Artificial noise (AN) transmission is a physical layer security technique in multi-antenna wireless communication systems. Synthetic noise is broadcast to all receivers except designated legitimate users via beamforming in the legitimate users' null space. We consider AN transmission employing a single RF chain and analog beamforming, where beamforming vectors maintain constant magnitude while allowing arbitrary phases. Our primary objective is to design a constant-magnitude vector capable of nullifying multiple users' channel vectors simultaneously. To tackle this zero-forcing problem, we propose a novel successive partition zero-forcing (SPZF) scheme, which transforms the multi-user zero-forcing task into optimizing channel partitioning to minimize outage probability. The SPZF scheme can be generalized to any number of users, but our analysis focuses on the two-user case. Theoretical analysis reveals that our proposed SPZF scheme can attain arbitrarily low outage probability in the limit of large number of transmit antenna. We present three partition algorithms (random, iterative, and genetic) to minimize the outage probability. The outage probabilities and secrecy rates of the three partition algorithms are compared via numerical simulations. We find that the more advanced partition algorithms (iterative and genetic) achieve higher secrecy rates than the random algorithm, particularly under conditions of high signal-to-noise ratio (SNR), large number of eavesdroppers, or small number of transmit antennas.

翻译：人工噪声传输是多天线无线通信系统中的一种物理层安全技术。通过在合法用户的零空间进行波束成形，将合成噪声广播给除指定合法用户外的所有接收者。我们考虑采用单射频链和模拟波束成形的人工噪声传输，其中波束成形向量保持恒定幅度，同时允许任意相位。我们的主要目标是设计一个能够同时抵消多个用户信道向量的恒定幅度向量。为解决这一迫零问题，我们提出了一种新颖的连续分区迫零方案，该方案将多用户迫零任务转化为优化信道分区以最小化中断概率。SPZF方案可推广至任意数量的用户，但我们的分析集中于两用户场景。理论分析表明，在发射天线数量趋于无穷大的极限情况下，我们提出的SPZF方案能够实现任意低的中断概率。我们提出了三种分区算法（随机、迭代和遗传）以最小化中断概率。通过数值仿真比较了三种分区算法的中断概率和保密速率。我们发现，更先进的分区算法（迭代和遗传）相比随机算法实现了更高的保密速率，特别是在高信噪比、窃听者数量多或发射天线数量少的条件下。