Secrecy rate study in two-hop relay channel with finite constellations

Two-hop security communication with an eavesdropper in wireless environment is a hot research direction. The basic idea is that the destination, simultaneously with the source, sends a jamming signal to interfere the eavesdropper near to or co-located with the relay. Similar as physical layer network coding, the friendly jamming signal will prevent the eavesdropper from detecting the useful information originated from the source and will not affect the destination on detecting the source information with the presence of the known jamming signal. However, existing investigations are confined to Gaussian distributed signals, which are seldom used in real systems. When finite constellation signals are applied, the behavior of the secrecy rate becomes very different. For example, the secrecy rate depends on phase difference between the input signals with finite constellations, which is not observed with Gaussian signals. In this paper, we investigate the secrecy capacity and derive its upper bound for the two-hop relay model, by assuming an eavesdropper near the relay and the widely used M-PSK modulation. With our upper bound, the best and worst phase differences in high SNR region are then given. Numerical studies verify our analysis and show that the derived upper bound is relatively tight.