MBT: Multi-Beam Strategy for Best Transmit Beamforming in mmWave Communications

Beamforming is pivotal for harnessing high data rates in millimeter wave (mmWave) multiple-input-single-output (MISO) systems. We present a learning algorithm, Multi-beam for Best Transmit Beamforming (MBT), that identifies the beam with the highest received signal strength at the user equipment. MBT uses the fixed-budget best arm identification (BAI) framework, where an optimal beam is learned by exploring the beams within a fixed number of time slots or pilot signals. During exploration, we allow the selection of multi-beams where concurrent transmission happens on all the beams selected and available power is distributed equally among all the beams. We show that the probability of misidentifying the optimal beam after using nBpilots decays exponentially fast as $\mathcal{O}\left( {{{\log }_2}K\exp \left\{ { - \frac{{{n_B}A}}{{{{\log }_2}K}}} \right\}} \right)$, where K is the number of beams, and A is a problem-dependent constant. Our error bound demonstrates that by employing the multi-beam transmission strategy for exploration, the error probability of MBT attains a better bound compared to the case where only a single beam is selected at each time slot. In particular, we achieve a factor K improvement in the error exponent. Extensive simulations and comparisons demonstrate the superior performance of our MBT algorithm. More specifically, MBT can enhance the average throughput by over 15% compared to state-of-the-art algorithms within 150 pilot symbols for 64 beams.