Diffusion Approximations to Output Processes of Non-Linear Systems with Wide Band inputs, and Applications.
Abstract
Many problems in communication theory involve approximations of a Markov type to outputs of non-linear (feedback or not) systems, often so that Fokker-Planck techniques can be used. A general and powerful method is presented for getting diffusion approximations to outputs of systems with wide band inputs. The input is parameterized by epsilon and as epsilon approaches 0 the band width goes to infinity (loosely speaking). It is proved, under reasonable conditions on the systems and noise,that the sequence of system output processes converges weakly to a Markov diffusion process, which is characterized completely. Many communication systems fit the model of the paper and, in order to make mathematical sense out of many common developments of system properties, assumptions such as those of this paper are often required. The usefulness and relative ease of use of the method is illustrated by application to three examples: (a) phase locked loop, where a Markov diffusion approximation of the error process is developed, (b) adaptive antenna system, where an asymptotic analysis of the equations for the system is given, (c) di-diffusion approximation to the output of a hard limiter followed by a band pass filter; input-output S/N ratios are developed ( a version of a classical problem of Davenport). Difficulties with the usual heuristic approaches to (a), (b) are discussed. The method is versatile and the models quite general. Since weak convergence methods are used, the approximate limits yield approximations to many types of functionals of the actual system. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA080207
Entities
People
- Harold J. Kushner
Organizations
- Brown University