Theoretical Analysis of Selective Relaying, Cooperative Multi-Hop Networks with Fairness Constraints

We consider the problem of selective relaying in multi-hop networks. At each slot, a relay and a node along the optimal non-cooperative path are opportunistically selected to transmit to the next-hop node in a cooperative manner. Being a promising scheme for fair resource allocation, the proportional fair scheduling (PFS) algorithm provides excellent balance between throughput and fairness via multi-user diversity and game-theoretic equilibrium. To maximize the overall utility along a cooperative multi-hop path, we apply the proportional fair (PF) criterion in selecting nodes and relays for cooperative transmission. Furthermore, we analyze and provide an analytical expression for end-to-end throughput of an opportunistic relaying, cooperative multi-hop path with proportional fairness constraints over a Rayleigh flat-fading channel. To our knowledge, it is the first time that a closed-form expression is obtained for the throughput of a proportional fair relaying, cooperative multi-hop path. This research is an extension of previous theoretical work on PF for cellular networks.