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The authors focus on the design of linear beamforming based on Quality-of-Service (QoS) power minimization and rate balancing in the DownLink (DL) of a satellite communication system with mobile and static users. Since only the rank-one covariance matrices of the channels to mobile users are known, they introduce average rate requirements for these users contrary to the perfect Channel State Information (CSI) rate requirements for the static users. Due to the structure of the ergodic rates, they cannot directly resort to the optimization techniques for the purely complete CSI vector Broadcast Channel (BC).
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