1912 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 10, OCTOBER 2013

Performance Analysis of AF Based Hybrid Satellite-TerrestrialCooperative Network over Generalized Fading Channels

Manav R. Bhatnagar, Senior Member, IEEE, and Arti M.K., Student Member, IEEE

Abstract—In this paper, the transmission of signals in ahybrid satellite-terrestrial link is considered. In particular, weaddress the problem of amplify-and-forward (AF) relaying ina hybrid satellite-terrestrial link, where a masked destinationnode receives the relayed transmission from a terrestrial linkand direct transmission from the satellite link. The satellite-relay and satellite-destination links are assumed to follow theShadowed-Rician fading; and the channel of the terrestriallink between the relay and destination is assumed to followthe Nakagami-m fading. The average symbol error rate of theconsidered AF cooperative scheme for M -ary phase shift keyingconstellation is derived for these generalized fading channels.Moreover, analytical diversity order of the hybrid system is alsoobtained.

Index Terms—Amplify-and-forward protocol, cooperative di-versity, hybrid satellite-terrestrial cooperative system, land mo-bile satellite (LMS) channel, M -ary phase-shift keying (M -PSK).

I. INTRODUCTION

SATELLITE systems provide services over a wide coveragearea; hence, theses systems are used in broadcasting,

navigation, disaster relief, and navigation. The masking effectis the main limitation of the mobile satellite systems; whenobstacles block the line of sight link (LOS) in between thesatellite and a terrestrial user, masking effect occurs. Thiseffect is more severe for the indoor users. Hybrid/integratedsatellite-terrestrial cooperative systems have been proposedin [1], [2], to overcome the masking effect. Integrated satellite-terrestrial systems are discussed in [3], while hybrid systemsfor satellite based unlimited mobile TV systems are proposedin [4]. Spatial diversity can be achieved in hybrid/integratedsatellite-terrestrial cooperative systems, because a ground userreceives two independent copies of the signal, one from thesatellite link and other from the satellite-terrestrial link. Thehybrid satellite-terrestrial cooperative systems have been stud-ied in [5], [6], [7], [8]. In [9], a limited channel model basedhybrid satellite-terrestrial cooperative system has been ana-lyzed, where the channel between the satellite and destinationuser follows the Shadowed-Rician land mobile satellite (LMS)model [10]; the channel between the satellite and relay nodefollows the Rician fading; whereas, the channel between therelay and destination is Rayleigh fading channel. Recently, in[11], the outage performance of a cooperative hybrid satellite-terrestrial system is analytically evaluated, where the satellite

Manuscript received May 12, 2013. The associate editor coordinating thereview of this letter and approving it for publication was A. Panagopoulos.

The authors are with the Department of Electrical Engineering, IndianInstitute of Technology - Delhi, Hauz Khas, New Delhi 110016, India (e-mail:{manav, arti.mk}@ee.iitd.ac.in). M. Bhatnagar is the corresponding author.

Digital Object Identifier 10.1109/LCOMM.2013.090313.131079

links are assumed to suffer from Shadowed-Rician fading,while the terrestrial link follows Nakagami-m fading.

In this paper, we analyze the error performance of a threenode amplify-and-forward (AF) hybrid satellite-terrestrial co-operative system with generalized fading channels, wherethe source-destination and source-relay satellite links followthe Shadowed-Rician LMS model; and the relay-destinationterrestrial link follows Nakagami-m fading. We derive themoment generating functions (m.g.f.s) for the direct and coop-erative links. By using these m.g.f.s, the average symbol errorrate (SER) of the considered cooperative system is obtained.In addition, we derive the analytical diversity order of theconsidered AF based hybrid satellite-terrestrial cooperativesystem.

