Massive MIMO attains high spectral and power efficiency transmission by leveraging a large number of transmit antennas. However, to capture the benefits of massive MIMO, each antenna should be accompanied with a dedicated RF chain, and consequently, the hardware costs would scale up tremendously with the increase of the antennas. Cheap implementations of massive MIMO have recently gained considerable attention, and constant modulus (CM) signaling is seen as a promising solution, owing to its low peak-to-average power ratio (PAPR). This paper investigates the physical-layer (PHY) security in massive MIMO with an emphasis on the CM signaling. In particular, we consider a transmitter with massive antennas broadcast common confidential information to a group of legitimate receivers, and a number of eavesdroppers overhear the transmission and attempt to intercept the information. Our goal is to design the CM beamforming at the transmitter so that the multicast secrecy rate is maximized. This secrecy rate maximization (SRM) problem is generally NP-hard. To tackle it, two tractable approaches are developed. The first one employs the semidefinite relaxation (SDR) technique and the Charnes-Copper transformation to obtain a convex relaxation of the SRM problem. However, due to the dimension lifting of SDR, this approach is feasible only for small to medium antenna sizes. The second approach leverages the Dinkelbach method to work directly over the beamformer domain; a custom-build nonconvex alternating direction method of multipliers (ADMM) algorithm is proposed to efficiently perform each Dinkelbach update. Simulation results demonstrate that the second approach is computationally more efficient and can achieve nearly optimal performance when the number of antennas is large.

中文翻译：

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组播大规模MIMO窃听通道的恒定模数安全波束形成

大规模MIMO通过利用大量的发射天线来实现高频谱和功率效率传输。但是，为了获得大规模MIMO的优势，每个天线都应配备专用的RF链，因此，硬件成本将随着天线的增加而大大增加。大规模MIMO的廉价实现最近受到了相当大的关注，并且恒定模量（CM）信令由于其峰均功率比（PAPR）低而被视为有前途的解决方案。本文研究了大规模MIMO中的物理层（PHY）安全性，重点是CM信令。特别是，我们考虑一种带有大天线的发射机向一组合法的接收机广播常见的机密信息，大量窃听者偷听了传输信息，并试图截获信息。我们的目标是在发射机处设计CM波束成形，以使多播保密率最大化。保密率最大化（SRM）问题通常是NP-难的。为了解决这个问题，开发了两种易于处理的方法。第一种方法采用半定松弛（SDR）技术和Charnes-Copper变换来获得SRM问题的凸松弛。但是，由于SDR的尺寸提升，这种方法仅适用于中小型天线。第二种方法利用Dinkelbach方法直接在波束成形器域上工作。提出了一种定制的非凸乘数交替方向方法（ADMM）算法，以有效执行每次Dinkelbach更新。