Abstract

In this paper, we investigate the outage performance of free-space optical mesh networks, which build upon the combination of serial (multi-hop) and parallel relaying. We assume log-normal atmospheric turbulence channels and derive outage probability expressions for the multi-hop parallel relaying scheme under consideration. Our outage probability analysis demonstrates substantial performance improvements with respect to both standalone serial and parallel relaying schemes. Furthermore, we present a diversity gain analysis and quantify the achievable diversity order in terms of the number of relays and the turbulence channel parameters.

© 2013 Optical Society of America

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  1. H. Willebrand and B. Ghuman, Free Space Optics: Enabling Optical Connectivity in Today’s Networks. Indianapolis, IN: Sams, 2002.
  2. D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol.  42, no. 5, pp. S2–S7, May 2004.
    [CrossRef]
  3. A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol.  2, pp. 345–396, 2005.
    [CrossRef]
  4. A. S. Acampora and S. V. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol.  6, no. 5, pp. 62–65, Oct. 1999.
  5. J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multihop free-space optical communication,” in Proc. of IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1771–1781.
  6. T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and N. C. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in Proc. of IEEE Int. Conf. on Communications (ICC), June 2006, vol. 6, pp. 2755–2759.
  7. G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
    [CrossRef]
  8. M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol.  7, no. 12, pp. 5441–5449, Dec. 2008.
    [CrossRef]
  9. M. Karimi and M. Nasiri-Kenari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol.  27, no. 24, pp. 5639–5647, 2009.
    [CrossRef]
  10. 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]
  11. C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: Performance analysis and optimal power allocation,” J. Lightwave Technol., vol.  29, no. 7, pp. 1058–1065, Apr. 2011.
    [CrossRef]
  12. S. M. Aghajanzadeh and M. Uysal, “Multi-hop coherent free-space optical communications over atmospheric turbulence channels,” IEEE Trans. Commun., vol.  59, no. 6, pp. 1657–1663, June 2011.
    [CrossRef]
  13. S. Kazemlou, S. Hranilovic, and S. Kumar, “All-optical multihop free-space optical communication systems,” J. Lightwave Technol., vol.  29, no. 18, pp. 2663–2669, Sept. 2011.
    [CrossRef]
  14. M. Safari, M. 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, Mar. 2012.
    [CrossRef]
  15. M. R. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  24, no. 7, pp. 545–547, Apr. 2012.
    [CrossRef]
  16. M. R. Bhatnagar, “Average BER analysis of differential modulation in DF cooperative communication system over gamma–gamma fading FSO links,” IEEE Commun. Lett., vol.  16, no. 8, pp. 1228–1231, Aug. 2012.
    [CrossRef]
  17. E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
    [CrossRef]
  18. M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
    [CrossRef]
  19. J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
    [CrossRef]
  20. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Bellingham, WA: SPIE, 2001.
  21. S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels: Fibers, Clouds, Water, and the Atmosphere. New York: Plenum, 1988.
  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, no. 9, pp. 1896–1906, 2004.
    [CrossRef]
  23. D. Tse and P. Viswanath, Fundamentals of Wireless Communication. London: Cambridge University Press, 2005.
  24. M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
    [CrossRef]
  25. J. G. Proakis, Digital Communication. New York: McGraw-Hill, 2001.
  26. M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
    [CrossRef]
  27. M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and diversity analysis of relay-assisted free-space optical communication systems,” J. Opt. Commun. Netw., vol.  5, pp. 37–47, 2013.
    [CrossRef]

2013

2012

M. Safari, M. 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, Mar. 2012.
[CrossRef]

M. R. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  24, no. 7, pp. 545–547, Apr. 2012.
[CrossRef]

M. R. Bhatnagar, “Average BER analysis of differential modulation in DF cooperative communication system over gamma–gamma fading FSO links,” IEEE Commun. Lett., vol.  16, no. 8, pp. 1228–1231, Aug. 2012.
[CrossRef]

