Studies On Super-Directivity With Realization For Small-Scale Sensor Array

This dissertation studies and analyses the principles and realization of the super-directivity beamforming for the small-scale sensor array. Based on the various existing methods or approaches, the dissertation divides the super-directivity beamforming research into three mathematical models: the super-directivity beamforming model based on maximum signal-to-noise principle, the super-directivity beamforming model based on pattern synthesis and the super-directivity beamforming model based on field reconstruction via mode components. The dissertation especially and carefully concentrates on the analysis and mathematical induction of these three models. Moreover, the proposed three models are more practical because of the introduction of the sound field modeling via boundary element method. The main contributions of this dissertation are presented as follows:1. The importance and intention of the super-directivity beamforming are presented, and the conception of the super-directivity is presented in this dissertation.2. The super-directivity forming model based on maximum signal-to-noise principle is carefully analyzed. The general weighting formula for the array elements to obtain maximum directivity index is also presented. The analysis of the super-directivity beamforming is carried out for linear array as well as circular array. Furthermore, the analytical formula for circular array weighting and beam pattern calculation are given.3. Much attention is paid on the super-directivity beamforming model based on pattern synthesis. The array weighting formula for beam pattern synthesis and the formulae for super-directivity together with the beam pattern calculation are also presented. Due to the use of the boundary element method, the model becomes more practical for the circular arrays mounted on arbitrary baffles. Water-tank experiments are carried out for several circular arrays mounted on baffles of different forms.4. The super-directivity beamforming model based on field reconstruction via mode components is also studied. The concepts of spherical harmonic mode decomposer, the Fourier decomposer for the incoming sound field etc. are presented. The optimum design procedures are also presented in the dissertation. Besides, the mathematical analysis for the super-directivity forming via the reconstruction of spherical mode and Fourier mode is also explained. Data...