A probabilistic downlink beamforming approach with multiplicative and additive channel errors

We study an outage constrained beamformer design in the multi-user vector downlink. The transmitter's statistical information about the fading channels is subject to an additive and a multiplicative random channel error. We split the outage probabilities and the optimization into two parts for the two types of channel errors. An inner problem takes the additive channel errors into account, assuming prior information of the multiplicative errors, and is solved in terms of convex conservative approximations. The outer optimization considers the multiplicative channel errors and adjusts the information for the inner problem. For the outer search, we compare an equal design with a locally optimal iterative search.