Vol. 6, No. 12 / December 2007 / JOURNAL OF OPTICAL NETWORKING 1323

Antenna aperture averaging withdifferent modulation schemes

for optical satellite communicationlinks

Anoop Kumar1 and V. K. Jain1,2,*1Department of Electrical Engineering, Indian Institute of Technology, Delhi,

New Delhi 110016, India2E-mail: vkjain@ee.iitd.ac.in

*Corresponding author: anoop_opto@yahoo.co.in

Received September 19, 2007; accepted October 8, 2007;published November 7, 2007 �Doc. ID 84710�

The performance of the optical satellite communication links is degraded inatmospheric environment. The degradation is more in the case of an on–offkeying (OOK) modulation scheme. The antenna aperture averaging method isused to improve system performance for different modulation schemes. Withthis method, it is found that improvement in system performance employingOOK modulation is higher as compared to subcarrier binary phase-shift key-ing and subcarrier quadrature phase-shift keying modulation schemes.© 2007 Optical Society of America

OCIS codes: 060.0060, 060.4510.

1. IntroductionSatellite-to-satellite communication links at optical wavelength in the free space isalready established [1,2]. Atmospheric optical links between an earth station and low-earth orbit satellite (as shown in Fig. 1) are in the research and development stage.Intensity modulation with direct detection system is widely used in both wireless andwired optical communication systems [3]. Communication through the atmosphereresults in signal distortion because the amplitude and phase of the beam are ran-domly varied over the propagation path. Atmospheric turbulence gives rise to distor-tions due to scintillation that are detected at the receiver and thereby corrupt the sig-nal information. Minimization of the phase distortion and subsequently the intensityvariations can be achieved by reducing the bandwidth or by using the aperture aver-aging method [4]. On the basis of the analysis given in this paper, it has been shownthat the on–off keying (OOK) signaling scheme, which was not usable due to severedegradation in the performance at high turbulence strength, can be used in satellitecommunication with aperture averaging. This is a very significant result from thepractical point of view.

2. Lognormal ScintillationIn an optical wireless communication for an intensity modulation system, the receivedoptical intensity P�t� can be written as

P�t� = X�t�Ps�t� + n�t�, �1�

where X�t� is a stationary random process with lognormal distribution due to turbu-lence, Ps�t� is the received optical intensity by the receiver without turbulence, andn�t� is the additive white Gaussian noise (AWGN). As random variable X has lognor-mal distribution, its probability density function (PDF) is given by [3]

fX�x� =1

�2��Xxe−��ln x + �X

2 �2/2�X2 �, �2�

where variance �X2 depends upon the turbulence condition and propagation path

length.

1536-5379/07/121323-6/$15.00 © 2007 Optical Society of America

Vol. 6, No. 12 / December 2007 / JOURNAL OF OPTICAL NETWORKING 1324

3. Aperture Averaging Factor and Atmospheric ScintillationAn optical receiver with a very small aperture will produce a random signal. If theaperture diameter is larger than the spatial width of the irradiance fluctuations, thereceiver will average out fluctuations over the aperture, and the signal fluctuationswill be less than those from a point receiver. This phenomenon is known as apertureaveraging.

The aperture averaging factor A is defined as the ratio of the variance of the signalfluctuations from a receiver with aperture diameter D to that from a receiver with aninfinitesimally small aperture. The factor A can be approximated as [4]

A ��1 + A0� D2

�h0 sec �7/6−1

, �3�

where A0�1.1 is a constant; � is the zenith angle; and h0 is the atmospheric turbu-lence aperture averaging scale height, which is given by

h0 = � �0

L

dzCn2�z�z2

�0

L

dzCn2�z�z5/6

6/7

. �4�

Equation (3) gives the aperture averaging factor in closed form for space-to-groundpropagation conditions and is applicable for a broad class of atmospheric turbulencemodels.

In this paper, the Hufnagel–Valley boundary model [5] of atmospheric turbulence isused for computation of h0. In weak turbulence, the irradiance variance �int

2 in termsof log-amplitude variance �X

2 without the aperture averaging method is given by [5]

�int2 = exp�4�X

2 � − 1. �5�

With aperture averaging, the right-hand side of Eq. (5) will get multiplied with thefactor A. In that case, corresponding variance of log-amplitude will become

�X�2 =

1

4ln�A�exp�4�X

2 � − 1� + 1�. �6�

4. Performance Evaluation4.A. OOK Modulation SchemeIn this case, the bit error rate (BER) is given by

Fig. 1. Laser communication between satellite and ground station [1].

