Abstract

In this paper we describe two new hybrid time and space integrating acoustooptic correlators and their use in spread spectrum applications. These systems employ 1-D or 2-D masks and are of use for many spread spectrum coding schemes and very long codes. Synchronization and demodulation of very long codes are achieved in these systems with an infinite range delay search and with nearly the full processing gain of the code. A statistical analysis of coherent and partially coherent output time integration is included (this appears to be most appropriate for any hybrid processor) together with initial simulation results.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).
  2. R. Denaro, IEEE Spectrum 18, 35 (May1981).
  3. D. Psaltis, D. Casasent, Appl. Opt. 19, 1546 (1980).
    [CrossRef] [PubMed]
  4. J. Upatnieks, C. Leonard, Appl. Opt. 8, 85 (1969).
    [CrossRef] [PubMed]
  5. E. W. Hansen, J. G. Verly, “Optical Processing in Polar Coordinates,” to be published in J. Opt. Soc. Am.73, in press (1983).
  6. P. Kellman, Opt. Eng. 19, 370 (1980).
    [CrossRef]
  7. D. Casasent, G. Silbershatz, Appl. Opt. 21, 2076 (1982).
    [CrossRef] [PubMed]
  8. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1 (Wiley, New York, 1968), pp. 273–286.
  9. J. J. Spilker, Inst. Navigation 25, No. 2, 121 (Summer1978).
  10. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1950), pp. 81–84.
  11. Special Issue on “Acousto-Optic Signal Processing,” Proc. IEEE 69 (Jan.1981).

1982 (1)

1981 (2)

R. Denaro, IEEE Spectrum 18, 35 (May1981).

Special Issue on “Acousto-Optic Signal Processing,” Proc. IEEE 69 (Jan.1981).

1980 (2)

1978 (1)

J. J. Spilker, Inst. Navigation 25, No. 2, 121 (Summer1978).

1969 (1)

Casasent, D.

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1950), pp. 81–84.

Denaro, R.

R. Denaro, IEEE Spectrum 18, 35 (May1981).

Dixon, R. C.

R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).

Hansen, E. W.

E. W. Hansen, J. G. Verly, “Optical Processing in Polar Coordinates,” to be published in J. Opt. Soc. Am.73, in press (1983).

Kellman, P.

P. Kellman, Opt. Eng. 19, 370 (1980).
[CrossRef]

Leonard, C.

Psaltis, D.

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1950), pp. 81–84.

Silbershatz, G.

Spilker, J. J.

J. J. Spilker, Inst. Navigation 25, No. 2, 121 (Summer1978).

Upatnieks, J.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1 (Wiley, New York, 1968), pp. 273–286.

Verly, J. G.

E. W. Hansen, J. G. Verly, “Optical Processing in Polar Coordinates,” to be published in J. Opt. Soc. Am.73, in press (1983).

Appl. Opt. (3)

IEEE Spectrum (1)

R. Denaro, IEEE Spectrum 18, 35 (May1981).

Inst. Navigation (1)

J. J. Spilker, Inst. Navigation 25, No. 2, 121 (Summer1978).

Opt. Eng. (1)

P. Kellman, Opt. Eng. 19, 370 (1980).
[CrossRef]

Proc. IEEE (1)

Special Issue on “Acousto-Optic Signal Processing,” Proc. IEEE 69 (Jan.1981).

Other (4)

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1950), pp. 81–84.

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1 (Wiley, New York, 1968), pp. 273–286.

R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).

E. W. Hansen, J. G. Verly, “Optical Processing in Polar Coordinates,” to be published in J. Opt. Soc. Am.73, in press (1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Product code generation concept: (a) short code u(t); (b) short code v(t); (c) long product code s(t).

Fig. 2
Fig. 2

Schematic diagram of a hybrid time and space integrating acoustooptic correlator for processing product code spread spectrum signals.

