Abstract

The performance of an optical heterodyne receiver for communication through the clear-air turbulent atmosphere is considered. Optimum and certain suboptimum adaptive processors are developed for receivers that synchronously demodulate the IF signal and those that use envelope demodulation. Error probabilities are presented demonstrating the effects of turbulence level, signal strength, and spatial diversity on binary orthogonal communication systems. In addition, a simple expression is developed for the optimum aperture size of an optical heterodyne receiver.

© 1980 Optical Society of America

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References

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  20. R. S. Kennedy, E. V. Hoversten, IEEE Trans. Inf. Theory IT-14, 716 (1968).
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  22. S. Solimeno, E. Corti, B. Nicoletti, J. Opt. Soc. Am. 60, 1245 (1970).
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  35. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1964).
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  38. D. L. Fried, “Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers/Average Antenna Gain and Antenna Gain Variation,” Optical Science Consultants Technical Report TR-027 (August1971).

1979 (1)

1978 (3)

1977 (1)

1976 (1)

C. B. Hogge, R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

1975 (2)

1974 (2)

1973 (3)

1971 (1)

1970 (3)

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

E. V. Hoversten, R. O. Harger, S. J. Halme, Proc. IEEE 58, 1626 (1970).
[CrossRef]

S. Solimeno, E. Corti, B. Nicoletti, J. Opt. Soc. Am. 60, 1245 (1970).
[CrossRef]

1969 (1)

1968 (1)

R. S. Kennedy, E. V. Hoversten, IEEE Trans. Inf. Theory IT-14, 716 (1968).
[CrossRef]

1967 (7)

D. L. Fried, J. B. Seidman, Appl. Opt. 6, 245 (1967).
[CrossRef] [PubMed]

D. L. Fried, IEEE J. Quantum Electron. QE-3, 213 (1967).
[CrossRef]

W. N. Peters, R. J. Arguello, C J. Quantum, Electron. QE-3, 532 (1967).

D. L. Fried, R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).
[CrossRef] [PubMed]

J. W. Strohbehn, S. F. Clifford, IEEE Trans. Antennas Propag. AP-15, 416 (1967).
[CrossRef]

T. J. Gilmartin, R. R. Horning, IEEE J. Quantum Electron. QE-3, 254 (1967).
[CrossRef]

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

1966 (1)

1965 (2)

Arguello, R. J.

W. N. Peters, R. J. Arguello, C J. Quantum, Electron. QE-3, 532 (1967).

Brown, C. M.

Butts, R. R.

C. B. Hogge, R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

Churnside, J. H.

Clifford, S. F.

Corti, E.

Fante, R. L.

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Fried, D. L.

D. L. Fried, G. E. Mevers, Appl. Opt. 13, 2620 (1974).
[CrossRef] [PubMed]

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

D. L. Fried, IEEE J. Quantum Electron. QE-3, 213 (1967).
[CrossRef]

D. L. Fried, R. A. Schmeltzer, Appl. Opt. 6, 1729 (1967).
[CrossRef] [PubMed]

D. L. Fried, J. B. Seidman, Appl. Opt. 6, 245 (1967).
[CrossRef] [PubMed]

D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
[CrossRef]

D. L. Fried, “Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers/Average Antenna Gain and Antenna Gain Variation,” Optical Science Consultants Technical Report TR-027 (August1971).

Gagliardi, R. M.

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

Gilmartin, T. J.

T. J. Gilmartin, R. R. Horning, IEEE J. Quantum Electron. QE-3, 254 (1967).
[CrossRef]

Haddad, A. H.

P. K. Varshney, A. H. Haddad, IEEE Trans. Commun. COM-26, 278 (1978).
[CrossRef]

Halme, S. J.

E. V. Hoversten, R. O. Harger, S. J. Halme, Proc. IEEE 58, 1626 (1970).
[CrossRef]

Hancock, J. C.

J. C. Hancock, P. A. Wintz, Signal Detection Theory (McGraw-Hill, New York, 1966).

Harger, R. O.

E. V. Hoversten, R. O. Harger, S. J. Halme, Proc. IEEE 58, 1626 (1970).
[CrossRef]

Hogge, C. B.

C. B. Hogge, R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

Hohn, D. H.

Horning, R. R.

T. J. Gilmartin, R. R. Horning, IEEE J. Quantum Electron. QE-3, 254 (1967).
[CrossRef]

Hoversten, E. V.

E. V. Hoversten, R. O. Harger, S. J. Halme, Proc. IEEE 58, 1626 (1970).
[CrossRef]

R. S. Kennedy, E. V. Hoversten, IEEE Trans. Inf. Theory IT-14, 716 (1968).
[CrossRef]

Jacobs, I. M.

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

Karp, S.

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

Kennedy, R. S.

R. S. Kennedy, E. V. Hoversten, IEEE Trans. Inf. Theory IT-14, 716 (1968).
[CrossRef]

Kerr, J. R.

Lawrence, R. S.

Marino, J. T.

