Abstract

The average bit error rate (BER) of optical communication systems is considered in the presence of random angular jitter. First, the received power and the BER in the absence of jitter are reviewed. Then the average BER is obtained in the presence of circularly symmetric, normally distributed jitter by using the probability density function of the optical signal. By minimizing the power penalty for average BER, the optimum ratio of the divergence angle of the laser beam to the random angular jitter at the desired BER is obtained. An analytic approximation of the optimum ratio is derived as a function of the desired average BER. The results can be used for designing the link budget of optical communication and tracking channels in the presence of jitter.

© 2002 Optical Society of America

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References

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    [CrossRef]
  2. C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
    [CrossRef]
  3. K. Araki, T. Aruga, “Space optical communication technologies—an overview,” Rev. Laser Eng. 24, 1264–1271 (1996).
    [CrossRef]
  4. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997), Chap. 4.5.
  5. K. Kiasaleh, “On the probability density function of signal intensity in free-space optical communications systems impaired by pointing jitter and turbulence,” Opt. Eng. 33, 3748–3757 (1994).
    [CrossRef]
  6. M. Toyoshima, K. Araki, “Far-field pattern measurement of an onboard laser transmitter by use of a space-to-ground optical link,” Appl. Opt. 37, 1720–1730 (1998).
    [CrossRef]
  7. M. Toyoshima, K. Araki, “Effects of time-averaging on optical scintillation in a ground-to-satellite atmospheric propagation,” Appl. Opt. 39, 1911–1919 (2000).
    [CrossRef]
  8. M. Toyoshima, K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the Engineering Test Satellite VI using laser communication equipment,” Opt. Eng. 40, 827–832 (2001).
    [CrossRef]
  9. R. D. Nelson, T. H. Ebben, R. G. Marshalek, “Experimental verification of the pointing error distribution of an optical intersatellite link,” in Selected Papers on Free-Space Laser Communications, D. L. Begley, B. J. Thompson, eds., Vol. 30 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1991), pp. 218–228.
  10. R. R. Hayes, “Fading statistics for intersatellite optical communication,” Appl. Opt. 36, 8063–8086 (1997).
    [CrossRef]
  11. D. L. Fried, “Statistics of laser beam fade induced by pointing jitter,” Appl. Opt. 12, 422–423 (1973).
    [CrossRef] [PubMed]
  12. P. J. Titterton, “Power reduction and fluctuations caused by narrow laser beam motion in the far field,” Appl. Opt. 12, 423–425 (1973).
    [CrossRef] [PubMed]
  13. H. T. Yura, W. G. McKinley, “Optical scintillation statistics for IR ground-to-space laser communication systems,” Appl. Opt. 22, 3353–3358 (1983).
    [CrossRef] [PubMed]
  14. L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751 (1994).
    [CrossRef]
  15. L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system: errata,” Appl. Opt. 36, 6068 (1997).
    [CrossRef]

2001 (1)

M. Toyoshima, K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the Engineering Test Satellite VI using laser communication equipment,” Opt. Eng. 40, 827–832 (2001).
[CrossRef]

2000 (1)

1998 (1)

1997 (2)

1996 (1)

K. Araki, T. Aruga, “Space optical communication technologies—an overview,” Rev. Laser Eng. 24, 1264–1271 (1996).
[CrossRef]

1995 (1)

1994 (2)

K. Kiasaleh, “On the probability density function of signal intensity in free-space optical communications systems impaired by pointing jitter and turbulence,” Opt. Eng. 33, 3748–3757 (1994).
[CrossRef]

L. C. Andrews, R. L. Phillips, P. T. Yu, “Optical scintillations and fade statistics for a satellite-communication system,” Appl. Opt. 34, 7742–7751 (1994).
[CrossRef]

1989 (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

1983 (1)

1973 (2)

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997), Chap. 4.5.

Andrews, L. C.

Araki, K.

M. Toyoshima, K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the Engineering Test Satellite VI using laser communication equipment,” Opt. Eng. 40, 827–832 (2001).
[CrossRef]

M. Toyoshima, K. Araki, “Effects of time-averaging on optical scintillation in a ground-to-satellite atmospheric propagation,” Appl. Opt. 39, 1911–1919 (2000).
[CrossRef]

M. Toyoshima, K. Araki, “Far-field pattern measurement of an onboard laser transmitter by use of a space-to-ground optical link,” Appl. Opt. 37, 1720–1730 (1998).
[CrossRef]

K. Araki, T. Aruga, “Space optical communication technologies—an overview,” Rev. Laser Eng. 24, 1264–1271 (1996).
[CrossRef]

Aruga, T.

K. Araki, T. Aruga, “Space optical communication technologies—an overview,” Rev. Laser Eng. 24, 1264–1271 (1996).
[CrossRef]

Chen, C. C.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Ebben, T. H.

R. D. Nelson, T. H. Ebben, R. G. Marshalek, “Experimental verification of the pointing error distribution of an optical intersatellite link,” in Selected Papers on Free-Space Laser Communications, D. L. Begley, B. J. Thompson, eds., Vol. 30 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1991), pp. 218–228.

