satellite - IEEE Xplore

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO. 5, SEPTEMBER 2004

Analysis of Optical Coherence Multiplexing Networks for Satellite Communication G. Kats and Schlomi Arnon

Abstract—Free-space optical communication between satellites networked together can enable a high data rate between the satellites. Coherence multiplexing (CM) is an attractive technique for satellite networking due to its ability to cope with the asynchronous nature of communication traffic and the dynamic changes taking place in the satellite constellation. The use of optical radiation for intersatellite links creates very narrow beam divergence angles. Due to the narrow beam divergence angle, the vibration of the pointing system, the movement of the satellite, and the large distance between them the pointing from one satellite to another is a complicated task. The vibration of the pointing system is caused by two stochastic fundamental mechanisms: 1) tracking noises created by the electrooptic tracker and 2) vibrations created by internal satellite mechanical mechanisms and external environments. We derive mathematical models of signal, noise, the approximate signal-to-noise ratio, and the approximate bit-error rates of optical communication satellite networks as functions of the system’s parameters, the number of satellites, and the vibration amplitude for frequency-shift keying coherence multiplexing (FSK-CM). Based on these models, we can calculate the negative impact of both the number of satellites and the optical terminal vibration on the system’s performance. Index Terms—Coherence multiplexing, laser communication, satellite, vibration.

I. INTRODUCTION

S

ATELLITE clusters, distributed satellite systems, or satellite flight formations are attractive options for achieving high performance in numerous applications, such as imaging, remote sensing, communication, synthetic aperture radar, and navigation [1]–[7]. The spatial separation of a satellite helps to achieve wider synthetic apertures for radar and interferometric applications, coverage in communication applications, and additional reference points in navigation applications, all of which improve performance dramatically. Clustering satellites makes it possible to design a very small, lightweight, and reduced power consumption space system, which reduces manufacturing and launch costs considerably. The idea of designing clusters of satellites with a possibility of communication between them is not new. For example, Iridium, the terrestrial planet finder (TPF) and the TechSat 21 are well-known satellite projects which use satellite clustering for communication, navigation, and imaging. Iridium provides a personal communications service (PCS) (typically voice, data, and fax) to users using small hand-held cellular-type telephones [2]. The TPF is a multiple spacecraft

Manuscript received June 1, 2003; accepted July 1, 2003. The editor coordinating the review of this paper and approving it for publication is A. Boucouvalas. This work was supported in part by the DIP Fund (Israeli–German Research Fund) for the BLISL Project. The authors are with the Satellite and Wireless Communication Laboratory, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TWC.2004.833476

telescope interferometer that searches for earth-like planets [3]. The U.S. Air Force TechSat 21 program envisions collaborative clusters of interdependent microsatellites, flying in close bird-like formations, which could replace many of today’s single larger satellites [4]. One way to achieve communication between satellites is by using optical intersatellite links (OISL). Compared to microwave intersatellite links, OISL are [1], [8], [9]: 1) smaller in size and terminal weight, 2) require less transmitter power, 3) have a higher immunity to interference, 4) have a larger data rate, and 5) require only a small transmitter beam divergence angle. However, a significant disadvantage is their complex pointing system, which is derived from the necessity to point from one satellite to another from a distance of tens of thousands of kilometers with a beam divergence angle of microradians during satellite movement and vibration. Vibration of the transmitted beam in the receiver plane decreases the received signal, which increases the bit-error rate (BER). In this paper, we analyze the performance of an frequency-shift keying coherence multiplexing (FSK-CM) in satellite networks. CM makes use of coherence matched filters. It has the same defining features and advantages of code division multiple access (CDMA), such as shared signal bandwidth and asynchronous operation [10], [11]. Therefore, it has attracted much attention, particularly because it allows multiple users to access the network asynchronously and simultaneously, so no scheduling is required, and new users can be easily added to the network. Furthermore, multiple users can gain access to the channel with no waiting time. For these reasons, it makes channel assignment easier than in time-division multiple-access (TDMA) or wavelength-division multiple-access (WDMA) systems [10]–[18]. Moreover, for space systems with a large distance separation between crafts, which results in long propagation delay, CM performs better than TDMA due to its asynchronic nature. The complexity of CM is similar to WDMA. A WDMA system requires a tunable laser in the transmitter and tunable filter in the receiver, while CM requires tunable Mach–Zender interferometers (MZI). We consider a scenario in which there is simultaneous communication from several picosatellites to one master satellite (Fig. 1). The picosatellites are orbiting the earth in low orbit (LEO), while the master satellite is orbiting the earth in a geostationary orbit (GEO). The picosatellites sense the space environment and the earth and transfer the information to the master satellite. However, due to the picosatellite orbit, some of these satellites enter the field of view (FOV) of the master satellite while others move out from it. Therefore, dynamic network resources need to be allocated and dismissed. The picosatellites use a narrow beam divergence angle laser transmitter, while the master satellite uses a wide FOV receiver that can receive signals from several picosatellites located far from each other. The

