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This paper studies an untrusted relay channel, in which the destination sendsartificial noise simultaneously with the source sending a message to the relay,in order to protect the source's confidential message. The traditionalamplify-and-forward (AF) scheme shows poor performance in this situationbecause of the interference power dilemma: providing better security by usingstronger artificial noise will decrease the confidential message power from therelay to the destination. To solve this problem, a modulo-and-forward (MF)operation at the relay with nested lattice encoding at the source is proposed.For this system with full channel state information at the transmitter (CSIT),theoretical analysis shows that the proposed MF scheme approaches the secrecycapacity within 1/2 bit for any channel realization, and hence achieves fullgeneralized security degrees of freedom (G-SDoF). In contrast, the AF schemecan only achieve a small fraction of the G-SDoF. For this system without anyCSIT, the total outage event, defined as either connection outage or secrecyoutage, is introduced. Based on this total outage definition, analysis showsthat the proposed MF scheme achieves the full generalized secure diversity gain(G-SDG) of order one. On the other hand, the AF scheme can only achieve a G-SDGof 1/2 at most.

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