https://hal.inria.fr/hal-00766295Chattopadhyay, ArpanArpanChattopadhyayECE - Department of Electrical Communication Engineering [Bangalore] - Indian Institute of ScienceSinha, AbhishekAbhishekSinhaECE - Department of Electrical Communication Engineering [Bangalore] - Indian Institute of ScienceCoupechoux, MarceauMarceauCoupechouxLTCI - Laboratoire Traitement et Communication de l'Information - Télécom ParisTech - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche ScientifiqueKumar, AnuragAnuragKumarECE - Department of Electrical Communication Engineering [Bangalore] - Indian Institute of ScienceOptimal Capacity Relay Node Placement in a Multi-hop Network on a LineHAL CCSD2012[INFO.INFO-MC] Computer Science [cs]/Mobile Computing[INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2012-12-18 09:48:152020-10-15 15:46:062012-12-18 15:44:15enConference papersapplication/pdf1We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node. The achievable rate formulas that we utilize are for full-duplex radios at the relays and decodeand- forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that a constant rate independent of the attenuation in the network can be achieved by placing a large enough number of relay nodes uniformly between the source and the destination, under the exponential path-loss model with total power constraint.