Fried, D. L.

Gardner, C. S.

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

Hayes, R. R.

Kiasaleh, K.

K. Kiasaleh, “On the probability density function of signal intensity in free-space optical communications systems impaired by pointing jitter and turbulence,” Opt. Eng. 33, 3748–3757 (1994).
[CrossRef]

Marshalek, R. G.

R. D. Nelson, T. H. Ebben, R. G. Marshalek, “Experimental verification of the pointing error distribution of an optical intersatellite link,” in Selected Papers on Free-Space Laser Communications, D. L. Begley, B. J. Thompson, eds., Vol. 30 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1991), pp. 218–228.

McKinley, W. G.

Nelson, R. D.

R. D. Nelson, T. H. Ebben, R. G. Marshalek, “Experimental verification of the pointing error distribution of an optical intersatellite link,” in Selected Papers on Free-Space Laser Communications, D. L. Begley, B. J. Thompson, eds., Vol. 30 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1991), pp. 218–228.

Phillips, R. L.

Titterton, P. J.

Toyoshima, M.

Yu, P. T.

Yura, H. T.

Appl. Opt. (8)

IEEE Trans. Commun. (1)

C. C. Chen, C. S. Gardner, “Impact of random pointing and tracking errors on the design of coherent and incoherent optical intersatellite communication links,” IEEE Trans. Commun. 37, 252–260 (1989).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

K. Kiasaleh, “On the probability density function of signal intensity in free-space optical communications systems impaired by pointing jitter and turbulence,” Opt. Eng. 33, 3748–3757 (1994).
[CrossRef]

M. Toyoshima, K. Araki, “In-orbit measurements of short term attitude and vibrational environment on the Engineering Test Satellite VI using laser communication equipment,” Opt. Eng. 40, 827–832 (2001).
[CrossRef]

Rev. Laser Eng. (1)

K. Araki, T. Aruga, “Space optical communication technologies—an overview,” Rev. Laser Eng. 24, 1264–1271 (1996).
[CrossRef]

Other (2)

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997), Chap. 4.5.

R. D. Nelson, T. H. Ebben, R. G. Marshalek, “Experimental verification of the pointing error distribution of an optical intersatellite link,” in Selected Papers on Free-Space Laser Communications, D. L. Begley, B. J. Thompson, eds., Vol. 30 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1991), pp. 218–228.

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Figures (6)

Fig. 1
Fig. 1

Average BER characteristics as a function of the required SNR and the ratio of the beam divergence angle to the random jitter.

Fig. 2
Fig. 2

Power penalty for the desired average BER as a function of the ratio of the beam divergence angle to the random jitter.

Fig. 3
Fig. 3

Total power penalty for the optical link with respect to average BER as a function of the ratio of the beam divergence angle to the random jitter when the transmitted power, the distance, and the random jitter are assumed to be constant against the beam divergence angle.

Fig. 4
Fig. 4

Optimum ratio of the beam divergence angle to the random jitter as a function of the desired average BER.

Fig. 5
Fig. 5

Fade level for several fade probabilities as a function of the ratio of the beam divergence angle to the random jitter.

Fig. 6
Fig. 6

Surge level for several surge probabilities as a function of the ratio of the beam divergence angle to the random jitter.

Tables (2)

Tables Icon

Table 1 Optimum Ratios of Beam Divergence Angle to Random Jitter for Each Desired BER

Tables Icon

Table 2 Coefficients for the Approximate Expression Describing the Optimum Ratio (w0/σ)opt for a Desired Average BER

Equations (23)

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I0(θ, R)=PtτtR22πw02exp-2θ2w02,
Pr=I0(θ, R)Arτr,
BER(Q)=12erfcQ2,
pj(θ, ϕ)=θσ2exp-θ2+ϕ22σ2I0θϕσ2,
pj(θ, 0)=θσ2exp-θ22σ2.
p(I)=βIβ-1 for0I1,
I¯=ββ+1,
BER¯(Qr)=01p(I)BERIQrβ+1βdI=Qr(β+1)201Iβ-1 erfcIQr2β+1βdI,
Lj=Q|BER(Q)=aQr|BER¯(Qr)=a.
I(0, R)=PtτtR22πw02ββ+1Lj=I0(0, R)τjLj,
Lp=-10 logI(0, R)I(0, R)|BER=10-6,max,-10 log Pt+20 log R+10 log(w02+4σ2)-10 log Lj.
(w0/σ)opt=a6t6+a5t5+a4t4+a3t3+a2t2+a1t+a0,
t=log10(BER¯),
Pr=PtτtGtLrGrτrτjLj,
Gt=8w02,Lr=λ4πR2,Gr=4πArλ2,
τj=w024σ2+w02,Lj=Q|BER(Q)=aQr|BER¯(Qr)=a.
Pr=PtτtGtLrGrτrsτj,
FT=β+1βPF1/β,
PF=0IFp(I)dI=IFβ.
ST=β+1β(1-PS)1/β,
PS=S1p(I)dI=1-ISβ.
D=ST/FT.
Dtotal=STFTRmaxRmin2,

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