Enhancing the coherence between virtual and physical signals in virtual sensing with a double-layer microphone arrangement

The coherence between virtual and physical signals is important in an active noise control system with virtual sensing techniques because it determines the upper limit of the noise reduction performance. In this paper, distributing physical microphones on two concentric hemispherical surfaces surrounding the virtual microphone is proposed to improve the coherence in practical applications. It is demonstrated that such a double-layer physical microphone arrangement outperforms the single-layer arrangement with the same number of physical microphones due to the added sound pressure gradient information obtained with microphones in two different layers. The simulation results in a diffuse field, and the experiment results in a reverberation room are presented to show that the upper limit frequencies below which the coherence is more than 0.9 is larger than the single-layer arrangement with the proposed double-layer arrangement. The upper limit frequency can be further increased by decreasing the distance between the two spherical surfaces and aligning the physical microphones radially for a better estimation of the radial sound pressure gradient. The findings are further supported with the experiment results obtained in a real car running on a typical asphalt road at a constant speed of 50 km/h.