RBF NN-Enabled Adaptive Filter for Any Type of Noise

The brief proposes a radial basis function (RBF) neural network (NN)-enabled adaptive filter (AF) algorithm, which consists of two stages. The first stage is a data-driven (DD) preprocessing part, and the RBF NN is to fit the probability density function (pdf) of the noise. The second stage is a model-driven filtering part, the RBF NN works as the cost function of the adaptive filtering, and an adaptive gradient ascent algorithm is obtained by maximizing the RBF NN. Since the RBF NN can fit any pdf of the noise, the proposed algorithm can work well in Gaussian, sub-Gaussian or light-tailed (uniform), and super-Gaussian or heavy-tailed (multipeak, pulse, and skewness) noises. Theoretical analysis shows the mean-value stability and mean square performance. Simulations verify the effectiveness of the proposed algorithm.