Secrecy capacity of single- and multi-antenna channels with simple helpers

Secrecy can be achieved on the physical layer in fading channels by smart resource allocation and transmit optimization. In this work, simple helper nodes creating artificial noise are applied to improve the secrecy of a point-to-point link. In the single-antenna case, the channel parameters and SNR determine whether a helper can increase the secrecy capacity. We derive a necessary and sufficient condition for optimality of a helper. The single-antenna helper provides only limited support for the single-antenna link. Therefore, we compute the optimal beamforming vectors of the transmitter in closed form for the multiple antenna link under ideal assumption of perfectly informed transmitters. The optimal beamforming vectors of the helpers are characterized and an algorithm is proposed which jointly optimizes transmitter and helper beamformers. It is shown that with increasing number of helpers the secrecy capacity approaches the capacity of the peaceful multiple-antenna link without secrecy constraints. Finally, numerical simulations illustrate the secrecy capacity gain by these simple helpers.