This paper generalizes the technique of spatial power combining to modulated signals and applies it to effectively strengthen or deny communications and navigation services in desired area. The system and mathematical model of coherent combining for direct-sequence spread spectrum (DSSS) signals are established. By using the method of transmitting delay precompensation and coherent combination, the coherent energy level after de-spreading at the receiving scales is the square of the number of nodes rather than being additive. Thus, the energy coherence is proposed to analyze the interference and superposition effects in the focusing area rather than the commonly used performance metric of front-end energy analysis. Then, the influences of beam pointing error and clock phase error of the sparse array on coherent combining are studied by theoretical and numerical analysis. The results show that by controlling the array error within a certain allowable range, the proposed method can achieve a precise projection of coherent energy. More specifically, we demonstrate that with further improvements in synchronization and pointing accuracy, the actual distribution of the focal spot and effective interference spots can be precisely manipulated.
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.
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