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the right-hand side, each MZI is used as the optical decoder. Each transmitter has a fixed large arms delay difference that exceeds the light source coherence time . Furthermore, the delay difference between each transmitter is larger than the . Fig. 3(a) and (b) illustrates the coherence time coherence [20] phenomena. In Fig. 3(a), we can see the signal at the output of MZI, the signal pattern decays exponentially as a function of the interferometer arms delay difference . In Fig. 3(b), we can a see the signal at the output of second the MZI. In this figure, we can also see that the signal increases as where is the arms delay difference of the first MZI; therefore, the information can be reconstructed. This configuration makes it possible to perform coherent multiplexing. We assume that the polarization maintaining mechanism or polarization diversity scheme is implemented. The system is presumed to have a stabilized mechanism that matches the encoder and decoder to the MZIs. Consequently, the photodetector normalized electrical power at detector can be expressed as [11] (1)

Fig. 1.

Satellite network.

receiver (master satellite) vibration and small pointing errors do not affect communication due to the wide FOV. We assume that the GEO FOV is in the order of miliradian in comparison to microradian of the picosatellites; therefore, it is reasonable to presume that the ranges between LEO satellites to the GEO are almost equal and as a result the average received power from the LEOs are equal. The objective of this paper is to derive mathematical models of signal, noise, the approximate noise-to-signal ratio (NSR) and the approximate BERs of coherence multiplexing optical communication satellite networks as functions of the system’s parameters, the number of satellites, and the vibration amplitude for FSK-CM. This paper is organized as follows: In Section II, we describe the basic concept and theory of coherence multiplexing. In Section III, we briefly review the vibration model. Section IV presents a mathematical analysis of the optical signal and noise model and the derivation of the signal-to-noise ratio (SNR) link performance parameter. Section V concludes the paper. II. BASIC CONCEPT AND THEORY OF COHERENCE MULTIPLEXING Fig. 2 depicts the architecture of a broadband coherence multiplexing -channel system [10], [11], [14], [15]. The left-hand side of the figure indicates that an MZI, which can be used as a coherence multiplexing encoder, follows each light source. On

where is the laser transmitters optical power (assuming all is the received optical power, the satellites are identical), is the delay difference between the encoder to the desired decoder, is the number of LEO satellites, is the central freis the beat noise of the coherent quency of the laser, and signal due to finite integration time of the receiver (we assume that information distortions of the rejected transmitters are negligible). The last term represents the dominant and detrimental noise factor. The division by 4 in the denominator is a result of the loss from both the transmitter and the receiver MZI. It easy to see from (1) that when the number of LEO satellites increases, the second term becomes smaller because the number of power splitters increases. The decoder arms delay is closely matched (within a small fraction of a wavelength) to the desired transmitter MZI arms delay. The cosine term carries the information. The cosine term takes the value of either 1 or 1. Phase shift keying (PSK) modulation is done by electrically modulating the [18], with being conMZI arms by changing the delay stant. FSK is done by changing the value of , using a chirp being constant. FSK-CM makes it easier to technique with chirp the laser source over the effective information bandwidth in comparison to PSK. III. VIBRATION MODEL In order to establish optical communication between two satellites, the line of sight of their optics must be aligned during the entire communication time. In order to meet this requirement, the satellites use Ephemerides data (the position of the satellite according to the orbit equation) for rough pointing and a tracking system for fine pointing to the other satellite. The basic and popular method of tracking between satellites includes use of a beacon signal on one satellite and a quadrant detector and tracking system on the other satellite. The fine elevation and azimuth angle of the pointing system evaluates the output signal of the quadrant detector. Due to noise in the tracking system and mechanical vibrations [8], [22], [23], the satellite transmitter beam to the receiver satellite vibrates.

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Fig. 2. Broadband

N channel OCDMA system.

