Abstract

In this paper, we consider a heterogenous scenario where free-space optical (FSO) and radio-frequency (RF) technologies are deployed together as a dual-hop communication system, and we investigate the end-to-end outage performance of this so-called mixed RF/FSO system. The RF and FSO links are, respectively, modeled as Rayleigh fading (due to multipath propagation) and M-distributed fading (due to atmospheric turbulence). We derive exact closed-form expressions for the outage probability and demonstrate that the existing outage results in the literature for mixed FSO systems can be obtained as special cases of our results. The effect of pointing errors in the FSO link is further investigated.

© 2013 Optical Society of America

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References

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  1. H. Hogan, “Data demands drive free-space optics,” Photonics Spectra, no. 2, pp. 38–42, Feb. 2013.
  2. E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
    [CrossRef]
  3. P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.
  4. S. Bloom and W. Hartley, “The last-mile solution: Hybrid FSO radio,” AirFiber Inc. White Paper, May 2002.
  5. I. I. Kim and E. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” Proc. SPIE, vol.  4530, pp. 84–95, Aug. 2001.
    [CrossRef]
  6. E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
    [CrossRef]
  7. J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
    [CrossRef]
  8. W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
    [CrossRef]
  9. H. Samimi and P. Azmi, “Subcarrier intensity modulated free-space optical communications in K-distributed turbulence channels,” J. Opt. Commun. Netw., vol.  2, no. 8, pp. 625–632, Aug. 2010.
    [CrossRef]
  10. I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” arXiv:1302.4225v1, 2013.
  11. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.
  12. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.
  13. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
    [CrossRef]
  14. H. Samimi, “Optical communication using subcarrier intensity modulation through generalized turbulence channels,” J. Opt. Commun. Netw., vol.  4, no. 5, pp. 378–381, 2012.
    [CrossRef]
  15. A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “Impact of pointing errors on the performance of generalized atmospheric optical channels,” Opt. Express, vol.  20, no. 11, pp. 12550–12562, 2012.
    [CrossRef]
  16. M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 1st ed. New York: Wiley, 2001.
  17. I. S. Gradshteyn, I. M. Ryzhic, and J. Alan, Table of Integrals, Series and Products, 5th ed. New York: Academia, 1994.
  18. E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol.  22, no. 9, pp. 1896–1906, Nov. 2004.
    [CrossRef]
  19. M. O. Hasna and M.-S. Alouini, “A performance study of dual-hop transmissions with fixed gains relays,” IEEE Trans. Wireless Commun., vol.  3, no. 6, pp. 1963–1968, Nov. 2004.
    [CrossRef]
  20. V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system,” in Proc. Int. Conf. Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.
  21. Mathematica 8.0, Champaign, Illinois: Wolfram Research, Inc., 2010.

2012

2011

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
[CrossRef]

2010

2009

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

2008

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

2007

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

2004

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol.  22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

M. O. Hasna and M.-S. Alouini, “A performance study of dual-hop transmissions with fixed gains relays,” IEEE Trans. Wireless Commun., vol.  3, no. 6, pp. 1963–1968, Nov. 2004.
[CrossRef]

2001

I. I. Kim and E. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” Proc. SPIE, vol.  4530, pp. 84–95, Aug. 2001.
[CrossRef]

Adamchik, V. S.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system,” in Proc. Int. Conf. Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

Alan, J.

I. S. Gradshteyn, I. M. Ryzhic, and J. Alan, Table of Integrals, Series and Products, 5th ed. New York: Academia, 1994.

Allen, J. I. H.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Alouini, M. S.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” arXiv:1302.4225v1, 2013.

Alouini, M.-S.

M. O. Hasna and M.-S. Alouini, “A performance study of dual-hop transmissions with fixed gains relays,” IEEE Trans. Wireless Commun., vol.  3, no. 6, pp. 1963–1968, Nov. 2004.
[CrossRef]

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 1st ed. New York: Wiley, 2001.

Ansari, I. S.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” arXiv:1302.4225v1, 2013.

Arimoto, Y.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Azmi, P.

Bloom, S.

S. Bloom and W. Hartley, “The last-mile solution: Hybrid FSO radio,” AirFiber Inc. White Paper, May 2002.

Chan, V. W. S.

