Formal deduction of a Volterra series model for complex-valued systems

This paper demonstrates a general model for nonlinear systems with complex-valued inputs and its application to communication systems modeling. Based on Wirtinger calculus and a double Volterra series approach, the proposed representation can also be considered as a generalization of the widely linear transformation to incorporate the description of nonlinear systems. The complete structure is pruned with the assistance of a compressive-sensing algorithm in order to reduce the number of parameters. To illustrate this approach, it has been experimentally implemented to model a transmitter for OFDM signals, which includes an I/Q modulator and a power amplifier.