Performance Analysis of Excess Mean Square Error of Adjusting Log-Based Stepsize for LMS Algorithm with High Variance Input

A high variance input excitation adversely impacts the performance of an adaptive filter for system identification problems. This occurs due to an increase in steady-state excess mean square error (EMSE) and consequently, an increase in the miss-adjustment value of the adaptive system. Reducing the miss-adjustment value at high variances of input excitation while maintaining fast convergence rate is being proposed by utilizing a new time-varying stepsize in this paper. A per tap time adjusting stepsize framework using a logarithmic function of the input to the adaptive filter is proposed. In the context of adaptive noise cancellation application, we present simulation results using various variances of AWGN input. We also present the statistical analysis of EMSE and miss-adjustment of the proposed technique. Simulation results show that this technique has the ability to terminate with a very small miss-adjustment for high variances of input excitation compared with others.