# Performance Analysis of Space Information Networks with Backbone Satellite Relaying for Vehicular Networks

Authors: Jian Jiao; Houlian Gao; Shaohua Wu; Qinyu Zhang
Journal: Wireless Communications and Mobile Computing
 (2017)

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## Abstract

Space Information Network (SIN) with backbone satellites relaying for vehicular network (VN) communications is regarded as an effective strategy to provide diverse vehicular services in a seamless, efficient, and cost-effective manner in rural areas and highways. In this paper, we investigate the performance of SIN return channel cooperative communications via an amplify-and-forward (AF) backbone satellite relaying for VN communications, where we assume that both of the source-destination and relay-destination links undergo Shadowed-Rician fading and the source-relay link follows Rician fading, respectively. In this SIN-assisted VN communication scenario, we first obtain the approximate statistical distributions of the equivalent end-to-end signal-to-noise ratio (SNR) of the system. Then, we derive the closed-form expressions to efficiently evaluate the average symbol error rate (ASER) of the system. Furthermore, the ASER expressions are taking into account the effect of satellite perturbation of the backbone relaying satellite, which reveal the accumulated error of the antenna pointing error. Finally, simulation results are provided to verify the accuracy of our theoretical analysis and show the impact of various parameters on the system performance.


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## Body

## 1. Introduction

Nowadays, the connected vehicles paradigm is to form a vehicular network (VN) to communicate with the surrounding environment and the VN plays a vital role in the next generation intelligent transportation system (ITS) [1]. Generally, the long-term evolution (LTE) can provide reliable access to the Internet for VN communications in the urban areas. However, LTE network has poor coverage in rural areas and highways due to the costly network infrastructure [2, 3]. Moreover, the high mobility of vehicles can suffer from frequent handovers as the networks become even denser.Space Information Network (SIN) is regarded as an effective strategy to provide diverse vehicular services in a seamless, efficient, and cost-effective manner in rural areas and highways. For instance, satellites and high altitude platforms (HAPs) in SIN can help achieve ubiquitous coverage in rural areas. Further, they can provide road information and transport information to assist ITS, entertainment services dissemination as relays, and relieve the demands on terrestrial networks through data offloading [4].The return channels of the low/medium Earth orbit (L/MEO) satellites are unstable and discontinuous intrinsically to the ground-based stations and vehicles, which limit the throughput as well as the delay sensitive services of SIN-assisted VN communications. Recently, high throughput backbone satellites (such as the Ka/Q/V-band geostationary Earth orbit (GEO) satellites) relaying for SIN communications are regarded as an effective strategy to improve the continuity of return channels as well as the throughput performance.Theoretically, three GEO satellites which are120∘ apart in the SIN backbone networks can provide coverage of the space between Earth ground and GEO orbit and achieve high-speed data relay through the intersatellite and satellite-terrestrial millimeter/terahertz/laser links.With the development of high throughput satellites (HTS), several GEO HTS can establish the backbone network of SIN, where the backbone HTS relaying for SIN-assisted VN is able to provide a global seamless broadband transmission by developing the intersatellite links. People believe that the SIN will enable a “terabit data rate capacity” broadband access, which was previously possible only with fiber-optic links, and offer the access availability of “anywhere and anytime” inherent to the satellites [5]. Furthermore, the SIN will be a significant enabling factor as well as an important component of the upcoming 5th-generation (5G) networks [6].Therefore, considering the backbone HTS relaying communication undergoes the large-scale and complex SIN dual-hop channel properties, such as rain attenuation [7], solar scintillation [8], perturbation factors [9], and interference [10–13], this paper investigates the performance of SIN return channel cooperative communications via an amplify-and-forward (AF) backbone satellite relaying for VN communications.


### 1.1. Background and Motivation

In our SIN communication scenario, space-based nodes (i.e., source nodes, like space mission explorers, orbiters and landers, space stations, spacecraft, manned and unmanned aircraft, etc.) can establish cooperative communications via an AF backbone HTS relaying.Recently, SINs have attracted considerable research interest, and substantial effort has been devoted to investigating the performance of the research works of the hybrid satellite-terrestrial cooperative/relay networks (HSTC/RNs) by analyzing the complex multihop channel models. For that, by applying maximal ratio combining (MRC) at the destination, [14, 15] studied the outage probability (OP) performance of HSTCNs with an AF relaying protocol. In [16], the decode-and-forward (DF) relaying protocols for HSTCNs was investigated. Further, with the help of the moment generating function (MGF), [14, 15, 17] have presented the analytical expression of average symbol error rate (ASER) for HSTCNs with an AF relaying protocol. Besides, the performance of optimal selection algorithm of multiple relays for HSTRNs was presented in [18, 19].Moreover, to achieve higher system capacity and energy efficiency, multiantenna technique was investigated in [20–22], and HTS with Ka/Q/V-band frequency with multiple antennas have attracted significant attention [23]. Authors in [24–31] investigate the performance of relay-based multiple antenna HSTC/RNs, since relay transmissions can effectively improve the throughput and the coverage of satellite communications. Further, the cognitive radio (CR) needs to be investigated since the HTS already suffer from spectrum scarcity in Ka band [32].Besides, the SINs backbone GEO satellites are subjected to various satellite perturbation forces (e.g., Earth oblateness perturbation, third-body gravitational perturbation, atmospheric perturbation, and solar perturbation), which leads to position drift and result in the beam center of the ground station antenna unfocused [33]. The accumulated error of the antenna pointing error will cause the satellite elevation error, which may deteriorate the signal-to-noise ratio (SNR), decrease link margin [34] and bit error rate (BER) [35], and so forth. To the best of our knowledge, this is the first work on GEO satellite perturbation that reveals the effect of satellite elevation error for SIN backbone satellite relaying.


