Performance Analysis and Optimization of Cooperative Satellite-Aerial-Terrestrial Systems

TL;DR: In this article, a cooperative satellite-aerial-terrestrial system including a satellite transmitter (S), a group of terrestrial receivers (D), and an aerial relay (R) is considered, and the outage performance of S-R link is investigated by deriving an approximated expression for the outage probability.

Abstract: Aerial relays have been regarded as an alternative and promising solution to extend and improve satellite-terrestrial communications, as the probability of line-of-sight transmissions increases compared with adopting terrestrial relays In this paper, a cooperative satellite-aerial-terrestrial system including a satellite transmitter (S), a group of terrestrial receivers (D), and an aerial relay (R) is considered Specifically, considering the randomness of S and D and employing stochastic geometry, the coverage probability of R-D links in non-interference and interference scenarios is studied, and the outage performance of S-R link is investigated by deriving an approximated expression for the outage probability Moreover, an optimization problem in terms of the transmit power and the transmission time over S-R and R-D links is formulated and solved to obtain the optimal end-to-end energy efficiency for the considered system Finally, some numerical results are provided to validate our proposed analysis models, as well as to study the optimal energy efficiency performance of the considered system

Summary

Introduction

• Aerial relays have been regarded as an alternative and promising solution to extend and improve satellite-terrestrial communications, as the probability of line-of-sight transmissions increases compared with adopting terrestrial relays.
• The ASER of a hybrid satellite-terrestrial decode-andforward (DF) relay network was evaluated in [7] while considering the effect of co-channel interference.
• 2) The approximated analytical expressions for the coverage probability (CP) of R-D links are derived for non-interference and interference scenarios, respectively;.
• 4) The optimal energy efficiency problem is formulated and solved via optimizing the transmit power and time allocation over the two hops to realize the optimal e2e energy efficiency performance of the considered CSATC system.
• In Section II, the considered CSATC system is described.

A. Non-Interference Scenario

• As one of the most important metrics to evaluate the performance of wireless networks (especially for some application scenarios, e.g., battlefield and hot-spots), CP is defined as the probability that a typical user can achieve some threshold of SNR/SINR.
• The authors will analyze the coverage performance of R-Di link, while considering the randomness of the positions of terrestrial receivers.
• The authors assume there is an interfering node existing in the neighbor area of the target terminal, Di, while R delivering information bits to Di.
• In order to facilitate the following analysis, spherical coordinates are adopted, while E is set as the original.
• As presented in Fig. 1, intuitively, there exists an optimal transmit power and transmission time allocation over S-R and R-D hops to achieve optimal e2e energy efficiency for the considered CSATC system.

A. Problem Formation

• Similar to [28], in this work energy efficiency is adopted to evaluate the efficiency of the energy consumption on delivering the information bits, which is defined as the number of delivered bits over S-R-Di link with unit-joule consumption.
• Therefore, the following optimization problem is considered:.
• How to optimally allocate the transmit power and transmission time over S-R and R-Di links so that the energy efficiency of the considered system is maximized.
• PmaxS and PmaxR denotes the maximum transmit power at S and R, respectively.
• C4 and C5 ensures the low bounds of the transmission time for the two hops, respectively.

B. Solution of the Problem OPT-2

• Moreover, there are some packets on various platforms to solve such a simple form transcendental equation, such as Mathematica.
• The proposed iterative algorithm consists of only one loop, it has a polynomial time complexity, i.e., O(N).
• Furthermore, the authors run 1 × 106 times of the realizations of the considered system and 1 × 106 trials of Monte-Carlo simulations, to model the randomness of the positions of the considered terminals and channel gains over each link.

A. Coverage Performance Over S-R Link

• Γth = 0 dB, and two scenarios, non-interference and interference scenarios, will be studied for various the average channel power gain of R-D link (ΩR), respectively.
• One can see that in both figures CP can be improved while ΩR increasing.
• It can be explained that a large T represents a large distribution area for the interfering node, which exhibits a large probability of large path-loss over the interfering link.
• This finding June 23, 2020 DRAFT 21 can also be explained by the reason proposed for the observations in Fig.
• Furthermore, one can clearly find that simulation and numerical results agree with each other very well, which verifies the accuracy of the proposed analytical model presented in Section III.

