Distributed antenna arrays are arbitrarily large groups of neighboring nodes which are controlled to form virtual antenna arrays for both transmission and reception. Distributed beamforming (DBF) is widely used in wireless sensor networks (WSNs) and distributed massive Multi-Input Multi-Output (MIMO) systems. The research in DBF has been divided into four major research trends: radiation pattern analysis, optimization of power and lifetime, nodes synchronization, and array design. In this paper, a new algorithm is introduced to synthesize the radiation pattern of an arbitrarily distributed array using reduced number of distributed nodes. In this context, the reduction in the number of nodes results in minimizing the synchronization complexity between the synthesized array nodes and in minimizing the number of RF front ends. Thus, the overall system cost is reduced. In this algorithm, the three antenna array parameters (number of nodes, nodes locations, and nodes excitations) are properly adjusted to construct a close copy of the original array pattern. Different nodes selection ways are utilized to select the nodes required to synthesize the array for a desired radiation pattern. Also, uniform feeding and non-uniform feeding scenarios are introduced. In simulations, the proposed algorithm is applied to the synthesis of pencil-beam patterns. The simulation results reveal that the synthesized radiation patterns highly agree with the ordinary distributed array pattern in the case of non-uniform feeding. Also, the proposed algorithm can be applied to the synthesis of shaped-beam patterns via controlling the three aforementioned antenna array parameters and taking the shaped-beam pattern as the desired pattern in the algorithm.
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