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Performance analysis of multiuser dualhop satellite relaying systems
EURASIP Journal on Wireless Communications and Networking volume 2019, Article number: 147 (2019)
Abstract
In this study, we investigate the outage probability (OP) of a multiuser dualhop satellite relaying system with decodeandforward (DF) protocol, where both uplink and downlink experience Shadowed Rician (SR) fading. Specifically,by taking the effects of antenna pattern and path loss into account, we first establish a practical satellite channel model and obtain the endtoend signaltonoise ratio (SNR) expression for the considered system, where the uplink employs opportunistic scheduling (OS) scheme while the downlink adopts selection combining (SC) or maximal ratio combining (MRC) approaches. Then, we derive the closedform OP expressions for the dualhop satellite relaying with OS/SC and OS/MRC schemes, respectively. Furthermore, the asymptotic OP formulas at high SNR are also developed to gain further insights conveniently. Finally, numerical results confirm the validity of the theoretical formulas and reveal the representative parameters on the system performance.
Introduction
Satellite communication (SatCom) has the potential of providing connectivity for fixed and mobile users especially in the areas where the terrestrial networks are challenging or infeasible to be deployed [1–4]. Meanwhile, it has been shown that relay technology is able to offer significant performance benefits, such as improving the system throughput via spatial diversity, extending signal coverage without consuming large transmitter power [5]. Therefore, the application of relay transmission in SatCom has been an active research topic both in academia and industry recently.
Previous works
In SatCom, the lineofsight (LoS) link between the satellite and the terrestrial user is prone to be blocked, which makes the satellite services unavailable in some scenarios, thus a novel network architecture termed as the hybrid satelliteterrestrial network (HSTN), which utilizes the terrestrial relay to assist the satellite signal transmission, has received significant attention recently. Until now, substantial effort has been devoted to investigating the performance of HSTNs. For example, in [6] and [7], the authors investigated the performance of a HSTN with decodeandforward (DF) protocol. The authors of [8] addressed the performance analysis problem of amplifyandforward (AF)based HSTN. Taking the interference power constraints imposed by satellite communications into account, the authors of [9] derived a closedform expression for the outage probability (OP) of a HSTN system. In [10], a partial relay selection scheme was studied in which satellite selects a relay earth station (ES) among multiple relay ESs (situated on ground) on the basis of maximum instantaneous signaltonoise ratio (SNR) in AFbased HSTN. Besides, the authors of [11] proposed a robust relay beamforming (BF) scheme for a HSTN, where a cognitive base station (BS) with multiantenna is utilized not only as a BS of a cellular network but also as a relay to assist the satellite signal transmission. However, the main drawback of the aforementioned works is that they only consider the downlink transmission of satellite systems.
In a practical scenario, the satellite is often exploited as a relay on the sky, which receives signals from a source ES through uplink channel and forward them to the destination ES via downlink channel [12]. Consequently, in order to measure the performance of a satellite system more accurately, both uplink and downlink channels should be taken into account. For this reason, the authors of [13] derived the closedform expressions of OP, ergodic capacity (EC), and average symbol error rate (ASER) for a dualhop AF satellite relaying network. In [14] and [15], the authors conducted performance evaluation of a dualhop AF system with satellite relaying. Although AF relaying protocol is a simple scheme, which is commonly employed in current bentpipe satellite system, it is foreseeable that DF protocol will be widely utilized in the future due to its advantage of better performance and the rapid development of satellite onboard processing technology. In this content, the authors of [16] analyzed the performance of a dualhop DF satellite relaying system over Shadowed Rician (SR) channels. However, it should be pointed out that all of the aforementioned works focus on the singleuser scenario, which is not in line with practical application, since SatCom often provides various services to a large number of terrestrial users with high quality of service (QoS). Under this situation, the authors of [17] investigated the performance of a multiuser AF HSTN with opportunistic scheduling (OS) scheme and verified that the system performance can be improved via the multiuser diversity. This work was later extended to the case of imperfect channel state information (CSI) and cochannel interference (CCI) in [18]. Besides, considering the interference at the terrestrial relay, the authors of [19] studied a multiantenna multiuser HSTN employing OS with outdated CSI and AF relaying with CCI. Furthermore, by making use of the complementary moment generating function (MGF) method, an accurate analytical expression for the EC of a HSTN with AF protocol was derived in [20], where the impacts of various system parameters on EC were also revealed. Nevertheless, to the best of our knowledge, the existing works conducting the performance of dualhop satellite relaying system with multiple users remain very limited, making it still an open yet interesting research topic. These observations motivate the work presented in this paper.
Methods and contributions
In this paper, we consider a dualhop satellite relaying network with multiple users, where both the uplinks and downlinks follow the SR fading. By applying OS scheme at the uplinks and selection combining (SC) or maximal ratio combining (MRC) schemes at the downlinks, the equivalent endtoend output SNR of the system is first obtained, then analytical expressions of OP as well as asymptotic results are derived to evaluate the system performance. Finally, simulation results are provided to validate our theoretical formulas and show the impact of various parameters on the system performance. The detailed contributions of this paper are outlined as follows:

