Behavior of the LMS algorithm with hyperbolic secant cost

Abstract This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise.