Capacity Scaling and Diversity Order for Secure Cooperative Relaying With Untrustworthy Relays

This paper presents an investigation of the secrecy performance of amplify-and-forward (AF) distributed beamforming (DBF) and opportunistic relaying (OR) through K untrustworthy relays. The capacity scaling and achievable diversity order of a secure communication are derived for K -> infinity and in high signal-to-noise-ratio (SNR) regimes, respectively. The DBF is shown to convey confidential messages with a capacity scaling of 1/2 logK regardless of the trustworthiness of the relays, even without intended jamming (IJ), where 1/2 logK corresponds to the maximal capacity scaling of cooperative relaying in non-eavesdropping environments. However, using multiple untrustworthy relays worsens the secrecy performance of the OR, and as K increases, the secrecy capacity converges to zero. When secrecy outage performance with IJ is considered, the achievable diversity order for both the DBF and OR is limited to one. However, only the DBF exploits the benefits using multiple untrustworthy relays, and its secrecy outage probability decreases exponentially as K increases.