Non-Gaussian noise models in signal processing for telecommunications: new methods and results for Class A and Class B noise models.

*(English)*Zbl 0959.94004From the introduction: The principal aims in this paper are: 1) to provide a concise, largely new, more compact and insightful development of the author’s original canonical non-Gaussian Class A and Class B noise models; 2) to present a variety of new results and statistical methods in this connection; 3) to examine the relationship of the more general Class B models to \(\alpha\)-stable distributions; 4) and to discuss the essential role of the physically additive Gauss noise component in modifying the purely Class A and Class B models themselves. Included also are samples of empirical data illustrating the typical close correspondence between theory and experiment. Only first-order \((q= 1)\) probability density functions (pdf’s) (and distributions (PDF’s)) are discussed here specifically, although the general \(q\)th-order \((q\geq 1)\) characteristic functions (c.f.’s) are also derived. The importance of an appropriate physical basis in the construction of canonical models is stressed, since it is the general physics of the noise mechanism which dictates the model’s structure and applicability. Moreover, from a practical viewpoint, the first-order pdf’s play an essential role in providing the structure of the limiting operations of threshold (or weak-signal) detection and estimation in generalized noise.