A two-gain NLMS algorithm for sparse system identification

• A modified normalized least-mean-square (NLMS) algorithm is proposed. • The proposed approach considers two different gains in the adaptation process. • The proposed algorithm focuses on sparse plant identification. • Different operating scenarios are considered to evaluate the proposed algorithm. • Simulation results confirmed the effectiveness of the proposed algorithm. This paper introduces a modified normalized least-mean-square (NLMS) algorithm for sparse system identification. The proposed approach is in line with the proportionate NLMS (PNLMS)-type algorithms in the sense that different gains are considered in the coefficient update equation. However, in contrast to the PNLMS-type algorithms, the proposed approach considers only two different gains, one related to the active coefficients and other related to the inactive ones. Such an approach allows obtaining closed-form expressions for both gains without relying on proportionality functions and activation factors. As a result of the proposed strategy, the new algorithm, termed here two-gain NLMS (TG-NLMS), leads to both fast convergence and low computational complexity. Simulation results are shown aiming to confirm the effectiveness of the proposed algorithm.