  A simple feedback control algorithm is presented for distributed beamforming
in a wireless network. A network of wireless sensors that seek to cooperatively
transmit a common message signal to a Base Station (BS) is considered. In this
case, it is well-known that substantial energy efficiencies are possible by
using distributed beamforming. The feedback algorithm is shown to achieve the
carrier phase coherence required for beamforming in a scalable and distributed
manner. In the proposed algorithm, each sensor independently makes a random
adjustment to its carrier phase. Assuming that the BS is able to broadcast one
bit of feedback each timeslot about the change in received signal to noise
ratio (SNR), the sensors are able to keep the favorable phase adjustments and
discard the unfavorable ones, asymptotically achieving perfect phase coherence.
A novel analytical model is derived that accurately predicts the convergence
rate. The analytical model is used to optimize the algorithm for fast
convergence and to establish the scalability of the algorithm.
