Abstract

We derive a model that optimizes the performance of a laser satellite communication link with an optical preamplifier in the presence of random jitter in the transmitter–receiver line of sight. The system utilizes a transceiver containing a single telescope with a circulator. The telescope is used for both transmitting and receiving and thus reduces communication terminal dimensions and weight. The optimization model was derived under the assumption that the dominant noise source was amplifier spontaneous-emission noise. It is shown that, given the required bit-error rate (BER) and the rms random pointing jitter, an optimal transceiver gain exists that minimizes transmitted power. We investigate the effect of the amplifier spontaneous-emission noise on the optimal transmitted power and gain by performing an optimization procedure for various combinations of amplifier gain and noise figure. We demonstrate that the amplifier noise figure determines the optimal transmitted power needed to achieve the desired BER but does not affect the optimal transceiver telescope gain. Our numerical example shows that for a BER of 10-9, doubling the amplifier noise figure results in an 80% increase in minimal transmitted power for a rms pointing jitter of 0.44 μrad.

© 2004 Optical Society of America

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References

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  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]
  2. S. Arnon, S. Rotman, N. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
    [CrossRef] [PubMed]
  3. J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant design parameter for satellite-borne, free-space optimal communication systems,” Opt. Eng. 24, 1049–1054 (1985).
    [CrossRef]
  4. A. Polishuk, S. Arnon, “Communication performance analysis of microsatellites with optical phased-array antenna,” Opt. Eng. 42, 2015–2024 (2003).
    [CrossRef]
  5. M. Toyoshima, T. Jono, K. Nakagawa, A. Yamamoto, “Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems,” J. Opt. Soc. Am. A 19, 567–571 (2002).
    [CrossRef]
  6. S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
    [CrossRef]
  7. S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
    [CrossRef]
  8. P. J. Winzer, A. Kalmar, W. R. Leeb, “Role of amplified spontaneous emission in optical free space communication links with optical amplification—impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” in Free-Space Laser Communication Technologies XI, G. S. Mecherle, ed., Proc. SPIE3615, 134–141 (1999).
    [CrossRef]
  9. S. Arnon, “Optical wireless communication,” in Encyclope-dia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, New York, 2003), pp. 1866–1886.
  10. J. D. Degnan, B. J. Klein, “Optical antenna gain. I. Transmitting antennas,” Appl. Opt. 13, 2134–2141 (1974).
    [CrossRef]
  11. J. D. Degnan, B. J. Klein, “Optical antenna gain. II. Receiving antennas,” Appl. Opt. 13, 2397–2401 (1974).
    [CrossRef] [PubMed]
  12. S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech House, Boston, Mass., 1995).
  13. S. B. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, Bellingham, Wash., 1997).
  14. E. Desurvire, Erbium-Doped Fiber Amplifier—Principles and Applications (Wiley, New York, 1994).
  15. G. P. Agrawal, Fiber Optic Communication (Wiley, New York, 1997).
  16. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, London, 1987).

2003 (2)

A. Polishuk, S. Arnon, “Communication performance analysis of microsatellites with optical phased-array antenna,” Opt. Eng. 42, 2015–2024 (2003).
[CrossRef]

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

2002 (1)

1998 (1)

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

1997 (1)

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]

1985 (1)

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant design parameter for satellite-borne, free-space optimal communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

1974 (2)

Agrawal, G. P.

G. P. Agrawal, Fiber Optic Communication (Wiley, New York, 1997).

Alexander, S. B.

S. B. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, Bellingham, Wash., 1997).

Arnon, S.

A. Polishuk, S. Arnon, “Communication performance analysis of microsatellites with optical phased-array antenna,” Opt. Eng. 42, 2015–2024 (2003).
[CrossRef]

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

S. Arnon, S. Rotman, N. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

S. Arnon, “Optical wireless communication,” in Encyclope-dia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, New York, 2003), pp. 1866–1886.

Barry, J. D.

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant design parameter for satellite-borne, free-space optimal communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Casey, W. L.

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech House, Boston, Mass., 1995).

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]

Degnan, J. D.

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifier—Principles and Applications (Wiley, New York, 1994).

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]

Jono, T.

Kalmar, A.

P. J. Winzer, A. Kalmar, W. R. Leeb, “Role of amplified spontaneous emission in optical free space communication links with optical amplification—impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” in Free-Space Laser Communication Technologies XI, G. S. Mecherle, ed., Proc. SPIE3615, 134–141 (1999).
[CrossRef]

Klein, B. J.

Kopeika, N.

Kopeika, N. S.

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

Lambert, S. G.

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech House, Boston, Mass., 1995).

Leeb, W. R.

P. J. Winzer, A. Kalmar, W. R. Leeb, “Role of amplified spontaneous emission in optical free space communication links with optical amplification—impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” in Free-Space Laser Communication Technologies XI, G. S. Mecherle, ed., Proc. SPIE3615, 134–141 (1999).
[CrossRef]

Mecherle, G. S.

