Abstract

Coherent wireless optical communication systems with heterodyne detection are analyzed for binary phase-shift keying (BPSK), differential PSK (DPSK), and M-ary PSK over Gamma-Gamma turbulence channels. Closed-form error rate expressions are derived using a series expansion approach. It is shown that, in the special case of K-distributed turbulence channel, the DPSK incurs a 3 dB signal-to-noise ratio (SNR) penalty compared to BPSK in the large SNR regime. The outage probability is also obtained, and a detailed outage truncation error analysis is presented and used to assess the accuracy in system performance estimation. It is shown that our series error rate expressions are simple to use and highly accurate for practical system performance estimation.

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References

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  1. V. W. S. Chan, “Free-space optical communications,” J. Lightwave Technol. 24, 4750–4762 (2006).
    [CrossRef]
  2. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (2002).
    [CrossRef]
  3. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of MIMO free-space optical systems in Gamma-Gamma fading,” IEEE Trans. Commun. 57, 3415–3424 (2009).
    [CrossRef]
  4. J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
    [CrossRef]
  5. W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).
  6. K. Kiasaleh, “Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence,” IEEE Trans. Commun. 54, 604–607 (2006).
    [CrossRef]
  7. M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K-distributed turbulence,” IEEE Trans. Commun. 59, 664–668 (2011).
    [CrossRef]
  8. A. Belmonte and J. M. Kahn, “Performance of synchronous optical receivers using atmospheric compensation techniques,” Opt. Express 16, 14151–14162 (2008).
    [CrossRef] [PubMed]
  9. G. P. Agrawal, Fiber-Optical Communication Systems (Wiley, 2002).
    [CrossRef]
  10. 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. 40, 1554–1562 (2001).
    [CrossRef]
  11. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
    [CrossRef]
  12. N. Wang and J. Cheng, “Moment-based estimation for the shape parameters of the Gamma-Gamma atmospheric turbulence model,” Opt. Express 18, 12824–12831 (2010).
    [CrossRef] [PubMed]
  13. Wolfram Mathworld. [Online]: http://functions.wolfram.com/03.04.06.0002.01 .
  14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, 2000).
  15. M. Niu, J. Schlenker, J. Cheng, J. F. Holzman, and R. Schober, “Coherent wireless optical communications with predetection and postdetection EGC over Gamma-Gamma atmospheric turbulence channels,” J. Opt. Commun. Netw. 3, 860–869 (2011).
    [CrossRef]

2011 (2)

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K-distributed turbulence,” IEEE Trans. Commun. 59, 664–668 (2011).
[CrossRef]

M. Niu, J. Schlenker, J. Cheng, J. F. Holzman, and R. Schober, “Coherent wireless optical communications with predetection and postdetection EGC over Gamma-Gamma atmospheric turbulence channels,” J. Opt. Commun. Netw. 3, 860–869 (2011).
[CrossRef]

2010 (1)

2009 (1)

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

2008 (1)

2007 (1)

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
[CrossRef]

2006 (2)

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

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

2002 (1)

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50, 1293–1300 (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. 40, 1554–1562 (2001).
[CrossRef]

1993 (1)

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optical Communication Systems (Wiley, 2002).
[CrossRef]

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. 40, 1554–1562 (2001).
[CrossRef]

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. 40, 1554–1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Bayaki, E.

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

Belmonte, A.

Chan, V. W. S.

Cheng, J.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, 2000).

Holzman, J. F.

M. Niu, J. Schlenker, J. Cheng, J. F. Holzman, and R. Schober, “Coherent wireless optical communications with predetection and postdetection EGC over Gamma-Gamma atmospheric turbulence channels,” J. Opt. Commun. Netw. 3, 860–869 (2011).
[CrossRef]

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K-distributed turbulence,” IEEE Trans. Commun. 59, 664–668 (2011).
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Huang, W.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

Kahn, J. M.

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

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

Kiasaleh, K.

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

Li, J.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
[CrossRef]

Liu, J. Q.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
[CrossRef]

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. 57, 3415–3424 (2009).
[CrossRef]

Nakagawa, M.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

Niu, M.

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K-distributed turbulence,” IEEE Trans. Commun. 59, 664–668 (2011).
[CrossRef]

M. Niu, J. Schlenker, J. Cheng, J. F. Holzman, and R. Schober, “Coherent wireless optical communications with predetection and postdetection EGC over Gamma-Gamma atmospheric turbulence channels,” J. Opt. Commun. Netw. 3, 860–869 (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. 40, 1554–1562 (2001).
[CrossRef]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, 2000).

Sakanaka, T.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

Schlenker, J.

Schober, R.

Takayanagi, J.

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

Taylor, D. P.

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
[CrossRef]

Wang, N.

Zhu, X.

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

IEEE Trans. Commun. (5)

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

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

J. Li, J. Q. Liu, and D. P. Taylor, “Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,” IEEE Trans. Commun. 55, 1598–1606 (2007).
[CrossRef]

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

M. Niu, J. Cheng, and J. F. Holzman, “Error rate analysis of M-ary coherent free-space optical communication systems with K-distributed turbulence,” IEEE Trans. Commun. 59, 664–668 (2011).
[CrossRef]

IEICE Trans. Commun (1)

W. Huang, J. Takayanagi, T. Sakanaka, and M. Nakagawa, “Atmospheric optical communication system using subcarrier PSK modulation,” IEICE Trans. Commun.  E76-B, 1169–1177 (1993).

