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The authors consider a wireless sensor network where a relay helps multiple source-destination pairs. The relay helps communication pairs in a probabilistic manner during several relaying slots. They formulate an optimization problem to find slot-sharing ratio maximizing an upper bound of the expected sum rate while the upper bound of each user's rate satisfying a predetermined target for the given number of relaying slots. An exact optimal value of slot-sharing ratio is provided by using Karush-Kuhn-Tucker (KKT) conditions. And they propose an algorithm to search the optimal number of relaying slots. Numerical results are presented to illustrate the optimal slot-sharing ratio and the optimal number of relaying slots.
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