Abstract

Relay-assisted free-space optical (FSO) transmission exploits the fact that atmospheric turbulence fading variance is distance dependent and yields significant performance gains by taking advantage of the resulting shorter hops. In this paper, we investigate how to determine optimal relay locations in serial and parallel FSO relaying so as to minimize the outage probability and quantify performance improvements obtained through optimal relay placement. We further present a diversity gain analysis for serial and parallel FSO relaying schemes and quantify their diversity advantages in terms of the number of relays and channel parameters.

© 2013 OSA

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  1. D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, pp. S2–S7, May2004.
    [CrossRef]
  2. S. Arnon, J. R. Barry, G. K. Karagiannidis, R. Schober, and M. Uysal, Eds., Advanced Optical Wireless Communication. Cambridge University Press, 2012.
  3. I. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol., vol. 26, pp. 478–487, Mar.2008.
    [CrossRef]
  4. T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
    [CrossRef]
  5. W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions,” IEEE Trans. Wireless Commun., vol. 8, pp. 2209–2213, May2009.
    [CrossRef]
  6. J. Anguita, M. Neifeld, B. Hildner, and B. Vasic, “Rateless coding on experimental temporally correlated FSO channels,” J. Lightwave Technol., vol. 28, pp. 990–1002, Apr.2010.
    [CrossRef]
  7. N. Chatzidiamantis, M. Uysal, T. Tsiftsis, and G. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol., vol. 28, pp. 1064–1070, Apr.2010.
    [CrossRef]
  8. H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
    [CrossRef]
  9. A. Acampora and S. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol. 6, pp. 62–65, Oct.1999.
    [CrossRef]
  10. J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multi-hop free-space optical communication,” in IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1777–1781.
  11. T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and N. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.
  12. G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
    [CrossRef]
  13. M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Nov.2008.
    [CrossRef]
  14. M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol. 27, pp. 5639–5647, Dec.2009.
    [CrossRef]
  15. M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Commun., vol. 4, no. 12, pp. 1423–1432, 2010.
    [CrossRef]
  16. C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: Performance analysis and optimal power allocation,” J. Lightwave Technol., vol. 29, pp. 1058–1065, Apr.2011.
    [CrossRef]
  17. M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
    [CrossRef]
  18. M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol. 24, pp. 545–547, Mar.2012.
    [CrossRef]
  19. L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation With Applications. Society of Photo-Optical Instrumentation Engineers, 2001.
  20. M. Safari and M. Uysal, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol. 7, pp. 1963–1972, May2008.
    [CrossRef]
  21. G. Osche, Optical Detection Theory. Wiley, New York, 2002.
  22. E. Lee and V. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, pp. 1896–1906, Nov.2004.
    [CrossRef]
  23. J. Strohbehn, “Laser beam propagation in the atmosphere,” in Topics in Applied Physics. Springer, Berlin, 1978.
  24. D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005.
  25. J. G. Proakis, Digital Communication. McGraw-Hill, 2001.
  26. R. Horst, P. Pardalos, and N. Van Thoai, Introduction to Global Optimization. Springer, 2000.
  27. D. Goldberg and J. Holland, “Genetic algorithms in search, optimization, and machine learning,” Mach. Learn., vol. 3, no. 2–3, pp. 95–99, Oct.1988.
    [CrossRef]
  28. L. Khanbary and D. Vidyarthi, “Reliability-based channel allocation using genetic algorithm in mobile computing,” IEEE Trans. Veh. Technol., vol. 58, pp. 4248–4256, Oct.2009.
    [CrossRef]
  29. M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
    [CrossRef]
  30. M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
    [CrossRef]

2012 (3)

H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
[CrossRef]

M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
[CrossRef]

M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol. 24, pp. 545–547, Mar.2012.
[CrossRef]

2011 (2)

C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: Performance analysis and optimal power allocation,” J. Lightwave Technol., vol. 29, pp. 1058–1065, Apr.2011.
[CrossRef]

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

2010 (3)

2009 (4)

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions,” IEEE Trans. Wireless Commun., vol. 8, pp. 2209–2213, May2009.
[CrossRef]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol. 27, pp. 5639–5647, Dec.2009.
[CrossRef]

L. Khanbary and D. Vidyarthi, “Reliability-based channel allocation using genetic algorithm in mobile computing,” IEEE Trans. Veh. Technol., vol. 58, pp. 4248–4256, Oct.2009.
[CrossRef]

