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We consider an ad hoc network consisting of d source-destination pairs and R relaying nodes. Each source wishes to transmit its data to its corresponding destination through the relay network. Each relay in the network transmits a properly scaled version of its received signal thereby cooperating with other relays to deliver each source's data to the corresponding destination. Assuming a minimal cooperation among the relaying nodes, we design a distributed beamformer such that the total relay transmit power dissipated by all relays is minimized while, at the same time, the quality of services at all destinations are guaranteed to be above certain pre-defined thresholds. We show that using a semi-definite relaxation approach, the power minimization problem can be turned into a semi-definite programming (SDP) optimization, and therefore, it can be solved efficiently using interior point methods. Our results show that the distributed relay multiplexing is possible and may be beneficial depending on the channel conditions. Index Terms-Distributed beamforming, relay networks, semidefinite programming, convex feasibility problem, distributed signal processing.

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