Limit distributions for imperfect electromagnetic reverberation

IEEE Transactions on Electromagnetic Compatibility

Volumn 45, Issue 2, 2003, Pages 357-377

  Arnaut, Luk R ^a  

^a NATIONAL PHYSICAL LABORATORY   (United Kingdom)

Author keywords

Bessel K distribution; Ensemble; Entropy; Meijer G distribution; Mode stirring; Mode tuning; Powered gamma distribution; Random walk; Reverberation chamber

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; REVERBERATION; STATISTICAL METHODS;

ELECTROMAGNETIC REVERBERATION; REVERBERATION CHAMBERS;

ELECTROMAGNETIC FIELDS;

EID: 0038519644     PISSN: 00189375     EISSN: None     Source Type: Journal    
DOI: 10.1109/TEMC.2003.811301     Document Type: Article

References (50)

1. L. R. Arnaut, "Uncertainty reduction and decorrelation of mode-stirred reverberation chamber data using transformation and expansion techniques," in Proc. 4th Eur. Symp. Electromagnetic Compatibility, Brugge, Belgium, Sept. 11-15, 2000, pp. 213-218.
2. ____, "Compound exponential distributions for undermoded reverberation chambers," IEEE Trans. Electromagn. Compat., vol. 44, pp. 442-457, Aug. 2002.
3. J. G. Kostas and B. Boverie, "Statistical model for a mode-stirred chamber," IEEE Trans. Electromagn. Compat., vol. 33, pp. 366-370, Nov. 1991.
4. B. V. Gnedenko and A. N. Kholmogorov, Predelnye Raspredelenya dlya Summ Nesavisimih Sluchanih Velichin, Gostechizdat, Moscow, Russia, 1949.
5. P. Beckmann, Probability in Communication Engineering. New York: Harcourt, Brace & World, 1967, ch. 4.
6. R. Holland and R. St. John, "Statistical response of enclosed systems to HPM environments," in Proc. 10th Annu. Rev. Appl. Comput. Electromagn. Soc., Monterey, CA, Mar. 1994, pp. 554-563.
7. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces. Oxford, U.K.: Pergamon, 1963.
8. R. H. Bolt, "Normal frequency spacing statistics," J. Acoust. Soc. Amer., vol. 18, no. 1, pp. 130-133, 1946.
9. O. Bohigas, M. J. Giannoni, and C. Schmit, "Characterization of chaotic quantum spectra and universality of level fluctuation laws," Phys. Rev. Lett., vol. 52, no. 1, pp. 1-4, 1984.
10. J. W. Gibbs, Elementary Principles in Statistical Mechanics. New Haven, CT: Yale Univ. Press, 1902, ch. IV, X, and XV.
11. L. R. Arnaut, "Effect of local stir and spatial averaging on the measurement and testing in mode-tuned and mode-stirred reverberation chambers," IEEE Trans. Electromagn. Compat., vol. 43, pp. 305-325, Aug. 2001.
12. D. ter Haar, Elements of Statistical Mechanics. New York: Holt, Rinehart & Winston, 1954, ch. IV-VI.
13. P. Pechukas, "Distribution of the energy eigenvalues in the irregular spectrum," Phys. Rev. Lett., vol. 51, no. 11, pp. 943-946, 1983.
14. T. Yukawa, "New approach to the statistical properties of energy levels," Phys. Rev. Lett., vol. 54, no. 17, pp. 1883-1886, 1985.
15. M. Wilkinson, "Statistics of multiple avoided crossings," J. Phys. A, vol. 22, no. 14, pp. 2795-2805, 1989.
16. P. Gaspard, S. A. Rice, H. J. Mikeska, and K. Nakamura, "Parametric motion of energy levels: Curvature distribution," Phys. Rev. A, vol. 42, no. 7, pp. 4015-4027, 1990.
17. T. Takami, "Curvature distribution of stadium billiard," J. Phys. Soc. Japan, vol. 60, no. 8, pp. 2489-2491, 1991.
18. L. R. Arnaut, "Operation of electromagnetic reverberation chambers with wave diffractors at relatively low frequencies," IEEE Trans. Electromagn. Compat., vol. 43, pp. 637-653, Nov. 2001.
19. H. Attias and Y. Alhassid, "Gaussian random-matrix process and universal parametric correlations in complex systems," Phys. Rev. E, vol. 52, no. 5, pp. 4776-4792, 1995.
20. L. R. Arnaut, "Statistical characterization of complex random media in random fields," Int. J. Electron. Comm. (Archiv Elektr. Übertr.), vol. 55, no. 4, pp. 211-223, 2001.
21. B. R. Lévine, Fondements Théoriques de la Radiotechnique Statistique. Moscow, Russia: Mir, 1973, vol. I.
22. I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th ed. New York: Academic, 1994.
23. K. Pearson, G. B. Jeffery, and E. M. Elderton, "On the distribution of the first product moment coefficient in samples drawn from an indefinitely large normal population," Biometrika, vol. XXI, pp. 164-201, 1929.