Considering the effects of antenna gain and path loss, we extend the channel model in [13] and [16] to a more practical one, and then obtain the endtoend SNR expression of the multiuser dualhop satellite relaying system with DF protocol, where the OS scheme is used in the uplink, while the SC and MRC schemes are used in the downlink, respectively.

Assuming that both uplink and downlink experience SR fading, we derive the OP expressions of the multiuser dualhop satellite relaying network with OS/SC and OS/MRC schemes, respectively. This is different from [13] and [16] focusing on the scenario of signal user, which do not coincide with the characteristics of SatCom, where a lot of terrestrial users are often served so that its benefits of wide coverage can be exploited.

To gain further insights, we present the asymptotic OP formulas at high SNR for the considered system, which are utilized to reveal the diversity order and coding gain of the satellite relaying system conveniently. Thus, our work provides useful guidelines for the engineers to implement satellite system design.
The rest of the paper is organized as follows. Section 2 describes the system and channel model. Section 3 derives the closedform OP expressions for the considered system with OS/SC and OS/MRC schemes, respectively. Section 4 presents the asymptotic OP expressions of the considered system. Moreover, based on these asymptotic OP expressions, the diversity order and coding gain expressions are also given. The numerical results and analyses are presented in Section 5, and the paper is concluded in Section 6.
Notation: E[·] denotes the expectation, · the absolute value, exp(·) the exponential function, and N_{c}(μ,σ^{2}) the complex Gaussian distribution with mean μ and variance σ^{2}.
System and channel model
The system model considered in this paper is illustrated in Fig. 1, which consists of N source ESs termed as source (S), M destination ESs termed as destination (D) and a satellite relaying (R). Similar to the existing works [13, 16], we assume that both of the uplink (SR) and downlink (RD) channels undergo SR fading, and the direct links between the sources and the destinations are unavailable, due to the heavy shadowing of the radio propagation. In addition, it is assumed that S and D have a directional antenna, while the satellite is equipped with a multibeam antenna to serve the multiple ESs. Similar to the previous works, such as [3], we suppose that the satellite channels experience slow fading and perfect CSIs of satellite links are available.^{Footnote 1}
Channel model
As shown in Fig. 1, we suppose that all of the ESs are within the coverage of satellite spot beam, and use \(g_{i}^{u}\) and \(g_{j}^{d}\) to denote the uplink channel response between the ith ES and R and downlink channel response between R and the jth ES, respectively. By taking the effects of practical parameters, such as antenna beam pattern, path loss, and channel fading into account, the satellite channel model of uplink and downlink can be uniformly expressed as
where the coefficient F_{l} is given by
where λ denotes the wavelength, d_{l} the distance between the satellite and the lth user. Besides, \(G_{s,l}^{}\) and \(G_{u,l}^{}\) represent the satellite and terrestrial user antenna patterns, respectively. According to [21], \(G_{s,l}^{}\) can be written as
where \(G_{s,l}^{\max }\) is the maximum satellite antenna gain, J_{1}(x) and J_{3}(x) the firstkind Bessel function of order 1 and 3, respectively, and u_{l}=2.07123sinϕ_{l}/sinϕ3 dB, where ϕ_{l} denotes the angle between the lth ES and the beam center with respect to the satellite, and ϕ3 dB the 3 dB angle of the main beam. The normalized satellite antenna pattern is illustrated in Fig. 2.
In (2), the array gain in dB, namely, \({\widehat G_{u,l}}(\theta,\varphi) = 10lo{g_{10}}\left ({{G_{u,l}}(\theta,\varphi)} \right)\) can be modeled as [22]
where \(G_{u,l}^{\max }\) is the maximum antenna gain of the lth ES and G_{h}(φ) and G_{v}(θ) the radiation patterns in horizontal and vertical angle directions, which are, respectively, given by
