  We consider a system with a single base station communicating with multiple
users over orthogonal channels while being assisted by multiple relays. Several
recent works have suggested that, in such a scenario, selection, i.e., a single
relay helping the source, is the best relaying option in terms of the resulting
complexity and overhead. However, in a multiuser setting, optimal relay
assignment is a combinatorial problem. In this paper, we formulate a related
convex optimization problem that provides an extremely tight upper bound on
performance and show that selection is, almost always, inherent in the
solution. We also provide a heuristic to find a close-to-optimal relay
assignment and power allocation across users supported by a single relay.
Simulation results using realistic channel models demonstrate the efficacy of
the proposed schemes, but also raise the question as to whether the gains from
relaying are worth the additional costs.
