Analysis of secure communications for a DF and RF relaying SIMO system with Gauss errors

This paper investigates a cooperative system for the typical four-node (source, relay, destination, and eavesdropper) scenario in physical-layer security. In the cooperative system, the source transmits its message to the destination via the relay, which adopts decode-and-forward (DF) and randomize-and-forward (RF) schemes to forward the information from the source to the destination, respectively. However, the eavesdropper wants to overhear the information of the source-relay link and the relay-destination link over the two hops. We consider single-input, multiple-output (SIMO) wiretap channels, where the source and the relay are equipped with a single antenna and the destination and eavesdropper are equipped with M and N antennas, and adopt a maximal ratio combining to deal with multipath signals. Considering Gauss channel estimation errors, we first derive the closed-form expressions for the probability density function and cumulative distribution function of the received signal-to-noise ratio at the destination and the eavesdropper, respectively, under the DF scheme; then, the closed-form expressions for the probability of non-zero secrecy capacity are derived under the DF and RF schemes, respectively. Finally, the accuracy of our proposed expressions is verified by simulation results.