

𝑒 = 𝐴

2√ 𝜋 sin 𝑀^𝜋

2𝑢+2 H₁

× 𝐺^1,2

2,2

F sin_𝑀^𝜋2

−𝑢 , −𝑢−¹

2

0, −𝑢−1

! . (33) It should be noted that the obtained OP and ASEP expres- sions are applicable for both downlink and uplink scenarios when using the corresponding expression for𝛽

ijand𝛼

ij in the Appendix.

IV. ASYMPTOTICANALYSIS

To provide further insights into the behavior of the SatCom system, we derive a simpler asymptotic expression for both OP and ASEP. In this context, the analytical expressions should be obtained in the formC (𝛾¯)^{− D}, where𝛾¯is the average SNR, C is the code gain that determines the shift of the curve in SNR, andD is the diversity gain that determines the slope of the curve [51, eq. (1)]. Note that at a very small value of its argument, the Meijer-G function can be represented in terms of the summation of basic elementary functions as [35, eq.

(9.303)]

𝐺_{𝑝 , 𝑞}^{𝑠 , 𝑡}

𝑋 | 𝑐₁, . . . , 𝑐_𝑡, . . . , 𝑐_𝑝 𝑑₁, . . . , 𝑑_𝑠, . . . , 𝑑_𝑞

=

𝑠

∑︁

𝑔=1

𝑋^𝑑𝑔

× Î^𝑠

𝑧=1;𝑧≠𝑔Γ 𝑑_𝑧−𝑑_𝑔 Î^𝑡

𝑧=1Γ 1+𝑑_𝑔−𝑐_𝑧 Î^𝑞

𝑧=𝑠+1Γ 1+𝑑_𝑔−𝑑_𝑧 Î^𝑝

𝑧=𝑡+1Γ 𝑐_𝑧−𝑑_𝑔, (34) where 𝑝 ≤𝑞 and no two 𝑑_𝑧 (for 𝑧 =1,2, ..., 𝑡) differ by an integer.

A. Outage Analysis

The asymptotic OP of the integrated transmission system is expressed by

𝑃

SatCom out, 𝑎 =𝑃

SAG out, 𝑎 𝑃

SH out, 𝑎 𝑃

RF

out, 𝑎 , (35)

where 𝑃

SAG

out, 𝑎 =1− 1−𝑃

GH

out, 𝑎 1−𝑃

HS out, 𝑎

. (36)

Using (34) and (13), the asymptotic OP of the ground-HAP hop is given by

𝑃

GH out, 𝑎=

3𝑏

∑︁

𝑔=1

X_GH B_GH^{2, 𝑔}

H₃

E_GH 𝛾

th

𝜇GH, 𝑏

B_GH^{2, 𝑔}

, (37)

where H₃ =

Î3𝑏 𝑧=1;𝑧≠𝑔Γ

B^{2, 𝑧} GH− B^{2, 𝑔}_GH Î𝑏

𝑧=1Γ

B_GH^{1, 𝑧}− B^{2, 𝑔}_GH . Similarly, 𝑃

HS

out, 𝑎 and 𝑃

GS out, 𝑎

can be obtained, using the corresponding parameters 𝜇

ij, 𝑏,𝜉

ij,

𝛽ij, and𝛼

ij. From (36) and (37), we can observe that 𝑃

SAG out, 𝑎 ∝ (𝛾¯

ij,b)^−DO,SAG, where the diversity gain with respect to outage D_O,SAG =min(^𝜉

2 GH 𝑏 ,

𝛼GH 𝑏 ,

𝛽GH 𝑏 ,

𝜉² HS 𝑏 ,

𝛼HS 𝑏 ,

𝛽HS

𝑏 ). Since𝜉

GH ≪𝜉

HS, 𝛼GH ≪ 𝛼

HS, and 𝛽

GH ≪ 𝛽

HS, D_O,SAG = min(^𝜉

2 GH 𝑏 ,

𝛼GH 𝑏 ,

𝛽GH 𝑏 ).

For the SH-FSO transmission, the diversity gain with respect to outage is given by D_O,SH=min(^𝜉

2 GS 𝑏 ,

𝛼GS 𝑏 ,

𝛽GS 𝑏 ).