II. SYSTEM MODEL

We consider a hybrid/integrated satellite-terrestrial cooper-ative system, where a satellite transmits data to a destinationnode at ground, with the assistance of a relay node situatedat ground. The transmission from satellite to the destinationis performed in two orthogonal phases. In the first phase, thesatellite broadcasts its signal to the relay and the destination.The signal received at the destination and the relay, respec-tively, will be

y0 = h0x+ e0, y1 = h1x+ e1, (1)

where h0 is the channel gain between the satellite and thedestination; h1 is the channel gain between the satellite andthe relay; x is the transmitted symbol with Es power; e0 ande1 are the zero-mean additive white Gaussian noise (AWGN)of the satellite-destination and satellite-relay links with σ2

0 andσ21 variance, respectively.In the next phase, the relay multiplies the received signal

y1 with a multiplication factor G > 0, in order to satisfyan average transmit power constraint.The amplified signal isforwarded to the destination; hence, the signal received at thedestination will be

y2 = Gh1h2x+Gh2e1 + e2, (2)

where h2 is the channel gain between the relay and thedestination, and e2 is the zero-mean AWGN noise with σ2

2

variance.The satellite-destination and the satellite-relay links are

modeled as Shadowed-Rician fading channels with the fol-lowing probability distribution function (p.d.f.) [10]

f|hi|2(x) = αie−βix

1F1(mi; 1; δix), x > 0, (3)

where i = 0, 1, αi = 0.5(2bimi/(2bimi + Ωi))mi/bi, βi =

(0.5/bi), δi = 0.5Ωi/(2b2imi + biΩi), the parameter Ωi is the

average power of LOS component, 2bi is the average power ofthe multipath component, and 0 ≤ mi ≤ ∞ is the Nakagami

1089-7798/13$31.00 c© 2013 IEEE

BHATNAGAR and ARTI M.K.: PERFORMANCE ANALYSIS OF AF BASED HYBRID SATELLITE-TERRESTRIAL COOPERATIVE NETWORK . . . 1913

parameter, for mi = 0 and mi = ∞, the envelope of hi

follows the Rayleigh and Rician distribution, respectively; and1F1(a; b; z) is the confluent Hypergeometric function [12, Eq.(9.210.1)].

The channel of the relay-destination link is assumed tofollow the Nakagami-m distribution; hence, |h2|2 follows theGamma distribution as

f|h2|2(x) = λ2xm2−1e−ε2x, x > 0, (4)

where λ2 = mm22 /(Ωm2

2 Γ(m2)), ε2 = m2/Ω2; and 1/2 ≤m2 ≤ ∞ and Ω2 denote the shape and scale parameters,respectively, of the relay-destination channel.

III. PERFORMANCE ANALYSIS

In this section, we will find the average SER of theconsidered AF based hybrid scheme. We follow the standardm.g.f. based approach.

Under the assumption of the maximal ratio combining(MRC) in the destination, the instantaneous received signal-to-noise ratio (SNR) can be written, by using (1) and (2), as

γe =|h1|2|h2|2|h2|2 + C

Es

σ21

+ |h0|2Es

σ20

= γc + γ0, (5)

where γc = |h1|2|h2|2Es/((|h2|2 + C

)σ21

)and γ0 =

|h0|2Es/σ20 denote the instantaneous received SNR of the co-

operative and direct link, respectively; and C = σ22/(G2σ2

1

).

From the definition of the m.g.f., we have

Mγe(s) = Mγc(s)Mγ0(s), (6)

where Mγ(s) denotes the m.g.f. of γ.

A. Calculation of the M.G.F. of the Direct Link

The m.g.f. of the direct link is given by

Mγ0(s) = Eγ0

{e−s|h0|2Es/σ

20

}=

∫ ∞

0

e−sxEs/σ20f|h0|2(x)dx, (7)

where E {·} represents the expectation. By using [12, Eq.(7.621.4)] in (7), it can be shown that

Mγ0(s) = α0(sEs

σ20

+ β0)−1F (m0, 1; 1; δ0(

sEs

σ20

+ β0)−1), (8)

where F (α, β; γ; z) is the Hypergeometric function [12, Eq.(9.100)]. Next, by using [12, Eq. (9.121.1)] in (8), we get

Mγ0(s) = α0(sEs

σ20

+ β0)−1(1− δ0(

sEs

σ20

+ β0)−1)−m0 . (9)

