This paper investigates joint secure beamforming design and receive antenna selection problem for large-scale multiple-input-multiple-output (MIMO) wiretap channels. A Branch-And-Bound (BAB) based algorithm is utilized to search the optimal receive antenna subset under both perfect and imperfect channel state information (CSI) scenarios. First, for the perfect CSI scenario, we formulate the secrecy rate optimization problem, and an equivalent monotonically decreasing objective function is established to make the problem suitable for efficient BAB search. In each search, we propose using the weighted mean squared error minimization (WMMSE) method to tackle the optimization problem. Then, we generalize the framework to the imperfect CSI case, and the robust problem is designed to maximize the worst-case secrecy rate, the problem is challenging to solve due to the channel uncertainties. A cutting-set method is devised to solve this non-convex problem by updating the worst-case secrecy rate and channel uncertainties alternately. To reduce the design complexity, we also present an antenna selection based on the alternating optimization (AO) method. The validity of the proposed antenna selection algorithms is evaluated through numerical simulations.

中文翻译：

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大规模 MIMO 窃听信道的联合波束成形设计和接收天线选择


本文研究了大规模多输入多输出（MIMO）窃听信道的联合安全波束成形设计和接收天线选择问题。利用基于分支定界（BAB）的算法在完美和不完美的信道状态信息（CSI）场景下搜索最佳接收天线子集。首先，针对完美的CSI场景，我们制定了保密率优化问题，并建立了等效的单调递减目标函数，使该问题适合高效的BAB搜索。在每次搜索中，我们建议使用加权均方误差最小化（WMMSE）方法来解决优化问题。然后，我们将该框架推广到不完美的 CSI 情况，鲁棒问题旨在最大化最坏情况的保密率，由于信道的不确定性，该问题很难解决。设计了一种割集方法，通过交替更新最坏情况保密率和信道不确定性来解决这个非凸问题。为了降低设计复杂性，我们还提出了一种基于交替优化（AO）方法的天线选择。通过数值模拟评估了所提出的天线选择算法的有效性。