  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.
