  In time-division-duplexing (TDD) massive multiple-input multiple-output
(MIMO) systems, channel reciprocity is exploited to overcome the overwhelming
pilot training and the feedback overhead. However, in practical scenarios, the
imperfections in channel reciprocity, mainly caused by radio-frequency
mismatches among the antennas at the base station side, can significantly
degrade the system performance and might become a performance limiting factor.
In order to compensate for these imperfections, we present and investigate two
new calibration schemes for TDD-based massive multi-user MIMO systems, namely,
relative calibration and inverse calibration. In particular, the design of the
proposed inverse calibration takes into account a compound effect of channel
reciprocity error and channel estimation error. We further derive closed-form
expressions for the ergodic sum rate, assuming maximum ratio transmissions with
the compound effect of both errors. We demonstrate that the inverse calibration
scheme outperforms the traditional relative calibration scheme. The proposed
analytical results are also verified by simulated illustrations.
