The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-231

“On Symmetric Stable Models for Impulsive Noise”

by Min Shao and Chrysostomos L. Nikias

February 1993

First-order statistics of impulsive noise processes are developed from the filtered-impulse mechanism. Under appropriate assumptions on the spatial and temporal distributions of noise sources and the propagation conditions, we show that the instantaneous amplitude of the received noise obeys the symmetric stable distribution, which is a natural generalization of the Gaussian distribution and enjoys many of its familiar properties. In the case of narrowband reception, the joint distribution of the quadrature components of the received noise is isotropic stable. The noise phase is then shown to be uniformly distributed on [0,2__ and independent of the envelope, as in the Gaussian case. The distribution of the envelope, on the other hand, is a heavy-tailed generalization of the Rayleigh distribution. Compared with existing models, such as Middleton's statistical-physical canonical models, the symmetric stable model is much simpler and mathematically more appealing. Direct comparisons with experimental data show that this model fits closely a variety of non-Gaussian noise.

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