  This paper analyzes the performance of linearly precoded time division duplex
based multi-user massive MIMO downlink system under joint impacts of channel
non-reciprocity (NRC) and imperfect channel state information (CSI). We
consider a generic and realistic NRC model that accounts for transceiver
frequency-response as well as mutual coupling mismatches at both user equipment
(UE) and base station (BS) sides. The analysis covers two most prominent forms
of linear precoding schemes, namely, zero-forcing (ZF) and maximum-ratio
transmission (MRT), and assumes that only the statistical properties of the
beamformed channel are used at the UE side to decode the received signal. Under
the approximation of i.i.d. Gaussian channels, closed-form analytical
expressions are derived for the effective signal to interference and noise
ratios (SINRs) and the corresponding capacity lower bounds. The expressions
show that, in moderate to high SNR, the additional interference caused by
imperfect NRC calibration can degrade the performance of both precoders
significantly. Moreover, ZF is shown to be more sensitive to NRC than MRT.
Numerical evaluations with practical NRC levels indicate that this performance
loss in the spectral efficiency can be as high as 42% for ZF, whereas it is
typically less than 13% for MRT. It is also shown that due to the NRC, the
asymptotic large-antenna performance of both precoders saturate to an identical
finite level. The derived analytical expressions provide useful tools and
valuable technical insight, e.g., into calculating the NRC calibration
requirements in BSs and UEs for any given specific performance targets in terms
of effective SINR or the system capacity bound.