The orthogonal direction error pointing angle models of the vibrations are based on a normal distribution. If the azimuth and elevation processes are independent and identically distributed, the radial pointing error angle model is Rayleigh distributed with probability density [23]

(2) is the elevation pointing standard deviation and is where the root sum square of the azimuth and elevation angles In the model presented in Section IV, the vibration amplitude of the pointing system of all satellites is identical and is described by . IV. COMMUNICATION SYSTEM MODEL A. Signal Model In this section, we derive a model that relates the transmitted optical received signal from the of LEO satellites to the GEO receiver satellite. Only LEO satellites that enter the GEO FOV can transfer information. The optical signal received from transmitter satellite at the GEO satellite [21] , where is the pointing loss factor and is , and where is is the optical power of satellite , is the the wavelength, optical splitter which is located in the receiver (causing is the transmitter receiver MZI’s power reduction and loss), loss, is the telescope gain of satellite , is the telescope is the distance between LEO gain of the master satellite, is the optics efficiency of satellite to the GEO satellite, is the optics the transmitter in satellite in the network, and efficiency of the receiver in master satellite. From the paragraph above and [22], the optical signal received from transmitter satellite at the GEO satellite is given by (3)

Fig. 3.

(a) Temporal coherence. (b) Coherence manipulation.

B. Noise Model In the coherence multiplexing system, the most dominant and detrimental noise factor is crosstalk, which is derived from the finite integration of two mutual fields [10], [14]. We assume that background noise is negligible in comparison to other noise sources since the satellite receiver is asumed to avoid direct sunlight. In this section, we evaluate the noise field variance that results from finite integration time of the photodetector on the mixed. The variance due to finite integration of two mutual fields is defined by [20] (4) where and are the optical power of the laser field and , respectively; is the complex coherence factor which is defined by (5) is the complex degree of coherence, tion time, and

is the finite integra-


Since the fields are generated by distinctive devices, they are . mutually incoherent, i.e., is and the Note that the width of the function width of function is twice the coherence time, hence . Consequently, it can be shown that for (6)

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If all the satellites are identical, the standard deviation of the radial pointing error angle of all the satellites equals (15) Consequently, density

is chi-square distributed with probability

(16)

If all the satellites are identical (7)

where

From (3), (6), and (7) the crosstalk between two mutual satellites field is (8) The total variance at the receiver satellite due to the sum of all the crosstalk terms can be expressed by

(17) The recursion formula of the gamma function is (18) We continue by evaluating

(9) The sum of all possible mutual fields (the number of combinations from which 2 can be chosen from ) is given by [24] (10) . Using If all the satellites are identical, (2)–(9) the total average variance in the FSK system due to the sum of all the crosstalk terms can be expressed by

(19) From (16) and (19) –

(20)

Calculating the integral in (20) [21]

(21) (11)

From (11)–(21), the total average variance is

To evaluate (11), the probability density function (PDF) of the random variable in the exponential term has to be calculated. We start with the evaluation of the PDF of the following: (12)

(22)

C. Performance Model In the following equation, we derive the NSR. We do not calculate the conventional SNR which cannot be represented by a closed form expression. The NSR model is

We then define a new variable (13) From (12) and (13)

(23) (14) Every includes two normal processes (azimuth and elevanormal processes. The distrition) and therefore includes bution of the process compounded from the sum square of the normal processes with equal variance is chi-square [24].

where is the photodetector responsivity. For simplicity, we select the signal from first satellite as the desire signal (responsivity is assumed to be equal to one). Using the same procedure as in Section IV-B, (23) can be expressed by (24), as shown at the bottom of the following page, by asuming that all satellite elevation pointing error angle are

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Fig. 4. NSR as a function of the normalized vibration amplitude for cluster sizes of 2, 9, 16, and 23 picosatellites: dashed, dotted, dashed-dotted, and solid lines, mark, respectively, the four cluster sizes. Spreading ratio T = is equal to 100.

