Exploiting Channel Sparsity for Beam Alignment in mmWave Systems via Exponential Learning

The large available spectrum in the millimeter wave (mmWave) band represents an attractive alternative for the congested sub-6 GHz spectrum. To overcome the difficult propagation conditions at high frequencies, directional communications via multiple antenna arrays and high-gain beams can be employed. Nevertheless, these beams need to be well aligned to reliably transmit data, which is a challenging task given the user mobility and the unpredictable changes of the wireless environment. In this paper, we propose a new distributed beam-alignment strategy relying on a single bit of feedback, which equals one if the signal-to-interference-plus-noise (SINR) reaches a predefined threshold. The novelty consists in a modified reward function, inspired from the sparse nature of the mmWave channel, coupled with the well-known exponential weights algorithm (EXP3). First, we show that our resulting adaptive policy comes with optimal theoretical guarantees in terms of sub-linear regret. Second, our numerical results demonstrate significant performance gains of our beam-alignment policy compared with the original EXP3 algorithm and other existing policies in a mmWave setting with user mobility.