where φ_{3 dB} and θ_{3 dB} are the 3 dB beamwidth of the horizontal and vertical patterns, respectively, θ_{tilt} the main beam tilting angle, SLL the sidelobe level of the antenna pattern.
In (1), h_{l} denotes the channel fading, which is often modeled as SR distribution described by \({h_{l}} = {\overline h_{l}}\exp \left ({j{\psi _{l}}} \right) + {\widetilde h_{l}}\exp \left ({j{\xi _{l}}} \right)\) [13, 16], where the LoS component \({\overline h_{l}}\) and the scattering component \({\widetilde h_{l}}\) satisfy Nakagamim and Rayleigh fading distribution, respectively. ψ_{l} is the deterministic phase of the LoS component and ξ_{l} the static random phase vector satisfying the uniform distribution among [0,2π). Since the value of ψ_{l} does not affect the envelope characteristics, we assume ψ_{l}=0 to simplify the notation. With this regard, the probability density function (PDF) of \({\left  {h_{l}^{~}} \right ^{2}}\) is given by [23]
where \({\alpha _{l}} = \frac {1}{{2{b_{l}}}}{\left (\frac {{2{b_{l}}{m_{l}}}}{{2{b_{l}}{m_{l}} + {\Omega _{l}}}}\right)^{{m_{l}}}}\), \({\beta _{l}} = \frac {1}{{2{b_{l}}}}\), \({\delta _{l}} = \frac {{{\Omega _{l}}}}{{2{b_{l}}(2{b_{l}}{m_{l}} + {\Omega _{l}})}}\), with Ω_{l} being the average power of LoS component, 2b_{l} the average power of the multipath component, and m_{l} the Nakagami parameter ranging from 0 to ∞. Meanwhile, the function _{1}F_{1}(a;b;z) is the confluent hypergeometric function having the expression as [24]
where (x)_{n}=x(x+1)…(x+n−1).
Signal model
The total communication occurs in two time phases. During the first time phase, the ith S sends its signal x(t) with E[x(t)^{2}]=1 to R via the uplink channel \({g_{i}^{u}}\). Then, the received signal at R can be written as
where P_{s,i} denotes the transmitted power of the ith source, n_{i} the noise at R that is often modeled as additive white Gaussian noise (AWGN) with zero mean and variance \(\sigma _{}^{2} = \kappa BT\), namely, \(n_{i}^{} \sim {N_{c}}\left ({0,\sigma _{}^{2}} \right)\), where κ is the Boltzman constant, B the carrier bandwidth, and T the receiver noise temperature. By using (1) into (6), the output SNR at R can be expressed as
where \({\bar \gamma _{s,i}} = \frac {{{P_{s,i}}F_{i}^{2}}}{{\sigma _{}^{2}}}\) is the average SNR of the ith SR link and \(h_{i}^{u}\) the channel fading of the ith SR link. Without loss of generality, we assume that the SR links have the same average SNR, namely, \({\bar \gamma _{s,i}} = {\bar \gamma _{s}}(i = 1,2, \ldots N)\). By adopting the OS scheme to select the user with the best channel link at each scheduling time, so that multiuser diversity can be achieved to improve the system performance, one can obtain the output SNR at R as
During the second time phase, since the DF relaying protocol is used, R decodes its received signal y_{s,i}(t) at first. Then, the reencoded signal is broadcasted to the destination within coverage. By supposing that the transmitted power at R is P_{r,j}, the received signal at the jth D can be written as
Similarly, n_{j} is AWGN satisfying \(n_{j}^{} \sim CN\left ({0,\sigma _{}^{2}} \right)\). As a result, According to (1) and (9), the received SNR at the jth D is given by
where \({\bar \gamma _{d,j}} = \frac {{{P_{r,j}}F_{j}^{2}}}{{\sigma _{}^{2}}}\) is the average SNR of the jth RD link and \(h_{j}^{d}\) the channel fading of the jth RD link. Similar to the uplink, it is also supposed that \({\bar \gamma _{d,j}} = {\bar \gamma _{d}}(j = 1,2, \ldots M)\). In this paper, we exploit two methods, namely, SC and MRC schemes at D, yielding the final output SNR as
Consequently, the endtoend SNR of multiuser dualhop satellite relaying with DF protocol can be expressed as
In the following section, we will derive the exact and asymptotic OP expressions to evaluate the considered satellite system, where the uplink exploits the OS scheme, while the downlink utilizes the SC and MRC schemes, respectively.
Performance analysis
