Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) seamlessly integrates two wireless technologies, mmWave communications and massive MIMO, which provides spectrums with tens of GHz of total bandwidth and supports aggressive space division multiple access using large-scale arrays. Though it is a promising solution for next-generation systems, the realization of mmWave massive MIMO faces several practical challenges. In particular, implementing massive MIMO in the digital domain requires hundreds to thousands of radio frequency chains and analog-to-digital converters matching the number of antennas. Furthermore, designing these components to operate at the mmWave frequencies is challenging and costly. These motivated the recent development of the hybrid-beamforming architecture, where MIMO signal processing is divided for separate implementation in the analog and digital domains, called the analog and digital beamforming, respectively. Analog beamforming using a phase array introduces uni-modulus constraints on the beamforming coefficients. They render the conventional MIMO techniques unsuitable and call for new designs. In this paper, we present a systematic design framework for hybrid beamforming for multi-cell multiuser massive MIMO systems over mmWave channels characterized by sparse propagation paths. The framework relies on the decomposition of analog beamforming vectors and path observation vectors into Kronecker products of factors being uni-modulus vectors. Exploiting properties of Kronecker mixed products, different factors of the analog beamformer are designed for either nulling interference paths or coherently combining data paths. Furthermore, a channel estimation scheme is designed for enabling the proposed hybrid beamforming. The scheme estimates the angles-of-arrival (AoA) of data and interference paths by analog beam scanning and data-path gains by analog beam steering. The performance of the channel estimation scheme is analyzed. In particular, the AoA spectrum resulting from beam scanning, which displays the magnitude distribution of paths over the AoA range, is derived in closed form. It is shown that the inter-cell interference level diminishes inversely with the array size, the square root of pilot sequence length, and the spatial separation between paths, suggesting different ways of tackling pilot contamination.