Use of satellite natural vibrations to improve performance of free-space satellite laser communication Shlomi Arnon
In some of the future laser communication satellites, it is plausible to assume that tracking and communication receivers will use the same detector array. The reason for dual use of the detector is to design simpler and less expensive satellites. Satellites vibrate continually because of their subsystems and environmental sources. The vibrations cause nonuniform spreading of the received energy on the detector array. In view of this, the information from the tracking system is used to adapt individually the communication signal gain of each of the detectors in the array. This adaptation of the gains improves communication system performance. It is important to emphasize that the communication performance improvement is achieved only by gain adaptation. Any additional vibrations decrease the tracking and laser pointing system performances, which decrease the return communication performances ~two-way communication!. A comparison of practical communication systems is presented. The novelty of this research is the utilization of natural satellite vibrations to improve the communication system performance. © 1998 Optical Society of America OCIS codes: 350.6090, 060.4510, 120.7280.
1. Introduction
Communication from any one place to another on Earth is an attractive goal. One method to achieve this aim is to network satellites that cover the globe. The use of optical intersatellite links has some advantages compared with microwave intersatellite links. The advantages of the optical intersatellite links are ~a! smaller size and weight of the terminal, ~b! less transmitter power, ~c! higher immunity to interference, and ~d! larger data rate. The main disadvantage of optical intersatellite links is the complex tracking and pointing system. The complexity of the pointing system derives from the necessity to point from one satellite to another over a distance of tens of thousands of kilometers with a beam divergence angle of microradians when the satellites move and vibrate. To meet the pointing requirement the satellites use the Ephemerides data ~the position of the satellite according to the orbit equation! and navigation system for rough pointing, and a tracking
The author is with the Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel. email address:
[email protected] Received 1 December 1997; revised manuscript received 24 March 1998. 0003-6935y98y215031-06$15.00y0 © 1998 Optical Society of America
system for fine pointing to another satellite. The basic and popular method of tracking between satellites includes the use of a beacon signal and tracking system with a quadrant detector on each satellite of the communication channel. In some future satellites, it is plausible to assume that tracking and communication receivers will use the same detector. The reason for dual use of the detector is the possibility to design simple satellites at a reduced cost. Satellites vibrate continually because of their subsystem operation and environmental sources. The satellite sources of vibrations and impacts1 can be split into two main groups: external sources and internal sources ~Fig. 1!. The external sources include the impact of micrometeorites; the gravitation fields of the Sun, the Moon, the Earth, and other celestial bodies; solar radiation pressure; and satellite structure bending that is due to temperature differences. The internal sources include vibration and impact that are due to navigation noise, thruster operation, the antenna pointing mechanism, the solar array driver, tracking noise, and operation of other satellite subsystems. From this short review it is easy to understand that satellites suffer continually from vibrations and impacts. The concept of optical intersatellite links in communication satellite networks is described in Refs. 2 and 3. Analyses of the performances of satellite optical communication networks are described in Refs. 4 and 5. Results of onboard measurements of satel20 July 1998 y Vol. 37, No. 21 y APPLIED OPTICS
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Fig. 1. Vibration and impact sources.
Fig. 2. Adaptive receiver.
lite vibration spectra are specified in Ref. 6. Skormin et al. described adaptive techniques to reduce the effects of vibrations on the pointing system.7 Chen and Gardner8 analyzed the effect of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links. Arnon and Kopeika9 have presented the concept of adaptive suboptimum detection of optical pulse position modulation ~PPM! signals with a detection matrix and centroid tracking. Lambert and Casey10 described most of the concepts of laser communication in space. In this research we deal with a system that uses a single detector array for both tracking and communication. The detector array includes four detectors ~quadrant detector!. Satellite vibrations cause nonuniform spreading of the received energy on the quadrant detector. In view of this, we use the signal from the tracking system to adapt individually the communication signal gain of each detection element. This adaptation of the gains improves the communication system performance. It is important to emphasize that it is the adaptive gain amplifiers that improve the communication system performance, not additional vibrations. Higher vibration amplitude decreases the tracking system performance, which decreases the return communication ~two-way communication! performance. Our model is derived for PPM. Comparison of practical communication systems is presented. For the parameters of the example, the bit error rate ~BER! improvement is more than twice that of the standard system under certain conditions. The novelty of our research is the utilization of natural satellite vibrations to improve the communication system performance.
