Distributed transmit beamforming: Phase convergence improvement using enhanced one-bit feedback

Transmission of signals using multiple antennas can significantly improve the energy efficiency of a wireless network, and the proper alignment of the transmitted signals' phases at the receiver is one of the key factors so this efficiency improvement can be realized. In a time-varying channel, due to the relative motion between the transmitters and the receiver, the development of a scheme that guarantees such alignment is very challenging. In this paper, considering a distributed transmit beamforming scenario, an algorithm to achieve such phase alignment of signals in a time-varying channel is proposed. A simple formula is derived, which can be adopted by each transmitter to compute its beamforming weight's phase, and it is shown that the use of this perturbation results in a significant improvement in terms of speed of convergence at the receiver. With simulation it is shown that, using the proposed scheme, the transmitted signals' phase aligned at the receiver 33% faster than the one-bit feedback scheme. The average theoretical bit error rate is achieved 50% faster relative to the one-bit feedback scheme with on average 18% less number of antennas at the transmitter.