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

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 are 120[degrees] 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 Kaband [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([mu], [[sigma].sup.2]) denotes a complex Gaussian distribution with mean [mu] and variance [[sigma].sup.2] * exp(*) represents the exponential function. [M.sub.[lambda]] (*) denotes the moment generating function (MGF) of [gamma]. [f.sub.x](*) and [F.sub.x](*) denote the probability distribution function (PDF) and cumulative distribution function (CDF) of x, respectively. [sub.1][F.sub.l] (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 [K.sub.n](*) represents the modified Bessel function of the second kind with order n [36, Eq. (8.446)]. [M.sub.a,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 Figure 1, where a source node (S),that is, space node, communicates with a terrestrial destination (D) via a GEO HTS relay (R) and [h.sub.0], [h.sub.1], and [h.sub.2] are the channel gains of the S-R, S-D, and R-D links, respectively.

The space node S 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 [h.sub.0] 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 [h.sub.1] and [h.sub.2] 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 Figure 1, 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 [h.sub.0] and [h.sub.1] are the channel gains of the S-R and S-D links, respectively. The received signals at the relay [y.sub.0] and the destination [y.sub.1] from S are given by

[y.sub.0] = [square root of ([E.sub.1])] [h.sub.0] x + [n.sub.0], (1)

[y.sub.1] = [square root of ([E.sub.1])] [h.sub.1] x + [n.sub.1], (2)

where x is the transmitted signal with unit power, [E.sub.1] is the transmitted power at S, and [n.sub.0] and [n.sub.1] are the AWGN of S-R and S-D links with zero mean and variance [[sigma].sup.2.sub.0] and [[sigma].sup.2.sub.1] respectively.

During the second time phase, R first amplifies the received signal [y.sub.0] by an amplifying factor G and then forwards it to D through R-D link of which the channel gain is [h.sub.2], and the received signal at the destination [y.sub.2] is given by

[y.sub.2] = [square root of ([E.sub.2])]G[h.sub.2][y.sub.0] + [n.sub.2] (3)

= G [square root of ([E.sub.1][E.sub.2])][h.sub.2][h.sub.0] x + G [square root of ([E.sub.2])][h.sub.2][n.sub.0] + [n.sub.2], where [E.sub.2] is the transmit power at R and [n.sub.2] is in AWGN at D obeying [n.sub.2] ~ N(0,[[sigma].sup.2.sub.2]).

Assuming that perfect channel state information (CSI) is available at D and R and MRC is applied at the destination, thus, the end-to-end SNR at D can be expressed as

[[gamma].sub.e2e] = [[gamma].sub.l] + [[gamma].sub.02], (4)

where [[gamma].sub.1] is the SNR of S-D link and [[gamma].sub.02] is the SNR of S-R-D link. From (2), we have

[[gamma].sub.1] = [E.sub.1] [absolute value of [h.sub.1]].sup.2] / [[sigma].sup.2.sub.1] = [[rho].sub.1] [absolute value of [h.sub.1]].sup.2]. (5)

From (3), [[gamma].sub.02] can be expressed as

[mathematical expression not reproducible], (6)

where C = l/[(G[[sigma].sub.0]).sup.2] and [[gamma].sub.0] = [E.sub.1] [absolute value of [h.sub.0]].sup.2] / [[sigma].sup.2.sub.0] = [[rho].sub.0] [absolute value of [h.sub.0]].sup.2] and [[gamma].sub.2] = [E.sub.2] [absolute value of [h.sub.2]].sup.2] / [[sigma].sup.2.sub.2] = [[rho].sub.2] [absolute value of [h.sub.2]].sup.2] denote the SNR of S-R and R-D link, respectively. Thus, (4) can be rewritten as

[[gamma].sub.e2e] = [[gamma].sub.0] [[gamma].sub.2] / [[gamma].sub.2] + C + [[rho].sub.1] [absolute value of [h.sub.1]].sup.2]. (7)

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 w 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 Figure 2, and let [theta] = [[theta].sub.e] + [[theta].sub.c] denote the elevation of a GEO HTS, where [[theta].sub.e] represents the elevation error, which is the angle between centerline of antenna beam pointed to [P.sub.1] and the real LOS channel between the actual position [P.sub.2] of the satellite to the destination. [[theta].sub.c] 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 [theta] can be calculated by [46]

[mathematical expression not reproducible] (8)

where [phi] is the latitude of the destination, [lambda] = [[lambda].sub.sat] - [[lambda].sub.des] is the longitude difference between the subsatellite point and the ground station, [[lambda].sub.sat] represents the longitude of subsatellite point, [[lambda].sub.des] is the longitude of destination, [DELTA] [phi] is the drift of satellite in the northsouth direction, and [DELTA] [lambda] is the drift of satellite in the eastwest direction. Therefore, the elevation error [[theta].sub.e] can be calculated as [[theta].sub.e] = [theta] - [[theta].sub.c].

