Fast One-Bit Feedback Beamforming Algorithms with Stage-Threshold Mechanism

In this paper, two new one-bit feedback beamforming algorithms are proposed to achieve carrier phase alignment at the receiver for distributed transmit beamforming. We term two algorithms as continuous-negative one-bit feedback algorithm (CN) and directional-negative one-bit feedback algorithm (DN), respectively. They both are based on a new mechanism, referred to as the stage-threshold mechanism, in which there is different threshold value for different stage to determine whether transmitters step into the next stage and transmitters adopt the corresponding perturbation size in certain stage. During the initial stages, the perturbation size of the proposed algorithms is larger to speed up the convergence of synchronization, while the value of perturbation size decreases gradually as the order of stage increasing to keep the stability of convergence. CN algorithm directly controls the perturbation size, but DN algorithm consists of two steps, first to determine the direction of the perturbation size and then to adjust its amplitude. In comparison with existing one-bit feedback beamforming algorithms, the proposed algorithms provide their superiority while the number of transmitters is small. The given simulation results illustrate the main characteristics of the proposed algorithms.