  This paper addresses the training signal design for the channel estimation in
two-way multiple-input-and-multipleoutput (MIMO) relay systems, where the
channels are correlated. We first derive the backward channel estimator with
the optimal training signal sent by the relay node. Given the estimated
backward channels and the probabilistic knowledge of the estimation error, we
mainly focus on the forward channel estimation and the related training signal
design. We further propose a novel training signal. The design criterion is to
minimize the relaxation of the total mean square error (MSE) of the forward
channel estimators, which is conditioned on the estimated backward channels.
Finally, the numerical results show that the proposed training signal can
improve the MSE performance.
