Network Formation Games Among Relay Stations in Next Generation Wireless   Networks
  The introduction of relay station (RS) nodes is a key feature in next generation wireless networks such as 3GPP's long term evolution advanced (LTE-Advanced), or the forthcoming IEEE 802.16j WiMAX standard. This paper presents, using game theory, a novel approach for the formation of the tree architecture that connects the RSs and their serving base station in the \emph{uplink} of the next generation wireless multi-hop systems. Unlike existing literature which mainly focused on performance analysis, we propose a distributed algorithm for studying the \emph{structure} and \emph{dynamics} of the network. We formulate a network formation game among the RSs whereby each RS aims to maximize a cross-layer utility function that takes into account the benefit from cooperative transmission, in terms of reduced bit error rate, and the costs in terms of the delay due to multi-hop transmission. For forming the tree structure, a distributed myopic algorithm is devised. Using the proposed algorithm, each RS can individually select the path that connects it to the BS through other RSs while optimizing its utility. We show the convergence of the algorithm into a Nash tree network, and we study how the RSs can adapt the network's topology to environmental changes such as mobility or the deployment of new mobile stations. Simulation results show that the proposed algorithm presents significant gains in terms of average utility per mobile station which is at least 17.1% better relatively to the case with no RSs and reaches up to 40.3% improvement compared to a nearest neighbor algorithm (for a network with 10 RSs). The results also show that the average number of hops does not exceed 3 even for a network with up to 25 RSs. 
Walid Saad, Zhu Han, Tamer Ba\c{s}ar, M\'erouane Debbah, and Are   Hj{\o}rungnes
cs.IT math.IT