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A high‐rate beamforming design is reported for amplify‐and‐forward wireless relay networks with simultaneous information and power transfer. To achieve high sum rate, a new relay beamformer is designed to support multi‐pair source–destination communication links as well as an energy receiver simultaneously, instead of serving one information transmitter at a time. An energy‐harvesting constrained sum‐rate maximisation problem for this design is formulated, then relaxed and reformulated into a series of convex problems, which can be iteratively solved in polynomial time, eventually leading to a high‐rate beamforming solution. Simulation results confirm the performance gain and fast convergence of the developed beamforming design. [ABSTRACT FROM AUTHOR]