B. Calculation of the M.G.F. of the Cooperative Link

The m.g.f. of the cooperative link can be written as

Mγc(s) = Eγc

{e−s

|h1|2|h2|2|h2|2+C

Esσ21

}

=

∫ ∞

0

∫ ∞

0

e−s xy

y+CEsσ21 f|h1|2(x)f|h2|2(y)dxdy. (10)

Let us now define the following integral:

I1 �=

∫ ∞

0

e−s xy

y+CEsσ21 f|h1|2(x)dx. (11)

By using [12, Eq. (7.621.4)] and [12, Eq. (9.121.1)] in (11),we get

I1 =(α1y + α1C)

((sEs

σ21+ β1

)y + Cβ1

)m1−1

((sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1. (12)

Let us now define the following functions:

f(α)�=

Γ(α+ 1)Cα+1−m1 (β1 − δ1)α+1−m1(

sEs

σ21+ β1 − δ1

)α+1

× Ψ(α+ 1, α+ 2−m1;

ε2C(β1 − δ1)sEs

σ21+ β1 − δ1

), (13)

where Ψ(a, b; z) is the confluent Hypergeometric function [12,Eq. (9.210.2)]; and

g(α, β(x))�=

λ2(Cβ1)m1+m2−1(

sEs

σ21+ β1

)m2

∫ 1

0

(α1Cβ1xsEs

σ21+ β1

+ α1C

)

×(( sEs

σ21+ β1 − δ1

)Cβ1x

sEs

σ21+ β1

+ C(β1 − δ1)

)−m1

×e− ε2Cβ1x

sEsσ21

+β1

xα−1(1 + β(x))dx, (14)

where β(x) denotes a function of x. It is shown in Appendix Athat by using the functions defined in (13) and (14), the m.g.f.of the cooperative link can be written as

Mγc∼=

c1∑l=0

(c1l

)g(m2 + l, ex)−

c1∑l=0

(c1l

)g(e+m2 + l, e/x)

+λ2

c1∑l=0

(c1l

)(sEs

σ21

+ β1

)e+l

(Cβ1)c1−l

×(α1C

(1 +

β1esEs

σ21+ β1

)f(e+m2 + l − 1)

+α1f(e+m2 + l) +α1C

2β1esEs

σ21+ β1

f(e+m2 + l − 2)

), (15)

where c1 = �m1� − 1 and e = m1 − �m1� for m1 > 1;c1 = 0 and e = m1 − 1 for m1 ≤ 1; and �x� denotes thelargest integer not greater than x. It can be noticed from (14)that g(α, β(x)) contains a finite integral, which can be easilycalculated by using MATLAB.

C. Calculation of SER

The SER of the considered generalized hybrid channelsbased AF scheme for M -ary phase-shift keying (M -PSK)constellation can be calculated, by using the relation [13]:

PMPSK =1

π

∫ θM

0

Mγc

(gMPSK

sin2θ

)Mγ0

(gMPSK

sin2θ

)dθ, (16)

where θM = π(M − 1)/M and gMPSK = sin2(π/M).Alternatively, the following approximation of (16) can beused [14, Eq. (10)]:

PMPSK =3∑

p=1

bpMγc (ap)Mγ0 (ap) , (17)

1914 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 10, OCTOBER 2013

TABLE ILMS CHANNEL PARAMETERS [10]

Shadowing bi mi Ωi

Frequent heavy shadowing 0.063 0.739 8.97× 10−4

Average shadowing 0.126 10.1 0.835Infrequent light shadowing 0.158 19.4 1.29

where b1 = θM/(2π) − 1/6, b2 = 1/4, b3 = θM/(2π) −1/4, a1 = gMPSK , a2 = 4gMPSK/3, and a3 =gMPSK/sin2(θM ).

