Weighted sum-MSE minimization for the multiuser MIMO relay system

We study a joint optimal design of the receive equalizer and relaying architecture in terms of the weighted sum of mean square errors for the multi-user multiple-input multiple-output (MIMO) relaying system. We show that the optimal relaying architecture depends on the weight factors and that conventional diagonal relaying is a special case of the proposed relaying architecture. Interestingly, for unequal weights, it turns out that the optimal relaying is different from the existing diagonal relaying schemes. By simulation, we show that the proposed joint design improves the weighted sum of mean square error (MSE) over the existing MIMO relaying schemes.