2008 (3)

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Nov.2008.
[CrossRef]

M. Safari and M. Uysal, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol. 7, pp. 1963–1972, May2008.
[CrossRef]

I. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. Neifeld, “LDPC-coded MIMO optical communication over the atmospheric turbulence channel,” J. Lightwave Technol., vol. 26, pp. 478–487, Mar.2008.
[CrossRef]

2006 (1)

G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
[CrossRef]

2004 (2)

E. Lee and V. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, pp. 1896–1906, Nov.2004.
[CrossRef]

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, pp. S2–S7, May2004.
[CrossRef]

1999 (1)

A. Acampora and S. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol. 6, pp. 62–65, Oct.1999.
[CrossRef]

1988 (1)

D. Goldberg and J. Holland, “Genetic algorithms in search, optimization, and machine learning,” Mach. Learn., vol. 3, no. 2–3, pp. 95–99, Oct.1988.
[CrossRef]

1981 (1)

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
[CrossRef]

Abou-Rjeily, C.

Acampora, A.

A. Acampora and S. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol. 6, pp. 62–65, Oct.1999.
[CrossRef]

Akella, J.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multi-hop free-space optical communication,” in IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1777–1781.

Andrews, L.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation With Applications. Society of Photo-Optical Instrumentation Engineers, 2001.

Anguita, J.

Arnon, S.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, pp. S2–S7, May2004.
[CrossRef]

Bhatnagar, M.

M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol. 24, pp. 545–547, Mar.2012.
[CrossRef]

Chan, V.

E. Lee and V. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, pp. 1896–1906, Nov.2004.
[CrossRef]

Chatzidiamantis, N.

Denic, S.

Djordjevic, I.

Flohberger, M.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions,” IEEE Trans. Wireless Commun., vol. 8, pp. 2209–2213, May2009.
[CrossRef]

Gappmair, W.

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions,” IEEE Trans. Wireless Commun., vol. 8, pp. 2209–2213, May2009.
[CrossRef]

Goldberg, D.

D. Goldberg and J. Holland, “Genetic algorithms in search, optimization, and machine learning,” Mach. Learn., vol. 3, no. 2–3, pp. 95–99, Oct.1988.
[CrossRef]

Green, R.

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

Grötschel, M.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
[CrossRef]

Haddad, S.

Higgins, M.

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

Hildner, B.

Hines, E.

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

Holland, J.

D. Goldberg and J. Holland, “Genetic algorithms in search, optimization, and machine learning,” Mach. Learn., vol. 3, no. 2–3, pp. 95–99, Oct.1988.
[CrossRef]

Hopen, C.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation With Applications. Society of Photo-Optical Instrumentation Engineers, 2001.

Horst, R.

R. Horst, P. Pardalos, and N. Van Thoai, Introduction to Global Optimization. Springer, 2000.

Kalyanaraman, S.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multi-hop free-space optical communication,” in IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1777–1781.

Karagiannidis, G.

N. Chatzidiamantis, M. Uysal, T. Tsiftsis, and G. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol., vol. 28, pp. 1064–1070, Apr.2010.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and N. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.

Karimi, M.

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Commun., vol. 4, no. 12, pp. 1423–1432, 2010.
[CrossRef]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol. 27, pp. 5639–5647, Dec.2009.
[CrossRef]

Kedar, D.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, pp. S2–S7, May2004.
[CrossRef]

Khanbary, L.

L. Khanbary and D. Vidyarthi, “Reliability-based channel allocation using genetic algorithm in mobile computing,” IEEE Trans. Veh. Technol., vol. 58, pp. 4248–4256, Oct.2009.
[CrossRef]

Krishnamurthy, S.

A. Acampora and S. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol. 6, pp. 62–65, Oct.1999.
[CrossRef]

Lee, E.

E. Lee and V. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, pp. 1896–1906, Nov.2004.
[CrossRef]

Leeson, M.

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

LoPresti, P.

H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
[CrossRef]

Lovász, L.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
[CrossRef]

Moradi, H.

H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
[CrossRef]

Nasiri-Kenari, M.

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Commun., vol. 4, no. 12, pp. 1423–1432, 2010.
[CrossRef]

M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol. 27, pp. 5639–5647, Dec.2009.
[CrossRef]

Neifeld, M.

Osche, G.

G. Osche, Optical Detection Theory. Wiley, New York, 2002.

Pardalos, P.

