Concatenated training in distributed transmit beamforming systems

Generating and feeding back beamforming vector are very challenging tasks in distributed transmit beamforming (DTB) systems. Phases of DTB nodes may vary rapidly due to residual carrier frequency offset and hence frequent updating of beamforming vector is required. Existing iterative training schemes that only require one bit training and one or two bits feedback in each iteration have low convergence speed and are not robust in noisy channels due to the lack of structure in the training sequences. In this paper, we consider a DTB system where the number of training bits N sent from each node is no more than the number of source nodes M, and propose a concatenated training scheme based on optimal design of training sequences in this case. For spatially uncorrelated channels, we show that the concatenated training scheme can optimally combine the N latest training signals and achieve beamforming gain approximately proportional to N/M. An algorithm which can adaptively determine the length of the combination in time-varying channels is also proposed. Simulation results demonstrate the proposed scheme can work efficiently even at very low signal-to-noise ratio, with the total feedback bits much less than those required in the iterative schemes.