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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 17, Iss. 22 — Nov. 15, 1978
  • pp: 3576–3583

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications

Paul R. Prucnal and Malvin Carl Teich  »View Author Affiliations


Applied Optics, Vol. 17, Issue 22, pp. 3576-3583 (1978)
http://dx.doi.org/10.1364/AO.17.003576


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Abstract

A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [ IEEE Trans. Inf. Theory IT-25, (March, 1979)].

© 1978 Optical Society of America

History
Original Manuscript: May 30, 1978
Published: November 15, 1978

Citation
Paul R. Prucnal and Malvin Carl Teich, "Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications," Appl. Opt. 17, 3576-3583 (1978)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-17-22-3576


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References

  1. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part 1 (Wiley, New York, 1968).
  2. B. Reiffen, H. Sherman, Proc. IEEE 51, 1316 (1963). [CrossRef]
  3. C. W. Helstrom, IEEE Trans. Inf. Theory IT-10, 275 (1964). [CrossRef]
  4. W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).
  5. Proc. IEEE (Special Issue on Optical Communications), 58 (1970).
  6. E. Hoversten, “Optical Communication Theory,” in Laser Handbook, F. T. Arrechi, E. O. Schulz-DuBois, Eds. (North-Holland, Amsterdam, 1972), Vol. 2.
  7. M. C. Teich, R. Y. Yen, IEEE Trans. Aerosp. Electron. Syst. AES-8, 13 (1972). [CrossRef]
  8. R. Y. Yen, P. Diament, M. C. Teich, IEEE Trans. Inf. Theory IT-18, 302 (1972). [CrossRef]
  9. M. C. Teich, S. Rosenberg, Appl. Opt. 12, 2616 (1973). [CrossRef] [PubMed]
  10. S. Rosenberg, M. C. Teich, Appl. Opt. 12, 2625 (1973). [CrossRef] [PubMed]
  11. E. V. Hoversten, D. L. Snyder, R. O. Harger, K. Kurimoto, IEEE Trans. Commun. COM-22, 17 (1974). [CrossRef]
  12. D. L. Snyder, Random Point Processes (Wiley, New York, 1975).
  13. R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).
  14. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976).
  15. S. D. Personick, Bell Syst. Tech. J. 50, 3075 (1971).
  16. S. D. Personick, Proc. IEEE 65, 1670 (1977). [CrossRef]
  17. S. D. Personick, P. Balaban, J. H. Bobsin, P. R. Kumar, IEEE Trans. Commun COM-25, 541 (1977). [CrossRef]
  18. M. C. Teich, P. R. Prucnal, G. Vannucci, Opt. Lett. 1, 208 (1977). [CrossRef] [PubMed]
  19. M. C. Teich, B. I. Cantor, IEEE J. Quantum Electron. QE-14 (December, 1978).
  20. G. W. Flint, IEEE Trans. Mil. Electron. MIL-8, 22 (1964). [CrossRef]
  21. J. W. Goodman, Proc. IEEE 53, 1688 (1965). [CrossRef]
  22. W. W. Peterson, T. G. Birdsall, W. C. Fox, Trans. IRE Prof. Group Inf. Theory PGIT-4, 171 (1954). [CrossRef]
  23. W. P. Tanner, J. A. Swets, Psychol. Rev. 61, 401 (1954). [CrossRef] [PubMed]
  24. H. B. Barlow, J. Opt. Soc. Am. 46, 634 (1956). [CrossRef] [PubMed]
  25. M. C. Teich, P. R. Prucnal, J. Opt. Soc. Am. 67, 1426 (1977).
  26. W. J. McGill, J. Math. Psychol. 4, 351 (1967). [CrossRef]
  27. M. C. Teich, W. J. McGill, Phys. Rev. Lett. 36, 754 (1976). [CrossRef]
  28. P. R. Prucnal, M. C. Teich, IEEE Trans. Inf. Theory IT-25, (March, 1979).
  29. The finite difference is Δ[f(n)]k ≡ f(n + k) − f(n). If no subscript is used, k is assumed to be unity. We employ the second difference Δ2[f(n)]k,j ≡ [f(n + j) − f(n)] − [f(n + j − k) − f(n − k)] with j = 1 to obtain Δ2[f(n)]k.
  30. D. C. Murdoch, Linear Algebra (Wiley, New York, 1970), p. 165.
  31. The product rule can be seen fromΔ[f(n)g(n)h(n)]=f(n+1)g(n+1)h(n+1)−f(n+1)g(n+1)h(n)+f(n+1)g(n+1)h(n)−f(n+1)g(n)h(n)+f(n+1)g(n)h(n)−f(n)g(n)h(n)=f(n+1)g(n+1)Δ[h(n)]+f(n+1)Δ[g(n)]h(n)+Δ[f(n)]g(n)h(n),which extends easily to the case of an N-fold product.
  32. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1957).
  33. M. C. Teich, P. R. Prucnal, unpublished.
  34. M. Woodroofe, Probability with Applications (McGraw-Hill, New York, 1975).
  35. R. J. Glauber, “Photon Counting and Field Correlations,” in Physics of Quantum Electronics, P. L. Kelley, B. Lax, P. E. Tannenwald, Eds. (McGraw-Hill, New York, 1966), pp. 788–811.
  36. P. Diament, M. C. Teich, J. Opt. Soc. Am. 60, 682 (1970). [CrossRef]
  37. P. R. Prucnal, M. C. Teich, J. Opt. Soc. Am., to be published.
  38. P. Diament, M. C. Teich, J. Opt. Soc. Am. 60, 1489 (1970). [CrossRef]
  39. P. Diament, M. C. Teich, Appl. Opt. 10, 1664 (1971). [CrossRef] [PubMed]
  40. B. I. Cantor, M. C. Teich, J. Opt. Soc. Am. 65, 786 (1975). [CrossRef]
  41. P. R. Prucnal, Proc. IEEE, to be published.

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