Abstract

This paper analytically investigates a bit error rate (BER) performance of radio over free space optical (FSO) systems considering laser phase noise under Gamma-Gamma turbulence channels. An external modulation using a dual drive Mach-Zehnder modulator (DD-MZM) and a phase shifter is employed because a DD-MZM is robust against a laser chirp and provides high spectral efficiency. We derive a closed form average BER as a function of different turbulence strengths and laser diode (LD) linewidth, and investigate its analytical behavior under practical scenario. As a result, for a given average SNR with normalized perturbation, it is shown that the difference of average BER corresponding to two LDs (with linewidth of 624MHz and 10MHz) under weak turbulence is almost 3 times larger than that under strong turbulence.

© 2009 Optical Society of America

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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. 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]
  3. G. H. Smith and D. Novak, "Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators," IEEE Trans. Microwave Theory Tech. 45, 1410-1415 (1997).
    [CrossRef]
  4. R. W. Tkach and A. R. Chraplyvy, "Phase noise and linewidth in an InGaAsP DFB laser," J. Lightwave Technol. LT-4, 1711-1716 (1986).
    [CrossRef]
  5. T. Cho, C. Yun, J. Song, and K. Kim, "Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator," J. Lightwave Technol. 23, 4093-4100 (2005).
    [CrossRef]
  6. J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
    [CrossRef]
  7. K. Kiasaleh, "Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence," IEEE Trans. Commun. 54, 604-607 (2006).
    [CrossRef]
  8. G. P. Agrawal, Fiber-Optic Communication Systems. (John Wiley and Sons, New York, 2002).
    [CrossRef]
  9. A. J. Viterbi, Principles of Coherent Communication. (McGraw-Hill, New York, 1966).
  10. The Wolfram function site (2004), http://functions.wolfram.com/.

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]

2005 (1)

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]

1997 (1)

G. H. Smith and D. Novak, "Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators," IEEE Trans. Microwave Theory Tech. 45, 1410-1415 (1997).
[CrossRef]

1990 (1)

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

1986 (1)

R. W. Tkach and A. R. Chraplyvy, "Phase noise and linewidth in an InGaAsP DFB laser," J. Lightwave Technol. LT-4, 1711-1716 (1986).
[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]

Barry, J. R.

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

Chan, V. W. S.

Cho, T.

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, "Phase noise and linewidth in an InGaAsP DFB laser," J. Lightwave Technol. LT-4, 1711-1716 (1986).
[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]

Kim, K.

Lee, E. A.

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

Novak, D.

G. H. Smith and D. Novak, "Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators," IEEE Trans. Microwave Theory Tech. 45, 1410-1415 (1997).
[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]

Smith, G. H.

G. H. Smith and D. Novak, "Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators," IEEE Trans. Microwave Theory Tech. 45, 1410-1415 (1997).
[CrossRef]

Song, J.

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, "Phase noise and linewidth in an InGaAsP DFB laser," J. Lightwave Technol. LT-4, 1711-1716 (1986).
[CrossRef]

Yun, C.

IEEE Trans. Commun. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

G. H. Smith and D. Novak, "Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators," IEEE Trans. Microwave Theory Tech. 45, 1410-1415 (1997).
[CrossRef]

J. Lightwave Technol. (3)

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]

Proc. IEEE (1)

J. R. Barry and E. A. Lee, "Performance of coherent optical receivers," Proc. IEEE 78, 1369-1394 (1990).
[CrossRef]

Other (3)

G. P. Agrawal, Fiber-Optic Communication Systems. (John Wiley and Sons, New York, 2002).
[CrossRef]

A. J. Viterbi, Principles of Coherent Communication. (McGraw-Hill, New York, 1966).

The Wolfram function site (2004), http://functions.wolfram.com/.

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Figures (2)

Fig. 1.
Fig. 1.

Overall architecture of the FSO system considering of optical transmitter, turbulence channels, and optical receiver.

Fig. 2.
Fig. 2.

Average BER according to average SNR when E[δ 2] = 1 according to (α, β,SI) ∈ {(4,1,1.5),(4,2,0.875),(4,4,0.5625)} and 624MHz and 10MHz of LD linewidth.

