Improvement of least mean square adaptive algorithm for non-monotonic systems

This paper introduces the zlLMS algorithm, an improvement over the traditional least mean square (LMS) algorithm, addressing its limitations in handling nonlinear and non-monotonic transfer functions commonly encountered in engineering systems. The proposed method replaces the LMS algorithm's error inputs with a function monotonically correlated with the controllable signal. Through mathematical derivations and simulations, the zlLMS algorithm demonstrates superior performance in nonlinear adaptive filtering scenarios, such as the raised-cosine transfer function of Mach-Zehnder modulators and the Lorentz transfer function of diode lasers. Simulation results reveal that the amplitude difference between the ideal and zlLMS-equalized signals is reduced to 1/1000th of the original input signal's amplitude, underscoring its effectiveness in optics and terahertz technologies. These findings highlight the algorithm's robustness and potential for broad applications in engineering, especially where nonlinear dynamics are involved.