In general, [[lambda].sub.des] can be calculated by the six elements of the satellite orbit [47]. When the satellite orbit is elliptical, the longitude ([L.sub.lon]) and the latitude ([L.sub.lat]) of the subsatellite point can be expressed as

[mathematical expression not reproducible] (9)

where [[omega].sub.e] is the average angular velocity of Earth, t is the time, [t.sub.N] 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

[mathematical expression not reproducible] (10)

where [tau] 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, [omega], and [tau]. If these variables have been affected by the satellite perturbation, the subsatellite point will have drift. Let [L.sup.lon.sub.p] and [L.sup.lat.sub.p] represent the longitude and latitude of subsatellite point considering the effect of satellite perturbation, respectively, and [L.sup.lon.sub.p] and [L.sup.lat.sub.p] 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

[DELTA] [phi] = [L.sup.lon.sub.p] - [L.sup.lon.sub.np] [DELTA] [lambda] = [L.sup.lat.sub.p] - [L.sup.lat.sub.p]. (11)

2.2. Channel Model

2.2.1. S-R Link. As the S-R link is modeled by using the Rician fading distribution, the probability distribution function (PDF) of [[gamma].sub.0] is given by [48]

[mathematical expression not reproducible] (12)

where [OMEGA] is the average power of received signal at R and [OMEGA] = ([A.sup.2] + 2[[sigma].sup.2])/2 and K = [A.sup.2]/(2[[sigma].sup.2]) are known as the Rician factor, A is the amplitude of LOS signal, [[sigma].sup.2] is the average power of multipath component, and [I.sub.0](*) is the modified Bessel function of the first kind with order zero.

Then, the cumulative distribution function (CDF) of [[gamma].sub.0] can be expressed as

[mathematical expression not reproducible], (13)

where [Q.sub.M] (*, *) is the Marcum Q-function of the Mth order, which is defined as

[Q.sub.M] (a,b) = [[integral].sup.[infinity].sub.b] [(x/a).sup.M-1] exp (- [x.sup.2] + [a.sup.2] / 2) [I.sub.M-1] (ax)dx. (14)

Moreover, the relationship between the Rician factor K of the Rician fading S-R link (12) and the satellite elevation ([[theta].sub.c]) was simulated in [49] through a large number of experiments. Then the relationship between the Rician factor and the satellite elevation ([[theta].sub.c] [member of] [10[degrees], 90[degrees]]) was fitted as an empirical formula

K([[theta].sub.c]) = [K.sub.0] + [K.sub.1] ([[theta].sub.c]) + [K.sub.2] ([[theta].sub.c]), (15)

where [K.sub.0], [K.sub.1], and [K.sub.2] are empirical constant and [K.sub.0] = 2.731, [K.sub.1] = -1.074 x [10.sup.-1], and [K.sub.2] = 2.771 x [10.sup.-3], respectively. Considering the effect of satellite perturbation, (15) can be rewritten as

K([[theta].sub.c], [[theta].sub.e], t) = [K.sub.0] + [K.sub.1] ([[theta].sub.c] + [[theta].sub.e] sin t) + [K.sub.2] ([[theta].sub.c] + [[theta].sub.e] sin t), (16)

where [[theta].sub.e] sin t indicates the elevation error [[theta].sub.e] affected by the satellite perturbation at time t.

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

Let [[gamma].sub.1] and [[gamma].sub.2] denote the SNR of the S-D and R-D links, respectively. The PDF of [[gamma].sub.i] (i = 1,2) is given by [39]

[mathematical expression not reproducible] (17)

where

[mathematical expression not reproducible], (18)

where [sub.1F.sub.1] (*; *; *) is the confluent hypergeometric function of first kind [36, Eq. (9.210.1)]. Moreover, [[OMEGA].sub.i] and 2[b.sub.i] are the average power of the LOS and the multipath components, respectively, and [m.sub.i] ([m.sub.i] [member of] [0, [infinity])) is the fading severity parameter.

