Abstract

We investigate transmission protocols for relay-assisted free-space optical (FSO) systems, when multiple parallel relays are employed and there is no direct link between the source and the destination. As alternatives to all-active FSO relaying, where all the available relays transmit concurrently, we propose schemes that select only a single relay to participate in the communication between the source and the destination in each transmission slot. The selection is based on the channel state information obtained either from all or from the last used FSO links. Thus, the need for synchronization of the relays’ transmissions is avoided, while the slowly varying nature of the atmospheric channel is exploited. For the considered relay selection and all-active relaying schemes, novel closed-form expressions for the outage performance are derived, assuming the versatile Gamma–Gamma channel model. In addition, based on the derived analytical results, the problem of optimizing the optical power resources of the FSO links is addressed. Optimal and more computationally attractive suboptimal solutions are proposed that lead to a power efficient system design. Numerical results for equal and non-equal length FSO links illustrate the merits of the proposed relay selection protocols compared to the all-active scheme and demonstrate the significant power savings offered by the proposed power allocation schemes.

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References

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  1. H. Willebrand and B. S. Ghuman, Free Space Optics: Enabling Optical Connectivity in Today’s Networks. Sams Publishing, 2002.
  2. L. Andrews and R. L. Philips, Laser Beam Propagation Through Random Media. SPIE Press, 2005.
  3. X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 51, pp. 1233–1239, Aug.2003.
    [CrossRef]
  4. M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
    [CrossRef]
  5. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, pp. 1293–1300, Aug.2002.
    [CrossRef]
  6. 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]
  7. S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
    [CrossRef]
  8. M. Safari and M. Uysal, “Relay-assisted free-space optical communication,” IEEE Trans. Wireless Commun., vol. 7, pp. 5441–5449, Dec.2008.
    [CrossRef]
  9. M. Kamiri and N. Nasiri-Kerari, “BER analysis of cooperative systems in free-space optical networks,” J. Lightwave Technol., vol. 27, pp. 5639–5647, Dec.2009.
    [CrossRef]
  10. M. Kamiri and N. Nasiri-Kerari, “Free-space optical communications via optical amplify-and-forward relaying,” J. Lightwave Technol., vol. 29, pp. 242–248, Jan.2011.
    [CrossRef]
  11. C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun., vol. 53, pp. 658–663, Mar.2011.
    [CrossRef]
  12. C. Abou-Rjeily and S. Haddad, “Cooperative FSO systems: Performance analysis and optimal power allocation,” J. Lighwave Technol., vol. 29, pp. 1058–1065, Apr.2011.
    [CrossRef]
  13. H. S. Nalwa, Handbook of Organic Electronics and Photonics. American Scientific Publishers, 2006.
  14. M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
    [CrossRef]
  15. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed.Academic, 2007.
  16. T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels,” Electron. Lett., vol. 44, pp. 372–373, Feb.2008.
    [CrossRef]
  17. D. S. Michalopoulos and G. K. Karagiannidis, “Two-relay distributed switch and stay combining (DSSC),” IEEE Trans. Commun., vol. 56, pp. 1790–1794, Nov.2008.
    [CrossRef]
  18. N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
    [CrossRef]
  19. M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 2nd ed.John Wiley & Sons, New York, 2005.
  20. P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
    [CrossRef]
  21. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed.McGraw Hill, 2002.
  22. D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
    [CrossRef]
  23. J. Nocedal and S. J. Wright, Numerical Optimization. Springer, 1999.
  24. B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
    [CrossRef]
  25. E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
    [CrossRef]

2011 (3)

C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun., vol. 53, pp. 658–663, Mar.2011.
[CrossRef]

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

M. Kamiri and N. Nasiri-Kerari, “Free-space optical communications via optical amplify-and-forward relaying,” J. Lightwave Technol., vol. 29, pp. 242–248, Jan.2011.
[CrossRef]

2009 (3)

E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
[CrossRef]

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

M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
[CrossRef]

