Design of beamforming in the satellite downlink with static and mobile users

We consider the downlink (DL) of a satellite communication system with single-antenna mobile receivers and static users that is modeled as a vector broadcast channel (BC). While for static users perfect channel state information (CSI) is available, only the rank-one covariance matrices of the channels to mobile users are known. In this scenario, we design beamforming techniques that are able to deal with full CSI users and statistical CSI users at the same time. In this paper, we employ zero-forcing (ZF) techniques with regard to the mobile users´ channels. Under this assumption, a duality w.r.t. the signal-to-interference-and-noise-ratio (SINR) between the vector BC and an appropriately constructed vector multiple-access channel (MAC) is established. Based on the observation that an interference function can be defined in the dual vector MAC that is standard, an iterative solution for the quality-of-service (QoS) power minimization and the rate balancing problem is found.