Abstract

Free-space optical communication between satellites in a distributed network can permit high data rates of communication between different places on Earth. To establish optical communication between any two satellites requires that the line of sight of their optics be aligned during the entire communication time. Because of the large distance between the satellites and the alignment accuracy required, the pointing from one satellite to another is complicated because of vibrations of the pointing system caused by two fundamental stochastic mechanisms: tracking noise created by the electro-optic tracker and vibrations derived from mechanical components. Vibration of the transmitter beam in the receiver plane causes a decrease in the received optical power. Vibrations of the receiver telescope relative to the received beam decrease the heterodyne mixing efficiency. These two factors increase the bit-error rate of a coherent detection network. We derive simple mathematical models of the network bit-error rate versus the system parameters and the transmitter and receiver vibration statistics. An example of a practical optical heterodyne free-space satellite optical communication network is presented. From this research it is clear that even low-amplitude vibration of the satellite-pointing systems dramatically decreases network performance.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Leopold, A. Miller, “The Iridium communications system,” IEEE Potential 12(2), 6–9 (1993).
    [CrossRef]
  2. P. P. Giusto, G. Quaglione, “Technical alternative for satellite mobile network,” in Mobile and Personal Satellite Communications, Proceedings of the First European Workshop on Mobile/Personal Satcoms, F. Ananasso, F. Vatalaro, eds., (Springer-Verlag, Berlin, 1995), pp. 15–27.
    [CrossRef]
  3. Motorola Global Communication, “Application for Celestri multimedia LEO system,” (Federal Communication Commission, Washington, D.C., 1997), p. 41.
  4. B. I. Edelson, G. Hyde, “Laser satellite communications, program technology and applications,” a report of the IEEE–USA Aerospace Policy Committee (IEEE, Piscataway, N.J., 1996).
  5. S. Arnon, N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646–1661 (1997).
    [CrossRef]
  6. S. Arnon, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—analog case,” Opt. Eng. 36, 175–182 (1997).
    [CrossRef]
  7. S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
    [CrossRef]
  8. M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.
  9. V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
    [CrossRef]
  10. C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
    [CrossRef]
  11. K. J. Held, J. D. Barry, “Precision pointing and tracking between satellite-borne optical systems,” Opt. Eng. 27, 325–333 (1988).
    [CrossRef]
  12. J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems,” Opt. Eng. 24, 1049–1054 (1985).
    [CrossRef]
  13. S. Arnon, S. Rotman, N. S. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
    [CrossRef] [PubMed]
  14. S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. (to be published).
  15. S. Arnon, N. S. Kopeika, “Adaptive bandwidth for satellite optical communication,” IEE Proc. Optoelectron. 145 (2) (April1998).
  16. S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech, Boston, Mass., 1995).
  17. R. M. Gagliardi, S. Karp, Optical Communication, 2nd ed. (Wiley, New York, 1995), pp. 32–34, 201–206, 247.
  18. L. Kazovsky, S. Benedetto, A. Willner, Optical fiber Communication Systems (Artech, Boston, Mass., 1996), pp. 78–79, 248, 401–426.
  19. S. Ryu, Coherent Lightwave Communication System (Artech, Boston, Mass., 1994), pp. 41–65.

1998 (1)

S. Arnon, N. S. Kopeika, “Adaptive bandwidth for satellite optical communication,” IEE Proc. Optoelectron. 145 (2) (April1998).

1997 (4)

S. Arnon, S. Rotman, N. S. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

S. Arnon, N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646–1661 (1997).
[CrossRef]

S. Arnon, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—analog case,” Opt. Eng. 36, 175–182 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
[CrossRef]

1995 (1)

V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
[CrossRef]

1993 (1)

R. J. Leopold, A. Miller, “The Iridium communications system,” IEEE Potential 12(2), 6–9 (1993).
[CrossRef]

1989 (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

1988 (1)

K. J. Held, J. D. Barry, “Precision pointing and tracking between satellite-borne optical systems,” Opt. Eng. 27, 325–333 (1988).
[CrossRef]

1985 (1)

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Arnon, S.

