Cognitive satellite-terrestrial networks (CSTNs) haveudbeen recognized as a promising network architecture for addressingudspectrum scarcity problem in next-generation communicationudnetworks. In this paper, we investigate the secure transmission forudCSTNs where the terrestrial base station (BS) serving as a greenudinterference resource is introduced to enhance the security of theudsatellite link. Adopting a stochastic model for the channel stateudinformation (CSI) uncertainty, we propose a secure and robustudbeamforming framework to minimize the transmit power, whileudsatisfying a range of outage (probabilistic) constraints concerningudthe signal-to-interference-plus-noise ratio (SINR) recorded at theudsatellite user and the terrestrial user, the leakage-SINR recorded atudthe eavesdropper, as well as the interference power recorded at theudsatellite user. The resulting robust optimization problem is highlyudintractable and the key observation is that the highly intractableudprobability constraints can be equivalently reformulated as theuddeterministic versions with Gaussian statistics. In this regard, weuddevelop two robust reformulation methods, namely S-Procedureudand Bernstein-type inequality restriction techniques, to obtain audsafe approximate solution. In the meantime, the computationaludcomplexities of the proposed schemes are analyzed. Finally, the effectivenessudof the proposed schemes are demonstrated by numericaludresults with different system parameters.
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