Theoretical Validation of a Single-Channel Air-Coupled PMUT With Multi-Frequency Operation for Compressed 3D Spatial Sensing

This paper proposes a new 3D spatial sensing approach via compressed sensing (CS) by using a single-channel air-coupled piezoelectric micromachined ultrasonic transducer (PMUT) operated with multi-frequency. Our study focuses on a single-channel transducer with a PMUT array composed of several diaphragms with different radius sizes. It is known that small variations in the radius size can cause distinct transmission signals of all diaphragms that are excited by the same excitation signal. In this way, the acoustic field distribution of a region of interest (ROI) can be distorted especially in the direction perpendicular to the wave propagation, which could help to obtain more distinctive information about the scatterers at different locations in any 3D ROI. Therefore, a compressed 3D spatial sensing approach is proposed and used for acquiring measurements of the designed single-channel transducer. The information of any object in a 3D ROI can be mapped onto a collection of basis functions constructed via the nearly mutual orthogonal echo signals from all scatterers in the ROI. Furthermore, the proposed approach is verified with simulated acoustic measurements obtained from the established PMUT equivalent circuit model and the K-Wave acoustic propagation model via an obstacle-sensing application. Based on the sparsity nature of objects in the ROI, the reconstruction of 2D/3D images of objects can be accomplished via a CS-based algorithm. The obtained image reconstruction results show that the proposed approach allows not only for detecting localization but also for reconstructing descriptive features of an object.