The Research Of Kernel Adaptive Filtering Algorithm

For the traditional linear adaptive filtering algorithm, they have a good performance in dealing with some linear problems, but the performance in dealing with nonlinear problems is not ideal. In reality, if there is a complicated nonlinear relationship between input and output in the system, the traditional linear methods are difficult to deal with them. In recent years, the kernel idea is more and more popular applied to the nonlinear field, it has a very strong ability to handle nonlinear signal adaptive filtering algorithm based on kernel method, it has become a mature implementation of nonlinear signal processing technique, with the solid foundation of mathematics of RKHS framework and kernel method in convex optimization problems, it has strong nonlinear problem ability. The new nonlinear algorithm based on kernel method are presented in the continuous, optimized algorithm is also in constant development.With researching aimed at the problems of adaptive filtering algorithm based on the idea of kernel methods, this paper puts forward some related algorithm to solve nonlinear problem of signal processing and communication:(1) With combining the RMN algorithm and the kernel method, I have proposed kernel sign-error mixed norm algorithm (KSEMN). With the noise environment of impulse noise, the RMN algorithm has the obvious advantage for LMS algorithm, so in this paper, we study the combination of RMN algorithm and kernel method, and developed the kernel sign-error mixed norm algorithm which is used to process the nonlinear signal. At the same time we also discussed normalized kernel sign-error mixed norm algorithm, and the derivation of the range of step size convergence of the KSEMN algorithm. And with different noise environment of impulse noise (Gauss distribution, binomial distribution, uniformly distributed), we have prove the superiority of KSEMN algorithm in the nonlinear channel equalization.(2) For the slow convergence of the sign-error algorithm, we improve the optimization of the sign-error algorithm, combined with the kernel method, and propose kernel segmentation sign-error algorithm (KSSE), kernel double sign-error algorithm (KDSIGN) and kernel segmentation sign-error mixed norm algorithm (KSISEMN). The MSE of the three algorithms in the nonlinear problem and the algorithm convergence speed are improved, and prove them with impulse noise and different distribution noise (Gauss distribution, binomial distribution, uniformly distributed) in relation to the traditional nonlinear algorithm (KLMS) of their respective advantages in the nonlinear channel equalization.