Calibration of Phase Shifter Network for Hybrid Beamforming in mmWave Massive MIMO Systems

For the millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid beamforming has been proposed to reap a great gain of the large number of antennas with a limited number of radio frequency (RF) chains. The hybrid beamforming relies on a phase shifter network (PSN) in the RF domain to steer the signal power along the desired direction (or subspace). However, the RF circuits connecting the antennas and the RF chains can introduce distinct phase deviations, which need to be calibrated for the effective hybrid beamforming. This paper develops two novel approaches to the estimation and calibration of the PSN in mmWave massive MIMO communication systems under line-of-sight (LOS) and non-LOS channel scenarios. Specifically, we formulate the core phase deviation estimation problem in the calibration task as an optimization program with constant modulus constraints. Efficient algorithms are then developed to estimate the phase deviations that need to be calibrated. To gauge the performance of the proposed schemes, we also derive the Cramer-Rao lower bounds (CRLBs) for the phase estimates. The numerical results validate the effectiveness of our approaches by showing that the proposed algorithms yield estimates whose mean squared errors (MSEs) are close to the CRLBs.