An efficient normalized LMS algorithm

The task of adaptive estimation in the presence of random and highly nonlinear environment such as wireless channel estimation and identification of non-stationary system etc. has been always challenging. The least mean square (LMS) algorithm is the most popular algorithm for adaptive estimation and it belongs to the gradient family, thus inheriting their low computational complexity and their slow convergence. To deal with this issue, an efficient normalization of the LMS algorithm is proposed in this work which is achieved by normalizing the input signal with an intelligent mixture of weighted signal and error powers which results in a variable step-size type algorithm. The proposed normalization scheme can provide both significant faster convergence in initial adaptation phase while maintaining a lower steady-state mean-square-error compared to the conventional normalized LMS (NLMS) algorithm. The proposed algorithm is tested on adaptive denoising of signals, estimation of unknown channel, and tracking of random walk channel and its performance is compared with that of the standard LMS and NLMS algorithms. Mean and mean-square performance of the proposed algorithm is investigated in both stationary and non-stationary environments. We derive the closed-form expressions of various performance measures by evaluating multi-dimensional moments. This is done by statistical characterization of required random variables by employing the approach of Indefinite Quadratic Forms. Simulation and experimental results are presented to corroborate our theoretical claims.