Among all the performance measures, OP is one of the most important criterions to measure the wireless communication service quality [25, 26], which is defined as the probability that the output SNR γ is below a certain threshold x. Thus, following (12), the OP of the considered system can be expressed as
where \({F_{{\gamma _{1}}}}\left (x \right)\) and \({F_{{\gamma _{2}}}}\left (x \right)\) denote the cumulative distribution function (CDF) of γ_{1} and γ_{2}, respectively. Obviously, the OP performance depends on the scheduling scheme, which will be investigated in the following subsection.
OS/SC scheme
In order to obtain the closedform OP expression of the considered system with OS/SC scheme, we will derive the analytical expressions of \({F_{{\gamma _{1}}}}\left (x \right)\) and \({F_{{\gamma _{2}}}}\left (x \right)\), respectively.
First of all, we focus on the closedform expression of \({F_{{\gamma _{1}}}}\left (x \right)\). By considering that the OS scheme is adopted in the uplink, the CDF of \(\gamma _{1}^{}\) in (8) can be expressed as
In deriving (14), we have used the fact that \(h_{i}^{u}(i = 1,2, \ldots N)\) is independent identically distributed (i.i.d.). Meanwhile, by using (5) and (7), the PDF of γ_{s,i} can be written as
After expanding exp(−x) with the Maclaurin series and utilizing the equation (2.01.1) in [24], the CDF of γ_{s,i} can be written as
where
and _{2}F_{2}(a_{1},a_{2};b_{1},b_{2};z) is the confluent hypergeometric function, which is given by
By substituting (16) into (14), the CDF of \(\gamma _{1}^{}\) can be obtained as
Next, when the SC scheme is used at D, only the ES with the maximal output SNR is selected [27], namely,
In a similar manner, by considering that \(h_{j}^{d}(j = 1,2, \ldots M)\) satisfies the condition of i.i.d., the CDF of \({F_{{\gamma _{2}}}}\left (x \right)\) can be written as
By substituting (17) and (19) into (13), the OP of the dualhop DF satellite relaying network with OS/SC scheme can be obtained as
where \(\Xi \left ({A,B,b,m,\bar \gamma,x} \right)\) is given by
OS/MRC scheme
Here, we focus on the OP of the considered system with OS/MRC scheme. Since the CDF of γ_{1}, namely, \({F_{{\gamma _{1}}}}(x)\), has already been obtained as in (17), here we aim at the closedform expression of \({F_{{\gamma _{2}}}}(x)\) with the MRC scheme used in the downlink. To this end, we first express the output SNR as
where \(\eta = \sum \limits _{j = 1}^{M} {{{\left  {h_{j}^{d}} \right }^{2}}}\). According to [28], the MGF of \({\left  {h_{j}^{d}} \right ^{2}}\) can be written as
By substituting (5) into (23) and employing the equations (7.621.4) and (9.121.1) in [24], (23) can be expressed as
Considering that \(h_{j}^{d}\left ({j = 1,2, \ldots M} \right)\) is i.i.d., we can obtain the MGF of η as
Since m_{d} may be a decimal, the power M(m_{d}−1) of the numerator can be written as
where
In (27), ⌊z⌋ means the largest integer that does not exceed z. In a similar manner, the power Mm_{d} of the denominator can be expressed as
where
Consequently, the MGF of η in (25) can be rewritten as
when β_{d}≫δ_{d}, then \(\frac {{{\delta _{d}}}}{{s + {\beta _{d}}  {\delta _{d}}}} \ll 1\), so we can get
By substituting (31) into (30), it follows that
With the help of the inverse Laplace transform of (32), the PDF of γ_{2} can be obtained as
where
In (34), M_{λ,μ}(z) represents the Whittaker function. Furthermore, the CDF of γ_{2} is given by
where
By substituting (17) and (35) into (13), the OP of the dualhop DF satellite relaying network with OS/MRC scheme can be expressed as
Remark 1
By taking the effects of antenna pattern and path loss into account, we have derived the closedform expressions of OP for the considered dualhop satellite relaying system with OS/SC and OS/MRC schemes, respectively. Therefore, we extend the existing works in [13] and [16] to a more practical scenario with multiple users.
Asymptotic OP at high SNR
