HoloBeam: Learning Optimal Beamforming in Far-Field Holographic Metasurface Transceivers

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a fixed-budget multi-armed bandit framework to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named Holographic Beam (HoloBeam) exploits the parametric form of channel gains of the beams, which can be expressed in terms of two phase-shifting parameters. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, HoloBeam works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of HoloBeam incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that HoloBeam outperforms state-of-the-art algorithms through extensive simulations.