A Variable Data Block Length LMS Algorithm for Second-Order Volterra Filter

The data block LMS algorithm for second-order Volterra filter uses the present moment and its previous moment abundant information of input signals and error signals to increase the algorithm’s convergence speed. However, the fixed data block lengths which are different from each other, lead to a reciprocal relationship between the algorithm’s convergence speed and steady-state error. To solve the problem, a variable data block length LMS algorithm for second-order Volterra filter is proposed, which improves the algorithm’s performance by changing the input data block length at each moment. In this algorithm, firstly，two parallel second-order Volterra filters are used and the difference of their input data block lengths is one unit forever. Then, the two filters’ output error signals are put into a data block length decision device to adaptively adjust the two input data block lengths in next moment. Lastly, the output signal of the first second-order Volterra filter is taken as the output signal of the whole filtering system to improve the algorithm’s performance. This algorithm is applied to nonlinear system identification. The computer simulation results of nonlinear system identification show that both convergence speed and steady-state performance of the algorithm are significantly improved in Gaussian noise environment.