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant design parameter for satellite-borne, free-space optimal communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

Nakagawa, K.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, London, 1987).

Polishuk, A.

A. Polishuk, S. Arnon, “Communication performance analysis of microsatellites with optical phased-array antenna,” Opt. Eng. 42, 2015–2024 (2003).
[CrossRef]

Rotman, S.

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

S. Arnon, S. Rotman, N. Kopeika, “Beam width and transmitter power adaptive to tracking system performance for free-space optical communication,” Appl. Opt. 36, 6095–6101 (1997).
[CrossRef] [PubMed]

Toyoshima, M.

Winzer, P. J.

P. J. Winzer, A. Kalmar, W. R. Leeb, “Role of amplified spontaneous emission in optical free space communication links with optical amplification—impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” in Free-Space Laser Communication Technologies XI, G. S. Mecherle, ed., Proc. SPIE3615, 134–141 (1999).
[CrossRef]

Yamamoto, A.

Appl. Opt. (3)

IEEE Trans. Aerosp. Electron. Syst. (1)

S. Arnon, S. Rotman, N. S. Kopeika, “Optimum transmitter optics aperture for satellite optical communication,” IEEE Trans. Aerosp. Electron. Syst. 34, 590–596 (1998).
[CrossRef]

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]

IEEE Trans. Wireless Commun. (1)

S. Arnon, “Optimization of urban optical wireless communication systems,” IEEE Trans. Wireless Commun. 2, 626–629 (2003).
[CrossRef]

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

Opt. Eng. (2)

J. D. Barry, G. S. Mecherle, “Beam pointing error as a significant design parameter for satellite-borne, free-space optimal communication systems,” Opt. Eng. 24, 1049–1054 (1985).
[CrossRef]

A. Polishuk, S. Arnon, “Communication performance analysis of microsatellites with optical phased-array antenna,” Opt. Eng. 42, 2015–2024 (2003).
[CrossRef]

Other (7)

S. G. Lambert, W. L. Casey, Laser Communication in Space (Artech House, Boston, Mass., 1995).

S. B. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, Bellingham, Wash., 1997).

E. Desurvire, Erbium-Doped Fiber Amplifier—Principles and Applications (Wiley, New York, 1994).

G. P. Agrawal, Fiber Optic Communication (Wiley, New York, 1997).

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, London, 1987).

P. J. Winzer, A. Kalmar, W. R. Leeb, “Role of amplified spontaneous emission in optical free space communication links with optical amplification—impact on isolation and data transmission; utilization for pointing, acquisition, and tracking,” in Free-Space Laser Communication Technologies XI, G. S. Mecherle, ed., Proc. SPIE3615, 134–141 (1999).
[CrossRef]

S. Arnon, “Optical wireless communication,” in Encyclope-dia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, New York, 2003), pp. 1866–1886.

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Figures (6)

Fig. 1
Fig. 1

Satellite transceiver.

Fig. 2
Fig. 2

BER as a function of the ratio of rms pointing jitter to angular beam width.

Fig. 3
Fig. 3

Power penalty for the desired BER as a function of the ratio of rms pointing jitter to angular beam width.

Fig. 4
Fig. 4

Minimal transmitted power for 10-9 BER as a function of transceiver gain for different rms pointing jitter values.

Fig. 5
Fig. 5

Parameter α=K1PT/σχ4 as a function of BER for three types of amplifiers.

Fig. 6
Fig. 6

Parameter β=G2σχ4 as a function of BER for three types of amplifiers.

Tables (1)

Tables Icon

Table 1 Communication System Parameters

Equations (63)