J. Lightwave Technol. (1)

J. Opt. Commun. Netw. (1)

Opt. Eng. (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. 40, 1554–1562 (2001).
[CrossRef]

Opt. Express (2)

Other (4)

G. P. Agrawal, Fiber-Optical Communication Systems (Wiley, 2002).
[CrossRef]

Wolfram Mathworld. [Online]: http://functions.wolfram.com/03.04.06.0002.01 .

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, 2000).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Exact and approximated BERs for BPSK and DPSK over turbulent Gamma-Gamma channels with J = 35; (b) Exact and approximated SERs for QPSK and 8PSK over turbulent Gamma-Gamma channels with J = 35.

Fig. 2
Fig. 2

(a) Exact and approximated outage probability over turbulent Gamma-Gamma channels with J = 30; (b) Outage truncation error over moderately turbulent Gamma-Gamma channels when α = 2.711, β = 2.319.

Equations (19)

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i ( t ) = i dc + i ac ( t ) + n ( t )
f I s ( I s ) = 2 Γ ( α ) Γ ( β ) ( α β ) α + β 2 I s α + β 2 K α β ( 2 α β I s ) , I s > 0
P e = 0 P e ( I s ) f I s ( I s ) d I s .
f I s ( I s ) = π sin [ π ( α β ) ] p = 0 [ a p ( α , β ) I s p + β 1 a p ( β , α ) I s p + α 1 ]
a p ( α , β ) ( α β ) p + β Γ ( α ) Γ ( β ) Γ ( p α + β + 1 ) p ! .
P e = 1 π 0 π 2 0 exp ( γ ¯ I s 2 sin 2 θ ) f I s ( I s ) d I s d θ .
P e BPSK = B ( α β , 1 α + β ) 2 π p = 0 [ a p ( α , β ) Γ ( p + β ) B ( 1 2 , p + β + 1 2 ) ( γ ¯ 2 ) ( p + β ) a p ( β , α ) Γ ( p + α ) B ( 1 2 , p + α + 1 2 ) ( γ ¯ 2 ) ( p + α ) ]
0 π 2 ( sin θ ) p + α d θ = 2 p + α 1 B ( p + α + 1 2 , p + α + 1 2 ) = 1 2 B ( 1 2 , p + α + 1 2 ) .
P e , asym BPSK = Γ ( α β ) B ( 1 2 , β + 1 2 ) 2 π Γ ( α ) ( γ ¯ 2 α β ) β .
P e MPSK = B ( α β , 1 α + β ) π × p = 0 [ a p ( α , β ) Γ ( p + β ) g p ( β ) sin 2 p + 2 β ( π M ) ( γ ¯ 2 ) ( p + β ) a p ( β , α ) Γ ( p + α ) g p ( α ) sin 2 p + 2 α ( π M ) ( γ ¯ 2 ) ( p + α ) ]
g p ( x ) M 1 M 0 π sin 2 p + 2 x ( M 1 M t ) d t = [ π 3 2 sec ( p π + π x ) 2 Γ ( p + x + 1 ) Γ ( 1 2 p x ) cos ( M 1 M π ) F 2 1 ( 1 2 , 1 2 p x ; 3 2 ; cos 2 ( M 1 ) π M ) ]
P e DPSK = B ( α β , 1 α + β ) 2 × p = 0 [ a p ( α , β ) Γ ( p + β ) ( γ ¯ 2 ) ( p + β ) a p ( β , α ) Γ ( p + α ) ( γ ¯ 2 ) ( p + α ) ] .
P e , asym DPSK = Γ ( α β ) 2 Γ ( α ) ( γ ¯ 2 α β ) β .
F I s ( I 0 ) = 0 I 0 f I s ( I s ) d I s = B ( α β , 1 α + β ) p = 0 [ a p ( α , β ) p + β I 0 p + β a p ( β , α ) p + α I 0 p + α ] .
P o ( γ th ) = B ( α β , 1 α + β ) p = 0 [ a p ( α , β ) ( p + β ) γ ¯ p + β γ t h p + β a p ( β , α ) ( p + α ) γ ¯ p + α γ th p + α ]
ε J = | B ( α β , 1 α + β ) | p = J + 1 | a p ( α , β ) ( p + β ) γ ¯ p + β γ th p + β a p ( β , α ) ( p + α ) γ ¯ p + α γ th p + α | .
ε J = | B ( α β , 1 α + β ) | Γ ( α ) Γ ( β ) p = J + 1 ( α β γ th γ ¯ ) p 1 p ! | b p ( α , β ) b p ( β , α ) |
b p ( α , β ) ( α β γ th ) β ( p + α ) Γ ( p α + β + 1 ) γ ¯ β .
ε J < | B ( α β , 1 α + β ) | Γ ( α ) Γ ( β ) max p > J { c p ( α , β ) } exp ( α β γ th γ ¯ )

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