S. Arnon, N. S. Kopeika, “Adaptive bandwidth for satellite optical communication,” IEE Proc. Optoelectron. 145 (2) (April1998).

S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

S. Arnon, N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646–1661 (1997).
[CrossRef]

S. Arnon, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—analog case,” Opt. Eng. 36, 175–182 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. (to be published).

Barry, J. D.

K. J. Held, J. D. Barry, “Precision pointing and tracking between satellite-borne optical systems,” Opt. Eng. 27, 325–333 (1988).
[CrossRef]

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Benedetto, S.

L. Kazovsky, S. Benedetto, A. Willner, Optical fiber Communication Systems (Artech, Boston, Mass., 1996), pp. 78–79, 248, 401–426.

Busch, T. E.

V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
[CrossRef]

Casey, W. L.

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech, Boston, Mass., 1995).

Chen, C. C.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Edelson, B. I.

B. I. Edelson, G. Hyde, “Laser satellite communications, program technology and applications,” a report of the IEEE–USA Aerospace Policy Committee (IEEE, Piscataway, N.J., 1996).

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communication, 2nd ed. (Wiley, New York, 1995), pp. 32–34, 201–206, 247.

Gardner, C. S.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Giusto, P. P.

P. P. Giusto, G. Quaglione, “Technical alternative for satellite mobile network,” in Mobile and Personal Satellite Communications, Proceedings of the First European Workshop on Mobile/Personal Satcoms, F. Ananasso, F. Vatalaro, eds., (Springer-Verlag, Berlin, 1995), pp. 15–27.
[CrossRef]

Held, K. J.

K. J. Held, J. D. Barry, “Precision pointing and tracking between satellite-borne optical systems,” Opt. Eng. 27, 325–333 (1988).
[CrossRef]

Hyde, G.

B. I. Edelson, G. Hyde, “Laser satellite communications, program technology and applications,” a report of the IEEE–USA Aerospace Policy Committee (IEEE, Piscataway, N.J., 1996).

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communication, 2nd ed. (Wiley, New York, 1995), pp. 32–34, 201–206, 247.

Kazovsky, L.

L. Kazovsky, S. Benedetto, A. Willner, Optical fiber Communication Systems (Artech, Boston, Mass., 1996), pp. 78–79, 248, 401–426.

Kopeika, N. S.

S. Arnon, N. S. Kopeika, “Adaptive bandwidth for satellite optical communication,” IEE Proc. Optoelectron. 145 (2) (April1998).

S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

S. Arnon, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—analog case,” Opt. Eng. 36, 175–182 (1997).
[CrossRef]

S. Arnon, N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646–1661 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. (to be published).

Lambert, S. G.

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech, Boston, Mass., 1995).

Leopold, R. J.

R. J. Leopold, A. Miller, “The Iridium communications system,” IEEE Potential 12(2), 6–9 (1993).
[CrossRef]

Mecherle, G. S.

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Miller, A.

R. J. Leopold, A. Miller, “The Iridium communications system,” IEEE Potential 12(2), 6–9 (1993).
[CrossRef]

Quaglione, G.

P. P. Giusto, G. Quaglione, “Technical alternative for satellite mobile network,” in Mobile and Personal Satellite Communications, Proceedings of the First European Workshop on Mobile/Personal Satcoms, F. Ananasso, F. Vatalaro, eds., (Springer-Verlag, Berlin, 1995), pp. 15–27.
[CrossRef]

Rotman, S.

S. Arnon, S. Rotman, N. S. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. (to be published).

Ryu, S.

S. Ryu, Coherent Lightwave Communication System (Artech, Boston, Mass., 1994), pp. 41–65.

Skormin, V. A.

V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
[CrossRef]

Tascillo, M. A.

V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
[CrossRef]

Tunbridge, D. E. L.

M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.

van Holtz, L.

M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.

Vermeulen, H. C.

M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.

Willner, A.

L. Kazovsky, S. Benedetto, A. Willner, Optical fiber Communication Systems (Artech, Boston, Mass., 1996), pp. 78–79, 248, 401–426.

Wittig, M.

M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.

