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White Gaussian Noise – Models for Engineers

  • Friedrich K. Jondral EMAIL logo
Published/Copyright: June 8, 2017
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Abstract

This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

References

[1] A. Einstein, “Zur Theorie der Brownschen Bewegung,” Ann Phys, vol. 4, Folge, Band, no. 19, pp. 371–381, 1906.10.1002/andp.19063240208Search in Google Scholar

[2] S. O. Rice, “Mathematical Analysis of Random Noise,” Bell Syst. Tech. J., vol. 23, pp. 282–332, 1944, and Vol. 24, pp. 46–156, 1945.10.1002/j.1538-7305.1944.tb00874.xSearch in Google Scholar

[3] P. Lévy, Processus Stochastiques Et Mouvement Brownien, 2ème éd. Paris: Gauthier-Villars, 1965.Search in Google Scholar

[4] T. Hida:, Brownian Motion. Berlin/Heidelberg/New York: Springer-Verlag, 1980.10.1007/978-1-4612-6030-1Search in Google Scholar

[5] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed. Reading (MA): Addison- Wesley Publishing Company, 1994.Search in Google Scholar

[6] W. Hengartner and R. Theodorescu, Einführung in Die Monte-Carlo-Methode, München/Wien: Carl Hanser Verlag, 1978.Search in Google Scholar

[7] S. W. Golomb, Shift Register Sequences, Revised ed. Laguna Hills (CA): Aegean Park Press, 1982.Search in Google Scholar

[8] A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. Tokyo: McGraw-Hill Kogakusha Ltd., 1974.Search in Google Scholar

Received: 2017-3-28
Published Online: 2017-6-8
Published in Print: 2018-4-25

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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