Cooperative Secure Transmission for Satellite Downlink: A Pas de Deux between Beam Pointings

In this letter, we propose a symbol-level spatial cooperative transmission scheme for secure communication in satellite downlink. Two beams are firstly superimposed around the target user to achieve transparent communication within a small intersection region while synthesizing the randomized signals elsewhere, using elaborately designed time-varying symbol mappings. On this basis, we observe that the random drifts of the beam pointings significantly influence the signals and the energy emitted in the undesired regions. Therefore, we propose a Pas de Deux between two cooperative beams, which can further enhance the system security by introducing symbol-level alterable beam pointings. A joint optimization problem for the symbol mappings, beam pointings and array partitioning is then proposed using spatially averaged secure capacity as the information-theoretic evaluation metric, aiming at shrinking the transparent communication region and minimizing the sidelobe leakage, simultaneously. To solve the non-trivial multi-objective optimization problem, a self-adaptive Armijo stepsize algorithm is developed to balance multiple coupled objectives and find an effective solution within high-dimensional space with convergence guarantee. The gain in mitigating sidelobe information leakage is also theoretically proved by analyzing the degradation of the effective signal-to-noise ratio at the eavesdropper. Simulations show that the proposed scheme can shrink the insecure region by 67.14% and reduce sidelobe information leakage by 18.19% compared with existing multi-beam cooperative schemes.