High-accuracy low-cost generalized complex pruned Volterra models for nonlinear calibration

Nonlinear calibration allows enhancing the performance of analog and radiofrequency circuits by digitally correcting nonlinearities. Often, calibration is performed in the complex baseband domain, and Volterra models are used These models have hundreds of coefficients, and easily become computationally unfeasible. This is worse in complex Volterra models, because high-order Volterra terms require summing multiple products of the input signal. We propose a generalized complex Volterra model based on one relaxation of Volterra theory: all the nonlinear monomial terms in the model are considered separately, even if they correspond to a single real coefficient in complex Volterra theory. This produces more accurate models, though with a larger number of coefficients. We thus extensively prune the model by means of OMP and OBS techniques. The resulting models have fewer coefficients and/or better accuracy than conventional Volterra models, resulting in a significantly improved accuracy-complexity tradeoff. These results are validated in the experimental calibration of a commercial IF amplifier. The resulting model achieves the same accuracy, with 9 free parameters and 34 multiplications, as the standard Volterra model with 12 parameters and 266 multiplications, resulting in a 25% reduction in the number of parameters, and an 87% reduction in the number of multipliers.