### 1.2. Contributions and Novelty

In this paper, we investigate the performance of SIN return channel cooperative communications via an AF backbone satellite relaying for VN, where both of the source-destination and relay-destination links undergo Shadowed-Rician fading, and the source-relay link follows Rician fading, respectively. By applying MRC at the destination, the equivalent end-to-end SNR of the system is first obtained, and then analytical expressions as well as the satellite perturbation effect are derived to evaluate the system performance. The detailed contributions of this paper are outlined as follows:(i)
The system model of SIN return channel cooperative communications via an AF backbone satellite relaying for VN is first built, and we present a new analytical expression for the approximate statistical distributions of the equivalent end-to-end SNR of system (7).(ii)
To gain further insight, the effect of the satellite perturbation of the relaying GEO satellite is considered for the first time, which reveals the accumulated error of the antenna pointing error leads to the satellite elevation error. And the accumulated satellite elevation error is taking into account the derivation of the ASER expression.(iii)
The closed-form expression for the end-to-end ASER (31) is derived, which can efficiently evaluate the system performance. Moreover, simulation results prove the rationality of our theoretical analysis.Notations. X-Y describes the link from node X to node Y. X-Y-Z represents the dual-hop link from node X to node Z through relay node Y. E[·] denotes the expectation operator. N(μ,σ2) denotes a complex Gaussian distribution with mean μ and variance σ2. exp(·) represents the exponential function. Mλ(·) denotes the moment generating function (MGF) of γ. fx(·) and Fx(·) denote the probability distribution function (PDF) and cumulative distribution function (CDF) of x, respectively. F11(a;b;c) represents the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. F(a,b;c;d) is Gauss hypergeometric function [36, Eq. (9.100)], and Kn(·) represents the modified Bessel function of the second kind with order n [36, Eq. (8.446)]. Ma,b(·) is the Whittaker function defined as [36, Eq. (9.220.2)].


## 1.1. Background and Motivation

In our SIN communication scenario, space-based nodes (i.e., source nodes, like space mission explorers, orbiters and landers, space stations, spacecraft, manned and unmanned aircraft, etc.) can establish cooperative communications via an AF backbone HTS relaying.Recently, SINs have attracted considerable research interest, and substantial effort has been devoted to investigating the performance of the research works of the hybrid satellite-terrestrial cooperative/relay networks (HSTC/RNs) by analyzing the complex multihop channel models. For that, by applying maximal ratio combining (MRC) at the destination, [14, 15] studied the outage probability (OP) performance of HSTCNs with an AF relaying protocol. In [16], the decode-and-forward (DF) relaying protocols for HSTCNs was investigated. Further, with the help of the moment generating function (MGF), [14, 15, 17] have presented the analytical expression of average symbol error rate (ASER) for HSTCNs with an AF relaying protocol. Besides, the performance of optimal selection algorithm of multiple relays for HSTRNs was presented in [18, 19].Moreover, to achieve higher system capacity and energy efficiency, multiantenna technique was investigated in [20–22], and HTS with Ka/Q/V-band frequency with multiple antennas have attracted significant attention [23]. Authors in [24–31] investigate the performance of relay-based multiple antenna HSTC/RNs, since relay transmissions can effectively improve the throughput and the coverage of satellite communications. Further, the cognitive radio (CR) needs to be investigated since the HTS already suffer from spectrum scarcity in Ka band [32].Besides, the SINs backbone GEO satellites are subjected to various satellite perturbation forces (e.g., Earth oblateness perturbation, third-body gravitational perturbation, atmospheric perturbation, and solar perturbation), which leads to position drift and result in the beam center of the ground station antenna unfocused [33]. The accumulated error of the antenna pointing error will cause the satellite elevation error, which may deteriorate the signal-to-noise ratio (SNR), decrease link margin [34] and bit error rate (BER) [35], and so forth. To the best of our knowledge, this is the first work on GEO satellite perturbation that reveals the effect of satellite elevation error for SIN backbone satellite relaying.


## 1.2. Contributions and Novelty

In this paper, we investigate the performance of SIN return channel cooperative communications via an AF backbone satellite relaying for VN, where both of the source-destination and relay-destination links undergo Shadowed-Rician fading, and the source-relay link follows Rician fading, respectively. By applying MRC at the destination, the equivalent end-to-end SNR of the system is first obtained, and then analytical expressions as well as the satellite perturbation effect are derived to evaluate the system performance. The detailed contributions of this paper are outlined as follows:(i)
The system model of SIN return channel cooperative communications via an AF backbone satellite relaying for VN is first built, and we present a new analytical expression for the approximate statistical distributions of the equivalent end-to-end SNR of system (7).(ii)
To gain further insight, the effect of the satellite perturbation of the relaying GEO satellite is considered for the first time, which reveals the accumulated error of the antenna pointing error leads to the satellite elevation error. And the accumulated satellite elevation error is taking into account the derivation of the ASER expression.(iii)
The closed-form expression for the end-to-end ASER (31) is derived, which can efficiently evaluate the system performance. Moreover, simulation results prove the rationality of our theoretical analysis.Notations. X-Y describes the link from node X to node Y. X-Y-Z represents the dual-hop link from node X to node Z through relay node Y. E[·] denotes the expectation operator. N(μ,σ2) denotes a complex Gaussian distribution with mean μ and variance σ2. exp(·) represents the exponential function. Mλ(·) denotes the moment generating function (MGF) of γ. fx(·) and Fx(·) denote the probability distribution function (PDF) and cumulative distribution function (CDF) of x, respectively. F11(a;b;c) represents the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. F(a,b;c;d) is Gauss hypergeometric function [36, Eq. (9.100)], and Kn(·) represents the modified Bessel function of the second kind with order n [36, Eq. (8.446)]. Ma,b(·) is the Whittaker function defined as [36, Eq. (9.220.2)].


