  This paper considers an interference network composed of K half-duplex
single-antenna pairs of users who wish to establish bi-directional
communication with the aid of a multi-input-multi-output (MIMO) half-duplex
relay node. This channel is referred to as the "MIMO Wireless Switch" since,
for the sake of simplicity, our model assumes no direct link between the two
end nodes of each pair implying that all communication must go through the
relay node (i.e., the MIMO switch). Assuming a delay-limited scenario, the
fundamental limits in the high signal-to-noise ratio (SNR) regime is analyzed
using the diversity multiplexing tradeoff (DMT) framework. Our results sheds
light on the structure of optimal transmission schemes and the gain offered by
the relay node in two distinct cases, namely reciprocal and non-reciprocal
channels (between the relay and end-users). In particular, the existence of a
relay node, equipped with a sufficient number of antennas, is shown to increase
the multiplexing gain; as compared with the traditional fully connected K-pair
interference channel. To the best of our knowledge, this is the first known
example where adding a relay node results in enlarging the pre-log factor of
the sum rate. Moreover, for the case of reciprocal channels, it is shown that,
when the relay has a number of antennas at least equal to the sum of antennas
of all the users, static time allocation of decode and forward (DF) type
schemes is optimal. On the other hand, in the non-reciprocal scenario, we
establish the optimality of dynamic decode and forward in certain relevant
scenarios.
