LLM-Empowered Adaptive Wavelet Denoising for Physical Layer Communications in Mixed Noise Environments

Abstract

Traditional fixed wavelet thresholding methods, such as VisuShrink, tend to be overly conservative. As a result, they fail to effectively suppress destructive impulsive spikes in harsh environments characterized by low Signal-to-Noise Ratio (SNR). While conventional adaptive algorithms attempt to address this, they suffer from the “Signal Edge Leakage” paradox: in high-SNR regimes, baseband square-wave transitions induce pseudo-kurtosis artifacts, misleading algorithms into “over-killing” and distorting the signal. To resolve this dilemma, a novel Physics-Informed Large Language Model (LLM) denoising agent is proposed. By formulating a low-complexity state space using the kurtosis of first-level wavelet detail coefficients and estimated SNR, the agent performs zero-shot non-linear threshold mapping. Leveraging prior physical knowledge, this agent achieves precise and efficient impulse suppression in critical regions with signal-to-noise ratios (SNR) below 10 dB, resulting in a significant performance breakthrough. In high SNR scenarios, an anti-deception gating mechanism is autonomously activated, effectively protecting signal edges. Extensive simulation results confirm that in mixed-noise channels, the proposed LLM agent achieves a significant performance leap in the low SNR range. Within a wide SNR range of $0-20 \text{dB}$, the global Mean Square Error (MSE) decreases by $\mathbf{1 8. 8 %}$, and the bit error rate (BER) decreases by $\mathbf{1 6. 8 %}$. In stationary Gaussian environments, the model also exhibits excellent robustness, without introducing additional interference to the signal.