Appl. Opt. (1)

IEE Proc. Optoelectron. (1)

S. Arnon, N. S. Kopeika, “Adaptive bandwidth for satellite optical communication,” IEE Proc. Optoelectron. 145 (2) (April1998).

IEEE Potential (1)

R. J. Leopold, A. Miller, “The Iridium communications system,” IEEE Potential 12(2), 6–9 (1993).
[CrossRef]

IEEE Trans. Commun. (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Opt. Eng. (3)

K. J. Held, J. D. Barry, “Precision pointing and tracking between satellite-borne optical systems,” Opt. Eng. 27, 325–333 (1988).
[CrossRef]

S. Arnon, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—analog case,” Opt. Eng. 36, 175–182 (1997).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “The performance limitations of free space optical communication satellite networks due to vibrations—digital case,” Opt. Eng. 36, 3148–3157 (1997).
[CrossRef]

Opt. Eng. (2)

V. A. Skormin, M. A. Tascillo, T. E. Busch, “Adaptive jitter rejection technique applicable to airborne laser communication systems,” Opt. Eng. 34, 1263–1268 (1995).
[CrossRef]

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant parameter for satellite borne, free-space optical communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Proc. IEEE (1)

S. Arnon, N. S. Kopeika, “Laser satellite communication networks-vibration effects and possible solutions,” Proc. IEEE 85, 1646–1661 (1997).
[CrossRef]

Other (9)

M. Wittig, L. van Holtz, D. E. L. Tunbridge, H. C. Vermeulen, “In orbit measurements of microaccelerations of ESA’s communication satellite OLYMPUS,” in Selected Papers on Free-Space Laser Communication II, D. L. Begly, B. J. Thompson, eds. Vol. 100 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994), pp. 389–398.

P. P. Giusto, G. Quaglione, “Technical alternative for satellite mobile network,” in Mobile and Personal Satellite Communications, Proceedings of the First European Workshop on Mobile/Personal Satcoms, F. Ananasso, F. Vatalaro, eds., (Springer-Verlag, Berlin, 1995), pp. 15–27.
[CrossRef]

Motorola Global Communication, “Application for Celestri multimedia LEO system,” (Federal Communication Commission, Washington, D.C., 1997), p. 41.

B. I. Edelson, G. Hyde, “Laser satellite communications, program technology and applications,” a report of the IEEE–USA Aerospace Policy Committee (IEEE, Piscataway, N.J., 1996).

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. (to be published).

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech, Boston, Mass., 1995).

R. M. Gagliardi, S. Karp, Optical Communication, 2nd ed. (Wiley, New York, 1995), pp. 32–34, 201–206, 247.

L. Kazovsky, S. Benedetto, A. Willner, Optical fiber Communication Systems (Artech, Boston, Mass., 1996), pp. 78–79, 248, 401–426.

S. Ryu, Coherent Lightwave Communication System (Artech, Boston, Mass., 1994), pp. 41–65.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Network of free-space optical communication satellites.

Fig. 2
Fig. 2

Basic schematics of (a) a satellite heterodyne optical communication transmitter and (b) a satellite heterodyne optical communication receiver.

Fig. 3
Fig. 3

Loss pattern as a function of misalignment angle.

Fig. 4
Fig. 4

Channel BER as a function of normalized vibration amplitude b. K 1 = 0.5.

Fig. 5
Fig. 5

Network BER as a function of normalized vibration amplitude and the number of satellites in the network.

Fig. 6
Fig. 6

Network BER versus vibration amplitude.

Fig. 7
Fig. 7

BER as a function of G R σθ 2.

Tables (2)

Tables Icon

Table 1 Parameters K1 and K2 for Detection Schemesa

Tables Icon

Table 2 Parameters of a Practical Optical Communication Satellite Network

Equations (57)

Equations on this page are rendered with MathJax. Learn more.