With the application of (34) and (18), the asymptotic OP of the RF link, after some algebraic manipulations, is given by

𝑃

RF out, 𝑎=

∞

∑︁

𝑢=0

exp(−𝐾) 𝐾

𝑢 (𝐾+1)^𝑢+1 (𝛾

th)^𝑢+1

(1+𝑢) (𝑢!)² (𝛾¯_𝑟)^{− (𝑢+1)}. (38) Because the higher-order terms are insignificant, just the first term is considered, 𝑃

RF

out, 𝑎 ∝ (𝛾¯_𝑟)⁻¹. Thus, the diversity gain of the RF link for outage is equal to unity.

To obtain the overall system diversity gain that defines the slope of the OP curve, we assume the FSO and RF links have equal average SNR (𝛾¯_ij=𝛾¯_𝑟). As a result, the overall system diversity gain in terms of OP is given by

D_O,SatCom =D_O,SAG + D_O,SH + 1. (39) B. Error Rate Analysis

The asymptotic ASEP of the integrated transmission system is as follows

¯ 𝑃

SatCom 𝑒, 𝑎 =𝑃¯

SAG 𝑒, 𝑎 + 𝑃

SAG out, 𝑎 𝑃¯

SH−h

𝑒, 𝑎 , (40)

where

¯ 𝑃

SAG 𝑒, 𝑎=𝑃¯

GH 𝑒, 𝑎 + 𝑃¯

HS 𝑒, 𝑎 − 𝑃¯

GH 𝑒, 𝑎 𝑃¯

HS

𝑒, 𝑎. (41)

The asymptotic ASEP of the FSO transmission over the ground-HAP hop is given by 𝑃¯

GH 𝑒, 𝑎=𝐼

1, 𝑎−𝐼

2, 𝑎, where 𝐼1, 𝑎 =

𝐴X_GH 2√

𝜋

3𝑏

∑︁

𝑔=1

H₃ Γ

1

2 + B_GH^{2, 𝑔} B_GH^{2, 𝑔}

E_GH sin _𝑀^𝜋2

𝜇GH, 𝑏

!B_GH^{2, 𝑔}

,

(42) and

𝐼2, 𝑎 =𝐴X_GH

3𝑏

∑︁

𝑔=1

H₃

E_GH 𝛾

th

𝜇GH, 𝑏

B^{2, 𝑔}_GH

× 1

2 B_GH^{2, 𝑔}

− H₂ 𝛾

𝑣+1 2

√ th

𝜋 (𝑣 + ¹₂ + B_GH^{2, 𝑔})

, (43) respectively. Similarly, 𝑃¯

HS

𝑒, 𝑎 can be obtained, using the cor- responding parameters 𝜇_{HS, 𝑏}, 𝜉_HS, 𝛽_HS, and 𝛼_HS. It is ob- served from the derived expressions in (42) and (43) that

¯ 𝑃

SAG 𝑒, 𝑎 ∝ (𝛾¯

ij)^−D𝑒,SAG. Thus, the diversity gain with respect to the

ASEP of the FSO transmission over the HAP, D_𝑒,SAG, is equal min(^𝜉

2 GH 𝑏 ,

𝛼GH 𝑏 ,

𝛽GH

𝑏 ). Similar to the SAG-FSO transmission, the diversity gain of the SH-FSO transmission is also obtained for ASEP as D_𝑒,SH=min(^𝜉

2 GS 𝑏 ,

𝛼GS 𝑏 ,

𝛽GS 𝑏 ).

For the RF link, the asymptotic ASEP is represented by

¯ 𝑃

RF 𝑒, 𝑎 =

∞

∑︁

𝑢=0

𝐴exp(−𝐾)𝐾

𝑢(𝐾+1)^𝑢+1Γ(³₂ +𝑢) 2√

𝜋 sin_𝑀^𝜋2𝑢+2

(1+𝑢) (𝑢!)²

(𝛾¯_𝑟)^{− (𝑢+1)}. (44)

Taking only the dominant term into account, we can deduce from (44) that 𝑃¯

RF

𝑒, 𝑎 ∝ (𝛾¯_𝑟)⁻¹. Thus, the RF diversity gain for ASEP equals unity. Note that the term with the smallest exponent of average SNR dominates the ASEP. Therefore, the overall system diversity gain for ASEP, considering (40), is obtained as

D_𝑒,SatCom =min

min(

𝜉²

GH

𝑏 ,

𝛼GH

𝑏 ,

𝛽GH

𝑏 ) , min(

𝜉²

GH

𝑏 ,

𝛼GH

𝑏 ,

𝛽GH

𝑏

) + D_𝑒,SH−h

, (45) whereD_𝑒,SH−h denotes the diversity gain with respect to ASEP of the SH-FSO/RF transmission and is calculated by

