Distributed beamforming with binary signaling

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