R. Horst, P. Pardalos, and N. Van Thoai, Introduction to Global Optimization. Springer, 2000.

Phillips, R.

L. Andrews, R. Phillips, and C. Hopen, Laser Beam Scintillation With Applications. Society of Photo-Optical Instrumentation Engineers, 2001.

Proakis, J. G.

J. G. Proakis, Digital Communication. McGraw-Hill, 2001.

Rad, M.

M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
[CrossRef]

Refai, H.

H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
[CrossRef]

Safari, M.

M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
[CrossRef]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Nov.2008.
[CrossRef]

M. Safari and M. Uysal, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol. 7, pp. 1963–1972, May2008.
[CrossRef]

Sagias, N.

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and N. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.

Sandalidis, H.

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and N. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.

Schrijver, A.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
[CrossRef]

Strohbehn, J.

J. Strohbehn, “Laser beam propagation in the atmosphere,” in Topics in Applied Physics. Springer, Berlin, 1978.

Tse, D.

D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005.

Tsiftsis, T.

N. Chatzidiamantis, M. Uysal, T. Tsiftsis, and G. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol., vol. 28, pp. 1064–1070, Apr.2010.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and N. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.

Uysal, M.

M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
[CrossRef]

N. Chatzidiamantis, M. Uysal, T. Tsiftsis, and G. Karagiannidis, “Iterative near maximum-likelihood sequence detection for MIMO optical wireless systems,” J. Lightwave Technol., vol. 28, pp. 1064–1070, Apr.2010.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Nov.2008.
[CrossRef]

M. Safari and M. Uysal, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol. 7, pp. 1963–1972, May2008.
[CrossRef]

Van Thoai, N.

R. Horst, P. Pardalos, and N. Van Thoai, Introduction to Global Optimization. Springer, 2000.

Vasic, B.

Vidyarthi, D.

L. Khanbary and D. Vidyarthi, “Reliability-based channel allocation using genetic algorithm in mobile computing,” IEEE Trans. Veh. Technol., vol. 58, pp. 4248–4256, Oct.2009.
[CrossRef]

Viswanath, P.

D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005.

Yuksel, M.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multi-hop free-space optical communication,” in IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1777–1781.

Combinatorica (1)

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol. 1, no. 2, pp. 169–197, 1981.
[CrossRef]

Electron. Lett. (1)

G. Karagiannidis, T. Tsiftsis, and H. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol. 42, no. 17, pp. 994–996, 2006.
[CrossRef]

IEEE Commun. Mag. (1)

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol. 42, pp. S2–S7, May2004.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

E. Lee and V. Chan, “Part 1: Optical communication over the clear turbulent atmospheric channel using diversity,” IEEE J. Sel. Areas Commun., vol. 22, pp. 1896–1906, Nov.2004.
[CrossRef]

IEEE Pers. Commun. (1)

A. Acampora and S. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol. 6, pp. 62–65, Oct.1999.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol. 24, pp. 545–547, Mar.2012.
[CrossRef]

IEEE Trans. Commun. (1)

M. Safari, M. Rad, and M. Uysal, “Multi-hop relaying over the atmospheric Poisson channel: Outage analysis and optimization,” IEEE Trans. Commun., vol. 60, no. 3, pp. 817–829, 2012.
[CrossRef]

IEEE Trans. Veh. Technol. (2)

H. Moradi, H. Refai, and P. LoPresti, “Circular MIMO FSO nodes with transmit selection and receive generalized selection diversity,” IEEE Trans. Veh. Technol., vol. 61, pp. 1174–1181, Mar.2012.
[CrossRef]

L. Khanbary and D. Vidyarthi, “Reliability-based channel allocation using genetic algorithm in mobile computing,” IEEE Trans. Veh. Technol., vol. 58, pp. 4248–4256, Oct.2009.
[CrossRef]

IEEE Trans. Wireless Commun. (4)

M. Safari and M. Uysal, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol. 7, pp. 1963–1972, May2008.
[CrossRef]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Nov.2008.
[CrossRef]

T. Tsiftsis, H. Sandalidis, G. Karagiannidis, and M. Uysal, “Optical wireless links with spatial diversity over strong atmospheric turbulence channels,” IEEE Trans. Wireless Commun., vol. 8, pp. 951–957, Feb.2009.
[CrossRef]

