Robust Secure Beamforming for the Downlink of Multibeam Satellite Communications

This paper investigates the physical layer security (PLS) of a multibeam satellite communication system where the satellite transmits the private signal to a legitimate user (LU) which is intercepted by multiple eavesdroppers (Eves). By considering the imperfect channel state information (CSI) of Eve channels, we formulate the constrained problem to maximize the LU achievable secrecy rate (ASR) subject to secrecy rate outage probability constraint, the total satellite transmit power constraint and the LU rate constraint. Firstly, we adopt golden section method to transform the difficult original problem into a series easier sub-problem. Then, considering the nonconvex of sub-problem, we employ Bernstein inequality and semidefinite programming (SDP) to transform the sub-problem into solvable one. Then, we use standard software package to get the optimal beamforming (BF) weight vector through an iterative penalty-based algorithm. Finally, simulation results confirm the superiority and robustness of the designed BF scheme.