  In this paper, collaborative use of relays to form a beamforming system and
provide physical-layer security is investigated. In particular,
decode-and-forward (DF) and amplify-and-forward (AF) relay beamforming designs
under total and individual relay power constraints are studied with the goal of
maximizing the secrecy rates when perfect channel state information (CSI) is
available. In the DF scheme, the total power constraint leads to a closed-form
solution, and in this case, the optimal beamforming structure is identified in
the low and high signal-to-noise ratio (SNR) regimes. The beamforming 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. A simplified
and suboptimal technique which reduces the computation complexity under
individual power constraints is also presented. In the AF scheme, not having
analytical solutions for the optimal beamforming design under both total and
individual power constraints, an iterative algorithm is proposed to numerically
obtain the optimal beamforming structure and maximize the secrecy rates.
Finally, robust beamforming designs in the presence of imperfect CSI are
investigated for DF-based relay beamforming, and optimization frameworks are
provided
