Towards Silent Open Windows

Abstract

Noise pollution is a major health threat to society. Active noise control systems that attenuate noise through open windows have the potential to create quieter homes while maintaining ventilation and sight. Such systems are commonly realized with closed-loop LMS algorithms. However, these algorithms require a large number of error microphones inside the room and provide only local attenuation. Using many error microphones leads to slow convergence and high computational effort, having additional disadvantages. Therefore, closed-loop active noise control algorithms are undesired for real-world application. In this study, we develop an open-loop wave-domain algorithm that converges instantaneously and operates with low computational effort. As it is open-loop, it does not require error microphones. We position a control region in the far-field that covers all directions from the aperture into the room. In the algorithm, we minimize the sound in that control region. Hence, it inherently ensures cancellation in the whole room. We derive acoustic transfer functions to obtain frequency responses of the aperture and loudspeakers. Those are used for soundfield calculation. The sum of the soundfields, from the aperture and the loudspeaker array, is then expressed in orthonormal basis functions. By minimizing this sum in least mean square sense, we can calculate the filter-weights that minimize the sound energy in the control region. Implementation of these filter-weights with block-wise processing using the Short-Time Fourier Transform generates the signals for the loudspeaker array. However, this processing induces a delay. To compensate for this algorithmic delay, two methods are compared. The first is positioning a reference microphone further in front of the aperture. The second method uses an autoregressive model for signal prediction. Both lead to a loss in attenuation performance compared to the optimal algorithm. We compare the optimal wave-domain algorithm with a LMS-based reference algorithm, as well as both the algorithmic delay compensation methods. The algorithms are tested with a sparse and grid loudspeaker array, and we use rumbler-siren, airplane, and white noise signals as incoming noise. Furthermore, we compare performance for three incident angles. Our simulation results indicate that wave-domain processing has the potential to outperform LMS-based methods in practical active noise control for apertures. More specifically, we obtain an average -10dB global reduction up to 2~kHz for all signal types with the optimal wave-domain approach. In comparison, the performance of the closed-loop algorithm ranges between -5.2 and -9.2dB, depending on the signal type. Furthermore, we indicate the limited impact of the incident angle on performance for the wave-domain algorithm. Positioning a reference microphone in front of the aperture outperforms the predictor approach in all scenarios, and its performance compares to that of the closed-loop LMS algorithms. Eventually, the absence of error microphones and inherent global control ensure that the wave-domain algorithm can be used for a practical active noise control system for apertures. Future work could improve the algorithm by reducing loss of performance with small window-sizes due to time-delay wrapping in the block-wise processing. Furthermore, a natural continuation of this study is to develop and test the wave-domain algorithm for scenarios with a moving primary noise source to further emphasize its advantage over the closed-loop LMS algorithm.