  In time-division duplexing (TDD) millimeter-wave (mmWave) massive
multiple-input multiple-output (MIMO) systems, the reciprocity mismatch
severely degrades the performance of the hybrid beamforming (HBF). In this
work, to mitigate the detrimental effect of the reciprocity mismatch, we
investigate reciprocity calibration for the mmWave-HBF system with a
fully-connected phase shifter network. To reduce the overhead and computational
complexity of reciprocity calibration, we first decouple digital radio
frequency (RF) chains and analog RF chains with beamforming design. Then, the
entire calibration problem of the HBF system is equivalently decomposed into
two subproblems corresponding to the digital-chain calibration and analog-chain
calibration. To solve the calibration problems efficiently, a closed-form
solution to the digital-chain calibration problem is derived, while an
iterative-alternating optimization algorithm for the analog-chain calibration
problem is proposed. To measure the performance of the proposed algorithm, we
derive the Cram\'er-Rao lower bound on the errors in estimating mismatch
coefficients. The results reveal that the estimation errors of mismatch
coefficients of digital and analog chains are uncorrelated, and that the
mismatch coefficients of receive digital chains can be estimated perfectly.
Simulation results are presented to validate the analytical results and to show
the performance of the proposed calibration approach.