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol.  22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

Ciaramella, E.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Contestabile, G.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

D’Errico, A.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Dat, P. T.

P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.

Gao, S.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Garrido-Balsells, J. M.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “Impact of pointing errors on the performance of generalized atmospheric optical channels,” Opt. Express, vol.  20, no. 11, pp. 12550–12562, 2012.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.

Ghassemlooy, Z.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhic, and J. Alan, Table of Integrals, Series and Products, 5th ed. New York: Academia, 1994.

Guarino, V.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Han, D.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

Hartley, W.

S. Bloom and W. Hartley, “The last-mile solution: Hybrid FSO radio,” AirFiber Inc. White Paper, May 2002.

Hasna, M. O.

M. O. Hasna and M.-S. Alouini, “A performance study of dual-hop transmissions with fixed gains relays,” IEEE Trans. Wireless Commun., vol.  3, no. 6, pp. 1963–1968, Nov. 2004.
[CrossRef]

Hogan, H.

H. Hogan, “Data demands drive free-space optics,” Photonics Spectra, no. 2, pp. 38–42, Feb. 2013.

Jurado-Navas, A.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “Impact of pointing errors on the performance of generalized atmospheric optical channels,” Opt. Express, vol.  20, no. 11, pp. 12550–12562, 2012.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.

Kazaura, K.

P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.

Kim, I. I.

I. I. Kim and E. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” Proc. SPIE, vol.  4530, pp. 84–95, Aug. 2001.
[CrossRef]

Korevaar, E.

I. I. Kim and E. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” Proc. SPIE, vol.  4530, pp. 84–95, Aug. 2001.
[CrossRef]

Lee, E.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

Lee, E. J.

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol.  22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

Leitgeb, E.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Li, J.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Marichev, O. I.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system,” in Proc. Int. Conf. Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

Matsumoto, M.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Paris, J. F.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “Impact of pointing errors on the performance of generalized atmospheric optical channels,” Opt. Express, vol.  20, no. 11, pp. 12550–12562, 2012.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.

Park, J.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

Popoola, W. O.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

Presi, M.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

Puerta-Notario, A.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “Impact of pointing errors on the performance of generalized atmospheric optical channels,” Opt. Express, vol.  20, no. 11, pp. 12550–12562, 2012.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “General analytical expressions for the bit error rate of atmospheric optical communication systems,” Opt. Lett., vol.  36, no. 20, pp. 4095–4097, 2011.
[CrossRef]

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.

Ryzhic, I. M.

I. S. Gradshteyn, I. M. Ryzhic, and J. Alan, Table of Integrals, Series and Products, 5th ed. New York: Academia, 1994.

Samimi, H.

Shah, A. M.

P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.

Simon, M. K.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 1st ed. New York: Wiley, 2001.

Tayler, D. P.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

Wakamori, K.

P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.

Yilmaz, F.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” arXiv:1302.4225v1, 2013.

Yoon, G.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

IEEE J. Sel. Areas Commun.

E. Ciaramella, Y. Arimoto, G. Contestabile, M. Presi, A. D’Errico, V. Guarino, and M. Matsumoto, “1.28 terabit/s (32×40 Gbit/s) WDM transmission system for free space optical communications,” IEEE J. Sel. Areas Commun., vol.  27, no. 9, pp. 1639–1645, 2009.
[CrossRef]

E. J. Lee and V. W. S. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol.  22, no. 9, pp. 1896–1906, Nov. 2004.
[CrossRef]

IEEE Photon. Technol. Lett.

E. Lee, J. Park, D. Han, and G. Yoon, “Performance analysis of the asymmetric dual-hop relay transmission with mixed RF/FSO links,” IEEE Photon. Technol. Lett., vol.  23, no. 21, pp. 1642–1644, Nov. 2011.
[CrossRef]

IEEE Trans. Commun.

J. Li, J. Q. Liu, and D. P. Tayler, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun., vol.  55, pp. 1598–1606, Aug. 2007.
[CrossRef]

IEEE Trans. Wireless Commun.

M. O. Hasna and M.-S. Alouini, “A performance study of dual-hop transmissions with fixed gains relays,” IEEE Trans. Wireless Commun., vol.  3, no. 6, pp. 1963–1968, Nov. 2004.
[CrossRef]

IET Optoelectron.

