Physics-informed adaptive filtering for acoustic echo cancellation

This paper introduces a physics-informed adaptive filtering framework for acoustic echo cancellation (AEC). Unlike conventional adaptive algorithms that rely solely on data-driven error minimization, the proposed method incorporates physically motivated priors derived from acoustic wave propagation and room impulse response structure. The echo path estimation problem is formulated as a composite stochastic optimization task, where the instantaneous squared error is regularized by constraints encoding causality, exponential energy decay, time-weighted sparsity of early reflections, spectral smoothness, and slow temporal variation of the acoustic path. The resulting Physics-Informed Normalized Least-Mean-Squares (PI-NLMS) algorithm performs stochastic gradient descent on the regularized cost while enforcing hard causality through projection. The proposed formulation restricts adaptation to a physically plausible echo-path manifold, improving conditioning and reducing variance without substantially increasing computational complexity. Theoretical analysis establishes mean convergence conditions and characterizes the bias-variance trade-off introduced by structured regularization. Simulation results under stationary and time-varying echo paths demonstrate faster convergence, improved steady-state misalignment, and enhanced echo return loss enhancement (ERLE) compared to conventional NLMS and sparsity-aware baselines.