Ergodic robust rate balancing for rank-one vector broadcast channels via sequential approximations

We focus on a linear beamformer design in the downlink with statistical channel state information (CSI) at the transmitter, where the users' ergodic rates are balanced. Simplifying the fading channels to given vectors with random scalar factors, which is a good approximation for rural mobile or satellite communications (SatCom), the stochastic model mismatch is kept small albeit the ergodic rate structure now allows for adapting the perfect CSI balancing algorithms. Although there is no equivalent signal-to-interference-and-noise-ratio (SINR) reformulation for the ergodic constraints, tight inner approximations with SINR structure are found. Based on this observation, a locally optimal sequential approximation strategy is proposed and a fixed point based implementation is provided that requires only few iterations.