## 2. System Model

Our system model of the SIN return channel cooperative communications via an AF GEO HTS relaying for VN is considered as shown in Figure1, where a source node (S), that is, space node, communicates with a terrestrial destination (D) via a GEO HTS relay (R) and h0, h1, and h2 are the channel gains of the S-R, S-D, and R-D links, respectively.Figure 1
The proposed system model of SIN return channel cooperative communications via an AF GEO HTS relaying for VN, where each node is equipped with a single antenna, the relay pointP1 with an arrow point to P2 shows the satellite drift effect caused by the satellite perturbation.The space nodeS is generally on the stratosphere layer and above, and R is a GEO HTS in our SIN communication scenario. In the S-R link, since the line of sight (LOS) signal is much stronger than the others, which is different from terrestrial networks, the channel gain h0 of the S-R link is considered as a Rician fading with additive white Gaussian noise (AWGN) [37, 38]. On the other hand, the channel gains h1 and h2 of satellite-terrestrial links S-D and R-D are usually modeled by Shadowed-Rician fading distribution [14–16, 24–27, 35]. It approaches the LOS communication using the Rician fading, whereas the amplitude is Nakagami-m distributed [39], and it sufficiently agrees with experimental data and is computationally less complex than other land mobile satellite channel models.As illustrated in Figure1, in such a backbone GEO HTS relaying SIN-assisted VN system, the communication occurs during two time phases. In the first time phase, the space node S broadcasts its signal to the relay R and the destination D, where h0 and h1 are the channel gains of the S-R and S-D links, respectively. The received signals at the relay y0 and the destination y1 from S are given by(1)y0=E1h0x+n0,(2)y1=E1h1x+n1,where x is the transmitted signal with unit power, E1 is the transmitted power at S, and n0 and n1 are the AWGN of S-R and S-D links with zero mean and variance σ02 and σ12, respectively.During the second time phase,R first amplifies the received signal y0 by an amplifying factor G and then forwards it to D through R-D link of which the channel gain is h2, and the received signal at the destination y2 is given by(3)y2=E2Gh2y0+n2=GE1E2h2h0x+GE2h2n0+n2,where E2 is the transmit power at R and n2 is in AWGN at D obeying n2~N(0,σ22).Assuming that perfect channel state information (CSI) is available atD and R and MRC is applied at the destination, thus, the end-to-end SNR at D can be expressed as(4)γe2e=γ1+γ02,where γ1 is the SNR of S-D link and γ02 is the SNR of S-R-D link. From (2), we have(5)γ1=E1h12σ12=ρ1h12.From (3), γ02 can be expressed as(6)γ02=E1h02/σ02·E2h22/σ22E2h22/σ22+1/G2σ02=γ0γ2γ2+C,where C=1/(Gσ0)2 and γ0=E1h02/σ02=ρ0h02 and γ2=E2h22/σ22=ρ2h22 denote the SNR of S-R and R-D link, respectively. Thus, (4) can be rewritten as(7)γe2e=γ0γ2γ2+C+ρ1h12.


### 2.1. Satellite Perturbation

In this paper, the GEO HTS satellite is considered as backbone relaying node for SIN-assisted VN communications to enhance the continuity as well as the throughput of the return channel. This is the first work to analyze the performance of cooperative communication for SIN dual-hop channel properties. To gain further insight, the effect of the satellite perturbation of the GEO HTS is analyzed, which reveals that the accumulated error of the antenna pointing error leads to the satellite elevation error.


#### 2.1.1. Principle and Law of Satellite Perturbation Drift

The satellite is always subjected to a variety of perturbation forces, especially to the GEO satellites, which will lead to perturbation drift and accumulate the antenna pointing error. The satellite perturbation forces include the Earth oblateness perturbation [40, 41], the third-body attraction perturbation [42] such as lunisolar gravitational perturbation [43], the solar radiation pressure perturbation [44, 45], and the atmospheric drag perturbation.The Earth oblateness perturbation is caused by the facts that the Earth is not an ideal sphere and it has uneven internal density distribution. It affects the long-term change of the right ascension of ascending node (RAAN)r and argument of perigee ω of satellite orbit. The lunisolar gravitational perturbation can reduce the satellite orbit radius and may increase the orbital inclination, while the semimajor axis changes with half-day cycle. On the contrary, the solar radiation pressure perturbation mainly affects the orbital eccentricity, which directly determines the satellite center distance and the satellite height.


#### 2.1.2. Satellite Elevation Error

The diagram of antenna pointing error is shown in Figure2, and let θ=θe+θc denote the elevation of a GEO HTS, where θe represents the elevation error, which is the angle between centerline of antenna beam pointed to P1 and the real LOS channel between the actual position P2 of the satellite to the destination. θc denotes the satellite elevation angle if the GEO satellite is not affected by the satellite perturbation. Considering the drift caused by satellite perturbation in the eastwest and northsouth directions, the elevation of satellite θ can be calculated by [46](8)θ=arctan⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ-0.151cos⁡arcsin⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ,θc=arctancos⁡ϕcos⁡λ-0.151cos⁡arcsin⁡cos⁡ϕcos⁡λΔφ=0,where ϕ is the latitude of the destination, λ=λsat-λdes is the longitude difference between the subsatellite point and the ground station, λsat represents the longitude of subsatellite point, λdes is the longitude of destination, Δφ is the drift of satellite in the northsouth direction, and Δλ is the drift of satellite in the eastwest direction. Therefore, the elevation error θe can be calculated as θe=θ-θc.Figure 2
The diagram of antenna pointing error caused by satellite perturbation,P1 means the satellite position located in antenna beam center, and P2 represents the satellite position offsets from antenna beam center.In general,λdes can be calculated by the six elements of the satellite orbit [47]. When the satellite orbit is elliptical, the longitude (Llon) and the latitude (Llat) of the subsatellite point can be expressed as(9)Llon=r+arctan⁡cos⁡itan⁡ω+2arctan⁡1+e1-etan⁡E2-ωet-tNLlat=arcsin⁡sin⁡isin⁡ω+2arctan⁡1+e1-etan⁡E2,where ωe is the average angular velocity of Earth, t is the time, tN is the time when the satellite passes the ascending node, E is the eccentric anomaly, i is the inclination of satellite orbit, and e is eccentricity. When the satellite orbit is a circle, (9) can be simplified as(10)Llon=r+arctan⁡cos⁡itan⁡ω+2πTt-τ-ωet-τ+Tω2πLlat=arcsin⁡sin⁡isin⁡ω+2πTt-τ,where τ is the time when the satellite perigee passes.Therefore, from (9) and (10), it is worth noting that the subsatellite point is related to the parameters r, i, ω, and τ. If these variables have been affected by the satellite perturbation, the subsatellite point will have drift. Let Lplon and Lplat represent the longitude and latitude of subsatellite point considering the effect of satellite perturbation, respectively, and Lnplon and Lnplat denote the longitude and latitude of unperturbed subsatellite point, respectively. It is clear that the drift of subsatellite point affected by satellite perturbation causes the elevation error of satellite, and we have(11)Δφ=Lplon-LnplonΔλ=Lplat-Lnplat.


