Abstract—We consider the problem of relay-assisted transmission for cellular networks. In the considered system, a source node together with relay nodes are selected in a proportionally fair (PF) manner to transmit to the base station (BS), which uses the maximal ratio combining (MRC) to combine the signals received from the source node in the first half slot and the relay nodes in the second half slot for successful reception. The proposed algorithm incorporates the PF criterion and cooperative diversity, and is called proportionally fair cooperation (PFC). Compared with the proportional fair scheduling (PFS) algorithm, PFC provides improved efficiency and fairness. The ordinary differential equation (ODE) analysis used to study PFS cannot be used for PFC; otherwise, one has to solve a large number of nonlinear and interrelated ODE equations which is time prohibited. In this paper, we present a mathematical framework for the performance of PFC. The cornerstone of our framework is a realistic yet simple model that captures node cooperation, fading, and fair resource allocation-induced dependencies. We obtain analytical expressions for the throughput gain of PFC over traditional PFS without node cooperation. Compared with the highly time-consuming ordinary differential equation analysis, our formulae are intuitive yet easy to evaluate numerically. To our knowledge, it is the first time that a closed-form expression is obtained for the throughput of relay-assisted transmission in a cellular network with the PF constraint.
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