A Variable Tap-Length Adaptive Algorithm for Second-Order Volterra Filter in α-stable Distribution Noise

The tap-length of a conventional adaptive Volterra filter is fixed. When the feature of a identifying system or equalizing channel is unknown or time varying, if the tap-length of the filter is too long, not only the amount of calculation increases, but also the error of system increases; if the tap-length of the filter is too short, the requirements of system performance can not be reached. In order to solve the problem, a variable tap-length adaptive algorithm for second-order Volterra is proposed. The input signal is orthogonalized using lattice filter and the quadratic terms are decoupled so that the weighting coefficients of the quadratic terms are reduced and the tap-length of linear part and nonlinear part is the same. So the structure of the traditional Volterra filter can be simplified. Based on least mean p-norm criterion, an adaptive algorithm using the concept of the pseudo-fractional tap-length is used to adjust tap-length, and the least mean p norm algorithm (LMP) is used to adjust the weighting coefficients. The simulation results indicate that the proposed algorithm for channel equalization has good convergence performance and can adaptively adjust to the optimal tap-length in Gaussian noise and -stable distribution noise under different SNR. Thus the results verify the validity of this method.