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We consider discrete-time (DT) systems S in which a DT input is first transformed to a continuous-time (CT) format by phase-amplitude modulation, then modified by a non-linear CT dynamical transformation F, and finally converted back to DT output using an ideal de-modulation scheme. Assuming that F belongs to a special class of CT Volterra series models with fixed degree and memory depth, we provide a complete characterization of S as a series connection of a DT Volterra series model of fixed degree and memory depth, and an LTI system with special properties. The result suggests a new, non-obvious, analytically motivated structure of digital compensation of analog nonlinear distortions (for example, those caused by power amplifiers) in digital communication systems. Results from a MATLAB simulation are used to demonstrate effectiveness of the new compensation scheme, as compared to the standard Volterra series approach.

Discrete-time models resulting from dynamic continuous-time perturbations in phase-amplitude modulation-demodulation schemes