Non-Gaussian noise models in signal processing for telecommunications: New methods and results for class A and class B noise models

The subject here is generalized (i.e., non-Gaussian) noise models, and specifically their first-order probability density functions (pdf's). Attention is focused primarily on the author's canonical statistical-physical Class A and Class B models. In particular, Class A noise describes the type of electromagnetic interference (EMI) often encountered in telecommunication applications, where this ambient noise is largely due to other, "intelligent" telecommunication operations. On the other hand, ambient Class B noise usually represents man-made or natural "nonintelligent"-i.e., nonmessage-bearing noise-and is highly impulsive. Class A noise is not an alpha-stable process, nor is it reducible to such, except in the limiting Gaussian cases of high-density noise (by the Central Limit Theorem). Class B noise is also asymptotically normal (before model approximation). Under rather broad conditions, principally governed by the source propagation and distribution scenarios, the pdf of Class B noise alone (no Gaussian component) can usually be approximated by 1) a symmetric Gaussian alpha-stable (S alpha S) model(1) in the case of narrowband reception, or when the pdf w(1)(a) of amplitude is symmetric; 2) a nonsymmetric alpha-stable (NS alpha S) model (no Gaussian component) can be constructed in broadband regimes. New results here include: i) Counting functional methods for constructing the general qth-order characteristic functions (c.f.'s) of Class A and Class B noise, from which tall) moments and tin principle), the pdf's follow. ii) The first-order c.f.'s, pdf's, and cumulative probabilities (APD's) of nonsymmetric broadband Class B noise, extended to include additive Gauss noise (AGN); iii) Proof of the existence of all moments in the basic Class A and Class B models; iv) The key physical role of AGN and the fact that AGN removes alpha-stability; v) The explicit roles of the propagation and distribution scenarios; vi) Extension to noise fields. Although telecommunication applications are emphasized, Class A and Class B noise models apply selectively, but equally well, to other physical regimes, e.g., underwater acoustics and EM (radar, optics, etc.). Supportive empirical data are included.