Study On The Algorithms Of Adaptive Volterra Filter

In the field of signal processing, linear adaptive filter is used widely for its simple structure, easy to analyze and realize. However, in the occasion of existing nonlinear interference, such as high-speed communication channels, satellite links, echo cancellation and another and etc, the performance of a linear adaptive filter is poor, which is due to the linear nature of the linear adaptive filter that restricts its capability of using higher-order non-linear signal redundancy and the ability of approximating nonlinear function. In solving nonlinear problems people have established many ways of non-linear adaptive filtering in recent years, such as neural network, homomorphic filtering, morphological filtering, Volterra filtering and so on. The Volterra filter is widely used in system recognition, chaos prediction, image processing, spread-spectrum communications and other fields. Studies have shown that the performance of the non-linear adaptive filter is better than that of the linear adaptive filter. The Volterra series is a kind of fonctionelle, and most nonlinear systems can use Volterra series to approximate any degree of accuracy if energy of input signal is limited. And because the output of a non-linear filter which is based on the Volterra series expansion is still a linear combination of the expansion'core, it is sufficient to ascertain the respond to any input in the system as long as the core of Volterra system is obtained. It is easy to analyze the performance of filtering.Three aspects'content are studied in this paper, including Volterra adaptive filtering algorithms in Gaussian noise environment andα-stable distribution noise environment respectively and the applications of Volterra filter in noise cancellation.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 environment. In order to improve the convergence speed and steady-state performance of the classic Volterra adaptive filtering algorithm (VLMS) based on minimum mean square error (MMSE) criterion in Gaussian noise environment, this paper utilizes two kinds of signal pre-processing methods. On the one hand, by decorrelating the input-related signal and using a variable step-size instead of the traditional fixed-step, a variable step-size decorrelation Volterra filtering algorithm is proposed. The steady-state performance and convergence speed are improved. On the other hand, this paper proposes an adaptive algorithm of second order Volterra filter using two lattice filters as pre-processing. This algorithm uses the orthogonalization property of backward prediction errors which can weaken the nonuniform convergence behavior and improve the convergence performance obviously.Then, adaptive Volterra filtering algorithms inα-stable distribution noise environment are studied. The nonlinearty of the filter increases the damaging effect of the impulse noise and spreads further eigen values of the correlation matrices of input signals. To solve the different convergence speed of linear terms and nonlinear terms, based on the minimum dispersion coefficient (MD) criterion, firstly, a novel divided-order adaptive Volterra least mean P norm filtering algorithm(DOVLMP) is proposed, which adopts two different convergence factors for linear items and nonlinear items respectively, and its convergence performance is proved theoretically. Then, VLMP algorithm with fully decoupled structure is proposed. Given the second Volterra filter, the first-order Volterra subsystem is adjusted to meet the MD criterion on condition that the second-order Volterra subsystem meets the MD criterion. The simulation results show that the two algorithms are superior to the traditional Volterra minimum P-norm algorithm in convergence speed and steady-state maladjustment. The divided-order adaptive Volterra filtering algorithm is simple, and the adaptive Volterra filtering algorithm with fully decoupled structure is realized cleverly and converges faster.Finally, to further improve the performance of non-linear noise cancellation, two kinds of adaptive Volterra noise cancelleres are studied. Using Lyapunov stability theory to reconstruct error performance surface, a kind of Volterra adaptive noise cancellation algorithm is proposed, which significantly improves the convergence performance, and increases the convergence precision. From the point of reducing the complexity of the algorithm, an improved Volterra adaptive noise cancellation algorithm is put forward. In order to prevent convergence instability, using non-linear function, the effect of product terms is reduced. This algorithm avoids computation of non-linear function differential, is simple and its performance is better than that of the algorithm in literature [61].