Subcarrier BPSK Modulated FSO Communications with ... - IEEE Xplore

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Ahstract-A free-space optical communication system using subcarrier binary phase-shift keying modulation is analyzed for Gamma-Gamma turbulence channels ...
2013

IEEE

Wireless Communications and Networking Conference (WCNC):

PHY

Subcarrier BPSK Modulated FSO Communications with Pointing Errors Xuegui Song, Student Member, IEEE, Fan Yang, and Julian Cheng, Member, IEEE School of Engineering The University of British Columbia, Kelowna, BC, Canada Email: {xuegui.song.fan.yang.julian.cheng}@ubc.ca

Ahstract-A free-space optical communication system using subcarrier binary phase-shift keying modulation is analyzed for Gamma-Gamma turbulence channels with pointing errors. We study the bit-error rate performance of such system and obtain highly accurate bit-error rate approximations using a series expansion approach. Asymptotic error rate analysis is also presented. Our asymptotic analysis reveals some unique transmission characteristics of such system.

I. INTRODUCTION Performance of free-space optical (FSO) communication systems in atmospheric turbulence has been studied exten­ sively in the literature. The turbulence induced fading is a major source of performance degradation for FSO cormnu­ nications. Besides the turbulence induced fading, the effects of pointing errors due to building sway caused by dynamic wind loads, thermal expansion, and weak earthquakes can also degrade the performance of FSO cormnunications [1]- [4].

Recently, FSO cormnunication systems with pointing errors have gained increasing attention. In [1]- [3], Arnon et al. studied the combined effect of atmospheric turbulence and misalignment on the bit-error rate (BER) performance of an on-off keying (OOK) based FSO system assuming the detector size is negligible. However, the authors did not propose a composite FSO channel model. This problem was tackled by Farid and Hranilovic [4] who explicitly considered the effect of beam width, detector size, and jitter variance, and derived a closed-form probability density function (PDF) of the composite channel with lognormal turbulence. However, the PDF of their composite channel model with Gamma­ Gamma turbulence was only presented by an integral with no closed-form expression. Later, Sandalidis et al. presented a closed-form expression for the PDF of composite FSO channel with K-distributed turbulence in terms of the Meijer's G­ function and studied the BER performance of such system [5]. The authors also extended their result to the Gamma-Gamma turbulence in [6]. Using this extended channel model and an approximation of the complementary error function, Gappmair et al. studied the error rate performance of a pulse position modulation (PPM) based system in [7]. In [8], Sandalidis also studied the error rate performance for coded FSO links over strong turbulence with misalignment. These works do not reveal any additional insights into the FSO systems with pointing errors due to the complex form of the Meijer's G­ function. More recently, Gappmair et al. considered different

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jitter in horizontal and vertical directions, and they modeled the composite FSO channel by a Hoyt distribution [9]. Based on this generalized composite channel model, they studied the BER performance of an OOK system by approximating the BER expression in terms of a finite series. Unfortunately, their series solution does not apply to all operation conditions. In [10], Garcia-Zambrana et al. studied the outage performance of a multiple-input and multiple-output OOK system over the exponential turbulence channels with pointing errors. Later, in [11], the same authors also studied the asymptotic BER performance for FSO systems using transmit laser selection over the Gamma-Gamma atmospheric turbulence channels with pointing errors. Their results are based on a Taylor series expansion of the Meijer's G-function. However, in both [10] and [11] the authors did not study the BER performance for finite signal-to-noise ratio (SNR) values, which is of practical interest. In this work, using the same series expansion formula [12] we study the BER performance for subcarrier binary phase­ shift keying (BPSK) modulated FSO systems in the Gamma­ Gamma atmospheric turbulence with pointing errors. We obtain highly accurate closed-form series BER expressions. Unlike previous work in [9], our novel series solutions are valid for any SNR values and can be applied to any operation conditions. Furthermore, our series solutions are suitable for asymptotic analysis. II. SUBC ARRlER INTENSIT Y MODUL ATION At the transmitter, an RF signal m(t) pre-modulated by the data source is used to modulate a continuous wave laser beam after being properly biased. The transmitted power, Pt(t), of the modulated laser beam can be written as

