How accurately should we calibrate a Massive MIMO TDD system?

We perform an analysis on the accuracy of the channel state information at the transmitter (CSIT) in a Massive MIMO time division duplex (TDD) system. In such a system, channel calibration is needed to compensate the hardware non-symmetry which breaks the TDD channel reciprocity. We consider the joint impact of calibration coefficients and uplink (UL) CSI on the calibrated downlink (DL) CSI accuracy. Moreover, we show the impact of these factors on both conjugate and zero-forcing (ZF) beamforming performance, which provides a useful tool to determine the accuracy level that TDD calibration coefficients should achieve. In this paper, we aim to answer the question: "How accurately should we calibrate a Massive MIMO TDD system to fully release its potential?"