Design and Analysis of Deterministic Distributed Beamforming Algorithms in the Presence of Noise

This paper presents a new deterministic closed-loop phase-alignment algorithm based on quantized feedback from the receiver for distributed beamforming. In contrast with previously proposed methods, which entailed repeated transmissions from all the nodes in the network, this new algorithm requires each node to transmit only once during the synchronization cycle. This drastically reduces the amount of power consumed to achieve phase alignment, yet the new algorithm converges at least as fast as all other existing schemes. In contrast with previous analyses of distributed beamforming based on random phase updates, where noise had been disregarded, here it is explicitly included in the models and shown to have a considerable effect that cannot be ignored. With and without noise, analytical expressions that characterize the performance of the new algorithm are provided, with emphasis on various limiting regimes of interest.