E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
[CrossRef]

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

2011

2010

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]

2009

2008

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol.  7, no. 12, pp. 5441–5449, Dec. 2008.
[CrossRef]

M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
[CrossRef]

2006

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

2005

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol.  2, pp. 345–396, 2005.
[CrossRef]

2004

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol.  42, no. 5, pp. S2–S7, May 2004.
[CrossRef]

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
[CrossRef]

E. Lee and V. 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, 2004.
[CrossRef]

1999

A. S. Acampora and S. V. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol.  6, no. 5, pp. 62–65, Oct. 1999.

1981

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
[CrossRef]

Abou-Rjeily, C.

Acampora, A. S.

A. S. Acampora and S. V. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol.  6, no. 5, pp. 62–65, Oct. 1999.

Aghajanzadeh, S. M.

S. M. Aghajanzadeh and M. Uysal, “Multi-hop coherent free-space optical communications over atmospheric turbulence channels,” IEEE Trans. Commun., vol.  59, no. 6, pp. 1657–1663, June 2011.
[CrossRef]

Akella, J.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multihop free-space optical communication,” in Proc. of IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1771–1781.

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Bellingham, WA: SPIE, 2001.

Arnon, S.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol.  42, no. 5, pp. S2–S7, May 2004.
[CrossRef]

Bayaki, E.

E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
[CrossRef]

Bhatnagar, M. R.

M. R. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  24, no. 7, pp. 545–547, Apr. 2012.
[CrossRef]

M. R. Bhatnagar, “Average BER analysis of differential modulation in DF cooperative communication system over gamma–gamma fading FSO links,” IEEE Commun. Lett., vol.  16, no. 8, pp. 1228–1231, Aug. 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, no. 9, pp. 1896–1906, 2004.
[CrossRef]

Gagliardi, R. M.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels: Fibers, Clouds, Water, and the Atmosphere. New York: Plenum, 1988.

Ghuman, B.

H. Willebrand and B. Ghuman, Free Space Optics: Enabling Optical Connectivity in Today’s Networks. Indianapolis, IN: Sams, 2002.

Grötschel, M.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
[CrossRef]

Haddad, S.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Bellingham, WA: SPIE, 2001.

Hranilovic, S.

Kalyanaraman, S.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multihop free-space optical communication,” in Proc. of IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1771–1781.

Karagiannidis, G. K.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

T. A. Tsiftsis, H. G. Sandalidis, G. K. Karagiannidis, and N. C. Sagias, “Multihop free-space optical communications over strong turbulence channels,” in Proc. of 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, no. 24, pp. 5639–5647, 2009.
[CrossRef]

Karp, S.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels: Fibers, Clouds, Water, and the Atmosphere. New York: Plenum, 1988.

Kashani, M. A.

M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and diversity analysis of relay-assisted free-space optical communication systems,” J. Opt. Commun. Netw., vol.  5, pp. 37–47, 2013.
[CrossRef]

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

Kazemlou, S.

Kedar, D.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol.  42, no. 5, pp. S2–S7, May 2004.
[CrossRef]

Krishnamurthy, S. V.

A. S. Acampora and S. V. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol.  6, no. 5, pp. 62–65, Oct. 1999.

Kumar, S.

Laneman, J.

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
[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, no. 9, pp. 1896–1906, 2004.
[CrossRef]

Lovász, L.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
[CrossRef]

Majumdar, A. K.

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep., vol.  2, pp. 345–396, 2005.
[CrossRef]

Michalopoulos, D.

E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
[CrossRef]

Moran, S. E.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels: Fibers, Clouds, Water, and the Atmosphere. New York: Plenum, 1988.

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, no. 24, pp. 5639–5647, 2009.
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation With Applications. Bellingham, WA: SPIE, 2001.

Proakis, J. G.

