Constant modulus beamforming for large-scale MISOME wiretap channel

The multi-input single-output multi-eavesdropper (MISOME) wiretap channel is one of the generic wiretap channels in physical layer security. In Khisti and Wornell's classical work [1], the optimal secure beamformer for MISOME has been derived under the total power constraint. In this work, we revisit the MISOME wiretap channel and focus on the large-scale transmit antenna regime and the constant modulus beamformer design. The former is motivated by the significant spectral efficiency gains provided by massive antennas, and the latter is due to the consideration of cheap hardware implementation of constant modulus beamforming. However, from an optimization point of view, the secrecy beamforming with constant modulus constraints is challenging, more specifically, NP-hard. In light of this, we propose two methods to tackle it, namely the semidefinite relaxation (SDR) method and the ADMM-Dinkelbach method. Simulation results demonstrate that the ADMM-Dinkelbach method outperforms the SDR method, and can attain nearly optimal secrecy performance for the large-scale antenna scenario.