2008 (4)

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

T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels,” Electron. Lett., vol. 44, pp. 372–373, Feb.2008.
[CrossRef]

D. S. Michalopoulos and G. K. Karagiannidis, “Two-relay distributed switch and stay combining (DSSC),” IEEE Trans. Commun., vol. 56, pp. 1790–1794, Nov.2008.
[CrossRef]

N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
[CrossRef]

2006 (1)

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

2005 (2)

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[CrossRef]

M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
[CrossRef]

2004 (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]

2003 (1)

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 51, pp. 1233–1239, Aug.2003.
[CrossRef]

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, pp. 1293–1300, Aug.2002.
[CrossRef]

1998 (2)

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[CrossRef]

B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
[CrossRef]

Abou-Rjeily, C.

C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun., vol. 53, pp. 658–663, Mar.2011.
[CrossRef]

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

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 2nd ed.John Wiley & Sons, New York, 2005.

Anderson, B.

B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
[CrossRef]

Andrews, L.

L. Andrews and R. L. Philips, Laser Beam Propagation Through Random Media. SPIE Press, 2005.

Bayaki, E.

E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
[CrossRef]

Bithas, P. S.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

Brandt-Pearce, M.

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[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]

Cochrane, P.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[CrossRef]

Cowley, W. G.

N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
[CrossRef]

Ghuman, B. S.

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

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed.Academic, 2007.

Haddad, S.

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

Heatley, D. J. T.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[CrossRef]

Holland, I.

N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
[CrossRef]

Jackson, J.

B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
[CrossRef]

Kahn, J. M.

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 51, pp. 1233–1239, Aug.2003.
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, pp. 1293–1300, Aug.2002.
[CrossRef]

Kamiri, M.

Karagiannidis, G. K.

D. S. Michalopoulos and G. K. Karagiannidis, “Two-relay distributed switch and stay combining (DSSC),” IEEE Trans. Commun., vol. 56, pp. 1790–1794, Nov.2008.
[CrossRef]

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

Lampe, L.

M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
[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]

Letzepis, N.

N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
[CrossRef]

Leveque, J. H.

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[CrossRef]

Mallik, R.

E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
[CrossRef]

Mathiopoulos, P. T.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

Michalopoulos, D. S.

D. S. Michalopoulos and G. K. Karagiannidis, “Two-relay distributed switch and stay combining (DSSC),” IEEE Trans. Commun., vol. 56, pp. 1790–1794, Nov.2008.
[CrossRef]

Nalwa, H. S.

H. S. Nalwa, Handbook of Organic Electronics and Photonics. American Scientific Publishers, 2006.

Nasiri-Kerari, N.

Neild, I.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[CrossRef]

Nocedal, J.

J. Nocedal and S. J. Wright, Numerical Optimization. Springer, 1999.

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed.McGraw Hill, 2002.

Philips, R. L.

L. Andrews and R. L. Philips, Laser Beam Propagation Through Random Media. SPIE Press, 2005.

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed.McGraw Hill, 2002.

Qianling, C.

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[CrossRef]

Riediger, M. L. B.

M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
[CrossRef]

Rontogiannis, A. A.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed.Academic, 2007.

Safari, M.

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

Sagias, N. C.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

Schober, R.

M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
[CrossRef]

E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
[CrossRef]

Simon, M. K.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 2nd ed.John Wiley & Sons, New York, 2005.

Sitharam, M.

B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
[CrossRef]

Slim, A.

C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun., vol. 53, pp. 658–663, Mar.2011.
[CrossRef]

Tsiftsis, T. A.

T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels,” Electron. Lett., vol. 44, pp. 372–373, Feb.2008.
[CrossRef]

Tsuda, T.

M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
[CrossRef]

Uysal, M.

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

Willebrand, H.

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

Wilson, S. G.

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[CrossRef]

Wisely, D. R.

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[CrossRef]

Wright, S. J.

J. Nocedal and S. J. Wright, Numerical Optimization. Springer, 1999.

Yamagishi, F.

