Chance constrained and ergodic robust QoS power minimization in the satellite downlink

We focus on the linear beamformer design based on quality-of-service (QoS) power minimization in the satellite downlink with perfect and statistical channel state information (CSI) users. Contrary to the usual rate requirements for the perfect CSI users, we consider either ergodic or outage constrained rate requirements for the statistical CSI users. Modeling the fading channels as zero-mean Gaussian vectors with rank-one covariance matrices, tractable ergodic mutual information and outage probability expressions are obtained. While the resulting outage constrained rate requirements can directly be reformulated to equivalent signal-to-interference-and-noise-ratios (SINRs) this is not possible for the ergodic rate constraints. However, representing the necessary useful signal power of each user as a function of the experienced interference and linearizing this interference function, the usual SINR representation is obtained. Based on this observation, a sequential approximation strategy is proposed that solves a QoS power minimization with standard SINR constraints in each iteration. In the numerical results section, the convergence properties and the achieved performance of this sequential QoS optimization are discussed.