Efficient Adaptive Learning via Partial-Update Variable Step-Size LMS for Real-Time ERP Denoising

Event-Related Potentials (ERPs) are low-amplitude neural responses elicited by sensory or cognitive stimuli, widely exploited as biomarkers in the early diagnosis of neurodevelopmental and neurodegenerative disorders such as autism spectrum disorder and Alzheimer’s disease, and as control signals in brain–computer interface (BCI) systems for severely disabled individuals. However, their extremely low signal-to-noise ratio (SNR) necessitates robust denoising, especially in real-time BCI applications where low latency, minimal computational overhead, and single-channel operation are critical constraints. While advanced offline methods like Independent Component Analysis (ICA) and wavelet-based thresholding offer effective denoising in multichannel settings, they are ill-suited for embedded, causal, and resource-constrained environments. To address this gap, we propose a Partial-Update Variable Step-Size LMS (PU-VSS-LMS) algorithm that complementarily combines dynamic step-size adaptation with a magnitude-driven partial-update strategy. Evaluated on synthetic ERP-like signals embedded in realistic EEG noise (SNR = 6 dB and 0 dB), PU-VSS-LMS achieves lower mean squared error (MSE: 0.0780 vs. 0.0850 at 6 dB) and higher output SNR (8.10 dB vs. 7.80 dB) than standard VSS-LMS, while outperforming ICA in waveform preservation and noise suppression. Importantly, it reduces computational load by 75% (updating only 4 of 16 coefficients), enabling faster execution without sacrificing accuracy. These results establish PU-VSS-LMS as a highly efficient and effective solution for real-time ERP denoising in embedded, single-channel biomedical systems.