Optimal Design of extended slot allocation for multiuser relay networks

We 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. We 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 we propose an algorithm to search the optimal number of relaying slots. Numerical results are presented to illustrate the optimal slotsharing ratio and the optimal number of relaying slots.