Equations (28)

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x LD ( t ) = V LD exp [ j ( ω c t + Φ LD ( t ) ) ] ,
x RF ( t ) = V RF cos ( ω rf t + θ ( t ) ) .
E T ( t ) = V LD 2 10 L 20 { exp [ j ( ω c t + π 2 + Φ LD ( t ) + επ cos [ ω rf t + θ ( t ) ] ) ]
+ exp [ j ( ω c t + Φ LD ( t ) + επ cos [ ω rf t + θ ( t ) + π 2 ] ) ] }
E T ( t ) = V LD exp [ j ( ω c t + Φ LD ( t ) ) ] 2 10 L 20 { j n = [ j n exp [ j n ( ω c t + Φ LD ( t ) ) ] J n ( επ ) ]
+ n = [ j n exp [ jn ( π 2 + ω RF t + θ ( t ) ) ] J n ( επ ) ] }
V LD 10 L 20 { J 0 ( επ ) exp [ j ( ω c t + π 4 + Φ LD ( t ) ) ]
2 J 1 ( επ ) exp [ j ( ω c t + ω rf t + Φ LD ( t ) + θ ( t ) ) ] } .
E R ( t ) V LD · δ ( t ) 10 L 20 { J 0 ( επ ) exp [ j ( ω c t + π 4 + Φ LD ( t τ 0 ) ψ 0 ) ]
2 J 1 ( επ ) exp [ j ( ω c t + ω rf t + Φ LD ( t τ 1 ) + θ ( t ) ψ 1 ) ] }
i ( t ) = R E R ( t ) 2 + n th ( t )
2 2 R ( V LD · δ ( t ) 10 L 20 ) 2 J 0 ( επ ) J 1 ( επ ) cos ( ω rf t + Φ LD ( t τ 1 )
Φ LD ( t τ 0 ) + θ ( t ) ψ 1 + ψ 0 ) + n th ( t )
i ( t ) = δ · ϒ · cos ( ω rf t + Ψ + θ ( t ) + ψ 2 ) + n th ( t ) , mT t ( m + 1 ) T
f δ ( δ ) = 2 ( αβ ) α + β 2 Γ ( α ) Γ ( β ) ( δ ) α + β 2 1 K α β ( 2 αβδ )
α = ( exp [ 0.49 σ R 2 ( 1 + 0.18 d 2 + 0.56 σ R 12 / 5 ) 7/6 ] 1 ) 1
β = ( exp [ 0.51 σ R 2 ( 1 + 0.69 σ 12 / 5 ) 5 / 6 ( 1 + 0.18 d 2 + 0.56 σ R 12 / 5 ) 7/6 ] 1 ) 1
SI = 1 α + 1 β + 1 αβ .
P b ( E Ψ , Λ ) = 1 2 erfc ( Λ cos 2 [ Ψ ] )
E [ P b ] = 0 P b ( E Ψ , Λ ) f Ψ ( Ψ ) f δ ( δ ) d Ψ d δ
E [ P b ] = 1 2 π 0 erfc ( μ δ 2 cos 2 [ 2 σx ] ) exp [ x 2 ] f δ ( δ ) d x d δ
= 1 2 π 0 i = 1 N w i erfc ( μ δ 2 cos 2 [ 2 σ x i ] f δ ( δ ) d δ
erfc ( x ) = 1 π G 1,2 2,0 [ x 0 , 1 2 1 ]
K ν ( x ) = 1 2 G 0,2 2,0 [ x 2 4 ν 2 , ν 2 ]
E [ P b ] = 1 2 π i = 1 N w i 0 erfc ( μ δ 2 cos 2 [ 2 σ x i ] 2 ( αβ ) α + β 2 Γ ( α ) Γ ( β ) ( δ ) α + β 2 1 K α β ( 2 αβδ ) ) d δ
= ( αβ ) α + β 2 2 π Γ ( α ) Γ ( β ) i = 1 N w i 0 ( δ ) α + β 2 1 G 1,2 2,0 [ μ δ 2 cos 2 [ 2 σ x i ] 0 , 1 2 1 ]
× G 0,2 2,0 [ αβ ( δ ) α β 2 , β α 2 ] d δ .
E [ P b ] = 2 α + β 3 π 2 Γ ( α ) Γ ( β ) i = 1 N w i G 5,2 2,4 [ 2 4 μ cos 2 [ 2 σ x i ] ( αβ ) 2 0 , 1 2 1 α 2 , 2 α 2 , 1 β 2 , 2 β 2 , 1 ] .

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