Abstract

A coherent multiple-input multiple-output architecture is proposed for optical wireless communications (OWCs) to mitigate atmospheric turbulence effects. Transmitter optical signals operate at distinct carrier frequencies to allow the received optical signals to be separately processed. The accumulated phase noise in each transmission branch can then be independently and electrically compensated. Based on the proposed architecture, several diversity combining techniques are used at the receiver end for system performance evaluation. Three different turbulence models are considered in this paper for different scintillation level ranges, including gamma–gamma turbulence, K-distributed turbulence, and negative exponential turbulence. Closed-form error rate expressions are derived using a series expansion approach. The diversity order in the gamma–gamma turbulence channel is found to depend only on the smaller channel parameter, while the K-distributed and negative exponential turbulence channels are found to have the same diversity order. The presented numerical results demonstrate substantial system performance improvement over single-link coherent OWC.

© 2013 Optical Society of America

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  9. N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optial wireless transmission with coherent detection,” J. Lightwave Technol., vol.  28, pp. 1218–1227, Apr. 2010.
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  14. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
    [CrossRef]
  15. J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol., vol.  30, pp. 1569–1577, June 2012.
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
    [CrossRef]
  24. R. Shechter, Y. Amitai, and A. A. Friesem, “Compact wavelength division multiplexers and demultiplexers,” Appl. Opt., vol.  41, pp. 1256–1261, Mar. 2002.
    [CrossRef]
  25. M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
    [CrossRef]
  26. S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, “Understanding the performance of free-space optics,” J. Opt. Netw., vol.  2, pp. 178–200, June 2003.
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2012 (1)

2011 (1)

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

2010 (2)

2009 (3)

2008 (3)

M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
[CrossRef]

T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over gamma–gamma atmospheric turbulence channels,” Electron. Lett., vol.  44, pp. 373–375, Feb. 2008.
[CrossRef]

A. Belmonte and J. M. Kahn, “Performance of synchronous optical receivers using atmospheric compensation techniques,” Opt. Express, vol.  16, pp. 14151–14162, Sept. 2008.
[CrossRef]

2006 (4)

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

K. Kiasaleh, “Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence,” IEEE Trans. Commun., vol.  54, pp. 604–607, Apr. 2006.
[CrossRef]

N. Cvijetic and T. Wang, “A MIMO architecture for IEEE 802.16d (WiMAX) heterogeneous wireless access using optical wireless technology,” Lect. Notes Comput. Sci., vol.  4003, pp. 441–451, 2006.
[CrossRef]

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol., vol.  24, pp. 4750–4762, Dec. 2006.
[CrossRef]

2005 (1)

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

2004 (1)

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, pp. 1896–1906, Nov. 2004.
[CrossRef]

2003 (2)

X. Zhu, J. M. Kahn, and J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” Photon. Technol. Lett., vol.  15, pp. 623–625, Apr. 2003.
[CrossRef]

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, “Understanding the performance of free-space optics,” J. Opt. Netw., vol.  2, pp. 178–200, June 2003.

2002 (2)

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact wavelength division multiplexers and demultiplexers,” Appl. Opt., vol.  41, pp. 1256–1261, Mar. 2002.
[CrossRef]

S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for wireless optical communications,” EURASIP J. Appl. Signal Process., vol.  2002, pp. 211–220, Jan. 2002.
[CrossRef]

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

1993 (1)

V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
[CrossRef]

1976 (1)

E. Jakeman and P. N. Pusey, “A model for non-Rayleigh sea echo,” IEEE Trans. Antennas Propag., vol.  AP-24, pp. 806–814, Nov. 1976.
[CrossRef]

Ahmadi, V.

Z. Ghassemlooy, W. O. Popoola, V. Ahmadi, and E. Leitgeb, “MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels,” in Communications Infrastructure. Systems and Applications in Europe (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering). Springer, Berlin, Heidelberg, 2009, vol. 16, part 2, pp. 61–73.

