A combinatorial approach to maximizing the sum rate in the MIMO BC with linear precoding

We investigate the sum rate maximization in the MIMO broadcast channel when linear filtering is applied. Our particular interest lies in usually not considered system configurations where the base station is equipped with less antennas than the user terminals have in sum. For such scenarios, conventional block-diagonalization or zero-forcing techniques cannot be applied and even asymptotic results on the sum rate do not seem to exist. We show that the nonconvex problem at hand is closely related to a combinatorial stream selection and that choosing the number of active streams too high reduces the multiplexing gain and can even lead to a saturation of the sum rate, i.e., a multiplexing gain of zero. Besides the full featured reference algorithm probing all feasible stream allocation combinations, a reduced complexity successive version is presented as well. Both variants are based on the projected gradient algorithm.