The optimal relay selection problem in multiuser cooperative wireless networks is considered in this paper. A general discrete time model for such networks is introduced which takes into account the dynamic variations of the channel state as well as stochastic arrival of data packets into the system. The model consists of a set of mobile users, one destination node and R relay nodes which may be either mobile or fixed. The system uses the benefit of cooperative diversity by relaying in decode and forward or amplify and forward mode. We assume that each user either transmits its packets directly to the destination or selects a relay node to cooperatively transmit its packets. It is not however trivial whether a user at each time slot has to cooperate with any relay node or not and if so, which relay node should be selected for cooperation. We will propose a throughput optimal relay selection policy that can stabilize the system for all the arrival rate vectors strictly inside the stability region. Then, we show that the optimal policy is equivalent to finding the maximum weighted matching in a weighted bipartite graph at each time slot. We also use simulations to compare the performance of the throughput optimal relay selection strategy with an instantaneous throughput optimal policy as well as a non-cooperative policy in terms of average queue occupancy (or equivalently, queueing delay).
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