Online Sampling Rate Offset Estimation via Real Part Maximization

Distributed acoustic sensor networks consist of independent acoustic nodes, each with its own clock, which introduces inherent clock skew issues, creating several challenges when processing acoustic and speech signals. Specifically, the sampling rate offset (SRO) caused by clock skew leads to time-varying phase drift between the output signals of different nodes. This phase drift disrupts signal coherence, impairing the performance of downstream algorithms such as echo cancellation, blind source separation, and beamforming. Despite substantial progress in SRO estimation and compensation, existing online SRO estimation methods still encounter limitations in low SNR or naturally alternating conversational environments. To address these challenges, we propose a novel online SRO estimation method, formulated on the fundamental two-node case, with the potential for extension to multi-node scenarios. First, we reconsider phase drift in the normalized cross-spectrum (NCS), taking into account noise and interfering signals, and investigate the statistical properties of the average secondary NCS (SNCS). Then, we formulate an objective function based on real part maximization, which attains its maximum when the estimated SRO aligns with the true value. To enable online estimation, we replace the averaged SNCS with a recursively smoothed version in the objective function, and employ Nesterov accelerated gradient for efficient optimization. Both simulations and experiments validate the effectiveness of the proposed method¹.