B. Outage Performance

• Fig. 9 presents the outage performance over S-R link for various Ψ, while Ω increasing.
• Because Ω represents the average power of the LOS components of the received signal at R. Finally, the authors can also easily see that simulation and numerical results match well with each other, which confirms the correctness of the proposed analytical model presented in Section IV.
• The authors will present some simulation results of the e2e outage performance of the considered system shown in Fig.

C. Optimal Energy Efficiency Design

• The authors will present the e2e energy efficiency for non-interference and interference scenarios by using the proposed optimization method, which is given in Section V.
• The authors can observe that the proposed Algorithm 1 achieves convergence within five iterations.
• This observation can be explained the fact that the path loss over S-R link will dominate the main power consumption over S-R-D link when d0 is sufficiently large, e.g., the value of d0 ranges from 1600 km to 1800 km considered in Fig. 15, which is quite larger than the one of H1 ranging from 5 km to 30 km.
• An et al., “Performance analysis of multi-antenna hybrid satellite-terrestrial relay networks in the presence of interference,” IEEE Trans.

Figures

Fig. 4: CP over R-D link for various H1.

Fig. 9: OP over S-R link for various Ψ.

Fig. 2: Interference scenario.

Fig. 14: The optimal energy efficiency for various L.

Fig. 13: The optimal energy efficiency versus the number of the iterations for Algorithm 1.

Fig. 16: The optimal energy efficiency for various T .

Fig. 15: The optimal energy efficiency for various d0.

Fig. 6: CP over R-D link for various T .

Fig. 7: CP over R-D link for various H1.

Fig. 8: OP over S-R link for various H1.

Fig. 10: OP over S-R link for various PS.

Fig. 3: Satellite-relay link.

Fig. 17: The optimal energy efficiency for various Pmaxs .

Fig. 11: The e2e OP for interference scenarios with various combinations of L and T .

Fig. 12: The e2e OP for non-interference scenarios with various L.

Fig. 5: CP over R-D link for various L.

Fig. 1: System model.

Full text

Performance Analysis and Optimization of
Cooperative Satellite-Aerial-Terrestrial Systems
Item Type Article
Authors Pan, Gaofeng; Ye, Jia; Zhang, Yongqiang; Alouini, Mohamed-Slim
Citation Pan, G., Ye, J., Zhang, Y., & Alouini, M.-S. (2020). Performance
Analysis and Optimization of Cooperative Satellite-Aerial-
Terrestrial Systems. IEEE Transactions on Wireless
Communications, 19(10), 6693–6707. doi:10.1109/
twc.2020.3004644
Eprint version Post-print
DOI 10.1109/TWC.2020.3004644
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Journal IEEE Transactions on Wireless Communications
Rights This is an accepted manuscript version archived with thanks to
IEEE Transactions on Wireless Communications.
Download date 10/08/2022 03:55:14
Link to Item http://hdl.handle.net/10754/663810

