A variable step-size transform-domain LMS algorithm based on minimum mean-square deviation for autoregressive process

In this paper, we investigate the optimal variable step-size approach for the transform-domain least-mean-square (TDLMS) algorithm to achieve fast convergence speed and low steady-state misadjustment. By minimizing the mean-square deviation (MSD) between the filter weight vector and the true vector, we derive and approximate the optimal variable step-size for the TDLMS algorithm given autoregressive (AR) process as input signals. The resulted variable step-size has simple formulation and easily-setting parameters. Computer simulation is demonstrated in the framework of adaptive system modeling with a fourth-order AR input process. The overall performance are observed superior to the existing popular variable step-size approaches of the TDLMS algorithm.