Vol. 6, No. 12 / December 2007 / JOURNAL OF OPTICAL NETWORKING 1325

Pe = P0P�r � T/OFF� + P1P�r � T/ON�, �7�

where P0 and P1 are the transmission probability of bits “0” and “1,” respectively. Fur-ther, P�r�T /OFF� and P�r�T /ON� are BERs corresponding to bits 0 and 1, respec-tively.

As the signal transmitted corresponding to bit 0 is zero, the received signal corre-sponding to this bit will have only AWGN. However, for bit 1 both scintillation andAWGN are present. Therefore, P�r�T /OFF� and P�r�T /ON� are given by [3]

P�r � T/OFF� =�T

�

p�r/OFF�dr, �8�

P�r � T/ON� =�−�

T

p�r/ON�dr, �9�

where p�r /OFF� and p�r /ON� are PDFs of the electrical signal when bits 0 and 1 aresent, respectively. If the variance of AWGN noise is �n

2, PDF of the electrical signalwhen bit 0 is sent is given by [3]

p�r/OFF� =1

�2��n

e�−r2/2�n2�. �10�

The PDF of the received signal when bit 1 is sent is given by convolution of two PDFsas

p�r/ON� = fX�x� � gn�x�, �11�

p�r/ON� =e−�X

2 /2

2��X�n�

0

� 1

x2 exp − �� ln2 x

2�X2 +

�r − 2x�2

2�n2 dx, x � 0, �12�

where fX�x� and gn�x� are PDFs of lognormal scintillation and AWGN, respectively, and� represents convolution. The mean value of the received signal corresponding to bit 1is equal to 2e−�X

2 /2. Using Eqs. (7) and (12), BER of OOK modulation scheme withoutaperture averaging in atmospheric environment is given by [3]

Pe = P0Q�T/�n� +e−�X

2 /2�1 − P0�

�2��X�

0

� 1

x2 exp�− � ln2 x

2�X2 +

�r − 2x�2

2�n2 Q�2x − T

�ndx,

�13�

where

Q�x� =�X

� 1

�2�e−t2/2dt.

For receiving antenna aperture diameter D, BER can be obtained by replacing �X2 in

Eq. (13) by �X�2 as

Pe = P0Q�T/�n� +e−�X�

2/2�1 − P0�

�2��X�2 �

0

� 1

x2 exp�− � ln2 x

2�X�2

+�r − 2x�2

2�n2 Q�2x − T

�ndx.

�14�

The Pe for this scheme when there is no turbulence and only AWGN is present, will be[3]

Pe = Q��Eb

�n2 , �15�

where E =1 for normalized bit energy.

b

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4.B. Subcarrier BPSK Modulation SchemeFor this modulation scheme, the threshold is chosen at 0, i.e., T=0 and BER in atmo-spheric environment is given by [3]

Pe =e−�X

2 /2

�2��X�

0

� 1

x2e−ln2 x/2�X2Q�mx

�ndx. �16�

Without turbulence and in presence of AWGN only, it will be [3]

Pe = Q��m2

�n2 , �17�

where m is the modulation index with m� �0,1�. For aperture diameter D, BER isobtained by replacing �X

2 in Eq. (16) by �X�2 as

Pe =e−�X�

2/2

�2��X�2�

0

� 1

x2e−ln2 x/2�X�2Q�mx

�ndx, �18�

where �X�2 and A are same as in the case of OOK modulation scheme.

4.C. Subcarrier QPSK Modulation SchemeAs for binary phase-shift keying (BPSK), in this case also the threshold is chosen at 0,i.e., T=0. With this threshold BER in atmospheric environment is given by [3]

Pe =e−�X

2 /2

�2��X�

0

� 1

x2e−ln2 x/2�X2Q� mx

�2�ndx. �19�

Without turbulence and in presence of AWGN only, the BER will be [3]

Pe = Q��m2

2�n2 . �20�

Following the same approach as in the case of OOK and BPSK signaling schemes,BER with aperture diameter D, is obtained by replacing �X

2 in Eq. (19) by �X�2 as

Pe =e−�X�

2/2

�2��X�2�

0

� 1

x2e−ln2 x/2�X�2Q� mx

�2�ndx, �21�

where �X�2 and A are same as defined earlier.