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

Amitai, Y.

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media. SPIE, Bellingham, WA, 1998.

Baedke, M.

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

Banerjee, D.

D. Banerjee, PLL Performance, Simulation, and Design Handbook, 4th ed.National Semiconductor, 2006.

Bayaki, E.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol., vol.  30, pp. 1569–1577, June 2012.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Belmonte, A.

Bloom, S.

Brandt-Pearce, M.

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

Cao, Q.

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

Chan, V. W. S.

V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol., vol.  24, pp. 4750–4762, Dec. 2006.
[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, pp. 1896–1906, Nov. 2004.
[CrossRef]

Cheng, J.

Cvijetic, N.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optial wireless transmission with coherent detection,” J. Lightwave Technol., vol.  28, pp. 1218–1227, Apr. 2010.
[CrossRef]

N. Cvijetic and T. Wang, “A MIMO architecture for IEEE 802.16d (WiMAX) heterogeneous wireless access using optical wireless technology,” Lect. Notes Comput. Sci., vol.  4003, pp. 441–451, 2006.
[CrossRef]

Czichy, R.

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

Edwards, D. J.

M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
[CrossRef]

Friesem, A. A.

Ghassemlooy, Z.

Z. Ghassemlooy, W. O. Popoola, V. Ahmadi, and E. Leitgeb, “MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels,” in Communications Infrastructure. Systems and Applications in Europe (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering). Springer, Berlin, Heidelberg, 2009, vol. 16, part 2, pp. 61–73.

Ghuman, B. S.

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

Giggenbach, D.

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed., Academic, San Diego, 2000.

Haas, S. M.

S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for wireless optical communications,” EURASIP J. Appl. Signal Process., vol.  2002, pp. 211–220, Jan. 2002.
[CrossRef]

Holzman, J. F.

Huang, Y.-K.

Jafar, M.

M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
[CrossRef]

Jakeman, E.

E. Jakeman and P. N. Pusey, “A model for non-Rayleigh sea echo,” IEEE Trans. Antennas Propag., vol.  AP-24, pp. 806–814, Nov. 1976.
[CrossRef]

Kahn, J. M.

Kevorkian, A.

V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
[CrossRef]

Kiasaleh, K.

K. Kiasaleh, “Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence,” IEEE Trans. Commun., vol.  54, pp. 604–607, Apr. 2006.
[CrossRef]

Korevaar, E.

Lange, R.

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

Lee, E.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 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, pp. 1896–1906, Nov. 2004.
[CrossRef]

Leitgeb, E.

Z. Ghassemlooy, W. O. Popoola, V. Ahmadi, and E. Leitgeb, “MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels,” in Communications Infrastructure. Systems and Applications in Europe (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering). Springer, Berlin, Heidelberg, 2009, vol. 16, part 2, pp. 61–73.

Li, G.

Mallik, R. K.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Minier, V.

V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
[CrossRef]

Niu, M.

O’Brien, D. C.

M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
[CrossRef]

Park, J.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media,” Opt. Eng., vol.  40, pp. 1554–1562, Aug. 2001.
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media. SPIE, Bellingham, WA, 1998.

Popoola, W. O.

Z. Ghassemlooy, W. O. Popoola, V. Ahmadi, and E. Leitgeb, “MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels,” in Communications Infrastructure. Systems and Applications in Europe (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering). Springer, Berlin, Heidelberg, 2009, vol. 16, part 2, pp. 61–73.

Pusey, P. N.

E. Jakeman and P. N. Pusey, “A model for non-Rayleigh sea echo,” IEEE Trans. Antennas Propag., vol.  AP-24, pp. 806–814, Nov. 1976.
[CrossRef]

Qian, D.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed., Academic, San Diego, 2000.

Schober, R.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol., vol.  30, pp. 1569–1577, June 2012.
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in gamma–gamma fading,” IEEE Trans. Commun., vol.  57, pp. 3415–3424, Nov. 2009.
[CrossRef]

Schuster, J.

