This paper discusses the resource allocation problem in an uplink multi-cell OFDMA system. The classical LTE model considers two areas in the cell: the cell center and the cell border and divides the resources in four sets. The users in the cells center zones use the same subset of subcarriers whereas the users of the border zones use the remaining resources with a Fractional Frequency Reuse (FFR) equal to 3. Considering the same cell zones, we present in this work a different FFR model and prove with a theoretical analysis that the system throughput can be improved. The resource allocation is then performed considering the Weighted Proportional Fair (WPF) algorithm. Simulation results illustrate the performance improvements of the proposed solution in comparison to the classical model. The fairness for the different models is also studied and compared.