  Given the critical dependence of broadcast channels by the accuracy of
channel state information at the transmitter (CSIT), we develop a general
downlink model with zero-forcing (ZF) precoding, applied in realistic
heterogeneous cellular systems with multiple antenna base stations (BSs).
Specifically, we take into consideration imperfect CSIT due to pilot
contamination, channel aging due to users relative movement, and unavoidable
residual additive transceiver hardware impairments (RATHIs). Assuming that the
BSs are Poisson distributed, the main contributions focus on the derivations of
the upper bound of the coverage probability and the achievable user rate for
this general model. We show that both the coverage probability and the user
rate are dependent on the imperfect CSIT and RATHIs. More concretely, we
quantify the resultant performance loss of the network due to these effects. We
depict that the uplink RATHIs have equal impact, but the downlink transmit BS
distortion has a greater impact than the receive hardware impairment of the
user. Thus, the transmit BS hardware should be of better quality than user's
receive hardware. Furthermore, we characterise both the coverage probability
and user rate in terms of the time variation of the channel. It is shown that
both of them decrease with increasing user mobility, but after a specific value
of the normalised Doppler shift, they increase again. Actually, the time
variation, following the Jakes autocorrelation function, mirrors this effect on
coverage probability and user rate. Finally, we consider space division
multiple access (SDMA), single user beamforming (SU-BF), and baseline
single-input single-output (SISO) transmission. A comparison among these
schemes reveals that the coverage by means of SU-BF outperforms SDMA in terms
of coverage.