Shapiro, J. H.

S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for wireless optical communications,” EURASIP J. Appl. Signal Process., vol.  2002, pp. 211–220, Jan. 2002.
[CrossRef]

Shechter, R.

Smutny, B.

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

Stevens, C. J.

M. Jafar, D. C. O’Brien, C. J. Stevens, and D. J. Edwards, “Evaluation of coverage area for a wide line-of-sight indoor optical free-space communication system employing coherent detection,” IET Commun., vol.  2, pp. 18–26, Jan. 2008.
[CrossRef]

Tarokh, V.

S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for wireless optical communications,” EURASIP J. Appl. Signal Process., vol.  2002, pp. 211–220, Jan. 2002.
[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. 373–375, Feb. 2008.
[CrossRef]

Wandernoth, B.

R. Lange, B. Smutny, B. Wandernoth, R. Czichy, and D. Giggenbach, “142 km, 5.625 Gbps free-space optical link based on homodyne BPSK modulation,” Proc. SPIE, vol.  6105, pp. 61050A, Mar. 2006.
[CrossRef]

Wang, J.

X. Zhu, J. M. Kahn, and J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” Photon. Technol. Lett., vol.  15, pp. 623–625, Apr. 2003.
[CrossRef]

Wang, T.

N. Cvijetic, D. Qian, J. Yu, Y.-K. Huang, and T. Wang, “Polarization-multiplexed optial wireless transmission with coherent detection,” J. Lightwave Technol., vol.  28, pp. 1218–1227, Apr. 2010.
[CrossRef]

N. Cvijetic and T. Wang, “A MIMO architecture for IEEE 802.16d (WiMAX) heterogeneous wireless access using optical wireless technology,” Lect. Notes Comput. Sci., vol.  4003, pp. 441–451, 2006.
[CrossRef]

Willebrand, H.

S. Bloom, E. Korevaar, J. Schuster, and H. Willebrand, “Understanding the performance of free-space optics,” J. Opt. Netw., vol.  2, pp. 178–200, June 2003.

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

Wilson, S. G.

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

Xu, J. M.

V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
[CrossRef]

Yoon, G.

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

Yu, J.

Zhu, X.

X. Zhu, J. M. Kahn, and J. Wang, “Mitigation of turbulence-induced scintillation noise in free-space optical links using temporal-domain detection techniques,” Photon. Technol. Lett., vol.  15, pp. 623–625, Apr. 2003.
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Electron. Lett. (1)

T. A. Tsiftsis, “Performance of heterodyne wireless optical communication systems over gamma–gamma atmospheric turbulence channels,” Electron. Lett., vol.  44, pp. 373–375, Feb. 2008.
[CrossRef]

EURASIP J. Appl. Signal Process. (1)

S. M. Haas, J. H. Shapiro, and V. Tarokh, “Space-time codes for wireless optical communications,” EURASIP J. Appl. Signal Process., vol.  2002, pp. 211–220, Jan. 2002.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

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, pp. 1896–1906, Nov. 2004.
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. Park, E. Lee, and G. Yoon, “Average bit-error rate of the Alamouti scheme in gamma–gamma fading channels,” IEEE Photon. Technol. Lett., vol.  23, pp. 269–271, Feb. 2011.
[CrossRef]

V. Minier, A. Kevorkian, and J. M. Xu, “Superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications,” IEEE Photon. Technol. Lett., vol.  5, pp. 330–333, Mar. 1993.
[CrossRef]

IEEE Trans. Antennas Propag. (1)

E. Jakeman and P. N. Pusey, “A model for non-Rayleigh sea echo,” IEEE Trans. Antennas Propag., vol.  AP-24, pp. 806–814, Nov. 1976.
[CrossRef]

IEEE Trans. Commun. (3)

K. Kiasaleh, “Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence,” IEEE Trans. Commun., vol.  54, pp. 604–607, Apr. 2006.
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Block diagram of an M×N coherent MIMO architecture operating in atmospheric turbulent channels.

