Comments on "Optimizations of a MIMO Relay Network"

In the above paper [1], Behbahani et al. proposed a closed-form solution (in Section III-B-1) for the optimal relay coefficients by minimizing the minimum mean-square error (MMSE) at the destination subject to a global power constraint at the relays. We provide corrections to this closed-form solution and a few comments. In [1], a closed-form solution to problem (14) was given in (21). However, this result is not correct as was mistakenly designated as an eigenvector of (cf. [1, eq. (17)]). In fact, should be assigned to the eigenvector of   . To clarify this fact, let