Ping Pong Beam Training for Multi Stream MIMO Communications with Hybrid Antenna Arrays

We propose an iterative training procedure that approximates multi-stream MIMO eigenmode transmission between two transceivers equipped with hybrid digital analog antenna arrays. The procedure is based on a series of alternate (ping pong) transmissions between the two devices in order to exploit the reciprocity of the wireless channel. During the ping pong iterations, the update of the devices' digital precoders/combiners is performed based on a QR decomposition of the received signal matrix. Concurrently, their analog precoders/combiners are progressively updated by a novel “multi-beam split and drop with backtracking” mechanism that tracks the channel's main spatial components. As shown throughout the paper, the proposed algorithm converges with only few iterations, has minimal computational complexity, and performs very closely to optimal singular value decomposition based precoding with sufficiently large signal-to-noise ratio.