M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
[CrossRef]

Yano, M.

M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
[CrossRef]

Zhu, X.

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 51, pp. 1233–1239, Aug.2003.
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, pp. 1293–1300, Aug.2002.
[CrossRef]

Am. Math. Monthly (1)

B. Anderson, J. Jackson, and M. Sitharam, “Descartes’ rule of sign revisited,” Am. Math. Monthly, vol. 105, pp. 447–451, May1998.
[CrossRef]

Electron. Lett. (1)

T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over Gamma–Gamma atmospheric turbulence channels,” Electron. Lett., vol. 44, pp. 372–373, Feb.2008.
[CrossRef]

IEEE Commun. Lett. (1)

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, “On the performance analysis of digital communications over generalized-K fading channels,” IEEE Commun. Lett., vol. 10, pp. 353–355, May2006.
[CrossRef]

IEEE Commun. Mag. (1)

D. J. T. Heatley, D. R. Wisely, I. Neild, and P. Cochrane, “Optical wireless: The story so far,” IEEE Commun. Mag., vol. 36, pp. 72–74, Dec.1998.
[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 J. Sel. Topics Quantum Electron. (1)

M. Yano, F. Yamagishi, and T. Tsuda, “Optical MEMS for photonic switching–compact and stable optical crossconnect switches for simple, fast, and flexible wavelength applications in recent photonic networks,” IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 383–394, Mar.2005.
[CrossRef]

IEEE Trans. Commun. (7)

D. S. Michalopoulos and G. K. Karagiannidis, “Two-relay distributed switch and stay combining (DSSC),” IEEE Trans. Commun., vol. 56, pp. 1790–1794, Nov.2008.
[CrossRef]

S. G. Wilson, M. Brandt-Pearce, C. Qianling, and J. H. Leveque, “Free-space optical MIMO transmission with Q-ary PPM,” IEEE Trans. Commun., vol. 53, pp. 1402–1412, Aug.2005.
[CrossRef]

C. Abou-Rjeily and A. Slim, “Cooperative diversity for free-space optical communications: transceiver design and performance analysis,” IEEE Trans. Commun., vol. 53, pp. 658–663, Mar.2011.
[CrossRef]

X. Zhu and J. M. Kahn, “Performance bounds for coded free-space optical communications through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 51, pp. 1233–1239, Aug.2003.
[CrossRef]

M. L. B. Riediger, R. Schober, and L. Lampe, “Fast multiple-symbol detection for free-space optical communication,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Apr.2009.
[CrossRef]

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun., vol. 50, pp. 1293–1300, Aug.2002.
[CrossRef]

E. Bayaki, R. Schober, and R. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma–Gamma fading,” IEEE Trans. Commun., vol. 57, pp. 1119–1128, Nov.2009.
[CrossRef]

IEEE Trans. Wireless Commun. (2)

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

N. Letzepis, I. Holland, and W. G. Cowley, “The Gaussian free space optical MIMO channel with Q-ary pulse position modulation,” IEEE Trans. Wireless Commun., vol. 27, pp. 1744–1753, May2008.
[CrossRef]

J. Lightwave Technol. (2)

J. Lighwave Technol. (1)

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

Other (7)

H. S. Nalwa, Handbook of Organic Electronics and Photonics. American Scientific Publishers, 2006.

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

L. Andrews and R. L. Philips, Laser Beam Propagation Through Random Media. SPIE Press, 2005.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels, 2nd ed.John Wiley & Sons, New York, 2005.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed.Academic, 2007.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed.McGraw Hill, 2002.

J. Nocedal and S. J. Wright, Numerical Optimization. Springer, 1999.

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Figures (4)

Fig. 1
Fig. 1

Block diagram of the relay-assisted FSO system under consideration.

Fig. 2
Fig. 2

Comparison of the relaying protocols for a relay-assisted FSO system with d S R i = d R i D = 2 km, i { 1 , , N } .

