In this paper, we address the problem of subchannel, rate and power allocation in OFDM-based two-tier femtocell networks, which comprise a conventional macrocell and multiple femtocells. Our objective is maximizing the multiple femtocell users' weighted rate sum by jointly adjusting their subchannel, rate and power allocation, under the constraints of cross-tier interference (CTI) between macrocell and multiple femtocells. Then we propose an optimal distributed resource allocation algorithm based on Lagrangian dual method, and interpret it from economics angle. In order to illustrate the benefit of allowing femtocells to share the subchannels occupied by macrocell, we compare our system with another one (macrocell guard system), in which the femtocells can only use the subchannels unoccupied by macrocell. Simulation results validate the proposed algorithm, and show that our system can obtain better performance than the macrocell guard system.
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