Synergistic Quantization for Generalized Cauchy Adaptive Filters in Acoustic Echo Cancellation

Abstract

This letter proposes GC-SQMCC, a computationally efficient robust adaptive filtering algorithm tailored for fixed-point acoustic echo cancellation (AEC) under impulsive noise. Departing from signal-driven quantizers, the proposed scheme synergistically aligns a nonlinear compression-mapping quantizer with the influence function of the generalized Cauchy (GC) kernel, allocating fine resolution near zero and gracefully coarsening for large impulses. An adaptive error envelope tracker (AEET) normalizes the dynamic range online, while a synergistic look-up table (LUT) fuses the kernel weighting and error scaling into a single memory access, enabling 16-bit integer arithmetic during the per-sample filtering stage by moving divisions and transcendental operations to the infrequent LUT-update process. A threshold-based adaptive LUT update (ALUT-U) further decouples high-frequency filtering from low-frequency grid adjustment. Mean and mean-square stability conditions are derived, and an asymptotic steady-state MSD is derived under high-resolution assumptions. Simulations on AEC under single-talk and double-talk scenarios show that GC-SQMCC achieves lower steady-state MSD than competing quantized baselines under various configurations.