Ping-Pong Beam Training with Hybrid Digital-Analog Antenna Arrays

In this article we propose an iterative training scheme that approximates optimal beamforming between two transceivers equipped with hybrid digital-analog antenna arrays. Inspired by methods proposed for digital arrays that exploit algebraic power iterations, the proposed training procedure is based on a series of alternate (ping-pong) transmissions between the two devices over a reciprocal channel. During the transmissions, the devices updates their digital beamformers by conjugation and normalization operations on the received digital signal, while the analog beamformers are progressively updated by a simple "beam split and drop" strategy that tracks the directions from which signals with largest magnitude are being received. The resulting scheme has minimal computational complexity and converges with only a handful of iterations. As shown in the numerical assessment, the method approximates the top singular mode of the channel, hence performing very closely to optimal beamforming.