Sampling frequency requirements for identification and compensation of nonlinear systems

Nonlinear systems usually cause spectral spreading resulting in an output signal bandwidth that is greater than the input signal bandwidth. When identifying and compensating such systems by digital processing methods, it has been common practice to see the sampling frequency at the Nyquist rate of the output signal. The aim of this paper is to show that sampling at the Nyquist rate of the output signal is usually not necessary, and that a nonlinear system can be identified and compensated at the Nyquist rate of the input signal. We do this by invoking Zhu's (see IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal Processing., vol.39, no.8, p.587-588, 1992) generalised sampling theorem, and by giving three examples of nonlinear system identification and compensation. The first two examples involve known nonlinearities, the first memoryless, the second with memory. The third example deals with real data from an unknown nonlinearity in a radio frequency amplifier. For each example, identification and compensation are carried out for two input signal bandwidths, one causing the distortion terms of interest to be aliased, while for the other, they are not. The results show successful identification and compensation in both cases.<>