Inverse Scattering for Discrete Transmission-Line Models

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Abstract
This paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform, discrete transmission-line from its response to a given forcing function. This problem is the prototype for a wealth of one-dimensional inverse scattering problems arising in various fields. A unified, straightforward approach is presented, providing all known inversion procedures and some novel ones. The derivations readily follow from causality of signal propagation on the transmission-line. It is shown that a direct exploitation of the signal propagation model leads to recursive, computationally efficient and reliable inversion algorithms. In particular, the relationships between layer peeling (Schur type, difference equation) and layer-adjoining (Levinson type, integral equation) algorithms are clearly displayed.