We propose a beam alignment algorithm that enables initial access establishment between two transceivers equipped with hybrid digital-analog antenna arrays operating in millimeter wave wireless channels. The proposed method builds upon an active channel learning method based on hierarchical posterior matching that was originally proposed for single-sided beam alignment on single path dominant channels. We extend it to the double-sided alignment problem and propose an estimation framework based on variational Bayesian inference that accounts for the uncertainties on the unknown channel complex gain and noise variance. The proposed approach is numerically shown to be resilient to the single path assumption and reaches near optimal beamforming gains with a moderate training overhead, even at low signal-to-noise ratios.
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.
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