Online Echo State Network Based On Kalman Filter And Its Application In The Blind Equalization

Based on the Kalman filter(KF)theory,this paper studies the online training algorithm of ESN based on Kalman filter and applies it to the field of blind equalization.The main work of this paper and the research results are as follows.(1)An online training algorithm of ESN(ESN-SRUKF)based on the square root unscented Kalman filter(SRUKF)is proposed in this paper.The parameters of ESN are updated online through high-precision SRUKF,and outlier detection function is added to deal with outliers.Furthermore,to reduce the computational complexity of the algorithm,an improved online ESN(R-ESN-SRUKF)is proposed by using Restricted Boltzmann Machine(RBM),which has a good feature extraction capability.Simulation results show that R-ESN-SRUKF algorithm has better performance in the fields of the system identification,time series prediction and channel equalization.(2)In order to improve the equalization performance of the existing blind equalization algorithm,an online blind equalization algorithm(ESN-PEF)of ESN based on the prediction principle is proposed in this paper.The finite-length linear prediction error filter is replaced by the complex ESN,and the Kalman filter is used to adjust the ESN parameters online according to the channel characteristics to obtain the minimum prediction error.Then,the automatic gain control device and phase adjustment factor are used to adjust the amplitude and phase of the signal respectively to recover the original transmission sequence.Simulation results show that compared with other blind equalization algorithms based on the prediction principle and traditional cost function,the ESN-PEF algorithm has lower mean square error,better convergence speed and can process high-order QAM signals.(3)A blind equalization algorithm(KF-ESN)based on the Kalman filter and online Echo State Network is proposed in this paper,which fully considers the inherent characteristics of chaotic signals.Taking advantage of the short-term predictability of chaotic signals,R-ESN-SRUKF network is used to approximate unknown chaotic maps and the trained network is used as the predictor of the algorithm to predict the equalizer output.In addition,to improve the performance of the equalizer,the Kalman filter combined with the finite impulse response(FIR)is used as the equalizer and its parameters are adjusted by minimizing the prediction error of ESN.Simulation results show that compared with other chaotic blind equalization methods,the KF-ESN algorithm has lower mean square error and better convergence speed,and can be applied to strongly nonlinear channels.