D_𝑒,SH−h =min

min(

𝜉²

GS

𝑏 ,

𝛼GS

𝑏 ,

𝛽GS

𝑏 ) , min(

𝜉²

GS

𝑏 ,

𝛼GS

𝑏 ,

𝛽GS

𝑏 ) +1

. (46) After simplification,D_𝑒,SatCom is given by

D_𝑒,SatCom = min

𝜉²

GH

𝑏 ,

𝛼GH

𝑏 ,

𝛽GH

𝑏

. (47)

V. SWITCHINGTHRESHOLDOPTIMIZATION

In this section, we derive the optimum switching thresholds for both FSO links in terms of minimizing the overall system ASEP. First, we obtain the optimum switching threshold for SH-FSO transmission, 𝛾^SH

opt, which is given by differentiating (31) for𝛾

th and equating it to zero, as 𝑑

𝛾th

¯ 𝑃

SH

𝑒 + 𝑑

𝛾th

𝑃

SH out 𝑃¯

RF

𝑒 =0. (48)

From (13) and (27), we can rewrite (48) as

−𝑃(𝑒|𝛾) 𝑓_𝛾

GS(𝛾) + 𝑓_𝛾

GS(𝛾) 𝑃¯

RF

𝑒 =0. (49)

With the application of (21), the optimum switching of the SH-FSO transmission is given by

𝛾^SH

opt = 1

sin_𝑀^𝜋 erfc⁻¹ 2

𝐴

¯ 𝑃

RF 𝑒

2

. (50)

Now, we derive the optimum switching threshold for FSO transmission over the HAP 𝛾^SAG

opt . By differentiating (25) for 𝛾th and equating it to zero, we can obtain

𝑑 𝛾th

¯ 𝑃

SAG

𝑒 + 𝑑

𝛾th

𝑃

SAG out 𝑃¯

SH−h

𝑒,opt=0, (51)

where 𝑃¯

SH−h

𝑒,opt denotes the ASEP of the SH-FSO/RF trans- mission with optimum switching threshold 𝛾^SH

opt. Given that aerosols are typically concentrated within 2 km of the ground [16], the HAP-SAT hop experiences extremely weak tur- bulence with very large fading parameters in the order of 10⁴. On the other hand, the ground-HAP hop is vulnerable to atmospheric turbulence effects and weather conditions.

Thus, it is more likely that 𝛾

HS > 𝛾

GH, and the effective instantaneous SNR of the FSO transmission over the HAP

TABLE I

SIMULATIONPARAMETERS[24].

Parameter Symbol Value

Ground station height ℎ

G 1 m

HAP relay altitude ℎ

H 20 km

SAT altitude ℎ

S 620 km

Ground-SAT and HAP-SAT zenith angle

𝜃HS, 𝜃

GS 30^o:80^o

Ground-HAP zenith angle 𝜃

GH 5^o

Wind speed 𝜔 21 m/s

Ground level turbulence 𝐶²

n(0) 1.7×10⁻¹⁴m⁻²³ FSO subsystem

Optical bandwidth BWf 1 GHz

Optical wavelength 𝜆_f 1550 nm

Telescope Tx gain 𝐺^tx

f 75 dB

Telescope Rx gain 𝐺^rx

f 75 dB

Background noise power 𝜎²

n 250𝜇W [52]

Pointing error coefficients 𝜉

GS,𝜉

GH, and 𝜉

HS 5.2, 5.2, and 13.07 Optical-to-electrical efficiency 𝜂 0.8

Beam divergence angle 𝜙 15𝜇rad [52]

Telescope aperture diameter 𝐷 0.2 m

Transmitting beam radius 𝑊^G 0,𝑊^H

0 0.02 m

Switching threshold 𝛾

th 10.5 dB

RF subsystem [53]

RF carrier frequency 𝑓_𝑟 28 GHz

RF link bandwidth 𝐵𝑊𝑟 300 MHz

RF Transmit antenna gain 𝐺^tx

𝑟 50dB

RF Receive antenna gain 𝐺^rx

𝑟 50dB

RF Noise power spectral density 𝑃_n

o -114 dBW/MHz

Noise figure 𝑁_𝑟 5 dB

Rician factor 𝐾 6

can be approximated as 𝛾

SAG ≈𝛾

GH [26]. Hence, (51) can be rewritten as

𝑑 𝛾_th

¯ 𝑃

GH

𝑒 + 𝑑

𝛾_th 𝑃

GH out 𝑃¯

SH−h

𝑒,opt≈0. (52)