Fig. 3
Fig. 3

Output detection system for Fig. 2 to realize the required time delay and summation of the partial output correlations.

Fig. 4
Fig. 4

Schematic diagram of a hybrid time and space integrating acoustooptic correlator for processing general spread spectrum codes.

Fig. 5
Fig. 5

Receiver operating characteristics of the various processors: (A) linear correlator; (B) coherent summation: (C) noncoherent summation.

Fig. 6
Fig. 6

Correlation plane outputs for the system of Fig. 2 using a product code (N = 30, N v = 31, N s = 930) with no input noise for the cases of (a) coherent summation and (b) noncoherent summation.

Fig. 7
Fig. 7

Correlation plane outputs for the system of Fig. 2 with a product code (N u = 30, N v = 31, N s = 930) with input noise added for the cases of (a) coherent summation with SNR i = −17.5 dB and (b) noncoherent sumation with SNR i = −13.75 dB.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

s ( t ) = u ( t ) v ( t ) .
u 1 ( t , ζ ) = s R ( t + ζ ) u ( ζ ) .
u 3 ( t , x ) = T A u 1 ( t , ζ ) v ( x + ζ ) d ζ ,
u 3 ( t , x ) = T u s R ( t + ζ ) u ( ζ ) v ( x + ζ ) d ζ .
s R ( t ) = s ( t - t d ) = u ( t - t d ) v ( t - t d ) .
u 3 ( t , x ) = T u u ( t - t d + ζ ) v ( t - t d + ζ ) u ( ζ ) v ( x + ζ ) d ζ .
u 3 ( m T u + t d , x ) = T u v ( ζ - m T p ) v ( x + ζ ) d ζ = C v ( x - m T p ) ,
s 0 ( t ) = m = 0 N v - 1 u 3 2 ( t + m T u , - m T p ) = m = 0 N v - 1 [ T u s ( t - t d + m T u + ζ ) u ( ζ ) v ( ζ - m T p ) d ζ ] 2 ,
s 0 ( t ) = [ N v T u s ( t - t d + ζ ) s ( ζ ) d ζ ] 2 .
u m ( t , ζ , m ) = s ( t - t d + ζ ) s ( ζ - m T A ) .
u 3 ( t , m ) = X A u m ( t , ζ , m ) d ζ = T A s ( t - t d + ζ ) s ( ζ - m T A ) d ζ ,
s 0 ( t ) = m = 1 M [ T A s ( t - t d + m T A + ζ ) s ( ζ + m T A ) d ζ ] 2 ,
s 0 ( t ) = [ M T A s ( t - t d + ζ ) s ( ζ ) d ζ ] 2 ,
R ( t , x ) = R 0 exp [ j ( ω 0 t + k r x ) ]
s R ( t ) = s ( t - t d ) + n ( t ) .
s 0 ( t ) = m = 0 N v - 1 { T u [ s ( t - t d + m T u + ζ ) + n ( t + m T u + ζ ) ] × u ( ζ ) v ( ζ - m T p ) d ζ } 2 .
s 0 ( t ) = m = 0 N v - 1 { T u [ s ( t - t d + m T u + ζ ) + n ( t + m T u + ζ ) ] s ( ζ + m T u ) d ζ } 2 .
s 0 ( t ) = { N v T u [ s ( t - t d + ζ ) + n ( t + ζ ) s ( ζ ) d ζ } 2 .
P D = erf ( N s SNR i - η ) ,
P F = erf ( - η ) ,
P D = erf ( N s SNR i - η ) + erf ( - N s SNR i - η ) ,
P F = 2 erf ( - η ) .
P D = erf { N s SNR i + N v - η 4 N s SNR i + 2 N v } ,
P F = erf ( N v - η 2 N v ) .
SNR i - 34.25 dB ( linear correlator ) ,
SNR i - 33.75 dB ( coherent summation TSI system ) ,
SNR i - 26.75 dB ( noncoherent summation TSI system ) .

Metrics