summation unit for communication signals. The communication flow is as follows. The messages arrive at the input of the transmitter. The transmitter converts electrical pulses to optical laser pulses. The transmitter telescope collimates the laser radiation in the receiver satellite direction. The optical pulse radiation is received by the telescope and focused on the center of the quadrant detector. The quadrant detector converts optical signal to electronic signals for tracking and communication. The communication amplifiers amplify the communication signals. The summation unit sums the communication signals. A decision unit decides on the kind of information received according to the summed signal amplitude and arrival time. The tracking system tracks the other satellite according to the proportion between the tracking signals from the quadrant detector. We use the tracking system for two main purposes: ~a! pointing the satellite receiver in the direction of the transmitter and ~b! pointing a laser beam from the receiver satellite to the transmitter satellite for the return communication ~two-way communication!. Because of vibration of the satellite the received beam spot moves from the center of the quadrant detector to the edge. The control unit adapts the gain of each amplifier according to information from the tracking system, which gives an update of the position of the beam spot on the detector surface and knowledge of the spot dimensions. In the limit, if the spot is on one quadrant, the control unit attenuates the gain of all the other quadrants to zero. This procedure improves the performance of the communication system. It is important to understand that we do not intend to add more vibrations to the satellite to improve the receiver performance. Additional vibrations or receiver dithers decrease the tracking and pointing system performance, which deteriorates the return communication system performance. In this research, we propose to use only the natural vibrations of the satellites. It is for these natural vibration amplitudes that the tracking and pointing system have been designed.
2. Model Description
In this section the scheme of the proposed communication system is defined. The receiver ~Fig. 2! includes a detector array with four detectors ~quadrant detector! for both tracking and communication and a tracking system. The receiver also includes an array of gain control amplifiers, a control unit, and a 5032
APPLIED OPTICS y Vol. 37, No. 21 y 20 July 1998
3. Range Equation Model
The range equation relates the transmitted power and the receiver and transmitter parameters to the received power. The distance between the transmitter and the receiver satellite is z meters. The received power is PR 5 PThRhT GR GT@ly~4pz!#2,
(1)
where hR, hT and GR, GT are the optical efficiencies and the telescope gain of the receiver and the trans-
where PR is the received optical power from Eq. ~1!. In this analysis the conditions ~b2 1 a2! # Rs2 and Rs ,, RD are satisfied, where a and b are the coordinates of the center of the spot on the x and y axes, respectively, and RD is the detector radius. The second condition means that no part of the incident energy is going to be lost in one or more quadrants. This is a practical requirement. In the following equations, we calculate the optical power on each of the detection elements. The optical power received by the first quadrant is given by
[
fR0.5[aRsa 1 bRsb 1 2ab 1 Rs2~sin 2 1 sin 1)] fR0.5~aRsa 1 bRsb 1 2ab 1 Rs2~sin 2 2 sin 1) 1 pRs2
P~1! 5
b,0 . b$0
(5)
The optical power received by the second quadrant is given by P~2) 5
[
fR0.5[2aRsa 1 bRsb 1 2ab 1 Rs2~sin 1 2 sin 2)] fR0.5~2aRsa 1 bRsb 2 2ab 2 Rs2~sin 1 1 sin 2) 1 pRs2!
b,0 . b$0
(6)
The optical power received by the third quadrant is given by P~3! 5
[
2 fR0.5~aRsa 1 bRsb 2 2ab 1 Rs2~sin 2 1 sin 1! 2 pRs2! 2 fR0.5[aRsa 1 bRsb 2 2ab 1 Rs2~sin 2 2 sin 1!]
b,0 . b$0
(7)
The optical power received by the fourth quadrant is given by P~4! 5
[
2 fR0.5~ 2 aRsa 1 bRsb 1 2ab 1 Rs2~sin 1 2 sin 2! 2 pRs2! 2 fR0.5[ 2 aRsa 1 bRsb 1 2ab 2 Rs2~sin 2 1 sin 1!]
mitter, respectively; the wavelength of the laser transmitter is l; and PT is the optical laser transmitter power. The gain of the receiver telescope is8
S D
(2)
4. Received Optical Power
Here the position of the laser beam spot center in the energy distribution model is assigned to estimate the received optical power by each detection element. For a circular lens of diameter DR we can approximate the Airy disk in the focal plane by the uniform intensity function, so the spot radius is RS 5 1.22lfcyDR, (3) where l is the wavelength and fc is the focal length. In practical applications the spot radius is much larger than the diffraction limit, which can be achieved by intentionally defocusing the spot in the focal plane. The optical power density on the detector surface is fR 5 PRy~pRs2!,
(4)
(8)
where
2
pDR GR 5 , l where DR is the receiver diameter aperture.
b,0 , b$0
Rsa 5 ~Rs2 2 a2!0.5,
(9)
Rsb 5 ~Rs2 2 b2!0.5,
(10)
sin 1 5 arc sin~RsbyRs!,
(11)
sin 2 5 arc sin~ayRs!.
