Coherent energy projection of modulated signals from a sparse array

Abstract

In this article, coherent energy projection is generalized to modulated signals, enabling the precise delivery of energy to a specific target area. The system and mathematical model are established to characterize the far-field energy interference from a randomized sparse transmitting array. By using the method of transmitting delay pre-compensation and spatial coherent combination, the coherent energy of the modulated signals increases significantly after demodulation at the receiving end. The coherent energy scape is presented to describe the spatial distribution of projected energy in the target area, rather than the commonly used performance metric of front-end energy analysis. Then the simulations set out to examine the spatial grating lobes and potential for expanding the focal spot using multi-foci accumulation. We also employ the particle swarm optimization to find the optimum distribution of foci to match the focal spot with the desired target area and energy level. Analysis and numerical results are provided to demonstrate the correctness of the theoretical results and effectiveness of the proposed coherent energy projection method.