Fig. 3
Fig. 3

Comparison of the relaying protocols for different relay-assisted FSO configurations: N = 2 , d SR = { 2 , 1 . 5 } , d RD = { 1 , 2 . 5 } (in km) and N = 3 , d SR = { 2 , 1 . 5 , 1 } , d RD = { 1 , 2 . 5 , 3 } (in km).

Fig. 4
Fig. 4

Comparison of the power allocation schemes for the relaying protocols under consideration.

Equations (57)

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r B = [ r s r n ] = [ R T b ( ρ A B P t h A B + P b ) + n s R T b P b + n n ] ,
h A B = h ̄ A B h ̃ A B ,
h ̄ A B = D R 2 ( D T + θ T d A B ) 2 exp ( v d A B ) ,
f h ̃ A B ( x ) = 2 ( α A B β A B ) α A B + β A B 2 Γ ( α A B ) Γ ( β A B ) x α A B + β A B 2 1 × K α A B β A B ( 2 α A B β A B x ) ,
F h ̃ A B ( x ) = 1 Γ ( α A B ) Γ ( β A B ) × G 1 , 3 2 , 1 [ α A B β A B x | 1 α A B , β A B , 0 ] ,
γ A B = γ ̄ A B h ̃ A B 2 ,
γ ̄ A B = R 2 ρ A B 2 T b 2 P t 2 h ̄ A B 2 2 σ n 2 .
r D = [ R T b ( m D ρ R m D h R m D P t + P b ) + n s R T b P b + n n ] ,
γ i = min ( γ S R i , γ R i D ) ,
b = argmax i { 1 , , N } γ i .
r D = [ R T b ( ρ R b D P t h R b D + P b ) + n s R T b P b + n n ] .
if  R b j 1 = R 1 ,  then  R b j = { R 1  when  γ 1 j T R 2  when  γ 1 j < T ,
if  R b j 1 = R 2 ,  then  R b j = { R 2  when  γ 2 j T R 1  when  γ 2 j < T .
r D = [ R T b ( ρ R b j D P t h R b j D + P b ) + n s R T b P b + n n ] .
d i = max ( d S R i , d R i D ) ,
P o = Pr { C ( γ ) < r 0 } ,
P o = Pr { γ < γ t h } ,
P o , A B = Pr { R 2 T b 2 ρ A B 2 P t 2 h A B 2 2 σ n 2 < γ t h } ,
P o , A B = Pr { h ̃ A B < 1 h ̄ A B ρ A B P M } ,
P o , A B = F h ̃ A B ( 1 h ̄ A B ρ A B P M ) .
P o , A B Γ ( p A B q A B ) Γ ( α A B ) Γ ( β A B ) ( α A B β A B h ̄ A B P M ρ A B ) q A B q A B , ( α A B β A B ) Z ,
P o , all - act = n = 1 2 N Pr { m S ( n ) ρ R m D h R m D < 1 P M } × Pr { S ( n ) } ,
Pr { S ( n ) } = m S ( n ) ( 1 P o , S R m ) m S ( n ) P o , S R m .
P o , all - act = n = 1 2 N m S ( n ) ( 1 F h ̃ S R m ( 1 h ̄ S R m ρ S R m P M ) ) × F h S ( n ) ( 1 P M ) m S ( n ) F h ̃ S R m ( 1 h ̄ S R m ρ S R m P M ) .
F h S ( n ) ( x ) m S ( n ) ( α R m D β R m D h ̄ R m D ρ R m D ) q R m D ( m S ( n ) q R m D ) Γ ( m S ( n ) q R m D ) × m S ( n ) ( Γ ( q R m D ) Γ ( p R m D q R m D ) Γ ( α R m D ) Γ ( β R m D ) ) × x ( m S ( n ) q R m D ) .