Although (20) and (37) are exact and valid for any given SNR, it is difficult to characterize the impact of key parameters on the system performance. To this end, we devote to investigating the asymptotic OP at high SNR to gain further insight. According to (13), the asymptotic OP of the considered system is given by
In this section, by supposing that \({\bar \gamma _{v}} \to \infty \left ({v = s,d} \right)\), we will derive the asymptotic OP expressions for the considered system, where the OS scheme is used in the uplink, while the SC and MRC schemes are used in the downlink, respectively.
OS/SC scheme
When OS/SC scheme is employed, the asymptotic OP behavior of the considered system is given by Theorem 1.
Theorem 1
The asymptotic OP at high SNR for the system with OS/SC scheme can be expressed as
Proof
See Appendix 1. According to [29, 30], the OP of a wireless system at high SNR can be approximated as
where \(G_{c}^{}\) represents the coding gain and \(G_{d}^{}\) the diversity order, which is determined by the slope of the OP curve against average SNR at high SNR in a loglog scale. By comparing (39) with (40), the diversity order and coding gain of the system applying OS/SC scheme are given by
□
OS/MRC scheme
As for the case of employing OS/MRC scheme, the asymptotic OP behavior of the considered system with OS/MRC scheme can be evaluated by Theorem 2.
Theorem 2
The asymptotic OP at high SNR for the considered system with the OS/MRC scheme is given by
Proof
See Appendix 2. Following the similar way, the diversity order and coding gain of the multiuser dualhop satellite relaying system applying OS/MRC scheme can be expressed as
□
Remark 2
It is interesting to find that while the diversity order does not depend on the scheme used at D, the coding gain of the considered system with OS/MRC scheme is greater than that with OS/SC scheme in the case of N>M. Since the number of sources (e.g., mobile users) is often more than that of destinations (e.g., gateway), our results verify that it is better to exploit OS/MRC scheme in a practical satellite system.
Results and dicussion
This section provides computer simulations to confirm the validity of our analytical results and investigates the impact of system parameters on the OP of the dualhop satellite relaying network with DF protocol. The simulation parameters used are listed in Table 1. In the simulations, both uplink and downlink are subject to SR fading, which can be different shadowing severities, including the frequent heavy shadowing (FHS) {m,b,Ω}={0.739,0.063,8.97×10^{−4}} and average shadowing (AS) {m,b,Ω}={10.1,0.126,0.835} [23]. In all the figures, it is assumed that \(\bar \gamma _{s} = \bar \gamma _{d} = \bar \gamma \), and the threshold equals to 0 dB. In addition, the label (N,M) denotes the number of the sources and destinations, respectively, and all of the Monte Carlo simulations are obtained by performing 10^{6} channel realizations.
By assuming that both uplink and downlink undergo FHS fading, we plot the exact and asymptotic OP versus \(\bar \gamma \) with OS/SC and OS/MRC schemes in Figs. 3 and 4, respectively. Theoretical results were obtained by truncating the infinite series of (20) and (37) to 20 terms, i.e., k=20. Just as we expect, the analytical results match well with Monte Carlo simulations, and the asymptotic curves sharply approach the corresponding analytical curves, verifying the effectiveness of the derived theoretical formulas.
Figure 5 illustrates the OP comparison between OS/SC scheme and OS/MRC schemes. As we see, the performance of OS/MRC scheme is better than that of OS/SC scheme, but the OP slope at high SNR of the consider system with downlink employing SC is similar with that employing MRC scheme, indicating that the diversity order only depends on the number of users. Furthermore, it is interesting to find that for the case of user combinations being (N,M)=(2,3) and (N,M)=(3,2), similar performance can be obtained when OS/SC scheme is used. However, when the relaying system employ OS/MRC scheme, the performance of (N,M)=(3,2) is better than that of (N,M)=(2,3). This is because the worst link dominates the performance in this dualhop system.
