Discrete-Time Block Models for Transmission Line Channels: Static and Doubly Selective Cases

Most methodologies for modeling Transmission Line (TL) based channels define the input-output relationship in the frequency domain (FD) and handle the TL resorting to a twoport network (2PN) formalism. These techniques have not yet been formally mapped into a discrete-time (DT) block model, which is useful to simulate and estimate the channel response as well as to design optimal precoding strategies. TL methods also fall short when they are applied to Time Varying (TV) systems, such as the power line channel. The objective of this paper is to establish if and how one can introduce a DT block model for the Power Line Channel. We prove that it is possible to use Lifting and Trailing Zeros (L&TZ) techniques to derive a DT block model that maps the TL-based input-output description directly in the time domain (TD) block channel model. More specifically, we find an interesting relationship between the elements of an ABCD matrix, defined in the FD, and filtering kernels that allow an elegant representation of the channel in the TD. The same formalism is valid for both the Linear Time Invariant (LTI) and the Linear TV (LTV) cases, and bridges communications and signal processing methodologies with circuits and systems analysis tools.