Pr { S ( n ) } m S ( n ) P o , S R m .
P o , all - act n = 1 2 N m S ( n ) ( π Γ ( p S R m q S R m ) Γ ( α S R m ) Γ ( β S R m ) ( α S R m β S R m h ̄ S R m ρ S R m ) q S R m q S R m ) × m S ( n ) ( α R m D β R m D h ̄ R m D ρ R m D ) q R m D Γ ( q R m D ) Γ ( p R m D q R m D ) Γ ( α R m D ) Γ ( β R m D ) ( m S ( n ) q R m D ) Γ ( m S ( n ) q R m D ) ( 1 P M ) ( m S ( n ) q S R m + m S ( n ) q R m D )
P o , sel - max = P o { R 1 R N } = b = 1 N P o , R b ,
P o , R b = Pr { ( γ S R b < γ t h ) ( γ R b D < γ t h ) } = 1 ( 1 P o , S R b ) ( 1 P o , R b D ) .
P o , sel - max = b = 1 N ( 1 ( 1 F h ̃ S R b ( 1 h ̄ S R b ρ S R b P M ) ) × ( 1 F h ̃ R b D ( 1 h ̄ R b D ρ R b D P M ) ) ) .
P o , sel - max b = 1 N ( Γ ( p S R b q S R b ) q S R b Γ ( α S R b ) Γ ( β S R b ) ( α S R b β S R b h ̄ S R b ρ S R b P M ) q S R b + Γ ( p R b D q R b D ) q R b D Γ ( α R b D ) Γ ( β R b D ) ( α R b D β R b D h ̄ R b D ρ R b D P M ) q R b D ) .
P o , R b P o , S R b + P o , R b D .
P o , D S S = Pr { ( R b j = R 1 ) ( γ 1 j < γ t h ) } + Pr { ( R b j = R 2 ) ( γ 2 j < γ t h ) } .
P o , D S S = { F h 1 ( 1 T ̃ ) F h 2 ( 1 T ̃ ) ( F h 1 ( 1 P M ) + F h 2 ( 1 P M ) ) F h 1 ( 1 T ̃ ) + F h 2 ( 1 T ̃ ) , T ̄ P M , F h 1 ( 1 T ̃ ) F h 2 ( 1 T ̃ ) ( F h 1 ( 1 P M ) + F h 2 ( 1 P M ) 2 ) F h 1 ( 1 T ̃ ) + F h 2 ( 1 T ̃ ) + F h 1 ( 1 P M ) F h 2 ( 1 T ̃ ) + F h 1 ( 1 T ̃ ) F h 2 ( 1 P M ) F h 1 ( 1 T ̃ ) + F h 2 ( 1 T ̃ ) , T ̄ > P M ,
F h i ( x ) = 1 ( 1 F h ̃ S R i ( 1 h ̄ S R i ρ S R i x ) ) × ( 1 F h ̃ R i D ( 1 h ̄ R i D ρ R i D x ) ) ,
P o , D S S = { F γ 1 ( T ) F γ 2 ( T ) ( F γ 1 ( γ t h ) + F γ 2 ( γ t h ) ) F γ 1 ( T ) + F γ 2 ( T ) , γ t h T , F γ 1 ( T ) F γ 2 ( T ) ( Pr { γ 1 < γ t h } + F γ 2 ( γ t h ) 2 ) F γ 1 ( T ) + F γ 2 ( T ) + ( F γ 1 ( γ t h ) F γ 2 ( T ) + F γ 1 ( T ) F γ 2 ( γ t h ) ) F γ 1 ( T ) + F γ 2 ( T ) , γ t h > T ,
F γ i ( x ) = Pr { γ i < x } .
F γ i ( x ) = 1 ( 1 Pr { γ S R i < x } ) × ( 1 Pr { γ S R i < x } ) ,
P o , D S S = i = 1 2 ( 1 ( 1 P o , S R i ) ( 1 P o , R i D ) ) .
min P o , all - act subject to  { m = 1 N ( ρ S R m + ρ R m D ) = 1 , 0 < ρ S R m , ρ R m D ρ o , m = 1 , , N ,
