Robust distributed beamforming for wireless relay networks

In this paper, we consider a robust distributed beamforming design that minimizes total relay transmit power with signal-to-noise ratio (SNR) constraint for a wireless relay network in the presence of imperfect channel state information (CSI) at the relays. We consider a system with a transmit and a receive node, and a set of relay nodes. We assume there is no direct link between the transmit and receive nodes. Each node is equipped with a single antenna. The relay nodes perform amplify-and-forward (AF) relaying. The distributed beamforming design based on the assumption of perfect CSI at the relays fails to guarantee the SNR when the CSI available at the relay nodes is imperfect. We present a robust design which ensures that the SNR constraint is satisfied in the presence of imperfect CSI. We adopt a worst-case design and formulate the problem as a convex optimization problem that can be solved efficiently. The robustness of the proposed design to imperfections in CSI is illustrated through simulations