Figure 6 shows the OP against \(\bar \gamma \) with (N,M)=(3,3), where the SR links experience FHS and AS, respectively. For the purpose of fair comparison, we assume that all RD links follow FHS. Obviously, the OP of the considered system depends on the shadowing parameter of the link, namely, the system performance decreases with the increase of heavy shadowing, and vice versa.
Conclusions
In this paper, we have investigated the performance of a dualhop satellite relaying system with multiple users. Specifically, based on a practical satellite channel, both the analytical and asymptotic OP expressions for the satellite relaying system with OS/SC and OS/MRC schemes have been derived. Our study reveals that OS/SC scheme and OS/MRC scheme have the same diversity gain and different coding gains, resulting in that the performance of OS/MRC scheme outperforms that of OS/SC scheme in the same condition. The validity of the theoretical analysis has been confirmed by comparison with Monte Carlo simulations. The obtained outage expressions and conclusions will provide valuable insight into the satellite relaying network.
Appendix 1
Proof of Theorem 1
Proof
In order to obtain the asymptotic OP expression with OS/SC scheme, we will derive the expressions of \(F_{{\gamma _{1}}}^{\infty } \left (x \right)\) and \(F_{{\gamma _{2}}}^{\infty } \left (x \right)\), respectively.
As for the derivation of \(F_{{\gamma _{1}}}^{\infty } \left (x \right)\), according to (14), we can get
where \(F_{{\gamma _{s,i}}}^{\infty } (x) = \int \limits _{0}^{x} {f_{{\gamma _{s,i}}}^{\infty } (\tau)} d\tau \). Using (15) yields
when x→0, _{1}F_{1}(;;) have the property _{1}F_{1}(a;b;x)→1. Besides, by applying the Maclaurin series representation of the exponential function, i.e., \({e^{ x}} = \sum \limits _{n = 0}^{\infty } {\frac {{{{\left ({  1} \right)}^{n}}}}{{n!}}} {x^{n}}\), when x→0, we have e^{−x}=1−x+O(x). Hence, in the case of high SNR, i.e., \({\bar \gamma _{s}} \to \infty \), we have \({\delta _{s}}\frac {x}{{{{\bar \gamma }_{s}}}} \to 0\), then \({}_{1}{F_{1}}\left ({{m_{s}};1;\frac {{{\delta _{s}}x}}{{{{\bar \gamma }_{s}}}}} \right) \to 1\) and \({e^{ \frac {{{\beta _{s}}x}}{{{{\bar \gamma }_{s}}}}}} = 1  \frac {{{\beta _{s}}x}}{{{{\bar \gamma }_{s}}}} + O\left (\frac {1}{{\bar \gamma }_{s}} \right)\).
Substituting the above properties to (45), the asymptotic PDF of γ_{s,i} at high SNR can be denoted as
where O(·) stands for higher order terms. Since the asymptotic performance of \(f_{{\gamma _{s,i}}}^{\infty } \left (x \right)\) is determined by the lowest order terms of \({\bar \gamma _{s}}\) at high SNR, we can further obtain
Then, the CDF of γ_{s} at high SNR can be obtained as
By substituting (48) into (44), the CDF of γ_{1} at high SNR can be obtained as
In a similar manner, the CDF of γ_{2} at high SNR can be obtained as
By substituting (49) and (50) into (38), the asymptotic OP of the dualhop DF satellite relaying network with OS/SC scheme can be obtained as in (39). □
Appendix 2
Proof of Theorem 2
Proof
Since the CDF of γ_{1} at high SNR, namely \(F_{{\gamma _{1}}}^{\infty } (x)\), has already been obtained as (49), here we only focus on \(F_{{\gamma _{2}}}^{\infty } (x)\) with OS/MRC scheme.
From (33), we can obtain
when x→0, _{1}F_{1}(;;) have the property _{1}F_{1}(a;b;x)→1. Substituting the property to (51), the asymptotic PDF of γ_{2} at high SNR can be denoted as
where O(·) stands for higher order terms. Since the asymptotic performance of \(f_{{\gamma _{2}}}^{\infty } \left (x \right)\) is determined by the lowest order terms of \({\bar \gamma _{d}}\) at high SNR, we further obtain
Then, the CDF of γ_{2} at high SNR can be obtained as
By substituting (49) and (54) into (38), the asymptotic OP of the dualhop DF satellite relaying network with OS/MRC scheme can be obtained as in (42). □
Notes
 1.
It is assumed that these channels are quasistatic, and channel information can be obtained by employing the channel estimation method proposed in [31].
Abbreviations
 AF:

