Study On The Algorithms Of Adaptive Volterra Filter

Linear filter has be used widely for its mature theories, simple mathematical analysis, easy to design and realize. However, in the occasion of nonlinear interference, such as satellite links, high-speed communication channels, echo cancellation and another and etc, the performance of a linear filter is not ideal, which is due to the intrinsically deficient of the linear adaptive. In order to overcome the shortcomings of linear filter and improve the performance of system, non-linear filters theory gradually becomes the focus of research. In recent years, people have established many ways of non-linear adaptive filter, such as morphological filter, homomorphic filter, order statistics filter, Volterra filter, other polynomial filter and so on. Volterra filter is very suitable to construct various systems of non-linear model and has broad application prospects for considering the structure of linear and non-linear system. Meanwhile, when the feature of system is unknown or time-varying in practical application, the conventional fixed tap-length adaptive algorithm is unable to meet the requirements of system performance because the tap-length of filter can not be known in advance. So the variable tap-length adaptive algorithm also becomes the focus of research.Three aspects'contents are studied in this thesis, including adaptive Volterra filtering algorithms in Gaussian noise background andα-stable distribution noise background respectively and the variable tap-length adaptive algorithm.At first, the basic theory of the Volterra filter is introduced, which is the foundation of full research work.Second, adaptive algorithms of Volterra filter are studied in the Gaussian noise background. In order to improve the convergence performance of the classic least mean square error algorithm of Volterra filter in Gaussian noise background, an adaptive algorithm of second-order Volterra filter based on orthogonal transformation is proposed. The input signal is orthogonalized and the quadratic terms are decoupled, thus the number of the weighting coefficients is reduced and the adaptive algorithm is simpler. The simulations results of the algorithm for channel equalization show that the convergence performance of equalization be improved. Meanwhile, the performance of adaptive algorithms of second-order Volterra using five kinds of orthogonal transformations is compared.Then, adaptive algorithms of Volterra filter inα-stable distribution noise background are studied. The convergence performance of the conventional adaptive algorithm of Volterra filter is not ideal for heavy bad-tail characteristics ofα-stable distribution, two aspects studies are fulfilled. On the one hand, an adaptive data block algorithm of Volterra filter is proposed. More information of the error and input signals are used, and the different convergence factors are used to the linear part and the nonlinear part of the coefficient vectors of Volterra filter, to improve the steady performance and convergence speed of the traditional algorithm of Volterra filter. One the other hand, a fully decoupled group adaptive algorithm of second-order Volterra filter is proposed, which reduces the computational complexity by grouping the input dates. Meanwhile, an adaptive fully decoupled algorithm is adopted at coefficients of each sub-filter to reduce the impact of nonlinear coupling effectively.Finally, variable tap-length adaptive algorithms are studied. Based on the study of variable tap-length adaptive algorithms of FIR, a variable tap-length adaptive algorithm of FIR inα-stable distribution noise is proposed. The three parallel filters are used to compare the average of p-order error and the tap-length is updated every K point data block, and the LMP algorithm is adopted to adjust the weights of filter in the every K point data block. And then a variable tap-length adaptive algorithm of Volterra filter is studied. A variable tap-length adaptive algorithm of second-order Volterra filter inα-stable distribution noise is proposed, whose tap-length is adjusted by an adaptive algorithm using the concept of the pseudo-fractional tap-length and whose weighting coefficients is adjusted by the LMP algorithm.