Abstract

The three basic atmospheric propagation effects, absorption, scattering, and turbulence, are reviewed. A simulation approach is then developed to determine signal fade probability distributions on heterodyne-detected satellite links which operate through naturally occurring atmospheric turbulence. The calculations are performed on both angle-tracked and nonangle-tracked downlinks, and on uplinks, with and without adaptive optics. Turbulence-induced degradations in communication performance are determined using signal fade probability distributions, and it is shown that the average signal fade can be a poor measure of the performance degradation.

© 1986 Optical Society of America

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References

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  1. J. W. Strohbehn, “Introduction,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), pp. 1–7.
    [CrossRef]
  2. D. L. Fried, “Optical Heterodyne Detection of an Atmospherically Distorted Signal Wave Front,” Proc. IEEE 55, 57 (1967).
    [CrossRef]
  3. D. L. Fried, “Atmospheric Modulation Noise in an Optical Heterodyne Receiver,” IEEE J. Quantum Electron. QE-3, 213 (1967).
    [CrossRef]
  4. J. H. Churnside, C. M. McIntyre, “Signal Current Probability Distribution for Optical Heterodyne Receivers in the Turbulent Atmosphere. 1: Theory,” Appl. Opt. 17, 2141 (1978).
    [CrossRef] [PubMed]
  5. J. H. Churnside, C. M. McIntyre, “Signal Current Probability Distribution for Optical Heterodyne Receivers in the Turbulent Atmosphere. 2: Experiment,” Appl. Opt. 17, 2148 (1978).
    [CrossRef] [PubMed]
  6. R. J. Noll, “Zernike Polynomials and Atmospheric Turbulence,” J. Opt. Soc. Am. 66, 207 (1976).
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  7. J. E. Kaufmann, L. L. Jeromin, “Optical Heterodyne Intersatellite Links Using Semiconductor Lasers,” in IEEE GLOBE-COM '84, Convention Record, Atlanta, GA (26–29 Nov. 1984).
  8. E. J. McCartney, Absorption and Emission by Atmospheric Gases (Wiley, New York, 1983), Chap. 1.
  9. R. K. Long, “Atmospheric Absorption and Laser Radiation,” Bulletin 199 (Engineering Experiment Station, Ohio State U., Columbus, OH).
  10. L. S. Rothman, “High Resolution Atmospheric Transmittance Radiance: hitran and the Data Compilation,” Proc. Soc. Photo-Opt. Instrum. Eng. 142, 2 (1978).
  11. E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), pp. 20–26.
  12. F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL Report AFGL-TR-80-0067 (Air Force Geophysics Laboratory, Lexington, MA, 1980), AD No. A088215.
  13. L. W. Fredrick, R. H. Baker, Astronomy(Van Nostrand, New York, 1976), p. 85.
  14. D. L. Fried, “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  15. R. M. Gagliardi, S. Karp, Optical Communications(Wiley, New York, 1976), Chap. 6.
  16. V. A. Banakh, G. M. Krekov, V. L. Mironov, S. S. Khmelevtsov, R.Sh. Tsvik, “Focused-Laser Beam Scintillations in the Turbulent Atmosphere,” J. Opt. Soc. Am. 64, 516 (1974).
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  17. G. P. Massa, “Fourth-Order Moments of an Optical Field that has Propagated Through the Clear Turbulent Atmosphere,” M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA (1975).
  18. D. L. Fried, “Anisoplanatism in Adaptive Optics,” J. Opt. Soc. Am. 72, 52 (1982).
    [CrossRef]
  19. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  20. M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1965), Chap. 26.
  21. I. Selin, Detection Theory (Princeton U.P., Princeton, NJ, 1965), pp. 23–28.
  22. W. B. Davenport, Probability and Random Processes (McGraw-Hill, New York, 1970), pp. 504–505.
  23. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, pp. 80–82.
  24. F. E. Hohn, Introduction to Linear Algebra (Macmillan, New York, 1972), Chap. 9.
  25. A. Kolmogorov, “Turbulence,” in Classic Papers in Statistical TheoryS. K. Friedlander, L. Topper, Eds. (Interscience, New York, 1961), pp. 151–155.
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  27. D. L. Fried, “Diffusion Analysis for the Propagation of Mutual Coherence,” J. Opt. Soc. Am. 58, 961 (1968).
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  28. J. H. Shapiro, “Reciprocity of the Turbulent Atmosphere,” J. Opt. Soc. Am. 61, 492 (1971).
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  29. D. L. Fried, H. T. Yura, “Telescope-Performance Reciprocity for Propagation in a Turbulent Medium,” J. Opt. Soc. Am. 62, 600 (1972).
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  30. R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652 (1971).
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  31. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–62.
  32. G. A. Tyler, “Turbulence-Induced Adaptive-Optics Performance Degradation: Evaluation in the Time Domain,” J. Opt. Soc. Am. A 1, 251 (1984).
    [CrossRef]
  33. K. A. Winick, “Signal Fade Probability Distributions for Optical Heterodyne Receivers on Atmospherically Distorted Satellite Links,” in IEEE GLOBECOM '84 Convention Record, Atlanta, GA (26–29 Nov. 1984).
  34. W. C. Lindsey, M. K. Simon, Telecommunication Systems Engineering (Prentice-Hall, Englewood Cliffs, NJ, 1973), pp. 483–499.