### 2.2. Channel Model

#### 2.2.1.S-R Link

As theS-R link is modeled by using the Rician fading distribution, the probability distribution function (PDF) of γ0 is given by [48](12)fγ0x=K+1ρ0Ωexp⁡-xK+1ρ0Ω-K·I02KK+1xρ0Ω,where Ω is the average power of received signal at R and Ω=(A2+2σ2)/2 and K=A2/(2σ2) are known as the Rician factor, A is the amplitude of LOS signal, σ2 is the average power of multipath component, and I0(·) is the modified Bessel function of the first kind with order zero.Then, the cumulative distribution function (CDF) ofγ0 can be expressed as(13)Fγ0x=1-Q12K,2K+1xρ0Ω,where QM(·,·) is the MarcumQ-function of the Mth order, which is defined as(14)QMa,b=∫b∞xxaM-1exp⁡-x2+a22IM-1axdx.Moreover, the relationship between the Rician factorK of the Rician fading S-R link (12) and the satellite elevation (θc) was simulated in [49] through a large number of experiments. Then the relationship between the Rician factor and the satellite elevation (θc∈[10∘,90∘]) was fitted as an empirical formula(15)Kθc=K0+K1θc+K2θc,where K0, K1, and K2 are empirical constant and K0=2.731, K1=-1.074×10-1, and K2=2.771×10-3, respectively. Considering the effect of satellite perturbation, (15) can be rewritten as(16)Kθc,θe,t=K0+K1θc+θesin⁡t+K2θc+θesin⁡t,where θesin⁡t indicates the elevation error θe affected by the satellite perturbation at time t.


#### 2.2.2.S-D and R-D Links

TheS-D link is usually modeled as a composite fading distribution to describe the amplitude fluctuation of the signal envelope. Considering the tradeoffs between accuracy and computational complexity, the satellite-destination S-D link and the relay-destination R-D link are modeled by using the Shadowed-Rician fading distribution [11–13] in our SIN-assisted VN system.Letγ1 and γ2 denote the SNR of the S-D and R-D links, respectively. The PDF of γi(i=1,2) is given by [39](17)fγix=αiρiexp⁡-βixρi·F11mi;1;δiρix,where(18)αi=2bimi/2bimi+Ωimi2bi,βi=12bi,δi=0.5Ωi2bi2mi+biΩi,where F11(·;·;·) is the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. Moreover, Ωi and 2bi are the average power of the LOS and the multipath components, respectively, and mi(mi∈[0,∞)) is the fading severity parameter.Recall the definition ofF11(·;·;·), and we have(19)F11mi;1;δiρix=∑n=0∞min1n1n!δiρixn.For the analytical tractability, we retain our focus in the case when the channel severity parameters take integer values in the rest of this paper; that is,mi∈N. Hence, with the aid of [50, Eq. (07.20.03.0009.01), Eq. (07.02.03.0014.01)], (19) becomes(20)F11mi;1;δiρix=exp⁡δiρix∑n=0mi-1-1n1-minn!2δiρixn,where (z)n=Γ(z+n)/Γ(z) denotes the Pochhammer symbol with n∈N [51, Eq. (6.1.22)].To solve the three parameters(Ωi,bi, and mi) in (18), we assume θci is the elevation at GEO HTS R, when the center line of the receiving antenna beam in different link aims at R. θeisin⁡t is the elevation error which affects the satellite perturbation. When θci∈(20°,30°), Ωi, bi, and mi can be calculated by the empirical formulas [39, Eq. (19)]. Therefore, considering the effect of satellite perturbation, Ωi, bi, and mi can be calculated as follows:(21)biθci,θei,t=-4.7943×10-8θci+θeisin⁡t3+5.5784×10-6θci+θeisin⁡t2-2.1344×10-4θci+θeisin⁡t+3.2710×10-2,miθci,θei,t=6.3739×10-5θci+θeisin⁡t3+5.8533×10-4θci+θeisin⁡t2-1.5973×10-4θci+θeisin⁡t+3.5156,Ωiθci,θei,t=1.4428×10-5θci+θeisin⁡t3-2.3798×10-3θci+θeisin⁡t2+1.2702×10-1θci+θeisin⁡t-1.4864.


## 2.1. Satellite Perturbation

In this paper, the GEO HTS satellite is considered as backbone relaying node for SIN-assisted VN communications to enhance the continuity as well as the throughput of the return channel. This is the first work to analyze the performance of cooperative communication for SIN dual-hop channel properties. To gain further insight, the effect of the satellite perturbation of the GEO HTS is analyzed, which reveals that the accumulated error of the antenna pointing error leads to the satellite elevation error.


### 2.1.1. Principle and Law of Satellite Perturbation Drift

The satellite is always subjected to a variety of perturbation forces, especially to the GEO satellites, which will lead to perturbation drift and accumulate the antenna pointing error. The satellite perturbation forces include the Earth oblateness perturbation [40, 41], the third-body attraction perturbation [42] such as lunisolar gravitational perturbation [43], the solar radiation pressure perturbation [44, 45], and the atmospheric drag perturbation.The Earth oblateness perturbation is caused by the facts that the Earth is not an ideal sphere and it has uneven internal density distribution. It affects the long-term change of the right ascension of ascending node (RAAN)r and argument of perigee ω of satellite orbit. The lunisolar gravitational perturbation can reduce the satellite orbit radius and may increase the orbital inclination, while the semimajor axis changes with half-day cycle. On the contrary, the solar radiation pressure perturbation mainly affects the orbital eccentricity, which directly determines the satellite center distance and the satellite height.