Fig. 2.
Fig. 2.

Performance comparison of coherent MIMO MRC and MIMO EGC in gamma–gamma turbulence channels with weak {α=3.92,β=3.78;σR2=0.6} and strong {α=2.23,β=1.70;σR2=2.0} turbulence conditions.

Fig. 3.
Fig. 3.

Outage probability for coherent SISO and MIMO systems using MRC/EGC reception in strongly turbulent gamma–gamma atmospheric channels {α=2.15,β=1.06;σR2=15.0} with Λ=6dB.

Fig. 4.
Fig. 4.

BER performance of coherent MIMO MRC and MIMO EGC in a K-distributed turbulence channel with α=1.65.

Fig. 5.
Fig. 5.

BER performance of coherent MIMO MRC and MIMO EGC in the negative exponential turbulence.

Fig. 6.
Fig. 6.

Outage probability of coherent MRC and EGC OWC systems in the negative exponential (saturated) turbulence with an outage threshold Λ=6dB.

Equations (42)

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fG(Is)=2Γ(α)Γ(β)(αβ)α+β2Isα+β21Kαβ(2αβIs),
α=[exp(0.49σI2(1+1.11σI125)76)1]1,
β=[exp(0.51σI2(1+0.69σI125)56)1]1.
fK(Is)=2Γ(α)αα+12Isα12Kα1(2αIs),Is0,
E[Isn]=(α)nΓ(n+1)αn=Γ(α+n)Γ(n+1)αnΓ(α),
σsi2=ΔE[Is2](E[Is])21,
α=2σsi21.
fNE(Is)=1I0exp(IsI0),Is0,
en(t)=m=1MEs,mnexp(jωmt+jϕ+jϕst,m(t)),m=1,2,,M,n=1,2,,N,
esum,mn(t)=Es,mnexp(jωmt+jϕ+jϕst,m(t))+ELOexp(jωLO,mnt+jϕLO,mn(t)),
Pe=1π0π20exp(γ2sin2θ)fγ(γ)dγdθ,
Kν(x)=π2sin(πν)p=0[(x/2)2pνΓ(pν+1)p!(x/2)2p+νΓ(p+ν+1)p!],
fY(y)=2p=0[ap(α,β)y2(p+β)1+ap(β,α)y2(p+α)1],
ap(α,β)=πcsc[π(αβ)](αβ)p+βΓ(α)Γ(β)Γ(pα+β+1)p!.
MIg(s)=2MNi=0MN(MNi)×p=0λp(MNi)(α,β,2)*λp(i)(β,α,2)(s)p+MNβ+i(αβ),
fIg(I)=i=0MN(MNi)p=0λp(MNi)(α,β,2)*λp(i)(β,α,2)Γ(p+MNβ+i(αβ))×2MNIp+MNβ+i(αβ)1.
fγ(γEGC)=2MN1γ¯×i=0MN(MNi)p=0λp(MNi)(α,β,2)*λp(i)(β,α,2)Γ(2κp(α,β,MN,i))×MN(γEGCMNγ¯)κp(α,β,MN,i)1,
fγ(γMRC)=1γ¯i=0MN(MNi)p=0λp(MNi)(α,β,1)*λp(i)(β,α,1)Γ(κp(α,β,MN,i))×(γMRCγ¯)κp(α,β,MN,i)1.