1984 (1)

1982 (1)

1981 (1)

1978 (3)

1976 (1)

1974 (1)

1972 (1)

1971 (2)

1968 (1)

1967 (2)

D. L. Fried, “Optical Heterodyne Detection of an Atmospherically Distorted Signal Wave Front,” Proc. IEEE 55, 57 (1967).
[CrossRef]

D. L. Fried, “Atmospheric Modulation Noise in an Optical Heterodyne Receiver,” IEEE J. Quantum Electron. QE-3, 213 (1967).
[CrossRef]

1966 (1)

Baker, R. H.

L. W. Fredrick, R. H. Baker, Astronomy(Van Nostrand, New York, 1976), p. 85.

Banakh, V. A.

Churnside, J. H.

Davenport, W. B.

W. B. Davenport, Probability and Random Processes (McGraw-Hill, New York, 1970), pp. 504–505.

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, pp. 80–82.

Fredrick, L. W.

L. W. Fredrick, R. H. Baker, Astronomy(Van Nostrand, New York, 1976), p. 85.

Fried, D. L.

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications(Wiley, New York, 1976), Chap. 6.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–62.

Hohn, F. E.

F. E. Hohn, Introduction to Linear Algebra (Macmillan, New York, 1972), Chap. 9.

Jeromin, L. L.

J. E. Kaufmann, L. L. Jeromin, “Optical Heterodyne Intersatellite Links Using Semiconductor Lasers,” in IEEE GLOBE-COM '84, Convention Record, Atlanta, GA (26–29 Nov. 1984).

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications(Wiley, New York, 1976), Chap. 6.

Kaufmann, J. E.

J. E. Kaufmann, L. L. Jeromin, “Optical Heterodyne Intersatellite Links Using Semiconductor Lasers,” in IEEE GLOBE-COM '84, Convention Record, Atlanta, GA (26–29 Nov. 1984).

Khmelevtsov, S. S.

Kneizys, F. X.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL Report AFGL-TR-80-0067 (Air Force Geophysics Laboratory, Lexington, MA, 1980), AD No. A088215.

Kolmogorov, A.

A. Kolmogorov, “Turbulence,” in Classic Papers in Statistical TheoryS. K. Friedlander, L. Topper, Eds. (Interscience, New York, 1961), pp. 151–155.

Krekov, G. M.

Lindsey, W. C.

W. C. Lindsey, M. K. Simon, Telecommunication Systems Engineering (Prentice-Hall, Englewood Cliffs, NJ, 1973), pp. 483–499.

Long, R. K.

R. K. Long, “Atmospheric Absorption and Laser Radiation,” Bulletin 199 (Engineering Experiment Station, Ohio State U., Columbus, OH).

Lutomirski, R. F.

Massa, G. P.

G. P. Massa, “Fourth-Order Moments of an Optical Field that has Propagated Through the Clear Turbulent Atmosphere,” M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA (1975).

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), pp. 20–26.

E. J. McCartney, Absorption and Emission by Atmospheric Gases (Wiley, New York, 1983), Chap. 1.

McIntyre, C. M.

Mironov, V. L.

Noll, R. J.

Rothman, L. S.

L. S. Rothman, “High Resolution Atmospheric Transmittance Radiance: hitran and the Data Compilation,” Proc. Soc. Photo-Opt. Instrum. Eng. 142, 2 (1978).

