LAUSR

We study the proportionally fair beamforming design for the downlink channel of multibeam satellite systems. Due to the channel phase uncertainty caused by oscillators and the long round trip delay, the beamforming design needs to be robust to the imperfect channel state information (CSI). We formulate an optimization problem with outage probability and per-antenna power constraints to maximize the weighted sum utility of the signal-to-interference-plus-noise (SINR) threshold to realize proportional fairness. The optimization problem is non-convex and we transformed it into the convex form through accurate approximation. We solve the optimization problem via a proposed sub-optimal algorithm. The simulation result shows that the proposed algorithm can converge within 30 iterations when the number of beams is 9. Furthermore, the proposed beamforming scheme obtains a 10% average performance gain in weighted sum utility over the robust max-min schemes in different levels of phase uncertainty.