Fig. 5. NSR as a function of the normalized vibration amplitude for cluster sizes of 2, 9, 16, and 23 picosatellites: dashed, dotted, dashed-dotted, and solid lines, mark, respectively, the four cluster sizes. Spreading ratio T = is equal to 100.

independent and that all satellites are identical . Equation (24) can be expressed by (mathematical steps for going from (24) to (25) are presented in Appendix A)

noise source. In this system, the average BER for an optimal threshold receiver [10], [13] is given by

(26) (25) as a function of the norIn Figs. 4 and 5, we show the and the number of satelmalized vibration amplitude lites in the network. We assume that the ratio is equal to 100 and 1000, respectively. We can verify our result for the case when is close to zero by a published model from [11], which is the similar to our result. These figures demonstrate that the number of satellites is the major source for performance degradation and that vibration is a minor source although it cannot be ignored. The receiver is assumed to include an optical detector in the direct detection mode and the multiuser noise is the dominant

From (3), (9), and (26) the average BER can be expressed by

(27) By asuming that all the satellites are identical, (27) can be expressed as in (28), shown at the bottom of the following page, where (29)

(24)


Fig. 6. BER as a function of the normalized vibration amplitude for cluster sizes of 2, 9, 16, and 23 picosatellites: dashed, dotted, dashed-dotted, and solid lines, mark, respectively, the four cluster sizes. Spreading ratio T = is equal to 100.

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Fig. 7. BER as a function of the normalized vibration amplitude for cluster sizes of 2, 9, 16, and 23 picosatellites: dashed, dotted, dashed-dotted, and solid lines, mark, respectively, the four cluster sizes. Spreading ratio T = is equal to 100.

V. CONCLUSION (Mathematical steps for going from (27) to (28) are presented in Appendix B.) , , From [25], (21), and (28) and substituting with , , , respectively, the simplified expression for the BER is given by (30), as shown at the bottom of the page. Figs. 6 and 7 depict the BER as a function of the normalized and the number of satellites in vibration amplitude the network. We assume that the ratio is equal to 100 and 1000, respectively. We truncate the BER at 10 . When the number of users increases from 2 to 23 and the normalized vibration increase from 0 to 0.5, the BER changes from lower than 10 to more than 10 . The results clearly indicate that the number of satellites and the vibration amplitude of the pointing system are major sources of performance degradation for loaded networks.

This paper analyzed the effects of vibrations of a pointing system on network performance of an optical communication as high satellite FSK-CM system. We show that a loss in as 10 dB and an increase of the BER of several orders of magnitude can arise due to vibration of the pointing system. Hence, vibration degrades the performance of the communication system and should be taken into consideration for synthesis and analysis of space communication systems. Moreover, our results indicate , which creates a that while increasing the spreading ratio budget advantage, it does not eliminate the effect of the pointing error. Furthermore, we found that the elevation pointing stan, otherwise the dard deviation has to be smaller than results will not be valid. Future work will be directed toward investigating the effect of mismatch between Tx and Rx MZI on communication system performance.

(28)

(30)

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APPENDIX A The mathematical steps required to progess from (24) to (25) are described below. By using (2) and by asuming that all satellite elevation pointing error angle are independent, (24) can be expressed as

By asuming that all the satellites are identical to , we get

(A.3)

(A.1) Rearranging (A.1) yields

The five integrals in (A.3) can be solved under the assumption that following the same procedure outlined in Section IV-B. APPENDIX B The mathematical steps required to progess from (27) to (28) are described below. By assuming that all satellites are identical and from (9), (24) can be expressed by

(B.1)

(A.2)

Rearranging the summations, yields (B.2), as shown at the bottom of the page. Then, calculating the summation value yields (B.3), also shown at the bottom of the page.

(B.2)

(B.3)


