On the Theory of Amplitude Distribution of Impulsive Random Noise

Abstract

Two phenomenological models are considered by which impulsive random noises can be described: (a) Poisson noise, consisting of the superposition of independent, randomly occurring elementary impulses. Much electronic noise belongs to this type and the familiar physical examples are precipitation noise, ignition noise, and solar ``static.'' (b) Poisson-Poisson noise, consisting of the superposition of independent, randomly occurring Poisson noise, each type of Poisson noise forming a wave packet of some duration. Atmospheric noise is a representative example of the latter type. The attempt at first is made to deduce the general amplitude distribution for each model; then, because the noise sources in nature are spatially distributed and noise strength decreases with distance so that the amplitude of the received noise sometimes depends seriously on this spatial distribution of noise sources, the amplitude probability distributions are considered according to the two typical cases of the discrete and continuous spatial distributions, and are compared with those of actual atmospherics. Moments of even order and correlation functions are also calculated for each model. Finally, the dependence of the assumptions used on amplitude probability distribution are discussed. The distributions obtained are, in some cases, found to be independent of the adopted models and some of the used assumptions in a wide range of noise amplitude.

Study of statistical model and power measurement results for distortions due to clipping in SCM optical transmission system

“…The result agrees with the characteristic function of the impulse noise derived in Ref. 15 by Furutsu and Ishida. In Ref.…”

“…In Ref. 15, the analysis is based on the exponential distribution, and in Ref. 17, it is based on the Rayleigh distribution.…”

“…Using the characteristic function Φ R+G (λ) of the sum amplitude of the distortion due to clipping and the Gaussian noise, the cumulative probability P 0 (R > R 0 ) that the amplitude exceeds the given amplitude R 0 is given as follows [14,15] 24) is written as Thus, the probability density function [f(R)] of the distortion amplitude due to clipping, with additive Gaussian noise, is finally obtained as follows: …”

“…Consequently, there must be studies of the appropriate correction to the measured signal power, and a comparison of the corrected power and the theoretical value, for the case in which the signal has an amplitude distribution as impulse noise. This paper is based on the classical papers of Middleton [14] and Furutsu [15]. Considering the generation process of the distortion due to clipping, the statistical model is theoretically derived, and it is shown that its amplitude distribution follows Middletons class A model.…”

Statistical Analysis of LF/VLF Communication Modems

“…This is always satisfied for communication problems and is not nearly as strong an assumption as a Gaussian assumption. Almost all the available experimental data 4 :,-' have be,,n obtained in narrow-band conditions.…”