f θ v = 1 2 π σ v exp - θ v 2 2 σ v ,
f θ H = 1 2 π σ H exp - θ H 2 2 σ H 2 ,
θ = θ v 2 + θ H 2 .
σ v = σ H = σ .
f T θ T = θ T σ T 2 exp - θ T 2 2 σ T 2 .
f R θ R = θ R σ R 2 exp - θ R 2 2 σ R 2 .
P R θ T ,   θ R ,   θ p = C 1 L T θ T L R θ R cos 2 θ p ,
C 1 = P T η R η T G R G T λ / 4 π z 2
G T = 2 π W λ 2 ,
L T θ i = exp - G T θ i 2 .
L R q 0 = 1 A A d   ϕ L q ϕ R * q - q 0 d q 2 ,
θ R q 0 / f 0 ,
L R θ R = 1 A A d   ϕ L q ϕ R * q - θ R f 0 d q 2 .
ϕ R q = 2 J 1 G R q / f 0 / G R q / f 0 ,
G R = π D R λ 2
L R θ R = 2 J 1 G R θ R / G R θ R 2 .
R = q e η h ν ,
S θ T ,   θ R ,   θ p = 4 R 2 P R θ T ,   θ R ,   θ p P LO ,
N = 2 qRP LO B W ,
SNR θ T ,   θ R ,   θ P = S θ T ,   θ R ,   θ P N = 2 RC 1 L T θ T L R θ R cos 2 θ P qB W .
BER = K 1 exp - K 2 SNR .
BER θ T ,   θ R ,   θ p = K 1 exp - K 2   SNR θ T ,   θ R ,   θ p .
BER = 0 0     K 1 exp - K 2 K 3 exp - G T θ T 2 L R θ R × cos 2 θ P θ T σ T 2 exp - θ T 2 2 σ T 2 θ R σ R 2 × exp - θ R 2 2 σ R 2 f p θ p d θ p d θ T d θ R ,
K 3 = 2 RP T η R η T G R G T λ / 4 π z 2 / qB W .
BER = 0 0     K 1 exp - K 2 K 3 exp - G T θ T 2 × 2 J 1 G R θ R G R θ R 2 cos 2 θ P θ T σ T 2 exp - θ T 2 2 σ T 2 θ R σ R 2 × exp - θ R 2 2 σ R 2   f p θ p d θ p d θ T d θ R .
BER = 0 0   K 1 exp - K 2 K 3 exp - G T θ T 2 × 2 J 1 G R   θ R G R   θ R 2 θ T σ T 2 exp - θ T 2 2 σ T 2 θ R σ R 2 × exp - θ R 2 2 σ R 2 d θ T d θ R .
T = θ T / σ T ,
R = θ R / σ R .
BER = 0 0   K 1 exp - K 2 K 3 exp - G T σ T 2 T 2 × 2 J 1 G R   R σ R G R   R σ R 2 - T 2 + R 2 2 TR d R d T .
L R θ R exp - G T θ R 2 .
D R = D T .
D R > 2 W .
BER = 0 0   K 1 exp - K 2 K 3 exp - G T σ T 2 T 2 × exp - G T σ R 2 R 2 - T 2 + R 2 2 TR d R d T .
σ T σ R .
BER = 0 0   K 1 exp - K 2 K 3 exp - G T σ T 2 T 2 + R 2 - T 2 + R 2 2 TR d R d T .
y = T 2 + R 2 .
y = R RV 2 + T TV 2 + R RH 2 + T TH 2 .
f y = C 2 y - 1 + n / 2 exp - y / 2 σ T 2 ,     y 0 ,
C 2 = 2 n Γ n / 2 - 1 ,
n = 4 .
C 2 = 1 / 4 σ T 4 .
f y = y / 4   exp - y / 2 ,     y 0 .
BER = 0   K 1 exp - a   exp - G T σ T 2 y - y 2 y 4 d y ,
a = K 2 K 3 .
Z = exp - y / 2 .
BER channel = BER = - K 1 0 1 ln Z exp - Z b a d Z ,
b = 2 G T σ θ 2 .
BER network 1 - i = 1 n 1 - BER channel i .
BER channel i     1 ,     i ,
BER network i = 1 n BER channel i .
BER network i = BER channel j ,     i ,   j ,
BER network n   BER channel 1 .
BER channel i     BER channel j ,     j ,
BER network BER channel i .
c = - 0 1 ln z exp - az b d z .
t = Z b .
c = - 1 b 2 0 1 ln t exp - at t 1 / b - 1 d t .

Metrics