W. Gappmair and M. Flohberger, “Error performance of coded FSO links in turbulent atmosphere modeled by gamma–gamma distributions,” IEEE Trans. Wireless Commun., vol. 8, pp. 2209–2213, May2009.
[CrossRef]

IET Commun. (2)

M. Higgins, R. Green, M. Leeson, and E. Hines, “Multi-user indoor optical wireless communication system channel control using a genetic algorithm,” IET Commun., vol. 5, pp. 937–944, May2011.
[CrossRef]

M. Karimi and M. Nasiri-Kenari, “Outage analysis of relay-assisted free-space optical communications,” IET Commun., vol. 4, no. 12, pp. 1423–1432, 2010.
[CrossRef]

J. Lightwave Technol. (5)

Mach. Learn. (1)

D. Goldberg and J. Holland, “Genetic algorithms in search, optimization, and machine learning,” Mach. Learn., vol. 3, no. 2–3, pp. 95–99, Oct.1988.
[CrossRef]

Other (9)

G. Osche, Optical Detection Theory. Wiley, New York, 2002.

S. Arnon, J. R. Barry, G. K. Karagiannidis, R. Schober, and M. Uysal, Eds., Advanced Optical Wireless Communication. Cambridge University Press, 2012.

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Figures (8)

Fig. 1
Fig. 1

FSO serial relaying configuration.

Fig. 2
Fig. 2

(Color online) FSO parallel relaying configuration.

Fig. 3
Fig. 3

(Color online) Outage probability of serial FSO relaying scheme for different scenarios.

Fig. 4
Fig. 4

(Color online) Outage probability of parallel FSO relaying scheme for K = 2 and 3.

Fig. 5
Fig. 5

(Color online) Outage probability of parallel FSO relaying scheme for K = 3 and 4.

Fig. 6
Fig. 6

(Color online) RDO of serial FSO relaying scheme for different numbers of relays.

Fig. 7
Fig. 7

(Color online) RDO of parallel FSO relaying scheme for (a) two relays and (b) three relays.

Fig. 8
Fig. 8

(Color online) Comparison of the maximum ARDO for serial and parallel relaying.

Tables (1)

Tables Icon

Table I Normalized Optimal Relay Locations for Parallel FSO Relaying

Equations (66)

