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Femtocell networks, consisting of a conventional macro cellular deployment and overlaying femtocells, forming a hierarchical cell structure, constitute an attractive solution to improving the macrocell capacity and coverage. However, the inter- and intra-tier interferences in such systems can significantly reduce the capacity and cause an unacceptably high level of outage. This paper treats the uplink interference problem in orthogonal frequency-division multiple-access (OFDMA)-based femtocell networks with partial cochannel deployment. We first propose an inter-tier interference mitigation strategy without the femtocell users power control by forcing the femto-interfering macrocell users to use only some dedicated subcarriers. The non-interfering macrocell users, on the other hand, can use either the dedicated subcarriers, or the shared subcarriers which are also used by the femtocell users. We then propose subcarrier allocation schemes based on the auction algorithm for macrocell users and femtocell users, respectively, to independently mitigate the intra-tier interference. The proposed interference mitigation scheme for femtocell networks offers significant performance improvement over the existing methods by substantially reducing the inter- and intra-tier inferences in the system.