Outage secrecy rate in wireless relay channels using cooperative jamming

A wireless relay channel is considered, consisting of a multi-antenna source, a single-antenna destination, a single-antenna eavesdropper and a set of multi-antenna relays (helpers) that act as jammers to the eavesdropper. Each helper knows only its own link to the receiver and independently transmits jamming noise, lying in the null space of its own link to the destination, thus causes no interference to the destination. The source, knowing the main channel explicitly and having statistical information on the eavesdropper channel, designs the input covariance matrix so that the secrecy rate is maximized subject to an outage probability constraint and a sum power constraint. We show that the optimal input covariance matrix has rank one. Assuming that the eavesdropper channels follow a zero-mean Gaussian distribution with known covariance, the outage probability and outage secrecy rate are derived in closed form. Simulation results in support of the analysis are provided.