A kurtosis-driven variable step-size LMS algorithm

A new technique for adjusting the step-size of the LMS algorithm is introduced. The proposed method adjusts the step-size sequence utilising the kurtosis of the estimation error, reducing therefore performance degradation due to the existence of significant Gaussian-distributed noise. The algorithm's behaviour is analysed and equations regarding the evolution of the weight-error correlation matrix and stability of the algorithm are established. The obtained theoretical results are shown to agree well with the experimental ones. Furthermore, the performance of the proposed algorithm compared to that of LMS and other existing time-varying step-size algorithms is found superior in terms of tracking speed and steady-state error.