  In this paper, collaborative use of relays to form a beamforming system with
the aid of perfect channel state information (CSI) and to provide
physical-layer security is investigated. In particular, a
decode-and-forward-based relay beamforming design subject to total and
individual relay power constraints is studied with the goal of maximizing the
secrecy rate. It is shown that the total power constraint leads to a
closed-form solution. The design under individual relay power constraints is
formulated as an optimization problem which is shown to be easily solved using
two different approaches, namely semidefinite programming and second-order cone
programming. Furthermore, a simplified and suboptimal technique which reduces
the computation complexity under individual power constraints is presented.
