  This paper considers multiple-input multiple-output (MIMO) relay
communication in multi-cellular (interference) systems in which MIMO
source-destination pairs communicate simultaneously. It is assumed that due to
severe attenuation and/or shadowing effects, communication links can be
established only with the aid of a relay node. The aim is to minimize the
maximal mean-square-error (MSE) among all the receiving nodes under constrained
source and relay transmit powers. Both one- and two-way amplify-and-forward
(AF) relaying mechanisms are considered. Since the exactly optimal solution for
this practically appealing problem is intractable, we first propose optimizing
the source, relay, and receiver matrices in an alternating fashion. Then we
contrive a simplified semidefinite programming (SDP) solution based on the
error covariance matrix decomposition technique, avoiding the high complexity
of the iterative process. Numerical results reveal the effectiveness of the
proposed schemes.