Amplifyandforward
 AS:

Average shadowing
 ASER:

Average symbol error rate
 AWGN:

Additive white Guassian noise
 BF:

Beamforming
 BS:

Base station
 CCI:

Cochannel interference
 CDF:

Cumulative distribution function
 CSI:

Channel state information
 DF:

Decodeandforward
 EC:

Ergodic capacity
 ES:

Earth station
 FHS:

Frequent heavy shadowing
 HSTN:

Hybrid satelliteterrestrial network
 LoS:

Lineofsight
 MGF:

Moment generating function
 MRC:

Maximal ratio combining
 OP:

Outage probability
 OS:

Opportunistic scheduling
 PDF:

Probability density function
 Qos:

Quality of service
 Satcom:

Satellite communication
 SC:

Selection combining
 SNR:

Signaltonoise ratio
 SR:

Shadowed Rician
References
 1
P. D. Arapoglou, K. P. Liolis, M. Bertinelli, A. D. Panagopoulos, P. G. Cottis, R. D. Gaudenzi, MIMO over satellite: a review. IEEE Commun. Surv. Tutor.13(11), 27–51 (2011).
 2
K. An, M. Lin, J. Ouyang, Secure transmission in cognitive satellite terrestrial networks. IEEE J. Sel. Areas Commun.34(11), 3025–3037 (2016).
 3
M. Lin, Z. Lin, W. P. Zhu, J. B. Wang, Joint beamforming for secure communication in cognitive satellite terrestrial networks. IEEE J. Sel. Areas Commun.36(5), 1017–1029 (2018).
 4
Z. Lin, M. Lin, J. B. Wang, Y. M. Huang, W. P. Zhu, Robust secure beamforming for 5G cellular networks coexisting with satellite networks. IEEE J. Sel. Areas Commun.36(4), 932–945 (2018).
 5
S. H. Zhong, H. J. Huang, R. Li, Performance analysis of energyharvestingaware multirelay networks in Nakagamim fading. EURASIP J. Wirel. Commun. Netw.2018(1), 63 (2018).
 6
S. Sreng, B. Escrig, M. L. Boucheret, in Proc. IEEE Int. Conf. Commun., Budapest, Hungary. Exact outage probability of a hybrid satellite terrestrial cooperative system with best relay selection, (2013), pp. 4520–4524. https://doi.org/10.1109/ICC.2013.6655280.
 7
K. An, M. Lin, J. Ouyang, Symbol error analysis of hybrid satellite–terrestrial cooperative networks with cochannel interference. IEEE Commun. Lett.18(11), 1947–1950 (2014).
 8
K. An, M. Lin, T. Liang, Performance analysis of multiantenna hybrid satelliteterrestrial relay networks in the presence of interference. IEEE Trans. Commun.63(11), 4390–4404 (2015).
 9
Y. H. Ruan, Y. Z. Li, C. X. Wang, R. Zhang, H. L. Zhang, Outage performance of integrated satelliteterrestrial networks with hybrid CCI. IEEE Commun. Lett.21(7), 1545–1548 (2017).
 10
M. K. Arti, V. Jain, Relay selectionbased hybrid satelliteterrestrial communication systems. IET Commun.11(17), 2566–2574 (2017).
 11
C. Yuan, M. Lin, J. Ouyang, Beamforming schemes for hybrid satelliteterrestrial cooperative networks. AEUInt. J. Electron. Commun.69(8), 1118–1125 (2015).
 12
K. F. Guo, M. Lin, B. N. Zhang, W. P. Zhu, et al., On the performance of LMS communication with hardware impairments and interference. IEEE Trans. Commun.67(2), 1490–1505 (2019).
 13
N. I. Miridakis, D. D. Vergados, A. Michalas, Dualhop communication over a satellite relay and Shadowed Rician channels. IEEE Trans. Veh. Technol.64(9), 4031–4040 (2015).
 14
A. M. Cvetkovic, J. Anastasov, S. Panic, M. Stefanovic, D. Mili, Performance of dualhop relaying over Shadowed Rician fading channels. J. Electr. Eng.62(4), 244–248 (2011).
 15
X. Wang, Y. C. Yang, Q. Guo, in Proc. 4th Int. Conf. Adv. Satellite Space Commun., Chamonix, France. Outage probability evaluation of land mobile satellite cooperative diversity communication system, (2012), pp. 26–30.
 16
M. R. Bhatnagar, Performance evaluation of decodeandforward satellite relaying. IEEE Trans. Veh. Technol.64(10), 4827–4833 (2015).
 17
K. An, M. Lin, T. Liang, On the performance of multiuser hybrid satelliteterrestrial relay networks with opportunistic scheduling. IEEE Commun. Lett.19(10), 1722–1725 (2015).
 18
P. K. Upadhyay, P. K. Sharma, in Proc. IEEE Eur. Conf. Netw. Commun., Athens, Greece. Multiuser hybrid satelliteterrestrial relay networks with cochannel interference and feedback latency, (2016), pp. 174–178. https://doi.org/10.1109/EuCNC.2016.7561027.
 19
V. Bankey, P. K. Upadhyay, D. B. Da Costa, Performance analysis of multiantenna multiuser hybrid satelliteterrestrial relay systems for mobile services delivery. IEEE Access. 6:, 24729–24745 (2018).