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f(θV)=12πσVexp-(θV-μV)22σV2,
f(θH)=12πσHexp-(θH-μH)22σH2,
θ=θV2+θH2.
σθ=σV=σH,
p(θ, ϕ)=θσθ2exp-θ2+ϕ22σθ2I0θϕσθ2,
f(θR)=θRσθR2exp-θR22σθR2,
f(θT)=θTσθT2exp-θT22σθT2,
PR(θT, θR)=PTηTηRλ4πZ2GTGRLT(θT)LR(θR),
GTπDTλ2,
GRπDRλ2,
LT(θT)=exp(-GTθT2)
LR(θR)=exp(-GRθR2)
R=ηqhν;
σS×ASE2(θT, θR)=4RqnspηG0(G0-1)PR(θT, θR)B,
nspFn2,
σASE×ASE2=4[nspη(G0-1)q]2ΔλB,
P(y/On, θT, θR)=yσS×ASE2(θT, θR)+σASE×ASE2×I0yRG0PR(θT, θR)σS×ASE2(θT, θR)+σASE×ASE2×exp-y2+[RG0PR(θT, θR)]22[σS×ASE2(θT, θR)+σASE×ASE2].
P(y/Off)=yσASE×ASE2exp-y22σASE×ASE2.
sˆ=maxsP(y/s)P(s)P(y),
BER=P(On)P(Off/On)+P(Off)P(On/Off),
P(Off/On)=Λ(y)<1P(y/On)dy,
P(On/Off)=Λ(y)>1P(y/Off)dy.
Λ(y, θT, θR)
=P(y/On, θT, θR)P(y/Off)
=σASE×ASE2σS×ASE2(θT, θR)+σASE×ASE2
×I0yRG0PR(θT, θR)σS×ASE2(θT, θR)+σASE×ASE2
×exp-y2+[RG0PR(θT, θR)]22[σS×ASE2(θT, θR)+σASE×ASE2]
+y22σASE×ASE2.
BER=1200-VtyσS×ASE2(θT, θR)+σASE×ASE2×I0yRG0PR(θT, θR)σS×ASE2(θT, θR)+σASE×ASE2×exp-y2+[RG0PR(θT, θR)]22[σS×ASE2(θT, θR)+σASE×ASE2]dy+VtyσASE×ASE2exp-y22σASE×ASE2dy×θTσT2exp-θT22σT2θRσR2exp-θR22σR2dθTdθR,
GT=GR=GπDλ2,
PR(θT, θR)=PTηTηRλ4πZ2G2exp[-G(θT2+θR2)].
χ=θT2+θR2.
f(χ)=aχ exp-χ2σχ2U(χ),
a=1/(σχ2)4Γ(2).
Γ(x)=0tx-1exp(-t)dt,1x2.
Γ(x+1)=xΓ(x).
BER=120-VtyσS×ASE2(χ)+σASE×ASE2× I0yG0RPR(χ)σS×ASE2(χ)+σASE×ASE2×exp-y2+[RG0PR(χ)]22[σS×ASE2(χ)+σASE×ASE2]dy+VtyσASE×ASE2exp-y22σASE×ASE2dy×aχ exp-χ2σχ2dχ.
K1=ηTηR(λ/4πZ)2,
K2=4qnspηG0(G0-1)B,
K3=σASE×ASE2.
α=K1PTσχ4,
β=G2σχ4,
BER=120-VtyRK2αβ exp(-2uβ)+K3 ×I0yG0Rαβ exp(-2uβ)RK2αβ exp(-2Guσχ2)+K3×exp-y2+[G0Rαβ exp(-2uβ)]22[RK2αβ exp(-2uβ)+K3]dy+VtyK3exp-y22K3dy×u exp(-u)du,
Λ=K3RK2αβ exp(-2uβ)+K3× I0yG0Rαβ exp(-2uβ)RK2αβ exp(-2uβ)+K3×exp-y2+[G0Rαβ exp(-2uβ)]22[RK2αβ exp(-2uβ)+K3]+y22K3,
dBERdG=0=ddG120-VtyRK2αβ exp(-2uβ)+K3× I0yG0Rαβ exp(-2uβ)RK2αβ exp(-2Guσχ2)+K3×exp-y2+[G0Rαβ exp(-2uβ)]22[RK2αβexp(-2uβ)+K3]dy+VtyK3exp-y22K3dyu exp(-u)du.
dBERdG=120G-VtyRK2αβ exp(-2uβ)+K3× I0yG0Rαβ exp(-2uβ)RK2αβ exp(-2Guσχ2)+K3×exp-y2+[G0Rαβ exp(-2uβ)]22[RK2αβ exp(-2uβ)+K3]dy+VtyK3exp-y22K3dy×u exp(-u)du.
dBERdG=120-Vt(G)G [F(PT, G, u)]dy+Vt(G)G F[Vt(G), G]-Vt(G)G F1u exp(-u)du,
F(PT, G, u)
=yRK2αβ exp(-2uβ)+K3
×I0yG0Rαβ exp(-2uβ)RK2αβ exp(-2Guσχ2)+K3
×exp-y2+[G0Rαβ exp(-2uβ)]22[RK2αβexp(-2uβ)+K3],
F1=y/K3exp(-y2/2K3).
120-Vt(G)F2dy+Vt(G)G F[Vt(G), G]
-Vt(G)G F1[Vt(G), G]}u exp(-u)du=0,
G=Gopt,PT=PTopt,
F2=1h43exp-y2h2+h1/h22h4αβσχ2y(-1+βu)×{[h1K2-h22K2(y2-2K3)+2h2αβ(K22+G02R2K3)]I0(yh1/h4)-2h22G0RyK3I1(yh1/h4)},
h1=G02R2α2β2,
h2=exp(2βu),
h3=K2αβ,
h4=h3+h2K3.
PT opt=ασχn4K1,
Gopt=βσχn2.
za(z)b(z)f(x, z)dx=a(z)b(z)fzdx+f[b(z), z] bz-f[a(z), z] az.

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