McIntyre, C. M.

Mevers, G. E.

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Nicoletti, B.

Ochs, G. R.

Peters, W. N.

W. N. Peters, R. J. Arguello, C J. Quantum, Electron. QE-3, 532 (1967).

Pratt, W. K.

W. K. Pratt, Laser Communications System (Wiley, New York, 1969).

Quantum, C J.

W. N. Peters, R. J. Arguello, C J. Quantum, Electron. QE-3, 532 (1967).

Rosenberg, S.

Ryznar, E.

Schmeltzer, R. A.

Seidman, J. B.

Solimeno, S.

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

J. W. Strohbehn, S. F. Clifford, IEEE Trans. Antennas Propag. AP-15, 416 (1967).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, (Israel Program for Scientific Translations, Jerusalem, 1971).

Teich, M. C.

Titterton, P. J.

Varshney, P. K.

P. K. Varshney, A. H. Haddad, IEEE Trans. Commun. COM-26, 278 (1978).
[CrossRef]

Webb, W. E.

Wintz, P. A.

J. C. Hancock, P. A. Wintz, Signal Detection Theory (McGraw-Hill, New York, 1966).

Wozencraft, J. M.

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

Appl. Opt. (13)

Electron (1)

W. N. Peters, R. J. Arguello, C J. Quantum, Electron. QE-3, 532 (1967).

IEEE J. Quantum Electron. (2)

D. L. Fried, IEEE J. Quantum Electron. QE-3, 213 (1967).
[CrossRef]

T. J. Gilmartin, R. R. Horning, IEEE J. Quantum Electron. QE-3, 254 (1967).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

C. B. Hogge, R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
[CrossRef]

J. W. Strohbehn, S. F. Clifford, IEEE Trans. Antennas Propag. AP-15, 416 (1967).
[CrossRef]

IEEE Trans. Commun. (1)

P. K. Varshney, A. H. Haddad, IEEE Trans. Commun. COM-26, 278 (1978).
[CrossRef]

IEEE Trans. Inf. Theory (2)

S. Rosenberg, M. C. Teich, IEEE Trans. Inf. Theory IT-19, 807 (1973).
[CrossRef]

R. S. Kennedy, E. V. Hoversten, IEEE Trans. Inf. Theory IT-14, 716 (1968).
[CrossRef]

J. Opt. Soc. Am. (4)

Proc. IEEE (4)

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

E. V. Hoversten, R. O. Harger, S. J. Halme, Proc. IEEE 58, 1626 (1970).
[CrossRef]

Other (9)

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1964).

J. C. Hancock, P. A. Wintz, Signal Detection Theory (McGraw-Hill, New York, 1966).

D. L. Fried, “Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers/Average Antenna Gain and Antenna Gain Variation,” Optical Science Consultants Technical Report TR-027 (August1971).

J. W. Strohbehn, Ed., Laser Beam Propagation in the Atmosphere (Springer, New York, 1978).
[CrossRef]

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, (Israel Program for Scientific Translations, Jerusalem, 1971).

W. K. Pratt, Laser Communications System (Wiley, New York, 1969).

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

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Figures (14)

Fig. 1
Fig. 1

Block diagram of the optimum adaptive receiver structure for N-channel diversity detection of Mary orthogonal signaling using synchronous demodulation.

Fig. 2
Fig. 2

Lower bound on performance of the approximate optimum receiver PLB(E) vs the inverse of the normalized aperture diam D/ro.

Fig. 3
Fig. 3

Error probability P(E) vs signal strength γ for moderate turbulence (σχ = 0.3). Both optimum (lower curve) and suboptimum (upper curve) receiver performance are shown for each value of normalized aperture diam D/ro. The lower bound for the suboptimum processor is indicated by a dashed-line segment. The no-turbulence case (NT) is included for reference.

Fig. 4
Fig. 4

Same as Fig. 3 except that σχ = 0.8.

Fig. 5
Fig. 5

Error probability P(E) vs signal strength γ for a two-channel diversity array.

Fig. 6
Fig. 6

Block diagram of the optimum adaptive receiver structure for N-channel diversity detection of Mary orthogonal signaling using envelope demodulation.

Fig. 7
Fig. 7

Error probability P(E) vs signal strength γ for the optimum processor using envelope demodulation under moderate turbulence conditions (σχ = 0.3).

Fig. 8
Fig. 8

Same as Fig. 7 except that σχ = 0.8.

Fig. 9
Fig. 9

Error probability P(E) vs signal strength γ for a two-channel diversity array using envelope demodulation.

Fig. 10
Fig. 10

Error probability P(E) vs normalized aperture diam D/ro for low signal level (α = 10). Curves are labeled by σχ values.

Fig. 11
Fig. 11

Same as Fig. 10 except that α = 50.

Fig. 12
Fig. 12

Same as Fig. 10 except that α = 200.

Fig. 13
Fig. 13

Optimum normalized aperture diam (D/ro)opt vs log-amplitude standard deviation σχ for α = 10 (▲), α = 50 (●), and α = 200 (■) along with predicted values from Eq. (28) (solid lines).