J. G. Proakis, Digital Communication. New York: McGraw-Hill, 2001.

Rad, M. M.

M. Safari, M. 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, Mar. 2012.
[CrossRef]

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

Safari, M.

M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and diversity analysis of relay-assisted free-space optical communication systems,” J. Opt. Commun. Netw., vol.  5, pp. 37–47, 2013.
[CrossRef]

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

M. Safari, M. 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, Mar. 2012.
[CrossRef]

M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
[CrossRef]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol.  7, no. 12, pp. 5441–5449, Dec. 2008.
[CrossRef]

Sagias, N. C.

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

Sandalidis, H. G.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

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

Schober, R.

E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
[CrossRef]

Schrijver, A.

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
[CrossRef]

Stotts, L. B.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels: Fibers, Clouds, Water, and the Atmosphere. New York: Plenum, 1988.

Tse, D.

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
[CrossRef]

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

Tsiftsis, T. A.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

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

Uysal, M.

M. A. Kashani, M. Safari, and M. Uysal, “Optimal relay placement and diversity analysis of relay-assisted free-space optical communication systems,” J. Opt. Commun. Netw., vol.  5, pp. 37–47, 2013.
[CrossRef]

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

M. Safari, M. 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, Mar. 2012.
[CrossRef]

S. M. Aghajanzadeh and M. Uysal, “Multi-hop coherent free-space optical communications over atmospheric turbulence channels,” IEEE Trans. Commun., vol.  59, no. 6, pp. 1657–1663, June 2011.
[CrossRef]

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol.  7, no. 12, pp. 5441–5449, Dec. 2008.
[CrossRef]

M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
[CrossRef]

Viswanath, P.

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

Willebrand, H.

H. Willebrand and B. Ghuman, Free Space Optics: Enabling Optical Connectivity in Today’s Networks. Indianapolis, IN: Sams, 2002.

Wornell, G.

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
[CrossRef]

Yuksel, M.

J. Akella, M. Yuksel, and S. Kalyanaraman, “Error analysis of multihop free-space optical communication,” in Proc. of IEEE Int. Conf. on Communications (ICC), May 2005, vol. 3, pp. 1771–1781.

Zhang, K.

M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
[CrossRef]

Combinatorica

M. Grötschel, L. Lovász, and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimization,” Combinatorica, vol.  1, pp. 169–197, 1981.
[CrossRef]

Electron. Lett.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, “Outage probability of relayed free space optical communication systems,” Electron. Lett., vol.  42, no. 17, pp. 994–995, Aug. 2006.
[CrossRef]

IEEE Commun. Lett.

M. A. Kashani, M. M. Rad, M. Safari, and M. Uysal, “All-optical amplify-and-forward relaying system for atmospheric channels,” IEEE Commun. Lett., vol.  16, no. 10, pp. 1684–1687, Oct. 2012.
[CrossRef]

M. R. Bhatnagar, “Average BER analysis of differential modulation in DF cooperative communication system over gamma–gamma fading FSO links,” IEEE Commun. Lett., vol.  16, no. 8, pp. 1228–1231, Aug. 2012.
[CrossRef]

IEEE Commun. Mag.

D. Kedar and S. Arnon, “Urban optical wireless communication networks: The main challenges and possible solutions,” IEEE Commun. Mag., vol.  42, no. 5, pp. S2–S7, May 2004.
[CrossRef]

IEEE J. Sel. Areas Commun.

E. Lee and V. 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, 2004.
[CrossRef]

IEEE Pers. Commun.

A. S. Acampora and S. V. Krishnamurthy, “A broadband wireless access network based on mesh-connected free-space optical links,” IEEE Pers. Commun., vol.  6, no. 5, pp. 62–65, Oct. 1999.

IEEE Photon. Technol. Lett.

M. R. Bhatnagar, “Performance analysis of decode-and-forward relaying in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  24, no. 7, pp. 545–547, Apr. 2012.
[CrossRef]

IEEE Trans. Commun.

