Chebyshev approximation of baseband Volterra series for wideband RF power amplifiers

The Volterra series represents a very powerful mathematical tool for system-level analysis to describe the input-output behavior of nonlinear devices such as RF power amplifiers, which generally incorporate memory effects. Starting from the most general complex baseband representation of a nonlinear RF power amplifier, an equivalent nonlinear system with lower complexity is developed. The complexity reduction is obtained by a bandwidth dependent approximation of the multi-dimensional Volterra kernels with orthogonal polynomials in the frequency-domain. The resulting nonlinear time-domain model consists of a cascade of complex linear pre-filters and a memoryless polynomial with complex parameters. If the input signal bandwidth becomes sufficiently small, we obtain a special well known system from the most general approximation which can be represented in the baseband region by purely static nonlinearities (AM/AM- and AM/PM-conversion). We show for a 3rd-order nonlinear system with typically smooth kernels that the number of free parameters can be reduced while maintaining the required modeling accuracy.