Hyperbolic tangent type logarithmic hyperbolic cosine adaptive filtering algorithm

In recent years, hyperbolic functions including hyperbolic cosine, hyperbolic sine and inverse hyperbolic sine have been increasingly used in the design of adaptive filters. However, the performance of these algorithms may still be surpassed. This paper introduces a tanh-based logarithmic hyperbolic cosine adaptive filtering algorithm, aimed at enhancing both the accuracy and minimizing steady-state errors in adaptive filters. Through rigorous theoretical analysis, we derive the step-size criteria essential for ensuring algorithm convergence. Subsequently, we validate the algorithm’s practical efficacy through simulation experiments, demonstrating its superior performance against comparable algorithms within the same category. The simulation outcomes conclusively show that our proposed algorithm outperforms its peers.