Complex‐Valued B‐Spline Neural Networks for Modeling and Inverse of Wiener Systems

Abstract

Many communication signal processing applications manifest as the problem of modeling and inverse of complex-valued (CV) Wiener systems. This contribution develops a CV B-spline neural network approach for efficient identification of the CV Wiener system as well as effective inverse of the estimated CV Wiener model. Specifically, the CV nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks. Following the use of a simple least squares parameter initialization, the Gauss-Newton algorithm is applied for estimating the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first-order derivative recursions. Moreover, an accurate inverse of the CV Wiener system can readily be obtained using the estimated model. In particular, the inverse of the CV nonlinear static function in the Wiener system can be calculated effectively using the Gauss-Newton algorithm based on the estimated B-spline neural network model with the aid of the inverse of De Boor algorithm. The effectiveness of our approach is demonstrated using the application of digital predistorter design for high-power amplifiers with memory.