Selin, I.

I. Selin, Detection Theory (Princeton U.P., Princeton, NJ, 1965), pp. 23–28.

Severo, N. C.

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1965), Chap. 26.

Shapiro, J. H.

Simon, M. K.

W. C. Lindsey, M. K. Simon, Telecommunication Systems Engineering (Prentice-Hall, Englewood Cliffs, NJ, 1973), pp. 483–499.

Strohbehn, J. W.

J. W. Strohbehn, “Introduction,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), pp. 1–7.
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Tsvik, R.Sh.

Tyler, G. A.

Walters, D. L.

Winick, K. A.

K. A. Winick, “Signal Fade Probability Distributions for Optical Heterodyne Receivers on Atmospherically Distorted Satellite Links,” in IEEE GLOBECOM '84 Convention Record, Atlanta, GA (26–29 Nov. 1984).

Yura, H. T.

Zelen, M.

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1965), Chap. 26.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

D. L. Fried, “Atmospheric Modulation Noise in an Optical Heterodyne Receiver,” IEEE J. Quantum Electron. QE-3, 213 (1967).
[CrossRef]

J. Opt. Soc. Am. (8)

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

Proc. IEEE (1)

D. L. Fried, “Optical Heterodyne Detection of an Atmospherically Distorted Signal Wave Front,” Proc. IEEE 55, 57 (1967).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

L. S. Rothman, “High Resolution Atmospheric Transmittance Radiance: hitran and the Data Compilation,” Proc. Soc. Photo-Opt. Instrum. Eng. 142, 2 (1978).

Other (19)

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), pp. 20–26.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance: Computer Code lowtran 5,” AFGL Report AFGL-TR-80-0067 (Air Force Geophysics Laboratory, Lexington, MA, 1980), AD No. A088215.

L. W. Fredrick, R. H. Baker, Astronomy(Van Nostrand, New York, 1976), p. 85.

J. E. Kaufmann, L. L. Jeromin, “Optical Heterodyne Intersatellite Links Using Semiconductor Lasers,” in IEEE GLOBE-COM '84, Convention Record, Atlanta, GA (26–29 Nov. 1984).

E. J. McCartney, Absorption and Emission by Atmospheric Gases (Wiley, New York, 1983), Chap. 1.

R. K. Long, “Atmospheric Absorption and Laser Radiation,” Bulletin 199 (Engineering Experiment Station, Ohio State U., Columbus, OH).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1965), Chap. 26.

I. Selin, Detection Theory (Princeton U.P., Princeton, NJ, 1965), pp. 23–28.

W. B. Davenport, Probability and Random Processes (McGraw-Hill, New York, 1970), pp. 504–505.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, pp. 80–82.

F. E. Hohn, Introduction to Linear Algebra (Macmillan, New York, 1972), Chap. 9.

A. Kolmogorov, “Turbulence,” in Classic Papers in Statistical TheoryS. K. Friedlander, L. Topper, Eds. (Interscience, New York, 1961), pp. 151–155.

J. W. Strohbehn, “Introduction,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), pp. 1–7.
[CrossRef]

R. M. Gagliardi, S. Karp, Optical Communications(Wiley, New York, 1976), Chap. 6.

K. A. Winick, “Signal Fade Probability Distributions for Optical Heterodyne Receivers on Atmospherically Distorted Satellite Links,” in IEEE GLOBECOM '84 Convention Record, Atlanta, GA (26–29 Nov. 1984).

W. C. Lindsey, M. K. Simon, Telecommunication Systems Engineering (Prentice-Hall, Englewood Cliffs, NJ, 1973), pp. 483–499.

G. P. Massa, “Fourth-Order Moments of an Optical Field that has Propagated Through the Clear Turbulent Atmosphere,” M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA (1975).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–62.

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Figures (8)

Fig. 1
Fig. 1

Absorption spectral line plot (0.82–0.84 μm).

Fig. 2
Fig. 2

Absorption spectral line plot (0.84–0.85 μm).

Fig. 3
Fig. 3

Optical heterodyne receiver structure.

Fig. 4
Fig. 4

hX coordinate system.

Fig. 5
Fig. 5

Refractive-index structure function profiles.

Fig. 6
Fig. 6

Point-ahead angle.

Fig. 7
Fig. 7

Fade depth cumulative probability distribution: (1) nighttime uplink or downlink; (2) daytime angle-tracked downlink.

