General Characterization of Bezout Space-Time Equalizers and Precoder

Abstract

This paper gives a general framework for the investigation of Bezout space-time equalizers, not only for finite impulse response (FIR) systems, but for general transfer functions. Necessary and sufficient conditions are given under which a matrix valued transfer function possess a left (or right) inverse with certain desired system theoretical properties (e.g. causality, stability, approximation behavior), and a parametrization of all left inverses is presented. Moreover, sufficient conditions for the existence of the canonical inner-outer factorization are given