  We consider the reciprocity of the information-theoretic channel of Time
Division Duplex (TDD) Multi-User-Multiple Input Multiple Output (MU-MIMO)
systems in the up- and downlink. Specifically, we assume that the transmit and
receive chains are reciprocal. We take the mutual coupling between the antenna
elements at the base station and at the mobiles into account. Mutual coupling
influences how to calculate transmit power and noise covariance. The analysis
is based on the Multiport Communication Theory, which ensures that the
information-theoretic model is consistent with physics. It also includes a
detailed noise model. We show that due to the coupling, the
information-theoretic up- and downlink channels do not fulfill the ordinary
reciprocity relation, even if the input-output relation of the transmit voltage
sources and the receive load voltages, i.e., the channel which is estimated
with the help of pilot signals in the uplink, is reciprocal. This is a
fundamental effect that is not considered otherwise. We show via Monte Carlo
simulations that both, using the ordinary reciprocity relation, and not taking
the coupling into account, significantly decreases the ergodic rates in
single-user and the ergodic sum rates in multi-user systems.
