Abstract

In this Letter we propose a closed-form expression for the average bit error rate of intensity modulation/direct detection free-space optical systems employing dual-branch equal-gain combining and operating over turbulence channels. To offer a realistic error performance of the considered system we assume that both branches undergo independent but not necessarily identically distributed gamma–gamma fading. Our newly developed formula is obtained in terms of the bivariate H-Fox function, which can be readily evaluated based on its two-fold Mellin–Barnes representation. Numerically evaluated and computer simulation results are presented that verify the accuracy of the proposed mathematical analysis.

© 2013 Optical Society of America

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  1. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
    [CrossRef]
  2. M. K. Simon and M. S. Alouini, Digital Communication over Fading Channels, 2nd ed. (Wiley, 2004).
  3. W. O. Popoola and Z. Ghassemlooy, J. Lightwave Technol. 27, 967 (2009).
    [CrossRef]
  4. E. Bayaki, R. Schober, and R. K. Mallik, IEEE Trans. Commun. 57, 3415 (2009).
    [CrossRef]
  5. K. P. Peppas, IEEE Photon. Technol. Lett. 23, 839 (2011).
    [CrossRef]
  6. N. D. Chatzidiamantis and G. K. Karagiannidis, IEEE Trans. Wireless Commun. 59, 1298 (2011).
    [CrossRef]
  7. M. B. Niu, J. Schlenker, J. L. Cheng, J. F. Holzman, and R. Schober, J. Opt. Commun. Netw. 3, 860 (2011).
    [CrossRef]
  8. A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications (Springer, 2010).
  9. K. P. Peppas, IEEE Wireless Commun. Lett. 1, 85 (2012).
    [CrossRef]
  10. P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
    [CrossRef]
  11. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Elsevier, 2007).
  12. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 3, More Special Functions (CRC, 1998).

2012 (1)

K. P. Peppas, IEEE Wireless Commun. Lett. 1, 85 (2012).
[CrossRef]

2011 (3)

K. P. Peppas, IEEE Photon. Technol. Lett. 23, 839 (2011).
[CrossRef]

N. D. Chatzidiamantis and G. K. Karagiannidis, IEEE Trans. Wireless Commun. 59, 1298 (2011).
[CrossRef]

M. B. Niu, J. Schlenker, J. L. Cheng, J. F. Holzman, and R. Schober, J. Opt. Commun. Netw. 3, 860 (2011).
[CrossRef]

2009 (2)

W. O. Popoola and Z. Ghassemlooy, J. Lightwave Technol. 27, 967 (2009).
[CrossRef]

E. Bayaki, R. Schober, and R. K. Mallik, IEEE Trans. Commun. 57, 3415 (2009).
[CrossRef]

2006 (1)

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Alouini, M. S.

M. K. Simon and M. S. Alouini, Digital Communication over Fading Channels, 2nd ed. (Wiley, 2004).

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Bayaki, E.

E. Bayaki, R. Schober, and R. K. Mallik, IEEE Trans. Commun. 57, 3415 (2009).
[CrossRef]

Bithas, P. S.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

Brychkov, Y. A.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 3, More Special Functions (CRC, 1998).

Chatzidiamantis, N. D.

N. D. Chatzidiamantis and G. K. Karagiannidis, IEEE Trans. Wireless Commun. 59, 1298 (2011).
[CrossRef]

Cheng, J. L.

Ghassemlooy, Z.

Gradshteyn, I. S.

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

Haubold, H. J.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications (Springer, 2010).

Holzman, J. F.

Karagiannidis, G. K.

N. D. Chatzidiamantis and G. K. Karagiannidis, IEEE Trans. Wireless Commun. 59, 1298 (2011).
[CrossRef]

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

Mallik, R. K.

E. Bayaki, R. Schober, and R. K. Mallik, IEEE Trans. Commun. 57, 3415 (2009).
[CrossRef]

Marichev, O. I.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 3, More Special Functions (CRC, 1998).

Mathai, A.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications (Springer, 2010).

Mathiopoulos, P. T.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

Niu, M. B.

Peppas, K. P.

K. P. Peppas, IEEE Wireless Commun. Lett. 1, 85 (2012).
[CrossRef]

K. P. Peppas, IEEE Photon. Technol. Lett. 23, 839 (2011).
[CrossRef]

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Popoola, W. O.

Prudnikov, A. P.

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 3, More Special Functions (CRC, 1998).

Rontogiannis, A. A.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

Ryzhik, I. M.

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

Sagias, N. C.

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

Saxena, R. K.

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications (Springer, 2010).

Schlenker, J.

Schober, R.

Simon, M. K.

