Distributed Beamforming for Wireless Sensor Networks with Improved Graph Connectivity and Energy Efficiency
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As the nodes in wireless sensor networks (WSNs) are independent units, an intensive communication among them is required to generate a common signal and synchronize before entering a distributed beamforming (DBF) phase. Therefore, it is crucial to select the participating nodes in DBF such that not only the resulting beampattern meets the beamforming design requirements but also the internode connectivity is retained. We consider a DBF technique for WSNs with uniformly distributed nodes and derive an average beampattern expression for a general scenario wherein the participating nodes in DBF are located on a ring with arbitrary inner and outer radii. It is proved that increasing the ring inner radius from zero to a value close to the ring outer radius, the width of the average beampattern mainlobe continuously decreases. Further, it is shown that selecting the nodes from a neighborhood close to a disc perimeter, that is, choosing the nodes from the narrow ring adjacent to the inner side of the disc boundary, facilitates a substantial decrease in the network energy waste and the node isolation probability compared to the case that the nodes are randomly selected from the whole disc. A simple approximate expression for the average beampattern is obtained in the case where the nodes are selected from a narrow ring and is used to derive the sidelobes' null and peak positions as well as a tight lower bound on the average beampattern directivity. The proposed technique is then extended to the case where the nodes are located on multiple concentric rings and the set of rings' radii are derived that guarantee an average beampattern null at a required position while substantially decreasing the sidelobe peak levels compared to the single-ring case. Finally, an average beampattern expression is obtained in the case that the nodes' signals are contaminated by noise to show that most properties of the average beampattern in the noise-free signal case carry over to the noisy signal scenario. 2010 IEEE.