### 2.1.2. Satellite Elevation Error

The diagram of antenna pointing error is shown in Figure2, and let θ=θe+θc denote the elevation of a GEO HTS, where θe represents the elevation error, which is the angle between centerline of antenna beam pointed to P1 and the real LOS channel between the actual position P2 of the satellite to the destination. θc denotes the satellite elevation angle if the GEO satellite is not affected by the satellite perturbation. Considering the drift caused by satellite perturbation in the eastwest and northsouth directions, the elevation of satellite θ can be calculated by [46](8)θ=arctan⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ-0.151cos⁡arcsin⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ,θc=arctancos⁡ϕcos⁡λ-0.151cos⁡arcsin⁡cos⁡ϕcos⁡λΔφ=0,where ϕ is the latitude of the destination, λ=λsat-λdes is the longitude difference between the subsatellite point and the ground station, λsat represents the longitude of subsatellite point, λdes is the longitude of destination, Δφ is the drift of satellite in the northsouth direction, and Δλ is the drift of satellite in the eastwest direction. Therefore, the elevation error θe can be calculated as θe=θ-θc.Figure 2
The diagram of antenna pointing error caused by satellite perturbation,P1 means the satellite position located in antenna beam center, and P2 represents the satellite position offsets from antenna beam center.In general,λdes can be calculated by the six elements of the satellite orbit [47]. When the satellite orbit is elliptical, the longitude (Llon) and the latitude (Llat) of the subsatellite point can be expressed as(9)Llon=r+arctan⁡cos⁡itan⁡ω+2arctan⁡1+e1-etan⁡E2-ωet-tNLlat=arcsin⁡sin⁡isin⁡ω+2arctan⁡1+e1-etan⁡E2,where ωe is the average angular velocity of Earth, t is the time, tN is the time when the satellite passes the ascending node, E is the eccentric anomaly, i is the inclination of satellite orbit, and e is eccentricity. When the satellite orbit is a circle, (9) can be simplified as(10)Llon=r+arctan⁡cos⁡itan⁡ω+2πTt-τ-ωet-τ+Tω2πLlat=arcsin⁡sin⁡isin⁡ω+2πTt-τ,where τ is the time when the satellite perigee passes.Therefore, from (9) and (10), it is worth noting that the subsatellite point is related to the parameters r, i, ω, and τ. If these variables have been affected by the satellite perturbation, the subsatellite point will have drift. Let Lplon and Lplat represent the longitude and latitude of subsatellite point considering the effect of satellite perturbation, respectively, and Lnplon and Lnplat denote the longitude and latitude of unperturbed subsatellite point, respectively. It is clear that the drift of subsatellite point affected by satellite perturbation causes the elevation error of satellite, and we have(11)Δφ=Lplon-LnplonΔλ=Lplat-Lnplat.


## 2.1.1. Principle and Law of Satellite Perturbation Drift

The satellite is always subjected to a variety of perturbation forces, especially to the GEO satellites, which will lead to perturbation drift and accumulate the antenna pointing error. The satellite perturbation forces include the Earth oblateness perturbation [40, 41], the third-body attraction perturbation [42] such as lunisolar gravitational perturbation [43], the solar radiation pressure perturbation [44, 45], and the atmospheric drag perturbation.The Earth oblateness perturbation is caused by the facts that the Earth is not an ideal sphere and it has uneven internal density distribution. It affects the long-term change of the right ascension of ascending node (RAAN)r and argument of perigee ω of satellite orbit. The lunisolar gravitational perturbation can reduce the satellite orbit radius and may increase the orbital inclination, while the semimajor axis changes with half-day cycle. On the contrary, the solar radiation pressure perturbation mainly affects the orbital eccentricity, which directly determines the satellite center distance and the satellite height.


## 2.1.2. Satellite Elevation Error

The diagram of antenna pointing error is shown in Figure2, and let θ=θe+θc denote the elevation of a GEO HTS, where θe represents the elevation error, which is the angle between centerline of antenna beam pointed to P1 and the real LOS channel between the actual position P2 of the satellite to the destination. θc denotes the satellite elevation angle if the GEO satellite is not affected by the satellite perturbation. Considering the drift caused by satellite perturbation in the eastwest and northsouth directions, the elevation of satellite θ can be calculated by [46](8)θ=arctan⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ-0.151cos⁡arcsin⁡sin⁡Δφsin⁡ϕ+cos⁡Δφcos⁡ϕcos⁡λ+Δλ,θc=arctancos⁡ϕcos⁡λ-0.151cos⁡arcsin⁡cos⁡ϕcos⁡λΔφ=0,where ϕ is the latitude of the destination, λ=λsat-λdes is the longitude difference between the subsatellite point and the ground station, λsat represents the longitude of subsatellite point, λdes is the longitude of destination, Δφ is the drift of satellite in the northsouth direction, and Δλ is the drift of satellite in the eastwest direction. Therefore, the elevation error θe can be calculated as θe=θ-θc.Figure 2
The diagram of antenna pointing error caused by satellite perturbation,P1 means the satellite position located in antenna beam center, and P2 represents the satellite position offsets from antenna beam center.In general,λdes can be calculated by the six elements of the satellite orbit [47]. When the satellite orbit is elliptical, the longitude (Llon) and the latitude (Llat) of the subsatellite point can be expressed as(9)Llon=r+arctan⁡cos⁡itan⁡ω+2arctan⁡1+e1-etan⁡E2-ωet-tNLlat=arcsin⁡sin⁡isin⁡ω+2arctan⁡1+e1-etan⁡E2,where ωe is the average angular velocity of Earth, t is the time, tN is the time when the satellite passes the ascending node, E is the eccentric anomaly, i is the inclination of satellite orbit, and e is eccentricity. When the satellite orbit is a circle, (9) can be simplified as(10)Llon=r+arctan⁡cos⁡itan⁡ω+2πTt-τ-ωet-τ+Tω2πLlat=arcsin⁡sin⁡isin⁡ω+2πTt-τ,where τ is the time when the satellite perigee passes.Therefore, from (9) and (10), it is worth noting that the subsatellite point is related to the parameters r, i, ω, and τ. If these variables have been affected by the satellite perturbation, the subsatellite point will have drift. Let Lplon and Lplat represent the longitude and latitude of subsatellite point considering the effect of satellite perturbation, respectively, and Lnplon and Lnplat denote the longitude and latitude of unperturbed subsatellite point, respectively. It is clear that the drift of subsatellite point affected by satellite perturbation causes the elevation error of satellite, and we have(11)Δφ=Lplon-LnplonΔλ=Lplat-Lnplat.


## 2.2. Channel Model

### 2.2.1.S-R Link

As theS-R link is modeled by using the Rician fading distribution, the probability distribution function (PDF) of γ0 is given by [48](12)fγ0x=K+1ρ0Ωexp⁡-xK+1ρ0Ω-K·I02KK+1xρ0Ω,where Ω is the average power of received signal at R and Ω=(A2+2σ2)/2 and K=A2/(2σ2) are known as the Rician factor, A is the amplitude of LOS signal, σ2 is the average power of multipath component, and I0(·) is the modified Bessel function of the first kind with order zero.Then, the cumulative distribution function (CDF) ofγ0 can be expressed as(13)Fγ0x=1-Q12K,2K+1xρ0Ω,where QM(·,·) is the MarcumQ-function of the Mth order, which is defined as(14)QMa,b=∫b∞xxaM-1exp⁡-x2+a22IM-1axdx.Moreover, the relationship between the Rician factorK of the Rician fading S-R link (12) and the satellite elevation (θc) was simulated in [49] through a large number of experiments. Then the relationship between the Rician factor and the satellite elevation (θc∈[10∘,90∘]) was fitted as an empirical formula(15)Kθc=K0+K1θc+K2θc,where K0, K1, and K2 are empirical constant and K0=2.731, K1=-1.074×10-1, and K2=2.771×10-3, respectively. Considering the effect of satellite perturbation, (15) can be rewritten as(16)Kθc,θe,t=K0+K1θc+θesin⁡t+K2θc+θesin⁡t,where θesin⁡t indicates the elevation error θe affected by the satellite perturbation at time t.


