Effect of target signals and delays on spatially selective active noise control for open-fitting hearables

TL;DR

This study analyzes how the definition of the target signal and the accompanying delays affect spatially selective active noise control for open-fitting hearables. By formulating a constrained optimization that preserves a desired spatial component via ReIR constraints and solving it in closed form, the authors compare target definitions at the error microphone versus a spatial reference microphone across delays. The key finding is that zero delay is optimal when the target is the error-m microphone component, whereas a small delay equal to the acoustic path between the reference and error microphones is advantageous when the target is defined at the reference microphone; large delays degrade performance and increase control effort. These results provide practical design guidance for implementing spatially selective ANC in hearables, balancing noise reduction, speech distortion, and computational burden in real-world use cases.

Abstract

Spatially selective active noise control (ANC) hearables are designed to reduce unwanted noise from certain directions while preserving desired sounds from other directions. In previous studies, the target signal has been defined either as the delayed desired component in one of the reference microphone signals or as the desired component in the error microphone signal without any delay. In this paper, we systematically investigate the influence of delays in different target signals on the ANC performance and provide an intuitive explanation for how the system obtains the desired signal. Simulations were conducted on a pair of open-fitting hearables for localized speech and noise sources in an anechoic environment. The performance was assessed in terms of noise reduction, signal quality and control effort. Results indicate that optimal performance is achieved without delays when the target signal is defined at the error microphone, whereas causality necessitates delays when the target signal is defined at the reference microphone. The optimal delay is found to be the acoustic delay between this reference microphone and the error microphone from the desired source.

Figures (5)

• Figure 1: Block diagram of an ANC system with $K$ reference microphones, one loudspeaker and one error microphone. The control filter is $\mathbf{w}$, the secondary path is denoted by $\mathbf{g}$ and its estimate is denoted by $\widehat{\mathbf{g}}$.
• Figure 2: Illustration of the open-fitting hearable, the considered microphones and the simulation setup.
• Figure 3: The NR level, SDI, NB-PESQ MOS-LQO score and control effort for $\Delta \in [0:1:140]$ sample delays in the target signal (desired speech component at the error microphone). The shaded areas indicate the recommended range for the delay.
• Figure 4: Illustration of the mechanism behind selective ANC for various delays between the original desired component at the error microphone $p_s(n)$ and the target signal $t(n)$.
• Figure 5: The NR level, SDI, NB-PESQ MOS-LQO score and control effort for $\Delta \in [0:1:140]$ sample delays in the target signal (desired speech component at the spatial reference microphone). The shaded areas indicate the recommended range for the delay.