Characterization of the optimum transmitter correlation matrix for MIMO with antenna subset selection

We give a simple and complete characterization of the optimum transmitter correlation matrix for multiple-input-multiple-output (MIMO) systems, when antenna subset selection is used. It is assumed that the receiver feeds back to the transmitter only the selected set of antennas without providing any kind of rank ordering of the selected antennas. It turns out that the optimal correlation matrix in this case must be a convex combination of an identity matrix and a matrix whose elements are all ones. This reduces the problem of finding the actual optimum to a one-dimensional search in any given scenario.