### 2.2.2.S-D and R-D Links

TheS-D link is usually modeled as a composite fading distribution to describe the amplitude fluctuation of the signal envelope. Considering the tradeoffs between accuracy and computational complexity, the satellite-destination S-D link and the relay-destination R-D link are modeled by using the Shadowed-Rician fading distribution [11–13] in our SIN-assisted VN system.Letγ1 and γ2 denote the SNR of the S-D and R-D links, respectively. The PDF of γi(i=1,2) is given by [39](17)fγix=αiρiexp⁡-βixρi·F11mi;1;δiρix,where(18)αi=2bimi/2bimi+Ωimi2bi,βi=12bi,δi=0.5Ωi2bi2mi+biΩi,where F11(·;·;·) is the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. Moreover, Ωi and 2bi are the average power of the LOS and the multipath components, respectively, and mi(mi∈[0,∞)) is the fading severity parameter.Recall the definition ofF11(·;·;·), and we have(19)F11mi;1;δiρix=∑n=0∞min1n1n!δiρixn.For the analytical tractability, we retain our focus in the case when the channel severity parameters take integer values in the rest of this paper; that is,mi∈N. Hence, with the aid of [50, Eq. (07.20.03.0009.01), Eq. (07.02.03.0014.01)], (19) becomes(20)F11mi;1;δiρix=exp⁡δiρix∑n=0mi-1-1n1-minn!2δiρixn,where (z)n=Γ(z+n)/Γ(z) denotes the Pochhammer symbol with n∈N [51, Eq. (6.1.22)].To solve the three parameters(Ωi,bi, and mi) in (18), we assume θci is the elevation at GEO HTS R, when the center line of the receiving antenna beam in different link aims at R. θeisin⁡t is the elevation error which affects the satellite perturbation. When θci∈(20°,30°), Ωi, bi, and mi can be calculated by the empirical formulas [39, Eq. (19)]. Therefore, considering the effect of satellite perturbation, Ωi, bi, and mi can be calculated as follows:(21)biθci,θei,t=-4.7943×10-8θci+θeisin⁡t3+5.5784×10-6θci+θeisin⁡t2-2.1344×10-4θci+θeisin⁡t+3.2710×10-2,miθci,θei,t=6.3739×10-5θci+θeisin⁡t3+5.8533×10-4θci+θeisin⁡t2-1.5973×10-4θci+θeisin⁡t+3.5156,Ωiθci,θei,t=1.4428×10-5θci+θeisin⁡t3-2.3798×10-3θci+θeisin⁡t2+1.2702×10-1θci+θeisin⁡t-1.4864.


## 2.2.1.S-R Link

As theS-R link is modeled by using the Rician fading distribution, the probability distribution function (PDF) of γ0 is given by [48](12)fγ0x=K+1ρ0Ωexp⁡-xK+1ρ0Ω-K·I02KK+1xρ0Ω,where Ω is the average power of received signal at R and Ω=(A2+2σ2)/2 and K=A2/(2σ2) are known as the Rician factor, A is the amplitude of LOS signal, σ2 is the average power of multipath component, and I0(·) is the modified Bessel function of the first kind with order zero.Then, the cumulative distribution function (CDF) ofγ0 can be expressed as(13)Fγ0x=1-Q12K,2K+1xρ0Ω,where QM(·,·) is the MarcumQ-function of the Mth order, which is defined as(14)QMa,b=∫b∞xxaM-1exp⁡-x2+a22IM-1axdx.Moreover, the relationship between the Rician factorK of the Rician fading S-R link (12) and the satellite elevation (θc) was simulated in [49] through a large number of experiments. Then the relationship between the Rician factor and the satellite elevation (θc∈[10∘,90∘]) was fitted as an empirical formula(15)Kθc=K0+K1θc+K2θc,where K0, K1, and K2 are empirical constant and K0=2.731, K1=-1.074×10-1, and K2=2.771×10-3, respectively. Considering the effect of satellite perturbation, (15) can be rewritten as(16)Kθc,θe,t=K0+K1θc+θesin⁡t+K2θc+θesin⁡t,where θesin⁡t indicates the elevation error θe affected by the satellite perturbation at time t.


## 2.2.2.S-D and R-D Links

TheS-D link is usually modeled as a composite fading distribution to describe the amplitude fluctuation of the signal envelope. Considering the tradeoffs between accuracy and computational complexity, the satellite-destination S-D link and the relay-destination R-D link are modeled by using the Shadowed-Rician fading distribution [11–13] in our SIN-assisted VN system.Letγ1 and γ2 denote the SNR of the S-D and R-D links, respectively. The PDF of γi(i=1,2) is given by [39](17)fγix=αiρiexp⁡-βixρi·F11mi;1;δiρix,where(18)αi=2bimi/2bimi+Ωimi2bi,βi=12bi,δi=0.5Ωi2bi2mi+biΩi,where F11(·;·;·) is the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. Moreover, Ωi and 2bi are the average power of the LOS and the multipath components, respectively, and mi(mi∈[0,∞)) is the fading severity parameter.Recall the definition ofF11(·;·;·), and we have(19)F11mi;1;δiρix=∑n=0∞min1n1n!δiρixn.For the analytical tractability, we retain our focus in the case when the channel severity parameters take integer values in the rest of this paper; that is,mi∈N. Hence, with the aid of [50, Eq. (07.20.03.0009.01), Eq. (07.02.03.0014.01)], (19) becomes(20)F11mi;1;δiρix=exp⁡δiρix∑n=0mi-1-1n1-minn!2δiρixn,where (z)n=Γ(z+n)/Γ(z) denotes the Pochhammer symbol with n∈N [51, Eq. (6.1.22)].To solve the three parameters(Ωi,bi, and mi) in (18), we assume θci is the elevation at GEO HTS R, when the center line of the receiving antenna beam in different link aims at R. θeisin⁡t is the elevation error which affects the satellite perturbation. When θci∈(20°,30°), Ωi, bi, and mi can be calculated by the empirical formulas [39, Eq. (19)]. Therefore, considering the effect of satellite perturbation, Ωi, bi, and mi can be calculated as follows:(21)biθci,θei,t=-4.7943×10-8θci+θeisin⁡t3+5.5784×10-6θci+θeisin⁡t2-2.1344×10-4θci+θeisin⁡t+3.2710×10-2,miθci,θei,t=6.3739×10-5θci+θeisin⁡t3+5.8533×10-4θci+θeisin⁡t2-1.5973×10-4θci+θeisin⁡t+3.5156,Ωiθci,θei,t=1.4428×10-5θci+θeisin⁡t3-2.3798×10-3θci+θeisin⁡t2+1.2702×10-1θci+θeisin⁡t-1.4864.


