A fast-convergence algorithm for distributed transmit beamforming

We propose a Groupwise algorithm for distributed transmit beamforming featuring high convergence rate based on the existing Pairwise algorithm. The source nodes are divided into K groups to adjust intergroup phase offsets in turn using the feedback from the receiver. Phase synchronization of all source nodes is achieved by iteratively generating new random grouping patterns. By theoretical modeling and numerical simulation, we find that the proposed algorithm saves 40% of convergence time of the Pairwise algorithm at K = 5, and more at larger K values. Larger group numbers also result in robustness against phase noise in the sense of steady-state mean and fluctuation. Costs and limitations of larger K values are pointed out as well: 2(K - 1)/K of the feedback used in Pairwise algorithm is now necessary, and performance degradation is observed in AWGN channels if each group has relatively small numbers of nodes at a given noise level.