Toward Optimal ANC: Establishing Mutual Information Lower Bound
This provides a theoretical ceiling for ANC performance, addressing a gap in assessing improvements for researchers and engineers in acoustics and signal processing, though it is incremental as it builds on existing information-theoretic and physical constraints.
The paper tackles the lack of theoretical limits for Active Noise Cancellation (ANC) algorithms by deriving a unified lower bound on cancellation performance, validated on the NOISEX dataset with robustness across varying reverberation times.
Active Noise Cancellation (ANC) algorithms aim to suppress unwanted acoustic disturbances by generating anti-noise signals that destructively interfere with the original noise in real time. Although recent deep learning-based ANC algorithms have set new performance benchmarks, there remains a shortage of theoretical limits to rigorously assess their improvements. To address this, we derive a unified lower bound on cancellation performance composed of two components. The first component is information-theoretic: it links residual error power to the fraction of disturbance entropy captured by the anti-noise signal, thereby quantifying limits imposed by information-processing capacity. The second component is support-based: it measures the irreducible error arising in frequency bands that the cancellation path cannot address, reflecting fundamental physical constraints. By taking the maximum of these two terms, our bound establishes a theoretical ceiling on the Normalized Mean Squared Error (NMSE) attainable by any ANC algorithm. We validate its tightness empirically on the NOISEX dataset under varying reverberation times, demonstrating robustness across diverse acoustic conditions.