A Scalable Feedback-Based Approach to Distributed Nullforming

We present a novel approach to the problem of distributed nullforming where a set of transmitters cooperatively transmit a common message signal in such a way that their individual transmissions precisely cancel each other at a designated receiver. Under our approach, each transmitter iteratively makes an adjustment to the phase of its transmitted RF signal, by effectively implementing a gradient descent algorithm to reduce the amplitude of the overall received signal to zero. We show that this gradient search can be implemented in a purely distributed fashion at each transmitter assuming only that each transmitter has an estimate of its own channel gain to the receiver. This is an important advantage of our approach and assures its scalability; in contrast any non-iterative approach to the nullforming problem requires centralized knowledge of the channel gain of every transmitter. We prove analytically that the gradient search algorithm converges to a null at the designated receiver. We also present numerical simulations to illustrate the robustness of this approach.