Complex-Valued Symmetric Radial Basis Function Network for Beamforming

Abstract

The complex-valued radial basis function (RBF) network proposed by Chen et al. (1994) has found many applications for processing complex-valued signals, in particular, for communication channel equalization and signal detection. This complex-valued RBF network, like many other existing RBF modeling methods, constitutes a black-box approach that seeks typically a sparse model representation extracted from the training data. Adopting black-box modeling is appropriate, if no a priori information exists regarding the underlying data generating mechanism. However, a fundamental principle in practical data modelling is that if there exists a priori information concerning the system to be modeled it should be incorporated in the modeling process. Many complex-valued signal processing problems, particularly those encountered in communication signal detection, have some inherent symmetric properties. This contribution adopts a grey-box approach to complex-valued RBF modeling and develops a complex-valued symmetric RBF (SRBF) network model. The application of this SRBF network is demonstrated using nonlinear beamforming assisted detection for multiple-antenna aided wireless systems that employ complex-valued modulation schemes. Two training algorithms for this complex-valued SRBF network are proposed. The first method is based on a modified version of the cluster-variation enhanced clustering algorithm, while the second method is derived by modifying the orthogonal-forward-selection procedure based on Fisher ratio of class separability measure. The effectiveness of the proposed complex-valued SRBF network and the efficiency of the two training algorithms are demonstrated in nonlinear beamforming application.