Using (13), (21), and (27), the optimum switching for FSO transmission over the HAP is obtained as

𝛾^SAG

opt ≈ 1

sin𝑀^𝜋

erfc⁻¹ 2

𝐴

¯ 𝑃

SH−h 𝑒,opt

2

. (53)

VI. NUMERICALRESULTS

We now illustrate the performance of the integrated trans- mission system using selected numerical examples. We also use Monte Carlo simulations to verify the obtained OP and ASEP expressions. Unless otherwise stated, we assume binary PSK modulation, an IM/DD scheme without losing generality, and the system parameters as listed in Table I. We also assume that FSO and RF links have equal average SNR. The infinite summations are truncated to 𝑣 =50 and𝑢 =30 since larger values have a minor impact on the obtained performance.

Fig. 2 compares the OP of the proposed system given by (19) with other transmission schemes as a function of average link SNR over uplink and downlink scenarios. We assume a 10.5 dB outage threshold and a60^o satellite zenith

Fig. 2. OP performance with varying average link SNRs.

Fig. 3. OP performance with varying transmission rate for uplink scenario.

angle. We can observe that the derived analytical expression exactly matches the Monte Carlo simulation. Because of the residual beam-wandering effects in the uplink scenario, all SatCom systems achieve better performance in the downlink than in the uplink. Also, the SAG-FSO/RF design in [24]

outperforms SH-FSO/RF transmission [20] over the uplink, while the downlink performance gain is negligible. With our integrated transmission system, we can achieve about 10 dB performance gain over the SAG-FSO/RF transmission [24] for both downlink and uplink scenarios, at an OP of1×10⁻⁹. The performance gain over downlink and uplink scenarios suggests that the proposed system is a promising solution for future SatCom systems.

In Fig. 3, we plot the OP as a function of targeted trans- mission rate with a 10 dB average SNR and a 45^o satellite zenith angle. In this figure, the SH-FSO link can achieve the target transmission rate at a much lower OP when compared to RF transmission. Therefore, employing the SH-FSO link

Fig. 4. Probability of the RF-link usage for different satellite zenith angles over uplink scenario.

as a backup improves the system’s capability to satisfy the target transmission rate. For example, the proposed system can achieve a transmission rate of 1 Gbps with an OP of 1.7×10⁻⁶ compared to 2.8×10⁻³ in the case of the SAG- FSO/RF transmission [24]. The obtained results are practical in the sense that they allow us to identify the capacity guaranteed to fulfill a particular QoS requirement, which is substantially interesting and beneficial to the end user.

Because FSO transmissions typically have higher through- put than RF transmissions, a lower probability of RF-link usage denotes higher system throughput. Therefore, we show the probability of RF-link usage in Fig. 4 to highlight the benefit of the suggested transmission system. To do so, we assume varying satellite zenith angles, an outage threshold of 10.5 dB, and a 20 dB average link SNR. For the sake of comparison, we also plot the probability of RF-link usage for SH-FSO/RF [20], SAG-FSO/RF [24], and our proposed system without SH-FSO transmission. From this figure, we can see that the integrated transmission system results in substan- tially lower RF-link usage than SAG-FSO/RF [24], whereas SAG-FSO/RF [24] slightly outperforms SH-FSO/RF [20]. The probability of RF-link usage is decreased from 2×10⁻² and 5×10⁻³ for SH-FSO/RF [20] and SAG-FSO/RF [24] systems to7×10⁻⁶ for our proposed system, at a 40^o satellite zenith angle. Importantly, the RF-link usage increases to 4×10⁻⁴ without the use of SH-FSO transmission as an additional backup. Despite its vulnerability to atmospheric turbulence, the SH-FSO contributes to improved system performance, particularly at lower satellite zenith angles.

Fig. 5 presents the diversity gain for the OP given by (39) over the uplink scenario. The diversity gain is plotted for different satellite zenith angles to highlight its critical- ity for SatCom system design. In this figure, the diversity gain of the SH-FSO link [17] degrades from 10 to 1 when the satellite zenith angle increases from 30^o to 80^o. The fading parameters 𝛽

GS and 𝛼

GS are changed from (24.41, 20.67) to (1.95,2.11). This outcome confirms that the longer

Fig. 5. Outage diversity gain for different satellite zenith angles.

