Synthesis of the driving functions of an array for propagating localized wave energy

This paper presents a framework for designing the driving functions of an array of radiating elements given a scalar representation of the desired propagating field at a finite number of remote spatial locations. Based on a point source propagation model in a homogeneous media, the relationship between the driving functions and the resulting field leads to a system of linear equations in the frequency domain. A least-squares solution to the inverse problem is obtained by solving the system of linear equations for the unknown array driving functions. The proposed framework is suitable for designing array driving functions that could be used to generate 'source- free' (homogeneous) solutions to the wave equation. This paper focuses on the use of the proposed technique for calculating array driving functions for generating localized wave energy. Two cases are discussed; one based on a source-free solution to the wave equation, and the other based on a numerical traveling impulse function. The results are compared to the beam generated by driving the array uniformly with a continuous-wave (cw) signal.