Abstract
We consider the discrete-time detection of a known time-varying deterministic signal in white noise, where the univariate noise density is known perfectly only on an interval about the origin. We present a method to enhance the asymptotic performance of the detector by exploiting this knowledge, and at the same time preserve robustness properties of the detector to the remaining inexact knowledge of the univariate noise density. We then provide examples to show that improved performance is indeed obtained.
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References
J. H. Fennick, “Amplitude distributions of telephone channel noise and a model for impulsive noise,”Bell Syst. Tech. J., Vol.48, pp. 3243–3263 (Dec. 1969).
P. Mertz, “Model of impulsive noise for data transmission,” IRETrans. Commun. Syst., Vol.CS-9, pp. 130–137, (June 1961).
P. Beckmann, “Amplitude probability distribution of atmospheric radio noise,”J. Res. Nat. Bur. Stand,68D, pp. 723–735, (June 1964).
K. Furutsu and T. Ishida, “On the theory of amplitude distribution of impulsive random noise,”J. Appl. Phys., Vol.32, pp. 1206–1221 (July 1961).
G. V. Trunk, “Small- and large-sample behavior of two detectors against envelope-detected sea clutter,”IEEE Trans. Inform. Theory, Vol.IT-16, pp. 95–99 (Jan. 1970).
A. A. Giordano and F. Haber, “Modeling of atmospheric noise,”Radio Sci., Vol.7, pp. 1011–1023 (1972).
G. V. Trunk and S. F. George, “Detection of targets in non-Gaussian sea clutter,”IEEE Trans. Aerosp. Electron. Syst., Vol.AES-6, pp. 620–628 (Sept. 1970).
O. Yue, R. Lugannani, and S. Rice, “Series approximations for the amplitude distribution and density of shot processes, ”IEEE Trans. Commun., Vol.COM-26, pp. 45–54 (Jan. 1978).
D. Middleton, “Man-made noise in urban environments and transportation systems: Models and measurements,”IEEE Trans. Commun., Vol.COM-21, pp. 1232–1241 (Nov. 1973).
R. J. Marks II, G. L. Wise, D. G. Haldeman, and J. L. Whited, “Detection in Laplace noise,”IEEE Trans. Aerosp. Electron. Syst., Vol.AES-14, no. 6, pp. 866–872 (Nov. 1978).
J. H. Miller and J. B. Thomas, “The detection of signals in impulsive noise modeled as a mixture process,”IEEE Trans. Commun., Vol.COM-24, pp. 559–563, (May 1976).
S. L. Bernsteinet al., “Long-range communications at extremely low frequencies,”Proc. IEEE, Vol. 62, pp. 292–312, (March 1974).
A. R. Milne, “Sound propagation and ambient noise under ice,” inUnderwater Acoustics, Vol. 2, V. M. Albers, Ed. New York: Plenum, 1962, pp. 103–138.
V. V. Olshevskie,Characteristics of Sea Reverberation. New York: Consultant's Bureau, 1967, pp. 55–58.
P. J. Huber,Robust Statistics. New York: Wiley, 1981, pp. 264–273.
S. A. Kassam and J. B. Thomas, “Asymptotically robust detection of a known signal in contaminated non-Gaussian noise,”IEEE Trans. Inform. Theory, Vol.IT-22, pp. 22–26, (Jan. 1976).
H. V. Poor, M. Mami, and J. B. Thomas, “On robust detection of discretetime stochastic signals,”J. Franklin Inst, Vol.309, pp. 29–53 (Jan. 1980).
J. H. Miller and J. B. Thomas, “Detectors for discrete-time signals in non-Gaussian noise,”Trans. Inform. Theory, Vol.IT-18, pp. 241–250, (March 1972).
G. E. Noether, “On a theorem of Pitman, ”Ann. Math. Stat., Vol.26, pp. 64–68 (1955).
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This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-82-0033.
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Halverson, D.R. Asymptotically robust detection in partially contaminated noise. Circuits Systems and Signal Process 3, 493–503 (1984). https://doi.org/10.1007/BF01599173
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DOI: https://doi.org/10.1007/BF01599173