April 1976 | NTIA Technical Report OTR-76-86
Statistical-Physical Models of Man-made and Natural Radio Noise Part II: First Order Probability Models of the Envelope and Phase
Most man-made and natural electromagnetic interferences are highly non-gaussian random processes, whose degrading effects on system performance can be severe, particularly on most conventional systems, which are designed for optimal or near optimal performance against normal noise. In addition, the nature, origins, measurement and prediction of the general EM interference environment are a major concern of an adequate spectral management program. Accordingly, this second study in a continuing series [cf. Middleton, 1974] is devoted to the development of analytically tractable, experimentally verifiable, statistical-physical models of such electromagnetic interference
Here, classification into three major types of noise is made: Class A (narrowband vis-à-vis the receiver), Class B (broadband vis-à-vis the receiver), and Class C (=Class A+Class B). First-order statistical models are constructed for the Class A and Class B cases. In particular, the APD (a posteriori probability distribution) or exceedance probability, PD, viz. P1 (e>eo)A,B, and the associated probability densities, pdf’s, w1(e)A,B, of the envelope are obtained; [the phase is shown to be uniformly distributed in (0,2p)]. These results are canonical, i.e., their analytic forms are invariant of the particular noise source and its quantifying parameter values, levels, etc. Class A interference is described by a 3-parameter model, Class B noise by a 6-parameter model. All parameters are deducible from measurement, and like the APD’s and pdf’s, are also canonical in form: their structure is based on the general physics underlying the propagation and reception processes involved, and they, too, are invariant with respect to form and occurrence of particular interference sources.
Excellent agreement between theory and experiment is demonstrated, for many types of EM noise, man-made and natural, as shown by a broad spectrum of examples. Results for the moments of these distributions are included, and more precise analytical conditions for distinguishing between Class A, B, and C interference are also given. Methods for estimating the canonical model parameters from experimental data (essentially embodied in the APD) are outlined in some detail, and a program of possible next steps in developing the theory of these highly nongaussian random processes for application to general problems of spectrum management is presented.
Keywords: man-made noise; radio noise models; Statistical communications theory
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