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g = | α | 2 L ( d ) ,
p ( | α | ) = 1 | α | 2 π σ χ 2 exp ( ( ln ( | α | ) + σ χ 2 ) 2 2 σ χ 2 ) .
σ χ 2 ( d ) = min { 0 . 124 k 7 / 6 C n 2 d 11 / 6 , 0 . 5 } ,
C n 2 ( h ) = 0 . 00594 ( v / 27 ) 2 ( 10 5 h ) 10 exp ( h / 1000 ) + 2 . 7 × 10 6 exp ( h / 1500 ) + A exp ( h / 1000 ) .
P out = Pr ( i = 1 K + 1 { γ i < γ th } ) = 1 i = 1 K + 1 ( 1 Pr ( γ i < γ th ) ) ,
P out = 1 i = 1 K + 1 ( 1 Q ( ln ( L ( d i ) P M K + 1 ) + 2 μ χ ( d i ) 2 σ χ ( d i ) ) ) ,
P out = i = 1 2 K P out-p ( W ( i ) ) = i = 1 2 K [ j W ( i ) ( 1 Q ( ln ( L ( d S , j ) P M 2 K ) + 2 μ χ ( d S , j ) 2 σ χ ( d S , j ) ) ) × j W ( i ) Q ( ln ( L ( d S , j ) P M 2 K ) + 2 μ χ ( d S , j ) 2 σ χ ( d S , j ) ) ] × Q ( ln ( P M e μ ξ 2 K ) σ ξ ( d ̄ W ( i ) ) ) ,
μ ξ ( d ̄ W ( i ) ) = ln i W ( i ) L ( d i , D ) σ ξ 2 ( d ̄ W ( i ) ) / 2 ,
σ ξ 2 ( d ̄ W ( i ) ) = ln ( 1 + i W ( i ) L 2 ( d i , D ) ( e 4 σ χ 2 1 ) ( i W ( i ) L ( d i , D ) ) 2 ) .
h ( d 1 , d 2 , , d K + 1 ) = i = 1 K + 1 Φ ( f ( d i ) ) ,
g ( d 1 , d 2 , , d K + 1 ) = i = 1 K + 1 d i ,
max d 1 , d 2 , , d K + 1 h ( d 1 , d 2 , , d K + 1 )
s.t . g ( d 1 , d 2 , , d K + 1 ) = d S , D .
f ( d i ) exp ( f ( d i ) 2 2 ) j = 1 j i K + 1 Φ ( f ( d j ) ) = 2 Λ 2 π ,
f ( d i ) exp ( f ( d i ) 2 2 ) Φ ( f ( d k ) ) = f ( d k ) exp ( f ( d k ) 2 2 ) Φ ( f ( d i ) ) .
d i = d k .
z ( d S , 1 , d S , 2 , , d S , K , d 1 , D , , d K , D ) = def i = 1 2 K [ j W ( i ) ( 1 Q ( u ( d S , j ) ) ) j W ( i ) Q ( u ( d S , j ) ) ] × Q ( v ( d ̄ W ( i ) ) ) ,
u ( d S , j ) = def ( ln ( L ( d S , j ) P M 2 K ) + 2 μ χ ( d S , j ) ) / 2 σ χ ( d S , j ) ,
v ( d ̄ W ( i ) ) = def ln ( P M e μ ξ 2 K ) / σ ξ ( d ̄ W ( i ) ) ,
min d S , j , d j , D , j = 1 , 2 , , K z ( d S , 1 , d S , 2 , , d S , K , d 1 , D , , d K , D )
s.t. d S , j + d j , D = d S , D j = 1 , 2 , , K .
d opt ( P M , d S , D , K ) = 0 . 5 d S , D + β P M ln ( ϖ P M κ + φ ) K 2 ,
RDO ( P M ) = ln P out / ln P M ln P out,SISO / ln P M ,
RDO ( P M ) = ln ( 1 i = 1 K + 1 ( 1 Pr ( γ i < γ th ) ) ) / ln P M ln ( Q ( ( ln ( P M ) + 2 μ χ ( d S , D ) ) / 2 σ χ ( d S , D ) ) ) / ln P M .
RDO ( P M ) ln ( i = 1 K + 1 Q ( ln ( L ( d i ) P M / K + 1 ) + 2 μ χ ( d i ) 2 σ χ ( d i ) ) ) / ln P M ln ( Q ( ( ln ( P M ) + 2 μ χ ( d S , D ) ) / 2 σ χ ( d S , D ) ) ) / ln P M ,
RDO ( P M ) i = 1 K + 1 P out-s ( i ) ( l n P out-s ( i ) / ln P M ) ln ( Q ( ( ln ( P M ) + 2 μ χ ( d S , D ) ) / 2 σ χ ( d S , D ) ) ) ln P M i = 1 K + 1 P out-s ( i ) ,
