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The authors consider a distributed beamforming problem in which nodes are restricted to sending binary phases to a receiver that has access to a one-bit feedback channel. Their simplified model allows one to prove lower bounds, as well as explore algorithmic techniques and analysis. They demonstrate both upper and lower bounds on the convergence time that are linear in the number of nodes in the system. Their upper bound is given by analyzing a simple randomized algorithm. They also discuss methods for accurately approximating the convergence time numerically that apply to their algorithm, as well as more general algorithms. Finally, they investigate modifications of the basic algorithm which improve the constant factor in the running time.
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