Pairwise Algorithm for Distributed Transmit Beamforming

In this paper, we present a novel algorithm for distributed transmit beamforming enabling multiple single-antenna nodes to simultaneously transmit a common message such that they constructively interfere at the receiver. In order to constructively interfere, the nodes iteratively estimate and adjust their carrier phases with the help of receiver feedback. The receiver's feedback is based on composite channel estimates calculated from two simultaneous transmissions initiated by the nodes at each iteration. We prove that starting from arbitrary carrier phases, the algorithm converges to the maximum gain almost surely. The algorithm is compared to the 1-Bit Feedback algorithm presented in [3] through simulation, and is shown to outperform it by margins of 4:1 and 3:1 on metrics reflecting power consumption and convergence rate, respectively. We simulate the impact of phase estimation errors on the algorithm's steady-state gain and show it to be robust to moderately large errors of plusmn 20deg. We analyze the causes of asynchrony in simultaneous message transmissions and simulate its contribution to phase estimation errors in the context of IEEE 802.15.4 packets. We show that the contribution falls within the acceptable plusmn 20deg range.