Closed-Loop Beam Alignment for Massive MIMO Channel Estimation.

Training sequences are designed to probe wireless channels to obtain channel state information for block-fading channels. Optimal training sounds the channel using orthogonal beamforming vectors to find an estimate that optimizes some cost function, such as mean square error. As the number of transmit antennas increases, however, the training overhead becomes significant. This creates a need for alternative channel estimation schemes for increasingly large transmit arrays. In this work, we relax the orthogonal restriction on sounding vectors. The use of a feedback channel after each forward channel use during training enables closed-loop sounding vector design. A misalignment cost function is introduced, which provides a metric to sequentially design sounding vectors. In turn, the structure of the sounding vectors aligns the transmit beamformer with the true channel direction, thereby increasing beamforming gain. This beam alignment scheme for massive MIMO is shown to improve beamforming gain over conventional orthogonal training for a MISO channel.