Theory of Periodically Time-Variant Linear Systems

In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital representation of such systems. In addition, we derive several interesting properties enabling useful equivalences to represent, simulate and compensate PTVs.

Linear Channel Estimation Based on a Low-Bandwidth Observation Channel with Unknown Response

We propose a novel system identification technique, based on a least-mean square algorithm, allowing for the estimation of a linear channel by using an unknown-response measurement channel. The key of the technique is a memoryless nonlinear function working as uncoupling block between the estimated and observation channels, conforming a Wiener-Hammerstein scheme. We prove that this estimation, only differing from the actual channel response by a scaling factor and a temporal shift, does not depend on the observation channel bandwidth. As a consequence, this technique enables the usage of low-cost measurement devices as feedback channel. We present numerical examples of the method, supporting the proposal and displaying excellent results.