Fig. 8
Fig. 8

Fade depth cumulative probability distribution: (1) daytime adaptive optics uplink (Γ = 21 μrad); (2) nighttime angle-tracked downlink; (3) nighttime adaptive optics uplink.

Tables (1)

Tables Icon

Table I Degradation in 8-ary FSK Communication Performance: 1 Actual Loss;2 Mean Loss

Equations (53)

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E s ( X ) = A s ( X ) exp [ i ϕ ( X ) ] exp ( i 2 π f s t ) ,
E o ( X ) = A o exp ( i ϕ o ) exp ( i 2 π f o t ) .
I = η W ( X ) [ E o ( X ) + E s ( X ) ] [ E o ( X ) + E s ( X ) ] * d X ,
W ( X ) = { 1 , | X | d 2 , 0 , | X | > d 2 ,
I = η W ( X ) A s 2 ( X ) d X + η W ( X ) A o 2 d X + η W ( X ) 2 A o A s ( X ) cos [ 2 π ( f s f o ) t + ϕ ( X ) ϕ o ] d X .
I η W ( X ) A o 2 d X + η W ( X ) 2 A o A s ( X ) × cos [ 2 π ( f s f o ) t + ϕ ( X ) ϕ o ] d X .
I s = η W ( X ) 2 A o A s ( X ) cos [ 2 π ( f s f o ) t + ϕ ( X ) ϕ o ] d X .
P s = ( G I s ) 2 R = 4 G 2 R η 2 A o 2 { W ( X ) A s ( X ) × cos [ 2 π ( f s f o ) t + ϕ ( X ) ϕ o ] d X } 2 ,
P s = 2 G 2 R η A o 2 W ( X ) W ( X ) A s ( X ) A s ( X ) × cos [ 4 π ( f s f o ) t + ϕ ( X ) + ϕ ( X ) 2 ϕ o ] d X d X + 2 G 2 R η 2 A o 2 W ( X ) W ( X ) A s ( X ) A s ( X ) × cos [ ϕ ( X ) ϕ ( X ) ] d X d X = 2 G 2 R η 2 A o 2 W ( X ) W ( X ) A s ( X ) A s ( X ) × cos [ ϕ ( X ) ϕ ( X ) ] d X d X .
P s = 2 G 2 R η 2 A o 2 | W ( X ) A s ( X ) exp [ i ϕ ( X ) ] d X | 2 .
υ loss = | W ( X ) A s ( X ) exp [ i ϕ ( X ) ] d X | 2 A 2 ( W ( X ) d X ) 2 ,
A s ( X ) = constant = A in the absence of turbulence .
υ ω 1 | W ( X ) exp [ i ϕ ( X ) ] d X | 2 ,
ω = ( W ( X ) d X ) 2 = ( area of collection aperture ) 2 .
υ ω 1 | W ( X ) exp [ i ϕ ( X ) ] d X | 2 ,
ω = [ W ( X ) d X ] 2
υ ω 1 | W ( X ) exp [ i θ ( X ) ] d X | 2 ,
θ ( X ) ϕ ( X ) ϕ ( O ) .
R θ ( X X ) θ ( X ) θ ( X ) ̅ ,
( a b ) ( c d ) = ½ ( a c ) 2 ½ ( b d ) 2 + ½ ( a d ) 2 + ½ ( b c ) 2 ,
R θ ( X X ) = 1 2 [ ϕ ( X ) ϕ ( X ) ] 2 ̅ + 1 2 [ ϕ ( X ) ϕ ( O ) ] 2 ̅ + 1 2 [ ϕ ( X ) ϕ ( O ) ] 2 ̅ = 1 2 D ϕ ( X X ) + 1 2 D ϕ ( X ) + 1 2 D ϕ ( X ) ,
D ϕ ( δ ) [ ϕ ( X + δ ) ϕ ( X ) ] 2 ̅ .
υ | 1 N j = 1 N exp [ i θ ( X j ) ] | 2 ,
4 ω 1 W ( X ) W ( Y ) exp [ 1 2 D ϕ ( X Y ) ] d X d Y 8 ω 1 / 2 1 N j = 1 N exp [ 1 2 D ϕ ( X X j ) ] d X + 4 1 N 2 j = 1 N K = 1 N exp [ 1 2 D ϕ ( X j X K ) ] .
