Multihop Relaying in Millimeter Wave Networks: A Proportionally Fair Cooperative Network Formation Game

Millimeter wave channels suffer from considerable degradation in the channel quality when the signal is Non Line of Sight (NLOS) between the source and the destination. Multihop relaying is thus anticipated to improve the communi- cation between a source and its destination. This is achieved by transmitting the signal to a sequence of relays in which a Line of Sight (LOS) signal exists between two nodes along the path, or more generally when the signal is better than the transmitted signal directly from the source to the destination. In this paper, we consider a millimeter wave network composed of multiple source- destination pairs and a set of deployed relays. We formulate the problem of multihop relaying as a cooperative network formation game in which each relay chooses which source-destination pair to assist in order to improve the end-to-end performance, that is, the multihop delay between the source and the destination. Further, we present an algorithm based on the Nash Bargaining Solution to ensure fairness among the different source-destination pairs and assess its efficiency on numerical simulations.