IV. DIVERSITY ORDER CALCULATION

Let σ20 = σ2

1 = σ22 = σ2, then γ = Es/σ

2 denotes theaverage SNR. If γ takes very large value, then it is shown inAppendix B that Mγc(s) can be approximated as

Mγc(s)∼= A1

(sγ)m2+1Ψ

(m2 +m1,m2 + 1;

ε2C(β1 − δ1)

sγ

)

+A2

(sγ)m2

Ψ(m2 +m1 − 1,m2;

ε2C(β1 − δ1)

sγ

), (18)

where A1 = λ2α1Cm2Γ(m2 + m1)(β1 − δ1)

m2 and A2 =λ2α1C

m2Γ(m2 +m1 − 1)(β1 − δ1)m2−1. From [15, Chapter

13], these are asymptotic conditions for Ψ(a, b; z), z → 0:

Ψ(a, b; z) ≈{

Γ(b−1)Γ(a) z1−b , if b ≥ 1,Γ(1−b)

Γ(1+a−b) , if 0 ≤ b < 1.(19)

From (18) and (19), it can be deduced that at high SNR,

Mγc(s) ≈{

A1+A2

sγ , if m2 ≥ 1,B1

(sγ)m2 , if 1/2 ≤ m2 < 1,(20)

where A1 = A1Γ(m2) (ε2C(β1 − δ1))−m2 /Γ(m1 +m2),

A2 = A2Γ(m2 − 1) (ε2C(β1 − δ1))1−m2 /Γ(m1 +m2 − 1),

and B1 = A2Γ(1−m2)/Γ(m1). Further, it can be shown from(9) that at very large value of γ, we have

Mγ0(s) =α0

sγ. (21)

From (17), (20), and (21), we can write the asymptotic SERof the considered cooperative scheme as

PMPSK ≈⎧⎨⎩∑3

p=1(A1+A2)bpα0

a2pγ

2 , if m2 ≥ 1,∑3p=1

B1bpα0

(apγ)m2+1 , if 1/2 ≤ m2 < 1.

(22)

It can be observed from (22) that the diversity order of theconsidered scheme is 1 + min {1,m2}.

V. NUMERICAL RESULTS

The analytical and simulated results of the consideredAF based hybrid scheme are plotted for QPSK and 8-PSK constellations, and G = 1, in Fig. 1. It is assumedthat σ2

0 = σ21 = σ2

2 ; and on the x-axis of Fig. 1, SNRdenotes γ. The parameters of the Shadowed-Rician LMSmodel are given in Table I. The source-relay LMS channelis assumed to experience average shadowing; whereas, thesource-destination LMS channel experiences infrequent lightshadowing to frequent heavy shadowing. The relay-destinationchannel is taken as Nakagami-m distributed with m2 = 5.1and Ω2 = 1; the analytical SER is plotted by using (17).It can be seen from Fig. 1 that the derived approximateanalytical SER is closely followed by the simulated SER, for

0 5 10 15 20 25 30 35 40

10−8

10−6

10−4

10−2

100

SNR [dB]

SE

R

AsymptoticAnalysisSimulation

QPSK

8−PSK

AS

FHS

ILS

Fig. 1. SER versus SNR performance of the satellite-terrestrial AF coop-erative system with satellite-relay channel experiencing average shadowing,relay-destination link with m2 = 5.1 and ω2 = 1, and satellite-destinationlink with frequent heavy shadowing (FHS), average shadowing (AS), andinfrequent light shadowing (ILS).

all shadowing scenarios and constellations, considered in thefigure; therefore, the approximations taken for the proposedanalysis are very tight. We have also plotted the asymptoticSER, given in (22), for different scenarios in Fig. 1. It canbe seen from Fig. 1 that the proposed asymptotic SER verytightly follows the analytical SER at high SNR values. Sincem2 > 1, the diversity order of the considered scheme is two,as seen in Fig. 1 and indicated analytically in Section IV.Due to this improvement in the diversity order, even when thedirect satellite link experiences heavy shadowing, the hybridcooperative system provides satisfactorily low value of SER,for moderate to high SNR range, as shown in Fig. 1.

