Mean square error beamforming in SatCom: Uplink-downlink duality with per-feed constraints

Balancing the per-user average mean square errors (MSEs) of a satellite communication (SatCom) system under per-feed limitations - linear transmit power constraints - is the focus of this work. We propose an uplink-downlink duality for this optimization via Lagrangian multiplier theory. Strong duality is proven. Simple fixed point methods are used for the uplink power allocation and the worst-case noise covariance calculation. Simulation results are used to compare the performance for the SatCom channel with that of a standard Gaussian channel model.