Fig. 6. ASEP performance with varying average link SNRs.

propagation distance through the atmosphere impacts SH- FSO transmission. Despite the variation in diversity gain, the SH-FSO link outperforms the RF link, which justifies our approach of employing the SH-FSO as a backup link. The diversity gain of both SH-FSO/RF [20] and SAG-FSO/RF [24] is also degraded as the satellite zenith angle increases.

Still, both systems can maintain better diversity gain than SH- FSO transmission. Remarkably, the integrated transmission system achieves a considerable gain over other transmission schemes. Integrating both SAG-FSO and SH-FSO links into a single system is the main reason for such a performance gain.

Adopting a single-threshold hard-switching technique for the operation of the system, on the other hand, reduces the transmit power and simplifies the design of the receiver.

In Fig. 6, we investigate the effect of the average SNR of the link on the overall system ASEP given by (25) over uplink and downlink scenarios. To do so, we consider a10.5dB switching threshold and a60^osatellite zenith angle. We can observe that

Fig. 7. ASEP performance for different wind speeds.

the obtained expression for the ASEP and the Monte Carlo simulation are perfectly matched. Also, the proposed SatCom system performs better than the SAG-FSO/RF [24] by about 8 dB in both downlink and uplink scenarios, at an ASEP of 10⁻⁹. The SAG-FSO/RF system [24], however, can only outperform the SH-FSO/RF over the uplink since the beam- wandering effect is evident.

Fig. 7 presents the ASEP of the integrated transmission system for different wind speeds, a switching threshold of10.5 dB, a20dB average link SNR, a60^osatellite zenith angle, and an uplink scenario. Note that high wind speeds cause vortex formation, which alters the refractive index structure of the air. Such a phenomenon leads to pointing errors and possible fluctuations in the amplitude of the received signal. Therefore, a degraded SatCom performance is expected. From this figure, the wind speed affects the SH-FSO link to a greater extent, and employing the RF link as a backup achieves a significant performance gain. The hybrid FSO/RF transmission benefits from the complementary property of available beamwidth. The SH-FSO beamwidth at the receiver can range from tens of meters to a few kilometers, while the RF beamwidth ranges from tens to hundreds of kilometers, depending on the satellite altitude and zenith angle. Furthermore, we can also see that the proposed SatCom system achieves the best ASEP among all transmission schemes thanks to the small zenith angle of HAP deployment. When the wind speed changes from 10 m/s to40 m/s, 𝛽

GH and𝛼

GH are changed from (66.37,46.31) to (23.13,19.79). Thus, the FSO transmission over the HAP experiences a weak turbulence effect.

Fig. 8 shows the ASEP of the integrated transmission system with HD and IM/DD for various pointing error coefficients.

We assume a 10.5 dB switching threshold, a ground level turbulence 𝐶_n²(0) = 4.69 ×10⁻¹³m⁻²³, and a 65^o satellite zenith angle. As we can see, both asymptotic and exact analytical expressions are matched at high SNR values. It is also observed that the increase in𝜉 leads to improved system performance. The system with HD scheme gains about 6 dB

Fig. 8. ASEP performance under the effect of pointing errors over uplink scenario.

Fig. 9. ASEP performance as a function of switching threshold values.

when 𝜉 increases from 1 to 2, at an ASEP of 1 ×10⁻⁹. Furthermore, the proposed system with the HD scheme is more sensitive to changes in𝜉value and suffers a larger SEP penalty compared to that with the IM/DD scheme. The HD scheme, however, can sustain better system performance due to its coherent detection nature.

Fig. 9 presents the ASEP of the proposed system with respect to the switching thresholds for different average SNRs.

We assume a65^o satellite zenith angle, a ground level turbu- lence𝐶²

n(0) =4.69×10⁻¹³m⁻²³, and an uplink scenario. It is observed that there are optimum switching thresholds, 𝛾^SAG

opt

and𝛾^SH

opt, at which the ASEP reaches its minimum value, and the optimal value choice increases with the average SNR.

Table II shows the obtained numerical results of the optimum switching thresholds compared to the analytical values given by (50) and (53), verifying the accuracy of the analytical expressions.