VI. CONCLUSIONS

We have derived the average SER of the AF hybrid satellite-terrestrial system with generalized fading channels. This anal-ysis has indicated that at the most second order diversity canbe achieved in the considered AF hybrid cooperative scheme.However, the AF cooperation allows for sufficiently low SEReven when the direct LMS link is under deep shadow.

APPENDIX ADERIVATION OF M.G.F. OF COOPERATIVE LINK

From (4), (10), (11), and (12), we get

Mγc(s)=λ2

∫ ∞

0

(α1y + α1C)((

sEs

σ21+ β1

)y + Cβ1

)c1((

sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1

×((

sEs

σ21

+ β1

)y + Cβ1

)e

ym2−1e−ε2ydy. (23)

By using the Binomial expansion, we can re-write (23), as

Mγc(s) = λ2

c1∑l=0

(c1l

)(sEs

σ21

+ β1

)l

(Cβ1)c1−l

×∫ ∞

0

(α1y+α1C)((

sEs

σ21+β1

)y+Cβ1

)eym2+l−1e−ε2y((

sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1dy. (24)

BHATNAGAR and ARTI M.K.: PERFORMANCE ANALYSIS OF AF BASED HYBRID SATELLITE-TERRESTRIAL COOPERATIVE NETWORK . . . 1915

By using the following approximation (1+x)η ≈ 1+ηx, x < 1in (24), and after some algebra, we get

Mγc(s)∼= J1 − J2 + J3, (25)where

J1=λ2

c1∑l=0

(c1l

)(sEs

σ21

+β1

)l

(Cβ1 )c1−l+e

∫ Cβ1/(sEsσ21

+β1)

0

ym2+l−1

×(α1y + α1C)

⎛⎝1 +

e

(sEsσ21

+β1

)y

Cβ1

⎞⎠ e−ε2y

((sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1dy,

J2=λ2

c1∑l=0

(c1l

)(sEs

σ21

+β1

)l+e

(Cβ1)c1−l∫ Cβ1/(

sEsσ21

+β1)

0

ym2+l+e−1

×(α1y + α1C)

⎛⎝1 + eCβ1(

sEsσ21

+β1

)y

⎞⎠ e−ε2y

((sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1dy,

J3=λ2

c1∑l=0

(c1l

)(sEs

σ21

+β1

)l+e

(Cβ1)c1−l∫ ∞

0

ym2+l+e−1

×(α1y + α1C)

⎛⎝1 + eCβ1(

sEsσ21

+β1

)y

⎞⎠ e−ε2y

((sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1dy. (26)

We can simplify J1 and J2 by using the following substitutionof variable: y = Cβ1x/(

sEs

σ21+β1). Further, J3 can be solved

by using [16, Eq. (2.3.6.9)].APPENDIX B

DERIVATION OF (18)

Let us assume that m1 is an integer; therefore, by using theBinomial expansion in (12), we have

I1 =

m1−1∑l=0

(m1 − 1

l

)

×(α1y + α1C)

(sEs

σ21+ β1

)lyl (Cβ1)

m1−l−1

((sEs

σ21+ β1 − δ1

)y + C(β1 − δ1)

)m1. (27)

From (10) and (27), we get

Mγc(s) = λ2

m1−1∑l=0

(m1 − 1

l

) ( sEs

σ21+ β1

)l(Cβ1)

m1−l−1

(sEs

σ21+ β1 − δ1

)m1

×∫ ∞

0

(α1y + α1C)⎛⎝y + C(β1−δ1)(

sEsσ21

+β1−δ1

)⎞⎠

m1ym2+l−1e−ε2ydy. (28)

By using [16, Eq. (2.3.6.9)], we can solve the integral in (28);and get

Mγc(s) = λ2

m1−1∑l=0

(m1 − 1

l

) ( sEs

σ21+ β1

)l(Cβ1)

m1−l−1

(sEs

σ21+ β1 − δ1

)m1

×[α1Γ(m2 + l + 1)

(C(β1 − δ1)(

sEs

σ21+ β1 − δ1

))m2+l+1−m1

×Ψ(m2 + l + 1,m2 + l+ 2−m1;

ε2C(β1 − δ1)sEs

σ21+ β1 − δ1

)

+α1CΓ(m2 + l)

(C(β1 − δ1)(

sEs

σ21+ β1 − δ1

))m2+l−m1

×Ψ(m2 + l,m2 + l+ 1−m1;

ε2C(β1 − δ1)sEs

σ21+ β1 − δ1

)]. (29)

By substituting σ20 = σ2

1 = σ22 = σ2 and γ = Es/σ

2 in (29);and considering the terms corresponding to l = m1 − 1, weget (18).

