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Distributed beamforming (DBF) schemes are receiving increased interest for military and commercial applications due to radio frequency spectral congestion, the possibility of system implementation in autonomous systems, reduced interference requirements to existing legacy systems and/or other co-site signals, and the desire for improvements in low probability of intercept (LPI) and low probability of detection (LPD) transmissions. In this work, it is assumed that distributed beamforming is composed of distributed and collaborative beamforming nodes such that a beamforming gain can be achieved either with or without feedback between transmitter and receiver nodes. Open-loop DBF produces coherent beamforming gain either from a set of collaborating distributed transmitters and/or from a set of collaborating distributed receivers, where no feedback channel is required or available between the DBF transmitters and DBF receivers. Closed-loop DBF produces coherent beamforming gain from both the DBF transmitters and DBF receivers, but assumes a feedback channel exists between the transmitters and receivers. This work develops and demonstrates a method that can reach the maximum theoretical beamforming gain available in open-loop and closed-loop systems while each set of distributed nodes experiences non-ideal geometric array variation and synchronization offsets between distributed elements. Beamforming gain degradation is shown for mobile channel velocity variation. This work should provide useful application to a wide array of distributed autonomous systems as well as future 5G commercial applications.
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