## 3. Performance Analysis

In order to exactly measure the effect of satellite perturbation on the SIN return channel cooperative communications via an AF GEO HTS relaying, the important quality-of-service (QoS) metric, that is, average symbol error probability (ASER), is analytically studied and evaluated in our proposed SIN-assisted VN systems.Since MRC is applied at the destination, we derive the close-form expression by using MGF according to [52], where the ASER of an M-ary phase-shift keying (MPSK) modulated system is given by(22)PMPSK=1π∫0θMMγe2egMPSKsin2⁡θ,where θM=π(M-1)/M and gMPSK=sin2(π/M). The MGF of instantaneous SNR (γ) is defined as(23)Mγ=Eγe-sγ=∫0∞e-sγfγγdγ.Consideringh0, h1, and h2 are independent and the relationship between γ1, γ02, and γe2e is presented in (4), we can express Me2e(s) as(24)Mγe2es=Mγ1sMγ02s,where Mγ1(s) and Mγ02(s) are the MGF of γ1 and γ02.In the following, we derive the expressions forMγ1(s) and Mγ02(s). Then, we use (22) and (24) to obtain the ASER of our SIN backbone satellite relaying VN system.


### 3.1. MGF of the SNR for theS-D Link

By using the definition of MGF and substituting (17) into (23), we can evaluate the MGF of the S-D link as follows(25)Mγ1s=Ee-sx=∫0∞e-sxα1ρ1e-β1/ρ1x·F11m1;1;δ1ρ1xdx=α1ρ1∫0∞e-β1/ρ1+sx·F11m1;1;δ1ρ1xdx.By using [36, Eq. (7.621.4)], the result of (25) can be easily obtained as follows:(26)Mγ1s=α1ρ1s+β1Fm1,1;1;δ1ρ1s+β1.


### 3.2. MGF of the SNR for theS-R-D Link

By substitutingγ02 in (6) into (23), we can evaluate the MGF of cooperative link as presented in (27). The proof is provided in the Appendix.(27)Mγ02s=u2sα2e-K+u2s+β2-δ2/ρ2u1sKρ2∑n=0m2-1-1n1-m2nn!2δ2ρ2n∑k=0n-u1sn-k2ερ2u2sβ2-δ2k+1/2·Kk+12εu2sβ2-δ2ρ2+2εερ2u2sβ2-δ2k/2Kk2εu2sβ2-δ2ρ2,where the definitions u1(s), u2(s), and ε are shown in (A.7).


### 3.3. Derivation of ASER

Based on the definition of ASER of an MPSK modulated system (i.e., (27) and (24)), (22) can be written as(28)PMPSK=1π∫0θMMγe2egMPSKsin2⁡θdθ=Eγ1π∫0π/2exp⁡gMPSKsin2⁡θdθ+1π∫π/2θMexp⁡gMPSKsin2⁡θdθ=1π∫0θMMγ1gMPSKsin2⁡θMγ02gMPSKsin2⁡θdθ.Alternatively, the following approximation of (28) can be used [37]:(29)PMPSK=1π∫0θMMγ1gMPSKsin2⁡θMγ02gMPSKsin2⁡θdθ≈∑j=13kjMγ1wjMγ02wj,where(30)k1=θM2π-16,w1=-gMPSK,k2=14,w2=-43gMPSK,k3=θM2π-14,w3=-gMPSKsin2θ.As shown in (26) and (27), the close forms of Mγ1(s) and Mγ02(s) have already been derived. By substituting these close forms into (29), we finally obtain the accurate closed-form expression of the ASER of a space downlink cooperative transmission system with relay GEO satellite as shown in (31)PMPSK=∑j=13kjα1ρ1wj+β1Fm1,1;1;δ1ρ1wj+β1u2wjα2e-K+u2wj+β2-δ2/ρ2u1wjKρ2×∑n=0m2-1-1n1-m2nn!2δ2ρ2n∑k=0n-u1wjn-k×2ερ2u2wjβ2-δ2k+1/2·Kk+12εu2wjβ2-δ2ρ2+2εερ2u2wjβ2-δ2k/2Kk2εu2wjβ2-δ2ρ2.


## 3.1. MGF of the SNR for theS-D Link

By using the definition of MGF and substituting (17) into (23), we can evaluate the MGF of the S-D link as follows(25)Mγ1s=Ee-sx=∫0∞e-sxα1ρ1e-β1/ρ1x·F11m1;1;δ1ρ1xdx=α1ρ1∫0∞e-β1/ρ1+sx·F11m1;1;δ1ρ1xdx.By using [36, Eq. (7.621.4)], the result of (25) can be easily obtained as follows:(26)Mγ1s=α1ρ1s+β1Fm1,1;1;δ1ρ1s+β1.


## 3.2. MGF of the SNR for theS-R-D Link

By substitutingγ02 in (6) into (23), we can evaluate the MGF of cooperative link as presented in (27). The proof is provided in the Appendix.(27)Mγ02s=u2sα2e-K+u2s+β2-δ2/ρ2u1sKρ2∑n=0m2-1-1n1-m2nn!2δ2ρ2n∑k=0n-u1sn-k2ερ2u2sβ2-δ2k+1/2·Kk+12εu2sβ2-δ2ρ2+2εερ2u2sβ2-δ2k/2Kk2εu2sβ2-δ2ρ2,where the definitions u1(s), u2(s), and ε are shown in (A.7).


