Widely Linear Complex-Valued Spline-Based Algorithm for Nonlinear Filtering

Over the past decade, spline adaptive filtering (SAF) has attracted much attention in nonlinear signal processing. In this paper, we investigate the WL complex-valued SAF (WL-CSAF) algorithm in the complex domain based on the cascaded architecture combining a widely linear (WL) model and a nonlinear lookup table (LUT), which is capable of exploiting the full second-order information of signals. Moreover, the steady-state mean square error (MSE) is analyzed to provide insights into the theoretical behavior of the WL-CSAF algorithm. Simulations of nonlinear system identification scenarios demonstrate the superiority of WL-CSAF against known algorithms, and validate the accuracy of the theoretical predictions.