1 2 π x 1 + x 2 exp ( x 2 / 2 ) < Q ( x ) < 1 2 π x exp ( x 2 / 2 ) .
RDO ( P M ) ̃ i = 1 K + 1 ρ ( i ) P ̃ out-s ( i ) C i = 1 K + 1 P ˆ out-s ,
RDO ( P M ) ̃ i = 1 K + 1 ρ ˆ ( i ) P ˆ out-s ( i ) C ̃ i = 1 K + 1 P ̃ out-s ( i ) ,
P ̃ out-s = 2 σ χ ( d i ) ln ( P M ) + ψ ( i ) exp ( ( ln ( P M ) + ψ ( i ) ) 2 8 σ χ 2 ( d i ) ) ,
P ˆ out-s = ( ln ( P M ) + ψ ( i ) 2 σ χ ( d i ) / ( 1 + ( ln ( P M ) + ψ ( i ) ) 2 4 σ χ 4 ( d i ) ) ) × exp ( ( ln ( P M ) + ψ ( i ) ) 2 8 σ χ 2 ( d i ) ) ,
ρ ( i ) = ( ln ( P M ) + ψ ( i ) 4 σ χ 2 ( d i ) + 2 σ χ ( d i ) ln ( P M ) + ψ ( i ) ) ,
ρ ˆ ( i ) = ln ( P M ) + ψ ( i ) 4 σ χ 4 ( d i ) + ( ( ln ( P M ) + ψ ( i ) ) 2 4 σ χ 4 ( d i ) 1 ) × ( ln ( P M ) + ψ ( i ) 2 σ χ ( d i ) ( 1 + ( ln ( P M ) + ψ ( i ) ) 2 4 σ χ 4 ( d i ) ) ) 1 ,
C = ln ( P M ) + 2 μ x ( d S , D ) 4 σ χ 2 ( d S , D ) + 2 σ χ ( d S , D ) ln ( P M ) + 2 μ x ( d S , D ) × ( ln ( P M ) + 2 μ x ( d S , D ) ) 2 4 σ χ 4 ( d S , D ) ( ln ( P M ) + 2 μ x ( d S , D ) ) 2 + 4 σ χ 4 ( d S , D ) ,
C ̃ = 2 σ χ ( d S , D ) ln ( P M ) + 2 μ x ( d S , D ) + ln ( P M ) + 2 μ x ( d S , D ) 4 σ χ 2 ( d S , D ) .
ARDO = lim P M σ χ 2 ( d S , D ) i = 1 K + 1 1 σ χ ( d i ) exp ( ( ln ( P M ) ) 2 8 σ χ 2 ( d i ) ) i = 1 K + 1 σ χ ( d i ) exp ( ( ln ( P M ) ) 2 8 σ χ 2 ( d i ) ) = σ χ 2 ( d S , D ) max d i ( σ χ 2 ( d i ) ) ,
ARDO = ( d S , D / d max ) 11 / 6 .
ARDO max = ( K + 1 ) 11 / 6 .
RDO ( P M ) = ln ( i = 1 2 K P out-p ( W ( i ) ) ) / ln P M ln ( Q ( ( ln ( P M ) + 2 μ χ ( d S , D ) ) / 2 σ χ ( d S , D ) ) ) / ln P M .
I = i = 1 2 K P out-p ( W ( i ) ) ln P M i = 1 2 K P out-p ( W ( i ) ) = i = 1 2 K P out-p ( W ( i ) ) ln P out-p ( W ( i ) ) ln P M i = 1 2 K P out-p ( W ( i ) ) .
ln P out-p ( W ( i ) ) ln P M = ln P M ( ln ( Q ( ln ( P M ) + υ ̃ ( W ( i ) ) σ ξ ( d ̄ W ( i ) ) ) ) + j W ( i ) ln ( 1 Q ( ln ( P M ) + υ ( j ) 2 σ χ ( d S , j ) ) ) + j W ( i ) ln ( Q ( ln ( P M ) + υ ( j ) 2 σ χ ( d S , j ) ) ) ) ,
RDO ( P M ) i = 1 2 K κ ( i ) P ̃ out-p ( W ( i ) ) C i = 1 2 K P ˆ out-p ( W ( i ) ) ,
RDO ( P M ) i = 1 2 K κ ̃ ( i ) P ˆ out-p ( S ( i ) ) C ̃ i = 1 2 K P ̃ out-p ( S ( i ) ) ,
P ̃ out-p ( W ( i ) ) = exp ( Θ ) j W ( i ) Γ ( j ) σ ξ ( d ̄ W ( i ) ) ln ( P M ) + υ ̃ ( W ( i ) ) × j W ( i ) 2 σ χ ( d S , j ) ln ( P M ) + υ ( j ) ,
P ˆ out-p ( W ( i ) ) = exp ( Θ ) j W ( i ) ( Γ ( j ) × ( ln ( P M ) + υ ̃ ( W ( i ) ) σ ξ ( d ̄ W ( i ) ) / ( 1 + ( ln ( P M ) + υ ̃ ( W ( i ) ) ) 2 σ ξ 2 ( d ̄ W ( i ) ) ) ) ) × j W ( i ) ln ( P M ) + υ ( W ( i ) ) σ χ ( d S , j ) / ( 1 + ( ln ( P M ) + υ ( W ( i ) ) ) 2 σ χ 2 ( d S , j ) ) ,