## 3.3. Derivation of ASER

Based on the definition of ASER of an MPSK modulated system (i.e., (27) and (24)), (22) can be written as(28)PMPSK=1π∫0θMMγe2egMPSKsin2⁡θdθ=Eγ1π∫0π/2exp⁡gMPSKsin2⁡θdθ+1π∫π/2θMexp⁡gMPSKsin2⁡θdθ=1π∫0θMMγ1gMPSKsin2⁡θMγ02gMPSKsin2⁡θdθ.Alternatively, the following approximation of (28) can be used [37]:(29)PMPSK=1π∫0θMMγ1gMPSKsin2⁡θMγ02gMPSKsin2⁡θdθ≈∑j=13kjMγ1wjMγ02wj,where(30)k1=θM2π-16,w1=-gMPSK,k2=14,w2=-43gMPSK,k3=θM2π-14,w3=-gMPSKsin2θ.As shown in (26) and (27), the close forms of Mγ1(s) and Mγ02(s) have already been derived. By substituting these close forms into (29), we finally obtain the accurate closed-form expression of the ASER of a space downlink cooperative transmission system with relay GEO satellite as shown in (31)PMPSK=∑j=13kjα1ρ1wj+β1Fm1,1;1;δ1ρ1wj+β1u2wjα2e-K+u2wj+β2-δ2/ρ2u1wjKρ2×∑n=0m2-1-1n1-m2nn!2δ2ρ2n∑k=0n-u1wjn-k×2ερ2u2wjβ2-δ2k+1/2·Kk+12εu2wjβ2-δ2ρ2+2εερ2u2wjβ2-δ2k/2Kk2εu2wjβ2-δ2ρ2.


## 4. Numerical Results

This section gives the numerical results to demonstrate the validity of the theoretical analysis and the effect of satellite perturbation on the SIN return channel cooperative communications via a GEO HTS relaying.We assume the nodeS is a space node and its position is Llat=10°N and Llon=0°W. The node R is a GEO HTS and, for the initial position (X,Y, and Z) and velocity vector (Vx,Vy, and Vz) in the Cartesian coordinate system, their initial values are (X,Y, and Z) = (-32299.6,-27102.6,0) km and (Vx,Vy, and Vz) = (1.97635,-2.35533,0) km/sec. We adopt high precision orbit propagator (HPOP) model and the parameters of the various perturbations are shown in Table 1. The GEO HTS R is mainly affected by the Earth gravity, the third-body gravity, and the solar radiation pressure perturbation [53]. In Table 1, the Earth gravity model [54], the solar radiation pressure perturbation, and the third-body gravity perturbation adopt general settings.Table 1
Initial position and velocity vector of GEO HTS and other system parameters.
Parameters
Description
Earth gravity model
WGS84_EGM96.grv
Satellite mass
1000 kg
Mass-area ratio of satellite
0.1 m2/kg
Reflection coefficient of spacecraft
1.2
Solar radiation pressure model
Spherical
Third-body gravity
Sun, MoonThe elevation error affected by the satellite perturbation is shown in Figure3, which is mainly considering the Earth nonspherical perturbation, the lunisolar gravitational perturbation, and the solar radiation pressure perturbation. The simulation duration is one lunar month and each step is 60 seconds.Figure 3
Elevation error caused by GEO satellite perturbation.As shown in Figure3, the elevation error accumulates on the R-D link which is about 1 degree after one lunar month. The elevation error fluctuates on the S-R link, where the range of fluctuation increases gradually and the simulation time accumulates, and the maximum of fluctuation is about 0.1 degrees at the end of the simulation.We assumeE1=E2 and ρ0=ρ1=ρ2=ρ. In S-R and R-D links, the elevations of TX ignoring satellite perturbation at nodes R and D are equal; that is, θc0=θc2=θ0. In order to simulate the influence of the elevation error caused by perturbation on the system ASER performance, the elevation error data is sampled at intervals of 12 hours due to the large amount of elevation error in Figure 3. The amplifying factor is G=30 and θc1=60° and QPSK modulation is implemented, and the rest of the simulation parameters are the same as above. The end-to-end ASER with satellite perturbation in the SIN return channel cooperative communications via an AF GEO HTS are shown in Figures 4, 5, and 6, respectively.Figure 4
ASER with satellite perturbation versus variousρ; (b) shows the elevation error fluctuation and accumulation process on the ASER under different θ0, where ρ = 5 dB and Ω = 5 W.
(a)
(b)Figure 5
ASER with satellite perturbation versus variousρ; (b) shows the elevation error fluctuation and accumulation process on the ASER under different Ω, where ρ = 5 dB and θ0 = 55°.
(a)
(b)Figure 6
ASER performance versus variousθ0 under ρ = 5 dB.Figures4 and 5 indicate the ASER performance is improving with the increasing of receiving SNR ρ. As one can expect, with the increasing of TX and average power of received signal at node R in the S-R and R-D links, the ASER performance is improving. Comparing with the cases of ignoring the effect of the satellite perturbation, the ASER performance deteriorates a little due to the satellite perturbation.Moreover, three subfigures in Figures4 and 5 show the fluctuation and error accumulation process of the ASER with satellite perturbation with ρ = 5 dB, under different θ0 and Ω, respectively. In Figure 4, when θ0=35°,55°, and 75°, the fluctuation of ASER is the same, and the fluctuation ranges are 2.2379e-5, 1.5260e-5, and 4.4567e-6, respectively, and the fluctuation range becomes tighter and θ0 increases. Similar to Figure 5, when Ω = 2 W, 5 W, and 10 W, the fluctuation of ASER is the same, and the fluctuation ranges are 2.9818e-5, 1.5260e-5, and 6.8832e-6, respectively, and the fluctuation range declines when Ω increases. To be clearer, we show the ASER performance with the increasing of Ω and θ0 as in Figure 6.


## 5. Conclusion

In this paper, we investigate the ASER performance of SIN return channel cooperative communications via an AF GEO HTS relaying for VN, where both of theS-D and R-D links undergo the Shadowed-Rician fading, and the S-R link follows Rician fading, respectively. By applying MRC at D, the equivalent end-to-end SNR of the system is first obtained, then the analytical expressions of ASER and the satellite perturbation effect are derived. The effect of the satellite perturbation of the relaying GEO satellite is considered for the first time, which reveals that the accumulated error of the antenna pointing error leads to the satellite elevation error. And the accumulated satellite elevation error is taking into account the derivation of the ASER expression. The closed-form expression for the end-to-end ASER can efficiently evaluate the system performance, and simulation results prove the rationality of our theoretical analysis.



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*Source: 4859835-2017-12-10.xml*