REFERENCES [1] D. Bushuev, D. Kedar, and S. Arnon, “Analyzing the performance of nano-satellite cluster—Detector array receiver laser communication,” IEEE/OSA J. Lightwave Technol., vol. 21, no. 2, pp. 447–455, 2003. [2] J. V. Evans, “Satellite systems for personal communications,” Proc. IEEE, vol. 86, pp. 1325–1341, 1998. [3] T. Nakajima and H. Matsuhara, “Sensitivity of an imaging space infrared interferometer,” Appl. Opt., vol. 40, no. 4, pp. 514–526, 2001. [4] H. Steyskal, J. K. Schindler, P. Franchi, and R. J. Mailloux, “Pattern synthesis for Techsat21—A distributed spacebased radar system,” in Proc. IEEE Aerospace Conf., vol. 2, 2001, pp. 725–732. [5] A. Polishuk and S. Arnon, “Communication performance analysis of satellites with optical phased array antenna,” Opt. Eng., July 2003, to be published. [6] F. Jonas, J. Staggs, R. Blackledge, and M. E. Kouba, “TRAM antenna space experiments on the road to SBR,” in Proc. IEEE Aerospace Conf., vol. 5, 2000, pp. 189–792. [7] G. Purcell, D. Kuang, S. Lichten, S. C. Wu, and L. Young, “Autonomous Formation Flyer (AFF) Sensor Technology Development,”, NASA TMO Progress Rep. 42-134, 1998. [8] S. Arnon and N. S. Kopeika, “Laser satellite communication networks—Vibration effects and possible solutions,” Proc. IEEE, vol. 85, pp. 1646–1661, 1997. [9] N. Karafolas and S. Baroni, “Optical satellite networks,” IEEE/OSA J. Lightwave Technol., vol. 18, pp. 1792–1806, Dec. 2000. [10] D. D. Sampson, R. A. Griffin, and G. J. Pendock, “Photonic code division multiple-access communications,” Fiber Integrated Opt., vol. 16, pp. 129–157, 1997. [11] G. Kats and D. Sadot, “Inclusive BER analysis for coherent optical CDMA systems,” Opt. Eng., vol. 41, no. 6, pp. 1227–1231, 2002. [12] J. A. Salehi, “Code division multiple-access techniques in optical fiber networks—Part I: Fundamental principles,” IEEE Trans. Commun., vol. 37, pp. 824–833, Aug. 1989. [13] H. M. H. Shalaby, “Chip-level detection in optical code division multiple access,” IEEE/OSA J. Lightwave Technol., vol. 16, pp. 1077–1087, June 1998. [14] R. H. Wentworth, “Theoretical noise performances of coherence-multipexing for interferometric sensors,” IEEE/OSA J. Lightwave Technol., vol. 7, pp. 941–956, June 1989. [15] G. J. Pendock and D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication system by using differential detection,” IEEE Photon. Technol. Lett., vol. 7, pp. 1504–1506, 1995. [16] A. J. Mendez and R. M. Gagliardi, “Lasercom crosslinking for satellite clusters,” in SPIE Conf. Free-Space Laser Communication Technologies XIII, vol. 4272, G. S. Mecherle, Ed., 2001, pp. 50–59. [17] S. Zahedi and J. A. Salehi, “Analytical comparison of various fiberoptic CDMA receiver structures,” J. Lightwave Technol., vol. 18, pp. 1718–1727, Dec. 2000.

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[18] K. W. Chow and F. M. Dickey, “Optical coherence multiplexing for inter processor communications,” Opt. Eng., vol. 30, no. 3, pp. 337–344, 1991. [19] G. Kats and D. Sadot, “A new FSK-based method for coherent optical SDMA systems,” in Proc. IEEE ISSTA Int. Symp. Spread Spectrum Techniques Application, Piscataway, NJ, Sept. 6–8, 2000. [20] J. W. Goodman, Statistical Optics. New York: Wiley, 1985. [21] S. Arnon and N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—Analog case,” Opt. Eng., vol. 36, no. 1, pp. 175–182, 1997. [22] C. C. Chen and C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical inter satellite communication links,” IEEE Trans. Commun., vol. 37, pp. 252–260, Mar. 1989. [23] M. Toyoshima, T. Jono, K. Nakagawa, and A. Yamamoto, “Optimum divergence angle of a gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Amer. A, vol. 19, no. 3, pp. 567–571, 2002. [24] A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. London, U.K.: McGraw Hill, 1987. [25] S. Arnon, “The effects of atmospheric turbulence and building sway on optical wireless communication systems,” Opt. Lett., vol. 28, no. 2, pp. 129–131, 2003.

G. Kats photograph and biography not available at the time of publication.

Schlomi Arnon received the Ph.D. degree from Ben Gurion University (BGU), Beer-Sheva, Israel. He is presently a member of the faculty in the Electrical and Computer Engineering Department, BGU. He was a Postdoctoral Associate at LIDS, Massachusetts Institute of Technology (MIT), Cambridge. He has published more than 30 journal papers in the area of laser satellite and wireless communication. He was invited and sponsored by the U.S. Air Force to consult at a Rome Laboratory. Dr. Arnon was a Fulbright Fellow at MIT. Recently, his paper with N. S. Kopeika was awarded the J. J. Thomson award. He served as Session Chair of Photonics for the Space Environment SPIE conference. He coinstructed a tutorial on laser satellite communication at the International Conference on Communications, IEEE Communications Society, ICC 2000 Global Convergence and Communications New Orleans, June 18-22, 2000. He was an invited speaker at the SPIE conference in Denver 2004. He was a Coeditor for a special issue on optical wireless communication in the OSA Journal of Optical Networking.