ABSTRACT: The least-mean fourth (LMF) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the least mean square (LMS) algorithms with variable step size. It is because the variable step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a variable step-size LMF algorithm is proposed, which adopts an algebraic optimal step size as a variable step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.Keywords: Acoustic communication, Channel estimation, LMF, Algebraic optimal step-sizePACS numbers: 43.60.Dh, 43.60.Mn†Corresponding author: Jun-Seok Lim (jslim@sejong.ac.kr) Department of Electrical Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea(Tel: 82-2-3408-3299, Fax: 82-2-3408-4329)