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

Area of Science:

• Engineering
• Signal Processing
• Nonlinear Dynamics

Background:

• Traditional least mean square (LMS) algorithms struggle with nonlinear and non-monotonic transfer functions in engineering systems.
• Adaptive filtering is crucial for signal processing, but limitations exist in handling complex system dynamics.

Purpose of the Study:

• Introduce the z-transformed least mean square (zlLMS) algorithm as an advancement over traditional LMS.
• Address the limitations of LMS in nonlinear adaptive filtering scenarios.
• Demonstrate the efficacy of zlLMS in engineering applications with nonlinear transfer functions.

Main Methods:

• Modified the LMS algorithm by replacing error inputs with a function monotonically correlated to the controllable signal.
• Employed mathematical derivations and simulations to validate the zlLMS algorithm's performance.
• Tested the algorithm using nonlinear transfer functions, including raised-cosine and Lorentz functions.

Main Results:

• The zlLMS algorithm shows superior performance in nonlinear adaptive filtering.
• Achieved a significant reduction in amplitude difference (to 1/1000th) between ideal and equalized signals.
• Demonstrated effectiveness in complex scenarios like Mach-Zehnder modulators and diode lasers.

Conclusions:

• The zlLMS algorithm offers a robust solution for nonlinear adaptive filtering.
• The algorithm has broad potential applications in optics, terahertz technologies, and other engineering fields involving nonlinear dynamics.
• zlLMS provides enhanced precision and effectiveness compared to traditional LMS in challenging signal processing environments.