Near-Optimal Modulo-and-Forward Scheme for the Untrusted Relay Channel

This paper studies an untrusted relay channel, in which the destination sends artificial noise simultaneously with the source sending a message to the relay, in order to protect the source's confidential message. The traditional amplify-and-forward (AF) scheme shows poor performance in this situation because of the interference power dilemma. Providing better security by using stronger artificial noise will consume more power of the relay, impairing the confidential message's transmission. To solve this problem, this paper proposes a modulo-and-forward (MF) operation at the relay with nested lattice encoding at the source. For the proposed MF scheme with full channel state information at the transmitter (CSIT), theoretical analysis shows that the MF scheme approaches the secrecy capacity within 1/2 bit for all channel realizations, and, hence, achieves full generalized security degrees of freedom (G-SDoF). In contrast, the AF scheme can only achieve a small fraction of the G-SDoF. For the MF scheme without CSIT, the total outage event, defined as either connection outage or secrecy outage, is introduced. Based on this total outage definition, analysis shows that the proposed MF scheme achieves the full generalized secure diversity gain (G-SDG) of order one. On the other hand, the AF scheme can achieve a G-SDG of only 1/2 at most.