W. O. Popoola, Z. Ghassemlooy, J. I. H. Allen, E. Leitgeb, and S. Gao, “Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel,” IET Optoelectron., vol.  2, no. 1, pp. 16–23, Feb. 2008.
[CrossRef]

J. Opt. Commun. Netw.

Opt. Express

Opt. Lett.

Proc. SPIE

I. I. Kim and E. Korevaar, “Availability of free space optics (FSO) and hybrid FSO/RF systems,” Proc. SPIE, vol.  4530, pp. 84–95, Aug. 2001.
[CrossRef]

Other

H. Hogan, “Data demands drive free-space optics,” Photonics Spectra, no. 2, pp. 38–42, Feb. 2013.

P. T. Dat, A. M. Shah, K. Kazaura, and K. Wakamori, “Investigation of suitability of RF signal transmission over FSO links,” in Proc. Int. Symp. on High Capacity Optical Networks and Enabling Technologies (HONET), 2007.

S. Bloom and W. Hartley, “The last-mile solution: Hybrid FSO radio,” AirFiber Inc. White Paper, May 2002.

I. S. Ansari, F. Yilmaz, and M. S. Alouini, “Impact of pointing errors on the performance of mixed RF/FSO dual-hop transmission systems,” arXiv:1302.4225v1, 2013.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” in Numerical Simulations of Physical and Engineering Processes, J. Awrejcewicz, Ed., Intech, 2011, ch. 8.

A. Jurado-Navas, J. M. Garrido-Balsells, J. F. Paris, and A. Puerta-Notario, “A unifying statistical model for atmospheric optical scintillation,” arxiv.org/abs/1102.1915v1, 2011.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 1st ed. New York: Wiley, 2001.

I. S. Gradshteyn, I. M. Ryzhic, and J. Alan, Table of Integrals, Series and Products, 5th ed. New York: Academia, 1994.

V. S. Adamchik and O. I. Marichev, “The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system,” in Proc. Int. Conf. Symbolic and Algebraic Computation, Tokyo, Japan, 1990, pp. 212–224.

Mathematica 8.0, Champaign, Illinois: Wolfram Research, Inc., 2010.

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Figures (4)

Fig. 1.
Fig. 1.

System model of an asymmetric mixed RF/FSO dual-hop communication system.

Fig. 2.
Fig. 2.

Outage performance of the mixed dual-hop communication system. The FSO link experiences the M-distributed fading with (α,β)=(4.2,2) and C=1. In all curves, the transmitted power is normalized, Ω+2b0=1. The cases of ρ=0 and ρ=1 correspond to the special cases of the K and the gamma–gamma distribution, respectively.

Fig. 3.
Fig. 3.

Outage performance of the mixed dual-hop communication system showing impact of pointing errors with g=1. The FSO link experiences the M-distributed fading with (α,β)=(4.2,2) and C=1. In all curves, the transmitted power is normalized, Ω+2b0=1. The cases of ρ=0 and ρ=1 correspond to the special cases of the K and the gamma–gamma distribution, respectively.

Fig. 4.
Fig. 4.

Outage performance of the mixed dual-hop communication system showing impact of pointing errors in the FSO link for different values of g. The FSO link experiences the M-distributed fading with (α,β,ρ)=(4.2,2,1) and C=1. In all curves, the transmitted power is normalized, Ω+2b0=1.

Equations (32)

