Performance Evaluation of Function-Controlled Variable Step-Size LMS in Delayed-Reference Adaptive Noise Cancellation

Cemil Turan, Rashid Baimukashev

2026

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DOI 10.1109/icecco67619.2026.11488815
Data confidence 85 high
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Abstract

This paper presents a systematic performance evaluation of three adaptive noise-cancellation algorithmsLeast Mean Squares (LMS), Normalized LMS (NLMS), and Function-Controlled Variable Step-Size LMS (FCLMS)within a delayed-reference adaptive filtering framework. While LMS-type algorithms are widely used, their behavior under delayed-reference conditions without an external noise measurement remains insufficiently explored. From a signalprocessing perspective, the delayed-reference configuration introduces temporal dependencies that influence convergence dynamics and steady-state performance. All algorithms are implemented in MATLAB and evaluated using a sinusoidal test signal contaminated by colored AR(1) noise. A delayed version of the noisy observation is employed as a partially decorrelated reference input, and performance is assessed using signal-tonoise ratio (SNR) and minimum mean-square error (MMSE). To improve reproducibility and statistical reliability, simulations are conducted within a controlled framework with repeated trials and clearly defined parameters. The results indicate that the function-controlled step-size strategy provides improved convergence behavior and reduced steady-state error compared with conventional LMS and NLMS under identical delayed-reference conditions. Rather than introducing a new adaptive algorithm, this study offers a practical signalprocessing analysis of variable step-size adaptation in scenarios where classical reference-based assumptions are relaxed.