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Despite its promising performance gain, the realization of mmWave massiveMIMO still faces several practical challenges. In particular, implementingmassive MIMO in the digital domain requires hundreds of RF chains matching thenumber of antennas. Furthermore, designing these components to operate at themmWave frequencies is challenging and costly. These motivated the recentdevelopment of hybrid-beamforming where MIMO processing is divided for separateimplementation in the analog and digital domains, called the analog and digitalbeamforming, respectively. Analog beamforming using a phase array introducesuni-modulus constraints on the beamforming coefficients, rendering theconventional MIMO techniques unsuitable and call for new designs. In thispaper, we present a systematic design framework for hybrid beamforming formulti-cell multiuser massive MIMO systems over mmWave channels characterized bysparse propagation paths. The framework relies on the decomposition of analogbeamforming vectors and path observation vectors into Kronecker products offactors being uni-modulus vectors. Exploiting properties of Kronecker mixedproducts, different factors of the analog beamformer are designed for eithernulling interference paths or coherently combining data paths. Furthermore, achannel estimation scheme is designed for enabling the proposed hybridbeamforming. The scheme estimates the AoA of data and interference paths byanalog beam scanning and data-path gains by analog beam steering. Theperformance of the channel estimation scheme is analyzed. In particular, theAoA spectrum resulting from beam scanning, which displays the magnitudedistribution of paths over the AoA range, is derived in closed-form. It isshown that the inter-cell interference level diminishes inversely with thearray size, the square root of pilot sequence length and the spatial separationbetween paths.

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