ρ S R i = 1 m = 1 N ( h ̄ S R i h ̄ S R m + h ̄ S R i h ̄ R m D )
ρ R i D = 1 m = 1 N ( h ̄ R i D h ̄ S R m + h ̄ R i D h ̄ R m D )
ρ S R i = ρ o and ρ R i D = ρ o , if  S R i , R i D T ,
ρ S R i = 1 | T | ρ o S R m T h ̄ S R i h ̄ S R m + R m D T h ̄ S R i h ̄ R m D , if  S R i T ,
ρ R i D = 1 | T | ρ o S R m T h ̄ R i D h ̄ S R m + R m D T h ̄ R i D h ̄ R m D , if  R i D T ,
min P o , R b subject to  { ρ S R b + ρ R b D = 1 , 0 < ρ S R b , ρ R b D ρ o ,
min ( Γ ( p S R b q S R b ) Γ ( α S R b ) Γ ( β S R b ) q S R b ( α S R b β S R b h ̄ S R b ρ S R b P M ) q S R b + Γ ( p R b D q R b D ) Γ ( α R b D ) Γ ( β R b D ) q R b D ( α R b D β R b D h ̄ R b D ρ R b D P M ) q R b D ) subject to  { ρ S R b + ρ R b D = 1 , 0 < ρ S R b , ρ R b D ρ o .
ρ S R b = { ζ S R b , if  ζ S R b < ρ o  and  ζ R b D < ρ o , ρ o , if  ζ S R b ρ o , 1 ρ o , if  ζ R b D ρ o ,
ρ R b D = { ζ R b D , if  ζ S R b < ρ o  and  ζ R b D < ρ o , 1 ρ o , if  ζ S R b ρ o , ρ o , if  ζ R b D ρ o ,
S ( t ) = δ S R b 1 q S R b + 1 t 1 q S R b + 1 + δ R b D 1 q R b D + 1 t 1 q R b D + 1 1 .
J = δ S R b ρ S R b q S R b + δ R b D ρ R b D q R b D Λ ( ρ S R b + ρ R b D ) ,
ρ S R b = { κ S R b , if  κ S R b < ρ o  and  κ R b D < ρ o , ρ o , if  κ S R b ρ o , 1 ρ o , if  κ R b D ρ o ,
ρ R b D = { κ R b D , if  κ S R b < ρ o  and  κ R b D < ρ o , ρ o , if  κ R b D ρ o , 1 ρ o , if  κ S R b ρ o ,
P o , A B = π sin ( π ( α A B β A B ) ) Γ ( α A B ) Γ ( β A B ) l = 0 ( 1 ( β A B + l ) l ! ( α A B β A B P M h ̄ A B ρ A B ) β A B Γ ( l α A B + β A B + 1 ) × ( α A B β A B P M h ̄ A B ρ A B ) l 1 ( α A B + l ) l ! ( α A B β A B P M h ̄ A B ρ A B ) α A B + l Γ ( l + α A B β A B + 1 ) ) .
M ξ m ( s ) = ( α R m D β R m D h ̄ R m D ρ R m D ) q R m D Γ ( p R m D q R m D ) Γ ( α R m D ) Γ ( β R m D ) × s q R m D + o ( s q R m D ) .
M h S ( n ) ( s ) = m S ( n ) ( α R m D β R m D h ̄ R m D ρ R m D ) q R m D Γ ( p R m D q R m D ) Γ ( α R m D ) Γ ( β R m D ) × s m S ( n ) q R m D + o ( 1 s m S ( n ) q R m D ) ,
f h S ( n ) ( x ) = m S ( n ) ( α R m D β R m D h ̄ R m D ρ R m D ) q R m D x ( m S ( n ) q R m D ) × m S ( n ) Γ ( q R m D ) Γ ( p R m D q R m D ) Γ ( α R m D ) Γ ( β R m D ) Γ ( m S ( n ) q R m D ) x + o ( x m S ( n ) q R m D + 1 ) .