1
Performance Analysis and Optimization of
Cooperative Satellite-Aerial-Terrestrial Systems
Gaofeng Pan, SeniorMember, IEEE, Jia Ye, Student M ember, IEEE, Yongqiang Zhang,
Student M ember, IEEE, and Mohamed-Slim Alouini, F ellow, IEEE
Abstract
Aerial relays have been regarded as an alternative and promising solution to extend and improve
satellite-terrestrial communications, as the probability of line-of-sight transmissions increases compared
with adopting terrestrial relays. In this paper, a cooperative satellite-aerial-terrestrial system including
a satellite transmitter (S), a group of terrestrial receivers (D), and an aerial relay (R) is considered.
Specifically, considering the randomness of S and D and employing stochastic geometry, the coverage
probability of R-D links in non-interference and interference scenarios is studied, and the outage per-
formance of S-R link is investigated by deriving an approximated expression for the outage probability.
Moreover, an optimization problem in terms of the transmit power and the transmission time over S-R and
R-D links is formulated and solved to obtain the optimal end-to-end energy efficiency for the considered
system. Finally, some numerical results are provided to validate our proposed analysis models, as well
as to study the optimal energy efficiency performance of the considered system.
Index Terms
Coverage probability, energy efficiency, outage probability, satellite-terrestrial communication, s-
tochastic geometry.
Manuscript received Nov. 15, 2019; revised Mar. 28 and June 18, 2020; accepted June 21, 2020. The associate editor
coordinating the review of this paper and approving it for publication was N. Yang. (Corresponding author: Gaofeng Pan.)
G. Pan is with Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science
and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia, and he is also with the School of Information and Electronics
Engineering, Beijing Institute of Technology, Beijing 100081, China.
J. Ye, Y. Zhang, and M.-S. Alouni are with Computer, Electrical and Mathematical Sciences and Engineering Division, King
Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
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I. INTRODUCTION
Benefiting from its inherent merits, including large-scale footprint, long communication distance,
abundant frequency resource, fast deployment and little dependence on terrestrial facilities, satellite com-
munication has already served as an irreplaceable role in long-distance communications (e.g., television
broadcasting), location and navigation, and disaster relief (e.g., weather forecasting). However, direct
communication links from the satellite to the ground terminals may not be always available, due to deep
fading (e.g., the shadows created by buildings and mountains).
To solve the aforementioned problems, cooperative transmission has been introduced and integrated
into satellite networks as an effective strategy to extend the coverage of satellite communications as well
as to increase the energy efficiency [1]. For example, generally, ground stations have been considered to
play as relays to aid the communications between the satellite and terrestrial terminals, which can not
only raise the coverage level of satellite signals but also provide diversity gain to improve the receiving
quality at terrestrial terminals.
So far, there are plenty of researches presented to design and study cooperative satellite-terrestrial
communications (CSTC) involving ground relays in terms of bit/symbol error performance [2]–[10],
outage performance [11]–[13], and physical layer security (PLS) [14]–[18].
As an important performance index to quantitatively reflect the event that the transmitted bits/symbols
are correctly received at the destination, bit/symbol error probabilities have been investigated for CSTC
systems. In integrated satellite and terrestrial networks, the average symbol error rate (ASER) of two
transmission modes with co-channel interference under composite multipath/shadowing fading was studied
in [2]. The closed-form expression was derived for the SER of M-ary phase-shift keying (MPSK) in
a two-way amplify-and-forward (AF) satellite system by using a moment-generating function (MGF)-
based approach [3]. The transmission of orthogonal space-time block codes over a shadowed Rician land
mobile satellite link was investigated in [4], by deriving the expressions of MGF, SER, diversity order,
and average capacity. The ASER of MPSK was analyzed for an AF hybrid CSTC network in the presence
of co-channel interference [5]. The performance of an AF hybrid satellite-terrestrial relay network was
investigated by deriving an approximate closed-form expression for ergodic capacity and the analytical
lower bound expressions for OP and ASER [6]. The ASER of a hybrid satellite-terrestrial decode-and-
forward (DF) relay network was evaluated in [7] while considering the effect of co-channel interference.
The approximate ASER of MPSK was analyzed for hybrid satellite-terrestrial free space optical AF
cooperative link [8]. The ASER was studied for AF relaying hybrid satellite-terrestrial links, while the
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channel of the terrestrial link between the relay and destination is assumed to suffer Nakagami-m fading
[9]. The authors of [10] evaluated the symbol error probability performance of a hybrid/integrated CSTC
network, while MPSK and M -ary quadrature amplitude modulation is employed.
Some other researchers paid their attention to the outage performance of CSTC systems to investigate
the benefits brought by the relays. In [11], outage probability (OP) and ergodic capacity were studied
for downlink hybrid satellite-terrestrial relay networks with a cooperative non-orthogonal multiple access
scheme. Closed-form expressions were derived in [12] for the OP of both primary and secondary networks
in a hybrid satellite-terrestrial spectrum sharing system. The application of random linear network coding
was studied for cooperative coverage extension in land mobile satellite vehicular networks [13].