PbEGC=2L2i=0MN(MNi)p=0λp(MNi)(α,β,2)*λp(i)(β,α,2)πΓ(2κp(α,β,MN,i))×Γ(κp(α,β,MN,i))B(12,κp(α,β,MN,i)+12)×(γ¯2MN)κp(α,β,MN,i),
PbMRC=i=0MN(MNi)p=0λp(MNi)(α,β,1)*λp(i)(β,α,1)2π×B(12,κp(α,β,MN,i)+12)×(γ¯2)κp(α,β,MN,i),
Poutage(Λ)=Pr(γ<Λ)=0Λfγ(x)dx,
PoutageEGC(Λ)=2MNi=0MN(MNi)×p=0λp(MNi)(α,β,2)*λp(i)(β,α,2)Γ(2κp(α,β,MN,i)+1)×(ΛMNγ¯)κp(α,β,MN,i),
PoutageMRC(Λ)=i=0MN(MNi)p=0λp(MNi)(α,β,1)*λp(i)(β,α,1)Γ(κp(α,β,MN,i)+1)×(γMRCγ¯)κp(α,β,MN,i).
PbEGC=2L3i=0MN(MNi)p=0Γ2(κp(α,1,MN,i)+12)Γ2(2κp(α,1,MN,i))×Γ(κp(α,1,MN,i))λp(MNi)(α,1,2)*λp(i)(1,α,2)πκp(α,1,MN,i)×(γ¯8MN)κp(α,1,MN,i),
PbMRC=i=0MN(MNi)Γ2(κp(α,1,MN,i)+12)Γ(2κp(α,1,MN,i)+1)×p=0λp(MNi)(α,1,1)*λp(i)(1,α,1)2π×(γ¯8)κp(α,1,MN,i).
PoutageEGC(Λ)=i=0MN(MN1)p=0λp(MNi)(α,1,2)*λp(i)(1,α,2)Γ(2κp(α,1,MN,i)+1)×2MN(ΛMNγ¯)κp(α,1,MN,i),
PoutageMRC(Λ)=i=0MN(MNi)p=0λp(MNi)(α,1,1)*λp(i)(1,α,1)Γ(κp(α,1,MN,i)+1)×(γMRCγ¯)κp(α,1,MN,i),
MIs(s)=p=0[mp(α)(s)(p+1)+np(α)(s)(p+α)],
mp(x)=Γ(2x)xp+1(x1)Γ(px+2),
np(x)=Γ(1x)xp+xp!.
MIs(s)=limαp=0[mp(α)(s)(p+1)+np(α)(s)(p+α)]=limαp=0[(1α)Γ(1α)αp+1(α1)Γ(pα+2)(s)(p+1)]=p=0[Γ(p+1)(1)pp!(s)(p+1)].
MV(s)=1+πI0s2exp(I0s24)erfc(I0s2),
MV(s)=p=0[(1)p2Γ(2p+2)p!(s)2(p+1)].
MR(s)=2MNp=0[((1)p2Γ(2p+2)p!)(MN)×(s)2(p+MN)].
fR(r)=2MNp=0[((1)p2Γ(2p+2)p!)(MN)×(r)2(p+MN)1Γ(2(p+MN))].
fW(w)=2MN1p=0[((1)p2Γ(2p+2)p!)(MN)×wp+MN1Γ(2(p+MN))].
PNEEGC=2MN2πp=0[((1)pΓ(2p+2)p!)(MN)×Γ(p+MN)B(12,p+MN+12)Γ(2p+2MN)×(γ¯4MN)(p+MN)].
MX(s)=p=0[(Γ(p+1)(1)pp!)(MN)(s)(p+MN)].
fX(x)=p=0[(Γ(p+1)(1)pp!)(MN)(x)p+MN1Γ(p+MN)].
PNEMRC=12πp=0[(Γ(p+1)(1)pp!)(MN)×B(12,p+MN+12)(γ¯4)(p+MN)].
PoutageEGC(Λ)=2MN1p=0[((1)p2Γ(2p+2)p!)(MN)×(γ¯MNΛ)(p+MN)(p+MN)Γ(2(p+MN))],
PoutageMRC(Λ)=p=0[(Γ(p+1)(1)pp!)(MN)×(γ¯Λ)(p+MN)Γ(p+MN+1)],