Distributed beamforming designs to improve physical layer security in wireless relay networks

This paper investigates security-oriented beamforming designs in a relay network composed of a source-destination pair, multiple relays, and a passive eavesdropper. Unlike most of the earlier works, we assume that only statistical information of the relay-eavesdropper channels is known to the relays. We propose beamforming solutions for amplify-and-forward (AF) and decode-and-forward (DF) relay networks to improve secrecy capacity. In an AF network, the beamforming design is obtained by approximating a product of two correlated Rayleigh quotients to a single Rayleigh quotient using the Taylor series expansion. Our study reveals that in an AF network, the secrecy capacity does not always grow as the eavesdropper moves away from the relays or as total relay transmit power increases. Moreover, if the destination is nearer to the relays than the eavesdropper is, a suboptimal power is derived in closed form through monotonicity analysis of secrecy capacity. While in a DF network, secrecy capacity is a single Rayleigh quotient problem which can be easily solved. We also found that if the relay-eavesdropper distances are about the same, it is unnecessary to consider the eavesdropper in a DF network. Numerical results show that for either AF or DF relaying protocol, the proposed beamforming scheme provides higher secrecy capacity than traditional approaches.