This paper investigates cognitive single-group multicast secure beamforming (SGMC-SBF) in multicast scenario where an eavesdropper who acts as a regular user seeks to intercept the multicast service without authorization. This study emphasizes that the transmitter iteratively learns the eavesdropper’s spatial correlation matrix from the accumulated binary feedback on received signal-to-noise-ratio. In each iteration, the transmitter learns the eavesdropper’s spatial correlation matrix based on the historical beamformings and the historical binary feedback information, which is then used to design the optimal beamforming that will be used to learn eavesdropper’s spatial correlation matrix in the next iteration. Without loss of generality, it is assumed that the transmitter knows instantaneous channel state information (CSI) of the legitimate users (LCSI), but not the instantaneous or statistical CSI of the eavesdropper (ECSI). For comparison, we also established the corresponding genie-aided SGMC-SBF with perfect ECSI and two traditional robust schemes with erroneous and statistical ECSI, respectively. The numerical results verify that the proposed cognitive SGMC-SBF are feasible solutions that provide excellent performance.

本文研究了多播场景中的认知单组多播安全波束成形（SGMC-SBF），其中充当普通用户的窃听者试图在未经授权的情况下拦截多播服务。本研究强调发射机从接收到的信噪比的累积二进制反馈中迭代地学习窃听者的空间相关矩阵。在每次迭代中，发射机根据历史波束形成和历史二进制反馈信息学习窃听者的空间相关矩阵，然后用于设计最佳波束形成，用于在下一次迭代中学习窃听者的空间相关矩阵。不失一般性，假设发射机知道合法用户的瞬时信道状态信息（CSI）（LCSI），但不知道窃听者的瞬时或统计 CSI（ECSI）。为了比较，我们还分别建立了具有完美 ECSI 的相应精灵辅助 SGMC-SBF 和两个具有错误和统计 ECSI 的传统鲁棒方案。数值结果验证了所提出的认知 SGMC-SBF 是提供出色性能的可行解决方案。