  In hybrid satellite-terrestrial networks (HSTNs), spectrum sharing is crucial
to alleviate the "spectrum scarcity" problem. Therein, the transmit beams
should be carefully designed to mitigate the inter-satellite-terrestrial
interference. Different from previous studies, this work considers the impact
of both nonlinear power amplifier (PA) and large-scale channel state
information at the transmitter (CSIT) on beamforming. These phenomena are
usually inevitable in a practical HSTN. Based on the Saleh model of PA
nonlinearity and the large-scale multi-beam satellite channel parameters, we
formulate a beamforming optimization problem to maximize the achievable rate of
the satellite system while ensuring that the inter-satellite-terrestrial
interference is below a given threshold. The optimal amplitude and phase of
desired beams are derived in a decoupled manner. Simulation results demonstrate
the superiority of the proposed beamforming scheme.