It has been proved that, since the information delivery process is extended, the probability that
the transmitted information is overheard by eavesdroppers will unavoidably increase when relays are
introduced. Then, it is meaningful and necessary to study the impacts of the relays on the information
security of CSTC systems. The PLS of a downlink hybrid satellite-terrestrial relay network was in [14],
while [15] studied the PLS performance of a hybrid satellite and free-space optical cooperative system.
The authors of [16] investigated secure communication in a coexistence system of a satellite-terrestrial
network and a cellular network through PLS techniques. Ref. [17] investigated the secure transmission
for cognitive satellite-terrestrial networks where the terrestrial base station serving as a green interference
resource is introduced to enhance the security of the satellite link. The authors of [18] investigated the
secure transmission in a cognitive satellite-terrestrial network with a multi-antenna eavesdropper, where
the interference from terrestrial base stations is introduced to enhance the security of the satellite link.
Recently, aerial relays, e.g., low-altitude platforms (LAPs) including unmanned aerial vehicles (UAV),
balloons and blimps, which operate at varying altitudes in the range of a few dozen meters to a few
kilometers, can also assist the communications between the satellite and terrestrial users, leading to
cooperative satellite-aerial-terrestrial communication (CSATC) systems. Compared with terrestrial relays,
aerial relays are more capable of providing reliable and fast coverage for hazardous scenarios without
terrestrial access infrastructure while suffering natural disasters such as floods and earthquakes, and cases
of poor communication quality incurred by the lack of line-of-sight (LOS) or deep shadowing, as LOS
transmissions can be achieved with high probability by using aerial relays. On the other hand, aerial relays
can help some terrestrial terminals (e.g., wireless sensors), which suffer hardware constraints and then
cannot directly communicate with the satellite, set up communication links with the satellite. Hence, aerial
relays are an alternative choice to realize dependable satellite-terrestrial communications. The authors of
[19] studied the joint relay selection and power allocation for an orthogonal frequency division multiple
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access-based hybrid CSATC networks.
Then, one can see that there is almost a blank on the study of CSATC systems. Though researchers
have well studied CSTC systems, none of them has considered the randomness of the positions of the
satellite and destinations. So, inspired by these observations and similar to our previous work [20], the
main purpose of this paper is to investigate the impacts of the randomness of the positions of terrestrial
terminals and the satellite to fully understand the performance of CSATC systems, as well as to offer a
useful reference to the readers who are interested in studying satellite communication systems.
In this study, a CSATC system consisting of a satellite transmitter (S), a group of terrestrial receivers
(D), and a LAP (R) acting as a relay. While employing stochastic geometry theory, the coverage
performance of R-D links and the outage performance of S-R link are respectively studied. Then, an
optimal problem for transmit power and transmission time allocations is formulated to achieve the optimal
end-to-end (e2e) energy efficiency performance. In a word, logically, the two main tasks of this work
is first to understand how system parameters affect the system performance (i.e., coverage and outage
performance), and then to optimize the system performance (i.e., energy efficiency).
Technically speaking, compared with existing works on traditional terrestrial cooperative systems,
Shadowed-Rician (SR) model presented in [21] is considered in this work, and other than existing works
on satellite-terrestrial communication systems, the impact of the randomness of the position of the satellite
in three-dimensional space on the performance of the considered system is first studied.
The main contributions of this paper are summarized as follows:
1) The probability density function (PDF) or/and cumulative distribution function (CDF) of the signal-
to-noise-ratio (SNR)/signal-to-interference (SIR) over S-R/R-D links are characterized while considering
the impacts of both small-scale fading and the randomness of the positions of the terminals;
2) The approximated analytical expressions for the coverage probability (CP) of R-D links are derived
for non-interference and interference scenarios, respectively;
3) The approximated analytical expression for the OP over S-R link is presented while considering
that the satellite is randomly distributed;
4) The optimal energy efficiency problem is formulated and solved via optimizing the transmit power
and time allocation over the two hops to realize the optimal e2e energy efficiency performance of the
considered CSATC system.
The rest of this paper is organized as follows. In Section II, the considered CSATC system is described.
In Section III and IV, the coverage and outage analyses are conducted for R-D and S-R links, respectively.
An optimal energy efficiency problem is formulated and solved in Section V. In Section VI, numerical
June 23, 2020 DRAFT

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Q1. What are the contributions in "Performance analysis and optimization of cooperative satellite-aerial-terrestrial systems" ?

In this paper, a cooperative satellite-aerial-terrestrial system including a satellite transmitter ( S ), a group of terrestrial receivers ( D ), and an aerial relay ( R ) is considered. Specifically, considering the randomness of S and D and employing stochastic geometry, the coverage probability of R-D links in non-interference and interference scenarios is studied, and the outage performance of S-R link is investigated by deriving an approximated expression for the outage probability.