(12)
5. Signal and Noise Model
In this section the electronic signals and noises for each detection element based on the previous equations are calculated. The receiver in our system includes an avalanche photodiode ~APD! detector. The electronic noise variance without optical signal is created by three different sources, i.e., Johnson noise, dark current noise, and background shot noise. Consequently11,12 s02~1! 5 2qRPB F~M! M 2B 1 2qID F~M! M 2B 1
4kB BTe , RL
(13)
where PB is the optical background power, ID is the photodiode dark current, RL is the load resistance, Te 20 July 1998 y Vol. 37, No. 21 y APPLIED OPTICS
5033
is the noise temperature of the electronic system, M is the avalanche multiplication value, q is the electron charge, B is the electronic bandwidth, h is Planck’s constant, F~M! is the excess noise factor, R is the response of the APD, and kB is Boltzmann’s constant. The electronic noise variance for the received signal includes the above three sources as well as the signal shot noise and the laser relative intensity noise.10,11 It is given by
7. Instantaneous Bit Error Rate
The mathematical model for BER probability for an N-ary PPM is8
3
2
2
1 10RINy10~RMP~i!!2B,
i 5 1 . . . 4, (14)
where RIN is the relative intensity noise factor. The electronic signal for a received optical signal is given by m1~i! 5 RMP~i!, i 5 1 . . . 4.
(15)
The electronic signal without the received optical signal is given by m1~i! 5 0,
i 5 1 . . . 4.
~ y 2 m0!2 exp 2 dy 2s02 2`
(17)
where h is the quantum efficiency and n is the optical radiation frequency. The excess noise factor is12 F~M! 5 KeffM 1 ~1 2 Keff!~@2 2 ~1yM!#,
(18)
where Keff is the effective ratio of the ionization coefficients.
NA 5
4
( A~i!m ~i!,
m1 5
(19)
1
dx
N , 2~N 2 1!
a~N! 5
, (23)
(24)
1
Î2p s1~ Î2p s0!N21
.
(25)
The A~i! in Eqs. ~19!–~22! that suboptimizes the BER in Eq. ~23! is m1~i! 2 m0~i! . 2s02~i!
(26)
Equation ~26!, as confirmed in Ref. 9, implies that one should weigh quadrant gain based on the ratios between the signal and noise. In the limit, if the laser spot is on one quadrant, one should attenuate the gain of all the other quadrants to zero. 8. Average Bit Error Rate
The average BER of the communication system is given by
6. Cumulative Signal and Noise
The sum of the signal and noise from the four detection elements is now calculated. The cumulative electronic signal for receiving the optical signal is given by
N21
where
A~i! 5
R 5 qhyhn,
~ x 2 m1!2 2s12
exp 2
x
(16)
The response of the APD is
`
2`
s1 ~i! 5 s0 ~1! 1 2qRP~i! F~M! M B 2
F S* F G H* F G J DG
BER 5 NA 1 2 a~N!
ABER 5 ~1 2 nTd!BERs 1 n
*
Td
BER~t!dt, (27)
0
where the BERs is calculated from Eqs. ~23! and ~19!– ~22! for a 5 b 5 0, n is the impact per second, and Td is the impact duration. A condition to be satisfied is
i51
where A~i! is a special spatial filter that can be used to determine the individual signal gain for each detection element. The cumulative electronic signal without an optical signal is given by 4
( A~i!m ~i!.
m0 5
(20)
0
i51
The cumulative noise standard deviation when one receives an optical signal is given by
H(
J
1y2
4
s1 5
@A~i!s1~i!#2
i51
.
(21)
The cumulative noise standard deviation without an optical signal is given by
H(
s0 5
i51
5034
J
1y2
4
@A~i!s0~i!#
2
H( J
1y2
4
5 s0~1!
@A~i!#
2
. (22)
i51
APPLIED OPTICS y Vol. 37, No. 21 y 20 July 1998
nTd # 1.
