Toward Optimal ANC: Establishing Mutual Information Lower Bound

TL;DR

This paper derives a theoretical lower bound on the performance of Active Noise Cancellation algorithms, combining information-theoretic and physical constraints, and validates it empirically across diverse acoustic conditions.

Contribution

It introduces a unified lower bound on ANC performance that integrates information theory and physical limitations, providing a benchmark for evaluating algorithms.

Findings

The bound accurately predicts the best achievable NMSE in various conditions.

Empirical validation shows the bound's tightness across different reverberation times.

Theoretical insights help understand fundamental limits of ANC performance.

Abstract

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.