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The authors consider a wireless communication scenario with K source-destination pairs communicating through several half-duplex relays that amplify the signals received from the sources and forward them to the destination nodes. They jointly design the relay beamforming matrices by minimizing the total power transmitted from the relays subject to a constraint on the received Signal to Interference-plus-Noise Ratio (SINR) at each destination node. Due to the non-convexity of this problem, several approximations have been used in the literature to find a computationally efficient solution. They propose a novel solution technique in which the problem is formulated as a group of Second-Order Cone Programs (SOCPs) parameterized by K real parameters.
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