(28)
9. Practical Example
The situation considered here is communication between two low Earth orbit satellites. The satellites are placed at an orbit altitude of approximately 1400 km. The distance between the satellites is assumed to be 4500 km. In this example we compare two systems: a standard and the adaptive. The standard system has constant and equal gain amplifiers. The adaptive system adapts the gain of the individual amplifiers according to Eq. ~26!. All the system parameters are described in detail in Table 1. The temporal response of the steering system10,13 was simulated by a second-order differential equation. The temporal response equations are a~t! 5
[email protected] exp~2300t!sin~p1600t! 1 exp~21500t!# and b~t! 5
[email protected] exp~2300t!sin~p1600t! 1 exp~21500t!#. The results of the simulation are presented in Fig. 3,
Table 1. Practical System Parameters
Parameter
Symbol
Value
Relative intensity noise Optical wavelength APD gain Dark current Effective ratio of the ionization Quantum efficiency Noise temperature of the electronic system Resistance of preamplifier resistor Optical background power Transmitter power Transmitter gain Receiver telescope diameter Receiver optics efficiency Transmitter optics efficiency Distance between the satellites Bit rate-electronic bandwidth PPM word length Impact duration
RIN l M ID Keff h T
2145 dByHz 0.8 mm 150 ln A 0.001 0.8 500 K
RL PB PT GT DR hR hT z BW N Td
100V 10 pW 100 mW 4 3 1010 0.2 m 0.8 0.8 4500 km 5 Gbitsys 4 0.5 ms
Fig. 4. Average BER as a function of impactys. Td is equal to 0.5 ms.
10. Discussion and Summary
where one can see the normalized temporal response of a and b @Eqs. ~5!–~8!# as a function of time. The received spot radius Rs is equal to unity. From Fig. 3 it is easy to see that the response converges to a very low value after 0.05 ms. Figure 4 shows the average BER @Eq. ~27!# as a function of impact per second and the impact duration of 0.5 ms. Figure 4 has two curves: the upper is for the standard system and the lower is for the adaptive system. Two interesting points are clear from Fig. 4: the increase in BER of the standard system and the improvement of the adaptive system, both as functions of impact per second. The increase in BER of the standard system is due to the RIN @see Eq. ~14!#. Figure 4 also shows that the adaptive system achieves an improvement of twice the BER of that of the standard system for an impact per second rate greater than 1500 impactys.
Fig. 3. Temporal response of a fast steering mirror as a function of time.
This analysis points out that by use of natural satellite vibrations it is possible to improve communication system performance. The implementation of this model is simple. Only two changes are required: the replacement of the amplifier array by a tunable gain amplifier array and the addition of a gain control unit. The author is grateful to N. S. Kopeika and S. R. Rotman of Ben Gurion University and for the support of the Ministry of Science and Technology, Jerusalem. References and Notes 1. S. Arnon and N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646 –1661 ~1997!. 2. B. I. Edelson and G. Hyde, “Laser satellite communications, program technology and applications,” report of the IEEE-USA Aerospace Policy Committee ~Institute of Electrical and Electronics Engineers, New York, 1996!. 3. Motorola Global Communication, “Application for Celestri multimedia LEO system” before the Federal Communication Commission, Washington, D.C. ~June 1997!. 4. S. Arnon and N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations: analog case,” Opt. Eng. 36, 175–182 ~1997!. 5. S. Arnon, S. Rotman, and N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations: digital case,” Opt. Eng. 36, 3148 – 3157 ~1997!. 6. M. Wittig, L. van Holtz, D. E. L. Tunbridge, and H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected papers on Free-Space Laser Communications II, D. L. Begly and B. J. Thompson, eds., Vol. MS100 of SPIE Milestone Series ~SPIE Press, Bellingham, Wash., ~1994!, pp. 389 –398. 7. V. A. Skormin, M. A. Tascillo, and T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 ~1995!. 8. C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent opti20 July 1998 y Vol. 37, No. 21 y APPLIED OPTICS
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cal intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 ~1989!. 9. S. Arnon and N. S. Kopeika, “Adaptive suboptimum detection of an optical pulse-position modulation signal with a detection matrix and centroid tracking,” J. Opt. Soc. Am. 15, 443– 448 ~1998!. 10. S. G. Lambert and W. L. Casey, Laser Communication in Space ~Artech House, Norwood, Mass., 1995!. 11. L. Kazovsky, S. Benedetto, and A. Willner, Optical Fiber Com-
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APPLIED OPTICS y Vol. 37, No. 21 y 20 July 1998
munication Systems ~Artech House, Norwood, Mass., 1996!, Chap. 1, pp. 78 –79; Chap. 3, pp. 163–252. 12. R. M. Gagliardi and S. Karp, Optical Communication, 2nd ed. ~Wiley, New York, 1995!, Chap. 3, p. 81; Chap. 4, pp. 119 –150. 13. V. A. Skormin, C. R. Herman, M. A. Tascillo, and D. J. Nicholson, “Mathematical modeling and simulation analysis of a pointing, acquisition, and tracking system for laser based intersatellite communication,” Opt. Eng. 32, 2749 – 2763 ~1993!.
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