S. M. Aghajanzadeh and M. Uysal, “Multi-hop coherent free-space optical communications over atmospheric turbulence channels,” IEEE Trans. Commun., vol.  59, no. 6, pp. 1657–1663, June 2011.
[CrossRef]

M. Safari, M. 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, Mar. 2012.
[CrossRef]

E. Bayaki, D. Michalopoulos, and R. Schober, “EDFA-based all-optical relaying in free-space optical systems,” IEEE Trans. Commun., vol.  60, no. 12, pp. 3797–3807, Dec. 2012.
[CrossRef]

IEEE Trans. Inf. Theory

J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3062–3080, 2004.
[CrossRef]

IEEE Trans. Wireless Commun.

M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol.  7, no. 12, pp. 5441–5449, Dec. 2008.
[CrossRef]

M. Safari, M. Uysal, and K. Zhang, “Cooperative diversity over log-normal fading channels: Performance analysis and optimization,” IEEE Trans. Wireless Commun., vol.  7, no. 5, pp. 1963–1972, May 2008.
[CrossRef]

IET Commun.

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Figures (10)

Fig. 1.
Fig. 1.

Multi-hop parallel FSO relaying network.

Fig. 2.
Fig. 2.

Configurations under consideration: (a) C1, three groups of relays; (b) C2, two groups of relays; and (c) C3, single group of relays.

Fig. 3.
Fig. 3.

(a) Multi-hop and (b) parallel relaying benchmarking schemes for C1.

Fig. 4.
Fig. 4.

(a) Multi-hop and (b) parallel relaying benchmarking schemes for C2.

Fig. 5.
Fig. 5.

Multi-hop relaying benchmarking scheme for C3.

Fig. 6.
Fig. 6.

Performance comparison of multi-hop parallel, serial, and parallel relaying for C1.

Fig. 7.
Fig. 7.

Performance comparison of multi-hop parallel, serial, and parallel relaying for C2.

Fig. 8.
Fig. 8.

Performance comparison of multi-hop parallel, serial, and parallel relaying for C3.

Fig. 9.
Fig. 9.

Effect of different number of groups on the outage performance.

Fig. 10.
Fig. 10.

RDO values for C1, C2, C3, and multi-hop relaying.

Equations (29)

