Encryption Over the Air: Securing Two-Way Untrusted Relaying Systems Through Constellation Overlapping

This paper proposes a novel technique called constellation overlapping to secure two-way untrusted relaying systems. We first consider the symmetric case where two terminal users adopt the same modulation type. For this case, a truncated-channel-inversion-based approach is developed to make the signals from different users experience the same equivalent channel, thereby realizing full constellation overlapping at the relay. Consequently, an error floor is created at the untrusted relay, and data confidentiality is protected. Then, the asymmetric case is investigated, where different modulations are employed at the two users and the constellation overlapping cannot be realized. To address this issue, we develop a constellation virtualization method, which exploits the intrinsic user-cooperation mechanism to “virtualize” two identical constellations at the two users. In this manner, the constellation overlapping effect can still be achieved, without sacrificing much reliability performance. We optimize the truncation threshold to maximize the sum rate for end-to-end information exchange, and design the bit-to-symbol mapping criterion and the signal detection method as well. Unlike the existing physical layer security approaches that guarantee secrecy with additional resource consumptions, this method realizes security enhancement by letting different users mutually encrypt their signals over the air, which is more resource-efficient.