proposed algorithms have low computational complexity, and are shown to outperform the heuristic scheme with considerable gains.

System Model and Problem Statement \[sec:mod3\]
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### System Model

Consider a femtocell network with an MBS (indexed $0$) and $M$ FBS’s (indexed from $1$ to $M$) deployed in the area. The $M$ FBS’s are connected to the MBS and the Internet via broadband wireline connections. Furthermore, we assume a spectrum band that is divided into two parts, one is allocated to the MBS with bandwidth $B_0$ and the other is allocated to the $M$ FBS’s. The bandwidth allocated to FBS $m$ is denoted by $B_m$. When there is no overlap between the coverages of two FBS’s, they can spatially reuse the same spectrum. Otherwise, the MBS allocates disjoint spectrum to the FBS’s with overlapping coverages. We assumed the spectrum allocation is known a priori.

There are $K$ mobile users in the femtocell network. Each user is equipped with one transceiver that can be tuned to one of the two available channels, i.e., connecting to a nearby FBS or to the MBS. The network is time slotted. We assume block-fading channels, where the channel condition is constant in each time slot [@Goldsmith06]. We 