Recall the definition of [sub.1F.sub.1] (*; *; *), and we have

[mathematical expression not reproducible]. (19)

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, [m.sub.i] [member of] N. Hence, with the aid of [50, Eq. (07.20.03.0009.01), Eq. (07.02.03.0014.01)], (19) becomes

[mathematical expression not reproducible], (20)

where [(z).sub.n] = [TAU](z + n)/[TAU](z) denotes the Pochhammer symbol with n [member of] N [51, Eq. (6.1.22)].

To solve the three parameters ([[OMEGA].sub.i], [b.sub.i], and [m.sub.i]) in (18), we assume [[theta].sub.ci] is the elevation at GEO HTS R, when the center line of the receiving antenna beam in different link aims at R. [[theta].sub.ei] sin t is the elevation error which affects the satellite perturbation. When [[theta].sub.ci] [member of] (20[degrees], 30[degrees]), [[OMEGA].sub.i], [b.sub.i], and [m.sub.i] can be calculated by the empirical formulas [39, Eq. (19)]. Therefore, considering the effect of satellite perturbation, [[OMEGA].sub.i], [b.sub.i], and [m.sub.i] can be calculated as follows:

[mathematical expression not reproducible]. (21)

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

[mathematical expression not reproducible]. (22)

where [[theta].sub.M] = [pi](M - 1)/M and [g.sub.MPSK] = [sin.sup.2] ([pi]/M). The MGF of instantaneous SNR ([gamma]) is defined as

[M.sub.[gamma]] = [E.sub. [gamma]] {[e.sup.-s[gamma]]} = [[integral].sup.[infinity].sup.0] [e.sup.-s[gamma]] [f.sub. [gamma]] ([gamma]) d[gamma]. (23)

Considering [h.sub.0], [h.sub.1], and [h.sub.2] are independent and the relationship between [[gamma].sub.1], [[gamma].sub.02], and [[gamma].sub.e2e] is presented in (4), we can express [M.sub.e2e](s) as

[mathematical expression not reproducible], (24)

where [mathematical expression not reproducible] and [mathematical expression not reproducible] are the MGF of [[gamma].sub.1] and [[gamma].sub.02].

In the following, we derive the expressions for [mathematical expression not reproducible] and [mathematical expression not reproducible]. 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 the S-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

[mathematical expression not reproducible]. (25)

By using [36, Eq. (7.621.4)], the result of (25) can be easily obtained as follows:

[mathematical expression not reproducible]. (26)

3.2. MGF of the SNR for the S-R-D Link. By substituting y02 in (6) into (23), we can evaluate the MGF of cooperative link as presented in (27). The proof is provided in the Appendix.

[mathematical expression not reproducible] (27)

where the definitions [u.sub.1](s), [u.sub.2](s), and [epsilon] 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

[mathematical expression not reproducible] (28)

Alternatively, the following approximation of (28) can be used [37]:

[mathematical expression not reproducible] (29)

where

[mathematical expression not reproducible]. (30)

As shown in (26) and (27), the close forms of [mathematical expression not reproducible] and [mathematical expression not reproducible] 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

[mathematical expression not reproducible]. (31)

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 node S is a space node and its position is [L.sub.lat] = 10[degrees]N and [L.sub.lon] = 0[degrees]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.

The elevation error affected by the satellite perturbation is shown in Figure 3, 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.

As shown in Figure 3, 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 assume [E.sub.1] = [E.sub.2] and [[rho].sub.0] = [[rho].sub.1] = [[rho].sub.2] = [rho]. In S-R and R-D links, the elevations of [T.sub.X] ignoring satellite perturbation at nodes R and D are equal; that is, [[theta].sub.c0] = [[theta].sub.c2] = [[theta].sub.0]. 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 [[theta].sub.c1] = 60[degrees] 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.

Figures 4 and 5 indicate the ASER performance is improving with the increasing of receiving SNR [rho]. As one can expect, with the increasing of [T.sub.X] 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 Figures 4 and 5 show the fluctuation and error accumulation process of the ASER with satellite perturbation with [rho] = 5 dB, under different [[theta].sub.0] and [OMEGA], respectively. In Figure 4, when [[theta].sub.0] = 35[degrees], 55[degrees], and 75[degrees], 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 [[theta].sub.0] increases. Similar to Figure 5, when [OMEGA] = 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 [OMEGA] increases. To be clearer, we show the ASER performance with the increasing of [OMEGA] and [[theta].sub.0] 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 the S-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.