5. Results and ConclusionsIn the computation of system performance, the value of �X

2 is varied from 0.1 to 0.5.However, with aperture averaging results are presented only for �X

2 =0.5, whichimplies high turbulence. The value of m is taken to be unity. The threshold for OOK

Fig. 2. Variation of BER with SNR for OOK signaling scheme (a) without apertureaveraging for different turbulence strength and (b) with aperture averaging for �X

2

=0.5.

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is chosen as adaptive, i.e., it depends upon turbulence strength and its value is takenas half of the mean of received signal corresponding to bit 1, i.e., T=e−�X

2 /2. The com-puted results are shown in Figs. 2–5.

It is observed from Figs. 2(a) and 3(a) that there is degradation in the performanceof OOK and BPSK signaling schemes due to atmospheric turbulence. Further, degra-dation in the performance of the OOK scheme is much more as compared to, BPSKscheme. With aperture averaging, improvement in the performance for both OOK andBPSK schemes occurs. However, the improvement in OOK is more than that in BPSK.The behavior of the quadrature phase-shift keying (QPSK) scheme is quite similar tothat of BPSK and therefore results for QPSK are not given here.

A comparative performance of all three modulation schemes (OOK, BPSK, andQPSK) for different turbulence strength �X

2 (=0.1 and 0.5) is shown in Fig. 4. For tur-bulence strength of �X

2 =0.5, the improvement in the performance of the above modu-lation schemes with aperture averaging (D=15 cm and 18 cm) is shown in Fig. 5. Thesystem performance with BPSK is always better than OOK and QPSK irrespective ofturbulence strength. At low turbulence, system performance with OOK signaling isbetter than QPSK as shown in Fig. 4(a). However, at high turbulence when the signal-to-noise ratio (SNR) is more than 9 dB [refer to Fig. 4(b)], the performance of OOKbecomes poorer than QPSK and therefore this signaling scheme will not be preferred.

With aperture averaging, improvement in the system performance for OOK is morethan that in QPSK. It is due to the fact that the aperture averaging method averagesout the intensity fluctuations, which are more in OOK signaling. For aperture diam-eter of 10 cm or less, the improvement in performance is not very much. The reasonfor this is that if D���L0 [4] (=12.5 cm for L0=10 km and �=1550 nm) then only theaperture averaging method is effective. For diameters less than this, the aperturesaveraging factor approaches unity and therefore gives no improvement. The perfor-mance of the OOK signaling scheme with aperture averaging �D=18 cm� becomes bet-ter than QPSK and is very close to the performance of BPSK. Therefore, the conclu-

Fig. 3. Variation of BER with SNR for BPSK signaling scheme (a) without apertureaveraging for different turbulence strength and (b) with aperture averaging for �X

2

=0.5.

Fig. 4. Comparison of OOK with subcarrier BPSK and QPSK modulation withoutaperture averaging for turbulence strength (a) �2 =0.1 and (b) �2 =0.5.

X X

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sion of this study is that the OOK signaling scheme, which was unusable because ofthe severe degradation in the performance, can be used in uplink and downlink satel-lite communication systems with the aperture averaging method even at high turbu-lence strength.

References1. M. Toyoda, “Intensity fluctuations in laser links between the ground and a satellite,” Appl.

Opt. 44, 7364–7370 (2005).2. M. Toyoshima, “Trends in satellite communications and the role of optical free-space

communications,” J. Opt. Netw. 4, 300–311 (2005).3. G. S. Mitchell and Q. Lu, “Performance analysis for optical wireless communication systems

using subcarrier PSK intensity modulation through turbulent atmospheric channel,” inIEEE Globecom (IEEE, 2004), pp. 1872–1875.

4. H. T. Yura and W. G. McKinley, “Aperture averaging of scintillation for space to groundoptical communication applications,” Appl. Opt. 22, 1608–1609 (1983).

5. R. K. Tyson “Adaptive optics and ground to space laser communication,” Appl. Opt. 35,3640–3646 (1996).

Fig. 5. Comparison of OOK with subcarrier BPSK and QPSK modulation with aper-ture averaging for turbulence strength �X

2 =0.5 for diameters (a) D=15 cm and (b) D=18 cm.