Constant Modulus Secure Beamforming for Multicast Massive MIMO Wiretap Channels

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.