P cum ( z ) probability υ < z ,
P cum ( z ) ( number of times υ < z ) M .
variance = P cum ( z ) [ 1 P cum ( z ) ] / M .
b j k θ ( X j ) θ ( X k ) ̅ = R θ ( X j X k ) .
B = ( C G ) ( C G ) t ̅ ,
( C G ) ( C G ) t ̅ = C G G t ̅ C t = C C t .
B T = T [ λ 1 λ 2 λ N ] , B = T [ λ 1 λ 2 λ N ] T t , B = T [ λ 1 1 / 2 λ 2 1 / 2 λ N 1 / 2 ] ( T [ λ 1 1 / 2 λ 2 1 / 2 λ N 1 / 2 ] ) t .
C = T | λ 1 1 / 2 λ 2 1 / 2 λ N 1 / 2 | .
E + ( 2 π λ ) 2 n 2 E = 0 ,
[ n ( h , X ) n ( h , X ) ] 2 ̅ = C n 2 ( h + h 2 ) [ | X X | 2 + ( h h ) 2 ] 1 / 3 ,
D ϕ ( δ ) [ ϕ ( X + δ ) ϕ ( X ) ] 2 = 2.91 ( sec 2 α ) | δ | 5 / 3 0 C n 2 ( h ) d h ,
D ϕ ( X 1 X 2 ) = 6.88 ( | X 1 X 2 | / r 0 ) 5 / 3 ,
r 0 transverse coherence length = [ 0.423 ( sec 2 α ) ( 2 π λ ) 2 0 C n 2 ( h ) d h ] 3 / 5
D ϕ A T ( δ ) 6.88 ( | δ | / r 0 ) 5 / 3 [ 1 ( | δ | / d ) 1 / 3 ] .
E u ( X ) W ( X ) exp [ i ϕ ( X ) ] exp [ i 2 π λ L X X ] d X ,
W ( X ) = { 1 , inside the earth−based transmitting aperture , 0 , elsewhere , } L = distance between top of atmosphere and satellite .
E u ( X ) W ( X ) exp [ i ϕ ( X ) ] d X .
loss = | W ( X ) exp [ i ϕ ( X ) ] d X | 2 | W ( X ) d X | 2 .
D ϕ A D ( δ ) = 2 ( 2.91 ) ( sec 2 α ) ( 2 π λ ) 2 0 C n 2 ( h ) [ | δ | 5 / 3 + ( Γ h ) 5 / 3 1 2 | δ + Γ h ( cos α ) e | 5 / 3 1 2 | δ Γ h ( cos α ) e | 5 / 3 ] d h ,
P cs turb ( S N ) = 0 1 P cs ( υ S N ) p ( υ ) d υ ,
P cs turb ( S / N ) =
mean loss = 0 1 υ p ( υ ) d υ .
U ω 1 / 2 W ( X ) exp [ i ϕ ( X ) ] d X ,
Q 1 N j = 1 N exp [ i ϕ ( X j ) ] .
mean−squared error = ( | U | 2 | Q | 2 ) 2 ̅ = ( | U | | Q | ) 2 ( | U | + | Q | ) 2 ̅ 4 ( | U | | Q | ) 2 ̅ 4 | U Q | 2 ̅ ,
U Q = ω 1 / 2 1 N j = 1 N W ( X ) { exp [ i ϕ ( X ) ] exp [ i ϕ ( X k ) ] } d X ,
| U Q | 2 = ω 1 1 N 2 j = 1 N k = 1 N W ( X ) W ( Y ) { exp [ i ϕ ( X ) i ϕ ( Y ) ] exp [ i ϕ ( X ) i ϕ ( X j ) ] exp [ i ϕ ( X k ) i ϕ ( Y ) ] + exp [ i ϕ ( X k ) i ϕ ( X j ) ] } d X d Y .
exp ( i a ) ̅ = exp ( 1 2 a 2 ̅ ) ,
4 | U Q | 2 = 4 ω 1 W ( X ) W ( Y ) exp [ 1 2 D ϕ ( X Y ) ] d X d Y 8 ω 1 / 2 1 N j = 1 N W ( X ) exp [ 1 2 D ϕ ( X X j ) ] d X + 4 1 N 2 j = 1 N k = 1 N exp [ 1 2 D ϕ ( X j X k ) ] .

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