Secrecy Rates and Optimal Power Allocation for Full-Duplex Decode-and-Forward Relay Wire-Tap Channels

This paper investigates the secrecy rates and optimal power allocation schemes for a decode-and-forward wiretap relay channel where the transmission from a source to a destination is aided by a relay operating in a full-duplex (FD) mode under practical residual self-interference. By first considering static channels, we address the non-convex optimal power allocation problems between the source and relay nodes under individual and joint power constraints to establish closed-form solutions. An asymptotic analysis is then given to provide important insights on the derived power allocation solutions. Specifically, by using the method of dominant balance, it is demonstrated that full power at the relay is only optimal when the power at relay is sufficiently smaller when compared with that of the source. When the power at the relay is larger than the power at the source, the power consumed at the relay saturates to a constant for an effective control of self-interference. The analysis is also helpful to demonstrate that the secrecy capacity of the FD system is twice as much as that of the half-duplex system. The extension to fast fading channels with channel state information being available at the receivers but not the transmitters is also studied. To this end, we first establish a closed-form expression of the ergodic secrecy rate using simple exponential integrals for a given power allocation scheme. The results also show that with optimal power allocation schemes, FD can significantly improve the secrecy rate in fast fading environments.