LMSK: a robust higher‐order gradient‐based adaptive algorithm

Abstract

It has been shown that, in intensely noisy environments, adaptive algorithms based on higher-order statistics can enjoy better performance, as compared with the well known second-order least-mean-square (LMS) algorithm. By contrast, this advantage diminishes for low signal-to-noise ratio (SNR) levels, where the LMS algorithm outperforms. One remedy is to employ the LMS algorithm in conjunction with a higher-order adaptation algorithm, in a mixed mode. Least-mean kurtosis (LMK) is a higher-order algorithm that has been shown to be advantageous to use if the noise distribution is Gaussian or super-Gaussian. In this study, the authors propose the LMS/kurtosis algorithm, a stochastic gradient-based adaptive algorithm that is a combination of the LMS and the LMK algorithms. Simulation results demonstrate the privilege of the proposed algorithm, in comparison with its counterparts, for a wide range of noise distributions and SNR levels. This improvement is achieved in spite of a negligible increase in computational complexity. An analytical model is also derived for the mean weight as well as the weight-error covariance matrix, from which the mean-square-error behaviour of the algorithm can be predicted. Simulation results show the high accuracy of the derived model in different conditions.