M. K. Simon and M. S. Alouini, Digital Communication over Fading Channels, 2nd ed. (Wiley, 2004).

IEEE Commun. Lett. (1)

P. S. Bithas, N. C. Sagias, P. T. Mathiopoulos, G. K. Karagiannidis, and A. A. Rontogiannis, IEEE Commun. Lett. 10, 353 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. P. Peppas, IEEE Photon. Technol. Lett. 23, 839 (2011).
[CrossRef]

IEEE Trans. Commun. (1)

E. Bayaki, R. Schober, and R. K. Mallik, IEEE Trans. Commun. 57, 3415 (2009).
[CrossRef]

IEEE Trans. Wireless Commun. (1)

N. D. Chatzidiamantis and G. K. Karagiannidis, IEEE Trans. Wireless Commun. 59, 1298 (2011).
[CrossRef]

IEEE Wireless Commun. Lett. (1)

K. P. Peppas, IEEE Wireless Commun. Lett. 1, 85 (2012).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Commun. Netw. (1)

Opt. Eng. (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, Opt. Eng. 40, 1554 (2001).
[CrossRef]

Other (4)

M. K. Simon and M. S. Alouini, Digital Communication over Fading Channels, 2nd ed. (Wiley, 2004).

A. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications (Springer, 2010).

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

A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 3, More Special Functions (CRC, 1998).

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Figures (1)

Fig. 1.
Fig. 1.

Average BER for dual-branch EGC over G–G turbulence channels.

Equations (12)

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Pe¯=120erfc(η4N0x)fI(x)dx,
fIi(x)=2(αiβi)(αi+βi)/2Γ(αi)Γ(βi)x(αi+βi)21Kαiβi(2αiβix),
MIi(t)=(αiβi/t)(αi+βi1)/2exp[αiβi/(2t)]×W(αi+βi1)/2,(αiβi)/2(αiβi/t),
MIi(t)=(αiβi/t)(αi+βi)/2Γ(αi)Γ(βi)12πjσijσi+jΓ(αiβi2s)×Γ(βiαi2s)Γ(αi+βi2+s)×(αiβi/t)sds,
MI(t)=i=12MIi(t)=[i=12(αiβi/t)(αi+βi)/2Γ(αi)Γ(βi)](12πj)2σ1jσ1+jσ2jσ2+j{i=12Γ(αiβi2si)Γ(βiαi2si)×Γ(αi+βi2+si)(αiβit)si}ds1ds2.
fI(x)=12πjσjσ+jMI(t)extdt.
fI(x)=[i=12(αiβi)(αi+βi)/2Γ(αi)Γ(βi)](12πj)2σ1jσ1+jσ2jσ2+j×{i=12Γ(αiβi2si)Γ(βiαi2si)×Γ(αi+βi2+si)(αiβi)si}×(12πjσjσ+jti=12[(αi+βi)2+si]extdt)ds1ds2.
fI(x)=[i=12(αiβi)(αi+βi)/2Γ(αi)Γ(βi)]x[i=12(αi+βi)2]1(12πj)2×σ1jσ1+jσ2jσ2+j1Γ(i=12[(αi+βi)/2+si])×{i=12Γ(αiβi2si)Γ(βiαi2si)×Γ(αi+βi2+si)(αiβix)si}ds1ds2.
Pe¯=[i=12(αiβi)(αi+βi)/2Γ(αi)Γ(βi)](12πj)2σ1jσ1+jσ2jσ2+j×1Γ(i=12[(αi+βi)/2+si]){i=12Γ(αiβi2si)×Γ(βiαi2si)Γ(αi+βi2+si)(αiβi)si}×{120xi=12[(αi+βi)2+si]1erfc(η4N0x)dx}×ds1ds2.
120xi=12[(αi+βi)2+si]1erfc(ηx4N0)dx=12π×(η4N0)i=12[(αi+βi)2+si]1i=12[(αi+βi)/2+si]×Γ(12+12i=12[(αi+βi)/2+si]).
Pe¯=12π[i=12(αiβi)(αi+βi)/2Γ(αi)Γ(βi)](η4N0)i=12[(αi+βi)2]×(12πj)2σ1jσ1+jσ2jσ2+j{i=12Γ(αiβi2si)×Γ(βiαi2si)Γ(αi+βi2+si)(4αiβiN0η)si}×Γ(12+12i=12[(αi+βi)/2+si])Γ(1+i=12[(αi+βi)/2+si])ds1ds2.
Pe¯=12π[i=12(αiβi)(αi+βi)/2Γ(αi)Γ(βi)](η4N0)i=12[(αi+βi)2]×H1,1:1,2;1,20,1:2,1;2,1[4α1β1N0η4α2β2N0η|(12i=12αi+βi4;12,12):(1α1+β12,1);(1α2+β22,1)(1i=12αi+βi2;1,1):(α1β12,1),(β1α12,1);(α2β22,1),(β2α22,1)].

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