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Interference control and quality-of-service (QoS) awareness are the major challenges for resource management in orthogonal frequency-division multiple access femtocell networks. This paper investigates a self-organization strategy for physical resource block (PRB) allocation with QoS constraints to avoid the co-channel and co-tiered interference. Femtocell self-organization including self-configuration and self-optimization is proposed to manage the large femtocell networks. We formulate the optimization problem for PRB assignments where multiple QoS classes for different services can be supported, and interference between femtocells can be completely avoided. The proposed formulation pursues the maximization of PRB efficiency. A greedy algorithm is developed to solve the resource allocation formulation. In the simulations, the proposed approach is observed to increase the system throughput by over 13% without femtocell interference. Simulations also demonstrate that the rejection ratios of all QoS classes are low and mostly below 10%. Moreover, the proposed approach improves the PRB efficiency by over 82% in low-loading scenario and 13% in high-loading scenario.