Appendix

Derivation the MGF of the Cooperative Link

By the definition of MGF, from (6) and (23), the MGF of the cooperative link can be evaluated:

[mathematical expression not reproducible]. (A.1)

Considering [h.sub.0] and [h.sub.2] are independent, we first calculate the following integral of variable x such that

[mathematical expression not reproducible] (A.2)

By using [36, Eq. (6.614.3)], we get

[mathematical expression not reproducible] (A3)

where [mathematical expression not reproducible] is the Whittaker functions defined as [36, Eq. (9.220.2)]'

[mathematical expression not reproducible], (A.4)

where [PHI]([alpha],[gamma];z) is a second notation of confluent hypergeometric function, and when [alpha] = [gamma], [PHI]([alpha],[gamma];z) has the relationship [36, Eq. (9.215)] as follows:

[PHI]([alpha], [alpha]; z) = [e.sup.z]. (A.5)

Thus, (A.3) can be rewritten as

[mathematical expression not reproducible] (A.6)

In order to make the derivation more clear, we define

[mathematical expression not reproducible] (A.7)

After some algebra manipulations, we can rewrite (A.6) as

[mathematical expression not reproducible] (A.8)

Now, we can rewrite [mathematical expression not reproducible] as the integral of variable y

[mathematical expression not reproducible] (A.9)

Let w(s) = y + [u.sub.1](s), and then we have y = w(s) - [u.sub.1](s) and dy = dw. After some algebra manipulations, (A.9) can )e written as the integral of variable w

[mathematical expression not reproducible] (A.10)

By substituting (20) into (A.10), we have

[mathematical expression not reproducible] (A.11)

Then, by using the Binomial expansion for (w(s)-u1 (s))n, we can rewrite (A.11) as

[mathematical expression not reproducible] (A.12)

The integral part of (A.12) can be solved by using [36, Eq. (3.471.9)] as follows:

[mathematical expression not reproducible] (A.13)

Therefore, by plugging (A.13) into (A.12), the result of [mathematical expression not reproducible] can be obtained as presented in (27).

https://doi.org/10.1155/2017/4859835

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Authors' Contributions

Jian Jiao, Houlian Gao, and Qinyu Zhang contributed equally to this work.

Acknowledgments

This work was supported in part by the National Natural Sciences Foundation of China (NSFC) under Grants 61771158, 61701136, 61525103, and 61371102, the National High Technology Research & Development Program no. 2014AA01A704, the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology under Grant HIT.NSRIF.2017051, and the Shenzhen Fundamental Research Project under Grants JCYJ20160328163327348 and JCYJ20150930150304185.

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Jian Jiao, Houlian Gao, Shaohua Wu, and Qinyu Zhang

Communication Engineering Research Centre, Harbin Institute of Technology, Shenzhen, Guangdong, China

Correspondence should be addressed to Shaohua Wu; hitwush@hit.edu.cn

Received 9 September 2017; Accepted 15 November 2017; Published 10 December 2017

Academic Editor: Tao Han

Caption: 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 point [P.sub.1] with an arrow point to [P.sub.2] shows the satellite drift effect caused by the satellite perturbation.

Caption: FIGURE 2: The diagram of antenna pointing error caused by satellite perturbation, [P.sub.1] means the satellite position located in antenna beam center, and [P.sub.2] represents the satellite position offsets from antenna beam center.

Caption: FIGURE 3: Elevation error caused by GEO satellite perturbation.

Caption: FIGURE 4: ASER with satellite perturbation versus various p; (b) shows the elevation error fluctuation and accumulation process on the ASER under different [[theta].sub.0], where [rho] = 5 dB and [OMEGA] = 5W.

Caption: FIGURE 5: ASER with satellite perturbation versus various [rho]; (b) shows the elevation error fluctuation and accumulation process on the ASER under different [OMEGA], where [rho] = 5 dB and [[theta].sub.0] = 55[degrees].

Caption: FIGURE 6: ASER performance versus various [[theta].sub.0] under [rho] = 5 dB.

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 [m.sup.2]/kg
Reflection coefficient of spacecraft          1.2
Solar radiation pressure model             Spherical
Third-body gravity                         Sun, Moon
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Title Annotation:Research Article
Author:Jiao, Jian; Gao, Houlian; Wu, Shaohua; Zhang, Qinyu
Publication:Wireless Communications and Mobile Computing
Article Type:Report
Date:Jan 1, 2017
Words:6846
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