Scalable feedback algorithms for distributed transmit beamforming in wireless networks

We explore a class of techniques for distributed transmit beamforming where the beamforming target sends cumulative feedback that is broadcast to all of the beamforming nodes. The simplest technique in this class is a 1-bit RSS feedback algorithm that has been studied in detail in the literature. Under this 1-bit algorithm, transmitters make random phase perturbations and the receiver periodically sends 1 bit of feedback indicating whether the received signal strength has increased or not compared to what was observed in the past. While this simple algorithm has very attractive properties such as dynamic tracking of time-varying phases, robustness to noise and other disturbances and is also simple to implement, we show in this paper that it also has serious limitations such as slow convergence and poor tracking performance in the presence of frequency offsets between the transmitters. We then show that enhanced feedback algorithms where the receiver sends as feedback several bits of feedback indicating the amplitude and phase of the received signal over time, are able to achieve beamforming in the presence of frequency offsets and large feedback channel latencies, while retaining the scalability and robustness of the 1-bit algorithm.