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r1=h1s+n1,
fγ1(γ1)=1γ¯1exp(γ1γ¯1),
sopt=G(1+ηr1),
r2=I{G(1+ηr1)}+n2=I{G(1+η[h1s+n1])}+n2,
r2=IGη(h1s+n1)+n2.
fI(I)=Ak=1βakIα+k21Kαk(2αβIγβ+Ω),
A=2αα2γ1+α2Γ(α)(γβγβ+Ω)β+α2,
ak=(β1k1)(γβ+Ω)1k2(k1)!(Ωγ)k1(αβ)k2.
fγ2(γ2)=Ak=1βak(γ2)α+k412(γ¯2)α+k4Kαk(2αβγβ+Ωγ2γ2¯).
Pout=P(γ1γ2γ2+C<γth),
Pout=0P(γ1γ2γ2+C<γth|γ2)fγ2(γ2)dγ2.
P(γ1γ2γ2+C<γth|γ2)=1exp(γthγ¯1)exp(Cγthγ¯1γ2).
Pout=1Aexp(γthγ¯1)×k=1βak2(γ¯2)α+k4Ψ(k,γth),
Ψ(k,γth)=0(γ2)α+k41exp(Cγthγ¯1γ2)Kαk(2αβγβ+Ωγ2γ¯2)dγ2.
Pout=1A8πexp(γthγ¯1)×k=1βak(Cγthγ¯1γ¯2)α+k4G0,55,0((αβγβ+Ω)2Cγth16γ¯1γ¯2|αk4,αk+24,αk4,α+k+24,α+k4).
Pout=1exp(γthγ¯1)(αβ)(α+β)/2Γ(α)Γ(β)(γ¯2)α+β4×E(γth),
E(γth)=14π(Cγthγ¯1)α+β4G0,55,0((αβ)2Cγth16γ¯1γ¯2|αβ4,αβ+24,αβ4,α+β+24,α+β4).
fI(I)=g2A2I1k=1βak(αβγβ+Ω)(α+k)2G1,33,0[αβγβ+ΩIA0|g2,α,kg2+1].
f(γ2)=g2A4γ2k=1βak(αβγβ+Ω)(α+k)2G1,33,0[αβγβ+Ωγ2γ¯2|g2,α,kg2+1].
Pout=1exp(γthγ¯1)g2A4×k=1βak(αβγβ+Ω)(α+k)2Ξ(k,γth),
Ξ(k,γth)=01γRDexp(Cγthγ¯1γ2)G1,33,0[αβγβ+Ωγ2γ¯2|g2,α,kg2+1]dγ2.
Ξ(k,γth)=01γRDG1,00,1(γ¯1γ2Cγth|1)G1,33,0[αβγβ+Ωγ2γ¯2|g2,α,kg2+1]dγ2.
Ξ(k,γth)=2α+k12πG1,66,0[(αβγβ+Ω)2Cγth16γ¯1γ¯2|g22,α2,α+12,k2,k+12,0g2+22].
Pout=1exp(γthγ¯1)g2A8π×k=1βak2α+k1(αβγβ+Ω)(α+k)2×G1,66,0[(αβγβ+Ω)2Cγth16γ¯1γ¯2|g22,α2,α+12,k2,k+12,0g2+22].
Pout=1exp(γthγ¯1)×g22α+β8πΓ(α)Γ(β)G1,66,0[(αβ)2Cγth16γ¯1γ¯2|g22,α2,α+12,β2,β+12,0g2+22],
limgPout=1exp(γthγ¯1)A8π×k=1βak2α+k1(αβγβ+Ω)(α+k)2×limgg2G1,66,0[(αβγβ+Ω)2Cγth16γ¯1γ¯2|g22,α2,α+12,k2,k+12,0g2+22].
limgPout=1exp(γthγ¯1)A16π×k=1βak(Cγth16γ¯1γ¯2)(α+k)4{(αβγβ+Ω)2(Cγth16γ¯1γ¯2)}(α+k)4×G0,55,0[(αβγβ+Ω)2Cγth16γ¯1γ¯2|α2,α+12,k2,k+12,0].
limgPout=1A8πexp(γthγ¯1)×k=1βak(Cγth16γ¯1γ¯2)(α+k)4×G0,55,0[(αβγβ+Ω)2Cγth16γ¯1γ¯2|αk2,αk+22,kα2,kα+22,(α+k)4],
exp(Cγthγ¯1γ2)=G1,00,1(γ¯1γ2Cγth|1).
Kαk(2αβγβ+Ωγ2γ2¯)=12G0,22,0(αβγβ+Ωγ2γ2¯|αk2,αk2).
Ψ(k,γth)=120(γ2)α+k41G1,00,1(γ¯1γ2Cγth|1)G0,22,0(αβγβ+Ωγ2γ¯2|αk2,αk2)dγ2.
Ψ(k,γth)=14π(Cγthγ¯1)α+k4×G0,55,0((αβγβ+Ω)2Cγth16γ¯1γ¯2|αk4,αk+24,αk4,α+k+24,α+k4).