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rk1=[rk1srk1n]=[RTb(PgS,k1+Pb)+nk1sRTbPb+nk1n],
rki=[rkisrkin]=[RTb(Pji1Di1kgji1,ki+Pb)+nkisRTbPb+nkin],
Pout=i1=12N1Pout,phase2(U1(i1))Pr(U1(i1)).
Pr(U1(i1))=Pr[(m1U1(i1)m1U1(i1))(m1U1(i)m1U1(i1))]=m1U1(i1)(1Pout,SISO(dS,m1))m1U1(i1)Pout,SISO(dS,m1),
Pout,phasej(Uj1(ij1))=ij=12|Wj|Pout,phasej+1(Uj(ij))Pr(Uj(ij))
Pr(Uj(ij))=mjUj(ij)(1Pout,MISO(d¯Uj1(ij1),mj))mjUj(ij)Pout,MISO(d¯Uj1(ij1),mj).
Pout=i1=12NiPr(U1(i1))i2=12|W2|Pr(U2(i2))iK=12|WK|Pr(UK(iK))Pout,MISO(d¯UK(iK),D).
H(di,j)def=Q(ln(L(di,j)PM/κ)+2μχ(di,j)2σχ(di,j)),
G(d¯)def=Q(ln(PM/κ)+μξ(d¯)σξ(d¯)),
Pout=i1=12N1Pout1(U1(i1))=i1=12N1m1U1(i1)(1H(dS,m1))m1U1(i1)H(dS,m1)×i2=12|W2|m2U2(i2)(1G(d¯U1(i1),m2))m2U2(i2)G(d¯U1(i1),m2)×ij=12|Wj|mjUj(ij)(1G(d¯Uj1(ij1),mj))mjUj(ij)G(d¯Uj1(ij1),mj)×iK=12|WK|mKUK(iK)(1G(d¯UK1(iK1),mK))mKUK(iK)G(d¯UK1(iK1),mK)G(d¯UK(iK),D).
Pout-Serial=H(dS,m1)+(1H(dS,m1))H(dm1,m2)++(1H(dS,m1))(1H(dm1,m2))××(1H(dmK2,mK1))H(dmK1,mK).
Pout-Serial=1(1H(dS,m1))+(1H(dS,m1))H(dm1,m2)++(1H(dS,m1))(1H(dm1,m2))××(1H(dmK1,mK))H(dmK,D)=1(1H(dS,m1))H(dmK,D)i=1K1(1H(dmi,mi+1)),
Pout-Parallel=i1=12N[m1U1(i1)(1H(dS,m1))m1U1(i1)H(dS,m1)]G(d¯U1(i1),D),
RDO(PM)=lnPout/lnPMlnPout,SISO/lnPM.
RDO(PM)=ln(i1=12N1Pout1(U1(i1)))/lnPMln(Q((ln(PM)+2μχ)/2σχ))/lnPM.
I=i1=12N1Pout1(U1(i1))lnPMi1=12N1Pout1(U1(i1)).
Poutj=ij=12|Wj|mjUj(ij)(1G(d¯Uj1(ij1),mj))mjUj(ij)G(d¯Uj1(ij1),mj)×iK=12|WK|mKUK(iK)(1G(d¯UK1(iK1),mK))mKUK(iK)G(d¯UK1(iK1),mK)G(d¯UK(iK),D).
PoutjlnPM=ij=12|Wj|Poutj(υj/lnPM+(lnPoutj+1/lnPM))ij=12|Wj|Poutj,
υ1=m1U1(i1)ln(1H(dS,m1))+m1U1(i1)ln(H(dS,m1)),
υj=mjUj(ij)ln(1G(d¯Uj1(ij1),mj))+mjUj(ij)ln(G(d¯Uj1(ij1),mj)),
υK=mKUK(iK)ln(1G(d¯UK1(iK1),mK))+mKUK(iK)ln(G(d¯UK1(iK1),mK))+ln(G(d¯UK(iK),D)).
12πx1+x2exp(x2/2)<Q(x)<12πxexp(x2/2).
ARDO=4σχ2(dS,D)minU1(i1)(m1U1(i1)(14σχ2(dS,m1))+minU2(i2)(m2U2(i2)(1σξ2(d¯U1(i1),m2))++minUj(ij)(mjUj(ij)(1σξ2(d¯Uj1(ij1),mj))++minUK(iK)(mKUK(iK)1σξ2(d¯UK1(iK1),mK)+1σξ2(d¯UK(iK),D))))).
ARDO=4σχ2(dS,D)min|U1(i1)|(N/K|U1(i1)|4σχ2(dS,D/(K+1))+min|U2(i2)|(|U1(i1)||U2(i2)|4σχ2(dS,D/(K+1))++min|Uj(ij)|(|Uj1(ij1)||Uj(ij)|4σχ2(dS,D/(K+1))++min|UK(iK)|(|UK1(iK1)||UK(iK)|4σχ2(dS,D/(K+1))+1σξ2(|UK(iK)|,dS,D/(K+1)))))),
σξ2(|UK(iK)|,dS,D/(K+1))=ln(1+(exp(4σχ2(dS,D/(K+1)))1)/|UK(iK)|).
σξ2(|UK(iK)|,dS,D/(K+1))4σχ2(dS,D/(K+1))/|UK(iK)|.
ARDO=(K+1)11/6NK.
ARDO=(N+1)11/6,
ARDO=211/6N,