κ ( i ) = j W ( i ) ( ln ( P M ) + υ ( j ) 4 σ χ 4 ( d S , j ) + 2 σ χ ( d S , j ) ln ( P M ) + υ ( j ) ) + j W ( i ) ln Γ ( j ) ln P M + ln ( P M ) + υ ̃ ( W ( i ) ) σ ξ 2 ( d ̄ W ( i ) ) + σ ξ ( d ̄ W ( i ) ) ln ( P M ) + υ ̃ ( W ( i ) ) ,
κ ̃ ( i ) = ln ( P M ) + υ ̃ ( W ( i ) ) σ ξ 2 ( d ̄ W ( i ) ) + j W ( i ) ln Γ ( j ) ln P M + j W ( i ) ( ln ( P M ) + υ ( j ) 4 σ χ 2 ( d s , j ) + 2 σ χ ( d s , j ) ln ( P M ) + υ ( j ) × ( ln ( P M ) + υ ( j ) ) 2 4 σ χ 4 ( d s , j ) ( ln ( P M ) + υ ( j ) ) 2 + 4 σ χ 4 ( d s , j ) + σ ξ ( d ̄ W ( i ) ) ( ln ( P M ) + υ ̃ ( W ( i ) ) ) × ( ln ( P M ) + υ ̃ ( W ( i ) ) ) 2 σ ξ 4 ( d ̄ W ( i ) ) ( ln ( P M ) + υ ̃ ( W ( i ) ) ) 2 + σ ξ 4 ( d ̄ W ( i ) ) ) ,
Γ ( j ) = 1 Q ( ln ( P M ) + υ ( j ) 2 σ χ ( d S , j ) ) ,
Θ = j W ( i ) ( ln ( P M ) + υ ( j ) ) 2 8 σ χ 2 ( d S , j ) + ( ln ( P M ) + υ ̃ ( W ( i ) ) ) 2 2 σ ξ 2 ( d ̄ W ( i ) ) .
ARDO = lim P M { ( 2 2 σ χ ( d S , D ) ln ( P M ) ) 2 × i = 1 2 K τ ( i ) σ ξ ( d ̄ W ( i ) ) exp ( τ ( i ) ) j W ( i ) ) 2 σ χ ( d S , j ) i = 1 2 K σ ξ ( d ̄ W ( i ) ) exp ( τ ( i ) ) j W ( i ) 2 σ χ ( d S , j ) } ,
τ ( i ) = ( ln ( P M ) ) 2 2 ( j W ( i ) ( 1 4 σ χ 2 ( d S , j ) ) + 1 σ ξ 2 ( d ̄ W ( i ) ) ) .
ARDO = 4 σ χ 2 ( d S , D ) min τ ( i ) .
ARDO = 4 σ χ 2 ( d S , D ) × min N S ( S ( i ) ) ( K N S ( S ( i ) ) 4 σ χ 2 ( d ) + 1 σ ξ 2 ( N S ( S ( i ) ) , d ) ) ,
σ ξ 2 ( N S ( S ( i ) ) , d ) = ln ( 1 + exp ( 4 σ χ 2 ( d S , D d ) ) 1 N S ( S ( i ) ) ) .
ARDO = σ χ 2 ( d S , D ) min τ ( N S ( S ( i ) ) ) ,
τ ( N S ( S ( i ) ) ) = K N S ( S ( i ) ) σ χ 2 ( d ) + N S ( S ( i ) ) σ χ 2 ( d S , D d ) .
ARDO = { K ( d S , D d S , D d opt ) 11 / 6 d d S , D / 2 K ( d S , D d opt ) 11 / 6 d d S , D / 2 .
ARDO max = 2 11 / 6 K .
ARDO max = N H 11 / 6 N D ,
h ( d 1 , , d i , d i + 1 , , d K + 1 ) h ( d 1 , , d i , d i + 1 , , d K + 1 ) ,
( Φ ( f ( d i ) ) Φ ( f ( d i + 1 ) ) Φ ( f ( d i ) ) Φ ( f ( d i + 1 ) ) ) × j = 1 j i , i + 1 K + 1 Φ ( f ( d j ) ) 0 .
z ( d S , 1 , , d S , i , , d i , D , , d K , D ) z ( d S , 1 , , d S , i , , d i , D , , d K , D ) ,
z ( ) = j = 1 2 K 1 P s ( j ) [ Q ( u ( d S , i ) ) Q ( v ( d ̄ W ( i ) ) ) + ( 1 Q ( u ( d S , i ) ) ) Q ( v ( d ̄ W ( i ) , d i , D ) ) ] .
[ Q 1 Q ˆ 1 ] Q M + ( 1 Q 1 ) Q ̃ M ( 1 Q ˆ 1 ) Q ˆ M 0 ,
[ Q 1 Q ˆ 1 ] Q M + ( 1 Q ˆ 1 ( Q 1 Q ˆ 1 ) ) × ( Q ˆ M + Q ̃ M Q ˆ M ) ( 1 Q ˆ 1 ) Q ˆ M 0 .
( Q 1 Q ˆ 1 ) ( Q M Q ˆ M ) + ( 1 Q 1 ) ( Q ̃ M Q ˆ M ) 0 .