In this paper, beam-domain (BD) anti-jamming transmission in a downlink massive multiple-input multiple-output (MIMO) system is investigated. A smart jammer with multiple antennas attempts to interfere with the signal reception of users with the desired energy efficiency (EE), whereas a base station (BS) tries to minimize the transmission cost while ensuring uninterrupted communication. A Bayesian Stackelberg game between the BS and jammer, where the jammer is the follower and the BS acts as the leader, is modeled. In the follower subgame, the optimal jamming precoding with a closed-form power solution is introduced. The optimal jamming power is proportional to the transmission power in the downlink, and thus, for the BS, the strategy of suppressing malicious attacks by increasing the transmission power fails. In the leader subgame, generalized zero-forcing (ZF), whose closed-form power solution constitutes the unique Stackelberg equilibrium (SE) with that of the jammer, is found to be the optimal anti-jamming precoding for robust transmission. The results show that there always exists a precoding solution for the BS that ensures reliable transmission when the SE is obtained. A proper increase in the minimum signal-to-interference-and-noise ratio (SINR) threshold or the BD channel approximation error helps the BS save power during the resistance against the jammer. Then, a simplified power solution without the instantaneous channel state information (CSI) of jamming channels is further introduced for practical implementation. Numerical results are provided to verify the proposed solutions.

中文翻译：

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下行大规模 MIMO 系统的波束域抗干扰传输：Stackelberg 博弈视角


本文研究了下行链路大规模多输入多输出（MIMO）系统中的波束域（BD）抗干扰传输。具有多个天线的智能干扰器试图以所需的能量效率（EE）干扰用户的信号接收，而基站（BS）则试图在确保通信不间断的同时最大限度地降低传输成本。对 BS 和干扰机之间的贝叶斯 Stackelberg 博弈进行了建模，其中干扰机是跟随者，BS 是领导者。在跟随子博弈中，引入了具有封闭形式功率解的最佳干扰预编码。最佳干扰功率与下行发射功率成正比，因此对于基站来说，通过提高发射功率来抑制恶意攻击的策略是失败的。在领导者子博弈中，广义迫零（ZF）的封闭式功率解与干扰机的功率解构成了独特的斯塔克尔伯格平衡（SE），被发现是鲁棒传输的最佳抗干扰预编码。结果表明，在获得SE时，基站始终存在保证可靠传输的预编码方案。适当提高最小信号干扰噪声比（SINR）阈值或BD信道近似误差有助于基站在抗干扰期间节省功率。然后，进一步引入了一种无需干扰信道的瞬时信道状态信息（CSI）的简化功率解决方案以供实际实施。提供数值结果来验证所提出的解决方案。