Equalization-Based Beamforming for Secure Multicasting in Multicast Wiretap Channels

In this paper, a beamforming scheme is proposed to maximize a secrecy multicast rate (SMR) in the multicast wiretap channel, in which the multiple unauthorized users overhear the multicast messages. The SMR is formulated by the ratio of multicast rate and information leakage in the numerator and denominator, respectively. By exploiting the SMR structure, we propose three doubly equalizing beamforming approaches: i) zero-forcing algorithm, ii) bottom-first algorithm, and iii) top-first algorithm. Depending on the algorithms, either the legitimate user channels or the unauthorized user channels are fully equalized, and the other set of channels are then equalized through a least-squares approach. While the zero-forcing algorithm optimizes the strength of legitimate user channels, the bottom-first and the top-first algorithms find the balance between the strengths of legitimate user channels and unauthorized user channels. The top-first algorithm encompasses the bottom-first algorithm, where the bottom-first algorithm encompasses the zero-forcing algorithm. Consequently, the proposed top-first algorithm outperforms the other two algorithms. The proposed top-first algorithm improves SMR by effectively preventing overhearing while sustaining almost maximum multicast rate and provide comparable SMR to the multicast rate obtained without unauthorized users. These results are verified by simulation.