Abstract

In an optically preamplified differential phase-shift keying (DPSK) receiver with Mach–Zehnder interferometer (MZI) demodulation, it is essential to couple free space light into a single-mode fiber, by which the received optical signal can be guided into the amplifier and MZI. Random angular jitter has a profound impact on fiber coupling efficiency, in that it would significantly deteriorate the receiver performance. In this paper, the average bit error rate (BER) of fiber-coupled DPSK receivers is obtained in the presence of random angular jitter. It is shown that the degradation is significant when the random angular jitter normalized by the mode field radius is larger than 0.3. We further analyze the impact of other factors, including central obstruction and optical filter transfer functions. Our results show that the super-Gaussian filter outperforms other filters and leads to lower average BER at a fixed optical signal-to-noise ratio. This work can be used to improve the design of fiber-coupled DPSK receivers.

© 2010 Optical Society of America

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References

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  1. F. David and C. Rapp, “Breadboard model of a coherent optical BPSK homodyne system with virtual pilot tone (ViP)-based receiver and MRC auxiliary channel,” Proc. SPIE 3932, 35–44 (2000).
    [CrossRef]
  2. S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
    [CrossRef]
  3. S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
    [CrossRef]
  4. V. A. Vilnrotter and C. Lau, “Quantum detection and channel capacity for communications applications,” Proc. SPIE 4635, 103–115 (2002).
    [CrossRef]
  5. R. Lange and B. Smutny, “Homodyne BPSK-based optical inter-satellite communication links,” Proc. SPIE 6457, 645703 (2007).
    [CrossRef]
  6. B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.
  10. 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. Am. A 19, 567–571 (2002).
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. J. Wang and J. M. Kahn, “Impact of chromatic and polarization-mode dispersions on DPSK systems using interferometric demodulation and direct detection,” J. Lightwave Technol. 22, 362–371 (2004).
    [CrossRef]
  15. E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering,” J. Lightwave Technol. 18, 1493–1503 (2000).
    [CrossRef]
  16. E. Forestieri and M. Secondini, “On the error probability evaluation in lightwave systems with optical amplification,” J. Lightwave Technol. 27, 706–717(2009).
    [CrossRef]

2009

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

J. Ma, F. Zhao, L. Tan, S. Yu, and Q. Han, “Plane wave coupling into single-mode fiber in the presence of random angular jitter,” Appl. Opt. 48, 5184–5189 (2009).
[CrossRef] [PubMed]

E. Forestieri and M. Secondini, “On the error probability evaluation in lightwave systems with optical amplification,” J. Lightwave Technol. 27, 706–717(2009).
[CrossRef]

2007

R. Lange and B. Smutny, “Homodyne BPSK-based optical inter-satellite communication links,” Proc. SPIE 6457, 645703 (2007).
[CrossRef]

2005

2004

2002

2000

S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
[CrossRef]

F. David and C. Rapp, “Breadboard model of a coherent optical BPSK homodyne system with virtual pilot tone (ViP)-based receiver and MRC auxiliary channel,” Proc. SPIE 3932, 35–44 (2000).
[CrossRef]

E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering,” J. Lightwave Technol. 18, 1493–1503 (2000).
[CrossRef]

1999

S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
[CrossRef]

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

1998

1989

C. C. Chen and 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]

Araki, T.

S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
[CrossRef]

S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
[CrossRef]

Arimoto, Y.

H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.

Arnon, S.

Boehmer, K.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Chen, C. C.

C. C. Chen and 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]

Czichy, R.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Dallmann, D.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

David, F.

F. David and C. Rapp, “Breadboard model of a coherent optical BPSK homodyne system with virtual pilot tone (ViP)-based receiver and MRC auxiliary channel,” Proc. SPIE 3932, 35–44 (2000).
[CrossRef]

Feldhaus, T.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Forestieri, E.

Freier, A.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Gardner, C. S.

C. C. Chen and 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]

Gnauck, A. H.

Greulich, P.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Habara, K.

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

Han, Q.

Heine, F.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Hildebrand, U.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Hisada, Y.

S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
[CrossRef]

Jono, T.

Kaempfner, H.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Kahn, J. M.

Kopeika, N. S.

Lange, R.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

R. Lange and B. Smutny, “Homodyne BPSK-based optical inter-satellite communication links,” Proc. SPIE 6457, 645703 (2007).
[CrossRef]

Lau, C.

V. A. Vilnrotter and C. Lau, “Quantum detection and channel capacity for communications applications,” Proc. SPIE 4635, 103–115 (2002).
[CrossRef]

Ma, J.

Meyer, R.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Mikami, H.

H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.

Morikawa, H.

S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
[CrossRef]

Muehlnikel, G.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Mueller, J.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Nakagawa, K.

Nizhizawa, H.

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

Rapp, C.

F. David and C. Rapp, “Breadboard model of a coherent optical BPSK homodyne system with virtual pilot tone (ViP)-based receiver and MRC auxiliary channel,” Proc. SPIE 3932, 35–44 (2000).
[CrossRef]

Reinhardt, M.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Rotman, S. R.

Secondini, M.

Seel, S.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Shibata, Y.

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

Smutny, B.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

R. Lange and B. Smutny, “Homodyne BPSK-based optical inter-satellite communication links,” Proc. SPIE 6457, 645703 (2007).
[CrossRef]

Sterr, U.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Suzuki, R.