Fig. 14
Fig. 14

Error probability P(E) vs normalized aperture diam D/ro for a two-channel array with α = 50. Curves are labeled by σχ values.

Equations (28)

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L j = ln [ p ( I 11 , , I N M H j , I ^ 1 , , I ^ N ) p ( I 11 , , I N M H 0 , I ^ 1 , , I ^ N ) ] .
L j = i = 1 N ln [ p ( I i j H j , I ^ i ) ] - ln [ p ( I i j H 0 , I ^ i ) ] .
P ( E ) = 1 - - d I ^ 1 - d I ^ N p ( I ^ 1 , , I ^ N ) × - d L 1 p ( L 1 I ^ 1 , , I ^ N ) × - L 1 d L 2 - L 1 d L M p ( L 2 , , L M I ^ 1 , , I ^ N ) .
L j = i = 1 N ( I i j I ^ i - ½ I ^ i 2 ) .
L = L 2 - L 1 = i = 1 N I ^ i ( I i 2 - I i 1 )
P ( E ) = d I ^ 1 p ( I ^ 1 ) d I ^ N p ( I ^ N ) × - 0 d L p ( L H 2 , I ^ 1 , , I ^ N ) .
P ( E ) = d I ^ 1 p ( I ^ 1 ) d I ^ N p ( I ^ N ) erfc [ ( ½ i = 1 N I ^ i 2 ) 1 / 2 ] ,
erfc ( x ) = 1 ( 2 π ) 1 / 2 x exp ( - ½ y 2 ) d y .
I ^ = ( π η 2 e B ) 1 / 2 A ¯ s D Z { J 1 [ 4 a L ( π ) 1 / 2 D ] / [ 4 a L ( π ) 1 / 2 D ] } ,
I ^ i = 2 γ i Z i [ J 1 ( Δ i ) / Δ i ] ,
σ Δ 2 = 1.72 ( D / r o ) 5 / 3 .
P ( E ) = d X 1 d X N d Δ 1 d Δ N erfc [ ( ½ i = 1 N I ^ i 2 ) 1 / 2 ] × { ( 2 π σ χ 2 ) - N / 2 exp [ - 1 2 σ χ 2 i = 1 N ( X i + σ χ 2 ) 2 ] × ( Δ 1 Δ N σ Δ 2 N ) exp ( - 1 σ Δ 2 i = 1 N Δ i 2 ) } .
P ( E ) = P ( E I ^ > 0 ) P ( I ^ > 0 ) + P ( E I ^ < 0 ) P ( I ^ < 0 ) .
P ( E ) P L B ( E ) = ½ P [ J 1 ( Δ ) < 0 ] = ½ [ exp ( - a 1 2 2 σ Δ 2 ) - exp ( - a 2 2 2 σ Δ 2 ) + exp ( - a 3 2 2 σ Δ 2 ) - ] ,
p ( I i j H j , I ^ i ) = I i j exp [ - ½ ( I i j 2 + I ^ i 2 ) ] J 0 ( I ^ i I i j ) ,
L j = i = 1 N ln [ J 0 ( I ^ i I i j ) ] - 1 / 2 I ^ i 2 .
y = ln [ J 0 ( x ) ] .
ln [ J 0 ( x ) ] ¼ x 2 ,
L j = 1 4 i = 1 N I ^ i 2 ( I i j 2 - 2 ) .
L = 1 4 i = 1 N I ^ i 2 ( I i 2 2 - I i 1 2 ) ,
P ( L < 0 H 2 , I ^ 1 ) = ½ exp ( - ¼ I ^ 1 2 ) ,
P ( L < 0 H 2 , I ^ 1 , I ^ 2 ) = 1 2 ( I ^ 2 4 - I ^ 1 4 ) × exp ( - ¼ 2 I ^ 1 4 + I ^ 1 2 I ^ 2 2 + I ^ 2 4 I ^ 1 2 + I ^ 2 2 ) × [ I ^ 2 4 exp ( - ¼ I ^ 1 4 I ^ 1 2 + I ^ 2 2 ) - I ^ 1 4 × exp ( - ¼ I ^ 2 4 I ^ 1 2 + I ^ 2 2 ) ] .
γ = α ( D / r o ) .
σ Δ 2 = 1.72 ( D / r o ) 5 / 3
P ( E ) = - 0.291 ( D / r o ) - 5 / 3 d Δ Δ × exp [ - α 2 ( D / r o ) 2 J 1 2 ( Δ ) / Δ 2 - 0.291 Δ 2 ( D / r o ) - 5 / 3 ]
( D / r o ) opt 1.6 α - 6 / 11
( D / r o ) opt 1.6 α - 6 / 11 + 0.56 σ χ .
D opt = 1.4 ( η A ¯ s 2 e B ) - 3 / 11 r o 5 / 11 + 0.5 ( L / k ) 5 / 12 r o 7 / 12 ,

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