Least Mean Square Algorithm Based on Hyperbolic Tangent Function Framework

‍ ‍Adaptive filters play an important role in applications such as adaptive control， noise cancellation， channel equalization， system identification， and biomedical fields. Due to its simplicity， low computational complexity， and ease of implementation， the most popular adaptive filtering algorithm is the least mean square （LMS） algorithm. The traditional LMS algorithm has good convergence performance when processing Gaussian signals. However， for the processing of non-Gaussian signals， the adaptive LMS algorithm has poor convergence or even cannot converge. In order to improve the convergence of the LMS algorithm under non-Gaussian noise interference， this paper defines a new cost function by embedding the cost function of the traditional LMS algorithm into the framework of hyperbolic tangent function， and thus proposes a robust hyperbolic tangent least mean square （HTLMS） algorithm. In addition， in response to the contradiction between convergence speed and steady-state error in the HTLMS algorithm， this paper designs a variable λ-parameter hyperbolic tangent least mean square （VHTLMS） algorithm. The simulation results show that in system identification application scenarios， compared with the LMS algorithm， generalized maximum correntropy criterion （GMCC） adaptive filtering algorithm， and logarithmic hyperbolic cosine adaptive filter （LHCAF） algorithm， the proposed HTLMS algorithm and VHTLMS algorithm in this paper have good robustness， faster convergence speed and smaller steady-state error under impulsive noise interference.