H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.

Tan, L.

Toyoshima, M.

Vilnrotter, V. A.

V. A. Vilnrotter and C. Lau, “Quantum detection and channel capacity for communications applications,” Proc. SPIE 4635, 103–115 (2002).
[CrossRef]

Wandernoth, B.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Wang, J.

Weichert, A.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Winzer, P. J.

Yamada, Y.

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

Yamakawa, S.

S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
[CrossRef]

S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
[CrossRef]

Yamamoto, A.

Yasuda, Y.

H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.

Yu, S.

Zhao, F.

Appl. Opt.

IEEE Photonics Technol. Lett.

H. Nizhizawa, Y. Yamada, Y. Shibata, and K. Habara, “10 Gb/s optical DPSK packet receiver proof against large power fluctuations,” IEEE Photonics Technol. Lett. 11, 733–735 (1999).
[CrossRef]

IEEE Trans. Commun.

C. C. Chen and 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]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Proc. SPIE

F. David and C. Rapp, “Breadboard model of a coherent optical BPSK homodyne system with virtual pilot tone (ViP)-based receiver and MRC auxiliary channel,” Proc. SPIE 3932, 35–44 (2000).
[CrossRef]

S. Yamakawa, T. Araki, and Y. Hisada, “Trade-off between IM/DD and coherent system in high-data-rate optical interorbit links,” Proc. SPIE 3615, 80–89 (1999).
[CrossRef]

S. Yamakawa, T. Araki, and H. Morikawa, “Analysis of noises generated in high-power-operated erbium-doped fiber amplifiers and their influences on IM-DD/Coherent OIC system performance,” Proc. SPIE 3932, 196–204 (2000).
[CrossRef]

V. A. Vilnrotter and C. Lau, “Quantum detection and channel capacity for communications applications,” Proc. SPIE 4635, 103–115 (2002).
[CrossRef]

R. Lange and B. Smutny, “Homodyne BPSK-based optical inter-satellite communication links,” Proc. SPIE 6457, 645703 (2007).
[CrossRef]

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[CrossRef]

Other

H. Mikami, R. Suzuki, Y. Arimoto, and Y. Yasuda, “DPSK-self homodyne detection system adopting PLC for optical inter-satellite link terminal,” in Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99 (IEEE, 1999), Vol. 1, pp. 293–294.

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Figures (7)

Fig. 1
Fig. 1

Schematic of fiber-coupled DPSK receiver.

Fig. 2
Fig. 2

Low-pass equivalent receiver model.

Fig. 3
Fig. 3

Average BER as a function of E b / N 0 ; solid and dotted curves correspond to optimum design parameter β opt in the presence of random angular jitter and β = 1.12 optimized for zero random jitter, respectively.

Fig. 4
Fig. 4

Average BER as a function of E b / N 0 and normalized random jitter σ r / ω 0 .

Fig. 5
Fig. 5

Power penalty as a function of normalized random jitter σ r / ω 0 .

Fig. 6
Fig. 6

Average BER as a function of normalized random jitter σ r / ω 0 at various central obstruction ε.

Fig. 7
Fig. 7

Average BER as a function of normalized random jitter σ r / ω 0 for different optical filters.

Equations (20)

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

x ( t ) = n Φ n p ( t n T b ) .
p ( t ) = { E b / T b t [ 0 , T b ) 0 otherwise ,
N 0 = n sp ( G 1 ) G h ν n sp h ν for     G 1.
H o ( f ) = 1 ( 1 + j 2 f B o ) ,
H o ( f ) = exp [ ( f 0.85 B 0 ) 2 ] ,
H o ( f ) = exp [ ( f 0.65 B 0 ) 4 ] ,
H c ( f ) = exp [ j 2 π f T b ] + 1 2 ,
H d ( f ) = exp [ j 2 π f T b ] 1 2 .
H e ( f ) = 945 j f ˜ 5 + 15 f ˜ 4 105 j f ˜ 3 420 f ˜ 2 + 945 j f ˜ + 945 ,
Δ r = θ f .
η Δ r = | E A ( r ) F A ( r , Δ r ) r d r d φ | 2 π R 2 ( 1 ε 2 ) ,
F A ( r , Δ r ) = 2 π ω a 2 exp ( r 2 ω a 2 ) exp [ j 2 π λ f cos ( φ Ω ) r Δ r ] .
J 0 ( x ) = 1 2 π 0 2 π exp ( j x cos θ ) d θ ,
η Δ r = | ε R R 8 π ω a 2 exp ( r 2 ω a 2 ) J 0 ( 2 π λ f r Δ r ) r d r | 2 π R 2 ( 1 ε 2 ) ,
η Δ r = | ε 1 8 π β exp ( β 2 ρ 2 ) J 0 ( 2 β Δ r ω 0 ρ ) ρ d ρ | 2 π ( 1 ε 2 ) ,
β opt = 1.2564 2 σ r 2 ω 0 2 + 1 ε = 0.
β opt = 1.1958 2 σ r 2 ω 0 2 + 1 ε = 0.15.
f ( Δ r ) = Δ r σ r 2 exp ( Δ r 2 2 σ r 2 )
BER = 0 BER ( η Δ r ) · f ( Δ r ) d Δ r .
BER ( η Δ r ) = 1 N k = 1 N P k ( η Δ r ) ,

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