Study On Online Blind Equalization Algorithm For Satellite Channel Based On Echo State Network

Echo State Network(ESN),as a new type of recurrent neural network,is widely used for modeling nonlinear dynamic systems,time series prediction,and channel equalization due to its unique dynamic reservoir structure and simple training method.In satellite communication systems,the non-linearity and group delay characteristics of the channel will cause serious distortion when the transmitted signal reaches the receiving end.Although the prior information of the channel is unknown,the blind equalization technique can recover the original transmitted signal without distortion only by using the statistical information of the transmitted signal,and overcome the distortion caused by the non-ideal characteristics of the channel while making full use of the frequency band resources of the satellite channel.This paper focuses on the non-linear channels represented by satellite channels,and studies the online blind equalization algorithm based on the echo state network.Main contributions are as follows:(1)After studying the network topology and training algorithm of ESN,a recursive least square constant modulus algorithm(ESN-RLS-CMA)based on ESN is proposed to solve the blind equalization problem of nonlinear channel represented by satellite channel.This algorithm takes ESN as the basic framework and constructs the cost function of the blind equalization by using the prior statistical information of sending signals,and updates the output weight of ESN through recursive least squares(RLS)online iterations so as to minimize the cost function of the network.The simulation results show that in the satellite channel modeled by Volterra series,ESN-RLS-CMA proposed in this paper has faster convergence speed and lower Mean Square Error(MSE)value compared with the traditional online algorithm for the normalized QPSK signal.(2)In order to solve the multimode signal blind equalization problem under satellite channel and the phase rotation problem of ESN-RLS-CMA,the paper uses the idea of minimizing the real and imaginary parts of the equalizer output from the Multi-Modulus Algorithm(MMA)to construct the blind equalization cost function of the network,and then combines it with the recursive least squares algorithm(RLS)to update the output weights of the ESN online.Besides this,a two-mode operation scheme is adopted to prevent the divergence of the algorithm.Based on all above,a recursive least squares multimode algorithm via the echo state network(ESN-RLS-MMA)is proposed.Simulation results show that the proposed ESN-RLS-MMA algorithm can effectively solve the online blind equalization problem of 16QAM multi-mode signals in satellite channel and correct the phase deflection.(3)In order to make full use of the high-dimensional statistical information output from the reservoir,as well as to further enhance the online blind equalization performance based on echo state network under strongly nonlinear channels,the paper reconstructs the readout layer in the Reproducing Kernel Hilbert Space(RKHS)by means of the kernel trick.Then the the optimal solution of network cost function is obtained by using the Kernel Recursive Least Squares(KRLS)Finally,the Kernel Recursive Least Squares Multimode Algorithm(ESN-KRLS-MMA)based on Echo State Network is proposed.The simulation results show that this algorithm has better performance than traditional Volterra filtering algorithm and BP network algorithm.