  Social awareness and social ties are becoming increasingly popular with
emerging mobile and handheld devices. Social trust degree describing the
strength of the social ties has drawn lots of research interests in many fields
in wireless communications, such as resource sharing, cooperative communication
and so on. In this paper, we propose a hybrid cooperative beamforming and
jamming scheme to secure communication based on the social trust degree under a
stochastic geometry framework. The friendly nodes are categorized into relays
and jammers according to their locations and social trust degrees with the
source node. We aim to analyze the involved connection outage probability (COP)
and secrecy outage probability (SOP) of the performance in the networks. To
achieve this target, we propose a double Gamma ratio (DGR) approach through
Gamma approximation. Based on this, the COP and SOP are tractably obtained in
closed-form. We further consider the SOP in the presence of Poisson Point
Process (PPP) distributed eavesdroppers and derive an upper bound. The
simulation results verify our theoretical findings, and validate that the
social trust degree has dramatic influences on the security performance in the
networks.
