Variable exponent nonlinearly processed correlation algorithm: analysis and simulations

A new algorithm for adaptive filters, named variable exponent nonlinearly processed correlation algorithm (VE-NPCA), is proposed and studied. The exponent, r, in the "r^th power function" of the correlation between the error and the filter input is adaptively controlled by an estimate of the error power. The variable exponent achieves a significant improvement in the convergence rate of the sign-sign algorithm that is known to be highly robust against disturbances but considerably slow in convergence. The results of simulations for some examples prove the effectiveness of the proposed VE-NPCA. Analysis yields a set of difference equations for calculating the theoretical convergence curves which appear to be in good agreement with the simulated ones.