基于统计信道状态信息的多波束卫星系统安全波束成形设计

由于卫星通信的广域覆盖特性和信道的广播特性，使得通信过程存在被窃听的风险。为增强多窃听场景下多波束卫星通信系统的安全性，在已知统计信道状态信息条件下，本文分别针对总发射功率最小化和安全速率最大化问题，提出了相应的波束成形（Beamforming, BF）方案。首先，以安全速率为约束建立总发射功率最小化问题，通过拉格朗日乘子法推导出最优BF权矢量的解析表达式；然后，以安全速率最大化为准则，分别建立了以总发射功率受限和单波束发射功率受限的优化问题。针对总功率约束下的优化问题，根据广义瑞利商方法求出最优BF权矢量的解析表达式；针对单波束发射功率约束下的优化问题，通过引用辅助变量将非凸优化问题转换为凸优化问题，进而提出了一种基于黄金分割法的BF算法计算出最优BF权矢量。最后，通过计算机仿真验证了所提方案的有效性与正确性，并进一步分析了系统参数对安全性能的影响。与传统的BF方案相比，所提BF方案能更好地抑制窃听过程，从而获得更高的安全性能。

Secure Beamforming Design for Multi-beam Satellite Systems Based on Statistical Channel State Information

In order to enhance the security of multi-beam satellite communication system with multiple eavesdroppers, under the condition of available statistical channel state information, this paper focus on the total transmit power minimization and secrecy rate maximization, and propose corresponding beamforming (BF) schemes. Firstly, an optimization problem was formulated to minimize the satellite total transmit power while satisfying the secrecy rate requirement, the analytical expression of optimal BF weight vector was obtained by adopting the Lagrange multiplier method. Then, two optimization problems were established to maximize secrecy rate with the constraint of total transmit power and per-antenna power budget, respectively. For the total transmit power constraint, the analytic expression of optimal BF weight vector was obtained by using generalized Rayleigh quotient method. For the per-antenna power constraint, the non-convex problem was converted into a convex one by introducing auxiliary variable, and further an iterative golden section-based algorithm was proposed to obtain the optimal BF weight vectors. Finally, simulation results confirmed that the effectiveness and validity of the proposed BF schemes, and the effect of the system parameters on the security performance was also analyzed. Compared to the traditional BF schemes, the proposed three BF schemes can obtain better secrecy performance.