REFERENCES

[1] P. Chini, G. Giambene, and S. Kota, “A survey on mobile satellitesystems,” Int. J. Sat. Commun., vol. 28, no. 1, pp. 29–57, Aug. 2009.

[2] G. G. Kota and S. Kim, “Satellite component of NGN: integrated andhybrid networks,” Int. J. Sat. Commun., vol. 29, no. 3, pp. 191–208,May 2010.

[3] B. Evans, M. Werner, E. Lutz, M. Bousquet, G. Corazza, G. Maral, andR. Rumeau, “Integration of satellite and terrestrial systems in futuremultimedia communications,” IEEE Trans. Wireless Commun., vol. 12,no. 5, pp. 72–80, Oct. 2005.

[4] N. Chuberre, O. Courseille, P. Laine, L. Roullet, T. Quignon, andM. Tatard, “Hybrid satellite and terrestrial infrastructure for mobilebroadcast services delivery: an outlook to the unlimited mobile TVsystem performance,” Int. J. Sat. Commun., vol. 26, no. 5, pp. 405–426, Aug. 2008.

[5] S. Morosi, S. Jayousi, and E. D. Re, “Cooperative delay diversityin hybrid satellite/terrestrial DVB-SH system,” in Proc. 2010 IEEEInternational Conference on Communications, pp. 1–5.

[6] D.-S. Ahn, S. Kim, H. W. Kim, and D.-C. Park, “A cooperative transmitdiversity scheme for mobile satellite broadcasting systems,” Int. J. Sat.Commun., vol. 28, no. 5-6, pp. 352–368, May 2010.

[7] G. Cocco, C. Ibars, and O. del Rio Herrero, “Cooperative satellite toland mobile gap-filler-less interactive system architecture,” in Proc. 5thAdvanced Satellite Multimedia Systems Conference and 11th SignalProcessing for Space Communications Workshop, pp. 309–314.

[8] B. Paillassa, B. Escrig, R. Dhaou, M.-L. Boucheret, and C. Bes,“Improving satellite services with cooperative communications,” Int. J.Sat. Commun., vol. 29, no. 6, pp. 479–500, Oct. 2011.

[9] A. Iqbal and K. M. Ahmed, “A hybrid satellite-terrestrial cooperativenetwork over non identically distributed fading channels,” J. Commun.,vol. 7, pp. 581–589, 2011.

[10] A. Abdi, W. Lau, M.-S. Alouini, and M. Kaveh, “A new simple modelfor land mobile satellite channels: first and second order statistics,” IEEETrans. Wireless Commun., vol. 2, no. 3, pp. 519–528, May 2003.

[11] V. K. Sakarellos and A. D. Panagopoulos, “Outage performance ofcooperative land mobile satellite broadcasting systems,” in Proc. 2013European Conference on Antennas and Propagation, pp. 473–476.

[12] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, andProducts, 6th ed. Academic Press, 2000.

[13] M. K. Simon and M.-S. Alouini, Digital Communication over FadingChannels. John Wiley & Sons, Inc., 2005.

[14] M. McKay, A. Zanella, I. Collings, and M. Chiani, “Error probabilityand SINR analysis of optimum combining in Rician fading,” IEEETrans. Commun., vol. 57, no. 3, pp. 676–687, Mar. 2009.

[15] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.Dover Publications, Inc., 1972.

[16] A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals andSeries, Vol. 1, 4th ed. Taylor and Francis, 2002.