 20
V. Bankey, P. K. Upadhyay, Ergodic capacity of multiuser hybrid satelliteterrestrial fixedgain AF relay networks with CCI and outdated CSI. IEEE Trans. Veh. Technol.67(5), 4666–4671 (2018).
 21
G. Zheng, S. Chatzinotas, B. Ottersten, Generic optimization of linear precoding in multibeam satellite systems. IEEE Trans. Wirel. Commun.11(6), 2308–2320 (2012).
 22
ITUR, Guidelines for evaluation of radio interface technologies for IMTAdvanced. International Telecommunication Union, Tech. Rep. ITUR, M. 21351 (2009). https://www.itu.int/dms_pub/itur/opb/rep/RREPM.213512009PDFE.pdf.
 23
A. Abdi, W. C. Lau, M. S. Alouini, A new simple model for land mobile satellite channels: first and secondorder statistics. IEEE Trans. Wirel. Commun.2(3), 519–528 (2003).
 24
I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals Series, and Products (Academic Press, New York, 2007).
 25
M. Li, M. Lin, Q. Yu, Optimal beamformer design for dualhop MIMO AF relay networks over Rayleigh fading channels. IEEE J. Sel. Areas Commun.30(8), 1402–1414 (2012).
 26
L. Han, B. Shi, W. X. Zou, Performance analysis and power control for fullduplex relaying with largescale antenna array at the destination. EURASIP J. Wirel. Commun. Netw.2017(1), 41 (2017).
 27
D. Skraparlis, V. K. Sakarellos, A. D. Panagopoulos, J. D. Kanellopoulos, Outage performance analysis of cooperative diversity with MRC and SC in correlated lognormal channels. EURASIP J. Wirel. Commun. Netw.2009(1), 707839 (2009).
 28
M. R. Bhatnagar, M. K. Arti, On the closedform performance analysis of maximal ratio combining in ShadowedRician fading LMS channels. IEEE Commun. Lett.18(1), 54–57 (2014).
 29
Z. Wang, G. B. Giannakis, A simple and general parameterization quantifying performance in fading channels. IEEE Trans. Commun.51(8), 1389–1398 (2018).
 30
M. Mohammadi, M. Ardebilipour, Z. Mobini, S. R. A. Zadeh, Performance analysis and power allocation for multihop multibranch amplifyandforward cooperative networks over generalized fading channels. EURASIP J. Wirel. Commun. Netw.2013(1), 160 (2013).
 31
M. K. Arti, Channel estimation and detection in satellite communication systems. IEEE Trans. Veh. Technol.65(12), 10173–10179 (2016).
Acknowledgements
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Funding
This work was supported by Key International Cooperation Research Project [grant number 61720106003], the National Natural Science Foundation of China [grant number 61801234], the Natural Science Foundation of Jiangsu Province [grant number BK20160911], Postgraduate Research & Practice Innovation Program of Jiangsu Province [grant number SJCX18 _0276], and the open research fund of Key Lab of Broadband Wireless Communication and Sensor Network Technology (Nanjing University of Posts and Telecommunications), Ministry of Education [No. JZNY201701].
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The datasets generated and analyzed during the current study are not publicly available, but are available from the corresponding author on reasonable request.
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XW derived the closedform and asymptotic OP expressions for the multiuser dualhop satellite relaying with OS/SC and OS/MRC schemes, respectively, and verified the correctness with Monte Carlo simulations. ML proposed an idea and provided the guidance for deriving these expressions. QH derived these expressions cooperatively. JO verified the correctness with Monte Carlo simulations cooperatively. ADP improved the presentation of the draft and provided valuable suggestions. All authors read and approved it.
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Correspondence to Min Lin.
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Wu, X., Lin, M., Huang, Q. et al. Performance analysis of multiuser dualhop satellite relaying systems. J Wireless Com Network 2019, 147 (2019) doi:10.1186/s1363801914718
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Keywords
 Dualhop satellite relaying
 Decodeandforward
 Outage probability
 Selection combining
 Maximal ratio combining