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.Index Terms: amplify-and-forward relaying, decode-and-forward relaying, physical-layer security, relay beamforming, robust beamforming, second-order cone programming, secrecy rates, semidefinite programming.The authors are with the secure transmission in the presence of an eavesdropper was first studied from an information-theoretic perspective in [1] where Wyner considered a wiretap channel model. Wyner showed that secure communication is possible without sharing a secret key if the eavesdropper's channel is a degraded version of the main channel, and identified the rate-equivocation region and established the secrecy capacity of the degraded discrete memoryless wiretap channel. The secrecy capacity is defined as the maximum achievable rate from the transmitter to the legitimate receiver, which can be attained while keeping the eavesdropper completely ignorant of the transmitted messages. Later, Wyner's result was extended to the Gaussian channel in [3] and recently to fading channels in [4] and [5]. In addition to the single antenna case, secrecy in multi-antenna models is addressed in [6] and [7]. One particular result in [6] and [7] that is related to our study is that for the MISO secrecy channel, the optimal transmitting strategy is beamforming based on the generalized eigenvector of two matrices that depend on the channel coefficients. Regarding multiuser models, Liu et al.[8] presented inner and outer bounds on secrecy capacity regions for broadcast and interference channels.The secrecy capacity of the multi-antenna broadcast channel is obtained in [9].Having multiple antennas at the transmitter and receiver has multitude of benefits in terms of increas...

No abstract