Pt(t)

=

P[l +�m(t)l

(1)

where P is the average power, and � is the modulation index satisfying the condition -1 < �m(t) < 1 in order to avoid overmodulation. For simplicity, the power of m(t) is normalized to unity. At the receiver, the received optical power is converted into electrical signal through direct detection at the photodetector. This electrical signal is used to recover the transmitted data by using a standard electrical demodulator. In most practical systems, the thermal noise and/or shot noise at the receiver can be modeled with high accuracy as additive white Gaussian

4261

noise (AWGN) [13]. For an atmospheric turbulence channel, the photocurrent at the receiver can be written as

(2)

ir(t)= PRI(t)[l +�m(t)l +n(t)

where R is the photodetector responsivity, I(t) is the instanta­ neous channel gain, n(t) is a zero-mean AWGN due to thermal noise and has variance ()�. I (t) is assumed to be a stationary random process which is caused by both atmospheric turbu­ lence and pointing errors. The sample I = I( ) t lt=to at time instant t= to gives the random variable (RV) I having PDF

parameter rp plays an important role when studying large SNR performance. The equivalent beam width WZeq can be calculated as

WZeq = Wz 2 (4)

Using

and

h(I)=

h(I)·

To study the BER performance of the considered system, we define the instantaneous SNR at the input of the electrical demodulator as the ratio of the time-averaged AC photocurrent power to the total noise variance [14], and it can be expressed as

! [ v exp( v ]

X

(5),

.j7rerf(v)

(6)

- 2)

we obtain the composite PDF of

"+13

I

as

2rp2(0: 13) 2

cp2

can be calculated as

p,oo

2

=

[21]

af( + t 3/2)__ (t+1) . 2fo( + t l) '

(32)

From (17), (28) and (32), we conclude that the diversity or­ der of subcarrier BPSK modulated FSO system in the Gamma­ Gamma turbulence channels with pointing errors depends on the smaller value of cp2 and 13. This observation agrees with the conclusion made in [11] for an OOK based IM/DD system. More specifically, the diversity order is Cd min{f3, cp2}. =



B. Numerical Results

We follow the numerical settings in Section IV-B and con­ sider a weak turbulence condition (0 4.03,13 3 .45) and the jitter standard deviation a sir 3. Under this operation condition, we have 0 > cp2. =

=

=

and

lim jy(y) y-+O

=

C

JL(JL - 1) ... (JL - k+1)

( x+yt

where the integral equals a constant. Using Proposition 1 in [21], we obtain diversity order Cd cp2/2 and coding gain

(29)

In Fig. 2, we set B 5, N J 30 in (28) to approximate the exact BER of Gamma-Gamma fading with pointing errors. It can be seen from Fig. 2 that the approximate BER obtained from (28) can achieve remarkable accuracy over a wide range of transmission power. Asymptotic BER is also presented to reveal the BER behavior in large transmitted optical power region. =

=

=

VI. CONCLUSIONS In this paper, we have developed highly accurate c1osed­ form BER expressions for subcarrier BPSK modulation in Gamma-Gamma turbulence with pointing errors. Unlike pre­ vious studies, our series solutions are valid under all operation conditions, and are more suitable for asymptotic analysis.

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}

(24)

(27)

(28)

10

-1

ITTT ' 'TT,. , , �I"TT" ", ITGITGITT"TGF=======I:jJ -- Exact ' '

o

Series approximation

- - - Asymptotic

:::::;:-::" . . . . . . � .

-8

. . . . . . . . . . . . . . .

:, :::::;:.:::::::.:::::::-:::::::, . ' ., . . . . . . . . . . . . . . .

. . . . . .

