Comments on “Cutset Bounds on the Capacity of MIMO Relay Channels”

We comment on the paper “Cutset Bounds on the Capacity of MIMO Relay Channels” by Jeong
et al.
and point out that, unlike what appears from a remark and some other contents by these authors, the matrix distribution for the sum of two complex random Wishart matrices has already been derived by Kumar for the general case of arbitrary covariance matrices and not only for the special case when one of them is assumed proportional to the identity matrix. The latter assumption has been made only for deriving the corresponding eigenvalue distribution. Furthermore, we draw attention to the result that when all covariance matrices are chosen proportional to the identity matrix, then it is possible to obtain exact and closed form expressions for the sum of an arbitrary number of Wishart matrices and not only for two as considered by Jeong
et al.