Capacity of the isotropic fading multiple antenna downlink with magnitude feedback

We determine the capacity region of a single-cell isotropic fading multiple antenna downlink with perfect channel knowledge at the mobiles and only the knowledge of the magnitudes of the users´ channel vectors at the base station. Using a scalar upperbound, we are able to prove the optimality of Gaussian codebooks on this vector broadcast channel. Numerical results are provided to compare magnitude feedback against opportunistic beamforming and antenna selection.