L-__�__-L____L-__�__-L____L-__�__-L____L-� 10 -8 4 2 -2 -6 6 8 o -4 -10

10

Transmitted Optical Power, P (dBm)

Fig, 2. BERs of subcanier BPSK modulated FSO system over Gamma­ Gamma turbulence channels with pointing errors for a 4.03, f3 3.45, wz/r 10, as/r 3 (a > r.p2). =

=

=

=

REFERENCES [I] S. Arnon, "Effects of atmospheric turbulence and building sway on optical wireless-communication systems," Opt. Lett. vol. 28, pp. 129131, Jan. 2003. [2] D. Kedar and S. Arnon, "Optical wireless communication through fog in the presence of pointing errors," Appl. Opt., vol. 42, pp. 4946-4954, Aug. 2003. [3] S. Arnon, "Optimization of urban optical wireless communications systems," IEEE Trans. Wireless Commun., vol. 2, pp. 626-629, July 2003. [4] A. A. Farid and S. Hranilovic, "Outage capacity optimization for free space optical links with pointing errors," IEEEIOSA 1. Lightwave Tee/mo/., vol. 25, pp. 1702-1710, July 2007. [5] H. G. Sandalidis, T. A. Tsiftsis, G. K. Karagiannidis, and M. Uysal, "BER performance of FSO links over strong atmospheric turbulence channels with pointing errors," IEEE Commun. Lett., vol. 12, pp. 44-46, Jan. 2008. [6] H. G. Sandalidis, T. A. Tsiftsis, and G. K. Karagiannidis, "Optical wireless communications with heterodyne detection over turbulence channels with pointing errors," 1. Lightwave Technol., vol. 27, pp. 44404445, Oct. 2009.

[7] w. Gappmair, S. Hranilovic, and E. Leitgeb, "Performance of PPM on terrestrial FSO links with turbulence and pointing errors," IEEE Commun. Lett., vol. 14, pp. 468-470, May 2010. [8] H. G. Sandalidis, "Coded free-space optical links over strong turbulence and misalignment fading channels," IEEE Trans. Commun., vol. 59, pp. 669-674, Mar. 2011. [9] w. Gappmair, S. Hranilovic, and E. Leitgeb, "OOK performance for ter­ restrial FSO links in turbulent atmosphere with pointing errors modeled by Hoyt distributions," IEEE Commun. Lett., vol. 15, pp. 875-877, Aug. 2011. [10] A. Garcia-Zambrana, C. Castillo-Vazquez, and B. Castillo-Vazquez, "Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels," Opt. Express, vol. 19, pp. 13480-13496, July 2011. [11] A. Garcia-Zambrana, B. Castillo-Vazquez, and C. Castillo-Vazquez, "Asymptotic error-rate analysis of FSO links using transmit laser selec­ tion over gamma-gamma atmospheric turbulence channels with pointing errors," Opt. Express, vol. 20, pp. 2096-2109, Jan. 2012. [12] X. Song, M. Niu, and 1. Cheng, "Error rate of subcarrier intensity modulations for wireless optical communications," IEEE Commun. Lett., vol. 16, pp. 540 - 543, Apr. 2012. [13] X. Zhu and J. M. Kahn, "Free-space optical communication through atmospheric turbulence channels," IEEE Trans. Commun., vol. 50, pp. 1293-1300, Aug. 2002. [14] G. P. Agrawal, Fiber-Optical Communication Systems, 3rd ed., New York: Wiley, 2002. [15] A. AI-Habash, L. C. Andrews, and R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Opt. Eng., vol. 40, pp. 1554-1562, Aug. 2001. [16] L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Bellingham, WA: SPIE Press, 2001. [17] N. Wang and J. Cheng, "Moment-based estimation for the shape parameters of the Gamma-Gamma atmospheric turbulence model," Opt. Express, vol. 18, pp. 12824-12831, June 2010. [18] M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques: Signal Design and Detection, New Jersey: Prentice-Hall, 1995. [19] M. K. Simon, Probability Distributions Involving Gaussian Random Variables, New York: Springer, 2002. [20] I. S. Gradshteyn and l. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. San Diego: Academic Press, 2000. [21] Z. Wang and G. Giannakis, "A simple and general parameterization quantifying performance in fading channels," IEEE Trans. Commun., vol. 51, pp. 1389-1398, Aug. 2003.

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