24. E. Jakeman and P. N. Pusey, "A model for non-Rayleigh sea echo," IEEE Trans. Antennas Propagat., vol. AP-24, pp. 806-814, Nov. 1976.
25. E. Jakeman, "On the statistics of K-distributed noise," J. Phys. A, vol. 13, no. 1, pp. 31-48, 1980.
26. R. Barakat, "Weak-scatter generalization of the K-density function with application to laser scattering in atmospheric turbulence," J. Opt. Soc. Amer. A, vol. 3, no. 4, pp. 401-409, 1986.
27. L. R. Arnaut and P. D. West, "Electric field probe measurements in the NPL untuned stadium reverberation chamber," NPL, Teddington, U.K., CETM 13 [Online] http://publications.npl.co.uk/npl_web/pdf/cetm13.pdf, 1999.
28. A. T. McKay, "A Bessel function distribution," Biometrika, vol. 24, pp. 39-44, 1932.
29. B. C. Bhattacharyya, "The use of McKay's Bessel function curves for graduating frequency distributions," Sankhya, vol. 6, pp. 175-182, 1942.
30. K. V. Krishna Sastry, "On a Bessel function of the second kind and Wilks's Z-distribution," in Proc. Indian Acad. Sci., vol. A28, 1948, pp. 532-536.
31. R. G. Laha, "On some properties of the Bessel function distributions," Bull. Calcutta Math. Soc., vol. 46, pp. 59-72, 1953.
32. D. Raj, "On a generalized Bessel function population," Ganita, vol. 3, pp. 111-115, 1953.
33. S. K. Bhattacharya, "A modified Bessel function model in life testing," Metrika, vol. 11, pp. 133-144, 1966.
34. G. Malécot, "Identical loci and relationship," in Proc. 5th Berkeley Symp. Mathematical Statistics, Population Biology and Problems of Health, vol. 4, San Francisco, CA, 1967, pp. 317-332.
35. F. McNolty, "Applications of Bessel function distributions," Sankhya, ser. B, vol. B29, pp. 235-248, 1967.
36. M. Nakagami, "The m-distribution - A general formula of intensity distribution of rapid fading," in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, Ed. London, U.K.: Pergamon, 1960, pp. 3-36.
37. S. M. Rytov, "The connection between the distribution of a quasi-monochromatic stationary process and the distribution of its envelope," Zh. Eksp. Teor. Fiz., vol. 29, pp. 702-703, 1955.
38. E. W. Stacy, "A generalization of the gamma distribution," Ann. Math. Stat., vol. 33, pp. 1187-1192, 1962.
39. M. J. Wasilewski, "Sur certaines propriétés de la distribution gamma généralisée," Rev. Stat. Appl., vol. XV, no. 1, pp. 95-105, 1967.
40. H. P. Yuen, "Two-photon coherent states of the radiation field," Phys. Rev. A, vol. 13, no. 6, pp. 2226-2243, 1976.
41. L. R. Arnaut, "Statistics of the quality factor of a rectangular reverberation chamber," IEEE Trans. Electromagn. Compat., vol. 45, pp. 61-76, Feb. 2003.
42. D. W. Scott, "On optimal and data-based histograms," Biometrika, vol. 66, p. 605, 1979.
43. C. F. Bunting, K. J. Moeller, C. J. Reddy, and S. A. Scearce, "A two-dimensional finite element analysis of reverberation chambers," IEEE Trans. Electromagn. Compat., vol. 41, pp. 280-289, Nov. 1999.
44. J. Zakrzewski, D. Delande, and M. Kuś, "Parametric motion of energy levels in quantum chaotic systems," Phys. Rev. E, vol. 47, no. 1, pp. 1650-1676, 1993.
45. L. R. Arnaut and O. C. Rochard, "Distributions of field magnitude and energy density in undermoded mode-tuned reverberation chambers," in Proc. 5th Eur. Symp. Electromagnetic Compatibility, Sorrento, Italy, Sept. 9-13, 2002, pp. 663-666.
46. R. Lentz and H. C. Anderson, "Reverberating chambers for EMC measurements," Proc. 1979 IEEE Symp. Electromagnetic Compatibility, pp. 446-451, Aug. 1979.
47. L. R. Arnaut, "Field anisotropy, field inhomogeneity and polarization bias in imperfect reverberation conditions," NPL-CEM-DGSS, Teddington, U.K., R980 614, 1998.
48. R. Barakat, "Isotropic random flights: Random numbers of flights," J. Phys. A, vol. 15, no. 10, pp. 3073-3082, 1982.
49. K. S. Gochelashvili and V. I. Shishov, "Strong fluctuations of laser radiation intensity in a turbulent atmosphere - The distribution function," Zh. Eksp. Teor. Fiz., vol. 74, pp. 1974-1978, 1978.
50. I. R. Joughin, D. B. Percival, and D. P. Winnebrenner, "Maximum likelihood estimation of K distribution parameters for SAR data," IEEE Trans. Geosci. Remote Sens., vol. 31, pp. 989-999, May 1993.