to the MBS or an FBS. The second property is because each user can connect to only one BS. The user subsets connecting to different BS’s do not overlap. Therefore, $\mathcal{U}_l^m$’s is a [*partition*]{} of $\mathcal{U}_l$ with respect to $m$.

In addition, we define $\mathcal{S}_l^m$ as the set of possible users that are [*covered*]{} by BS $m$ and request the level $l$ packet. These sets have the following properties. $$\label{eq:SetProp2}
\left\{ \begin{array}{l}
\bigcup_{m=1}^M \mathcal{S}_l^m = \mathcal{S}_l^0=\mathcal{U}_l  \nonumber \\
\mathcal{S}_l^m \bigcap \mathcal{S}_l^0 = \mathcal{S}_l^m, \; \mbox{ for all } m \neq 0 \nonumber \\
\mathcal{S}_l^m \bigcap \mathcal{S}_l^{m'} = \emptyset, \; \mbox{ for all } m' \neq m \mbox{ and } m, m'\neq 0. \nonumber
        \end{array} \right.$$ The first property is because all users in each femtocell are covered by the MBS. The second property indicates that the users covered by FBS $m$ are a subset of the users covered by the MBS. The third property shows that the user subsets in different femtocells do not overlap. We can see that the $\mathcal{S}_l^m$’s, for $m=1,\cdots,M$, are also a partition of $\mathcal{U}_l$.

Define $W_m(\mathcal{U})=\max_{k\in\mathcal{U}}\left\{ 1/H_m^k \right\}$, where $\mathcal{U}$ is the set of users and $m=0,\cdots,M$. If the set $\mathcal{U}$ is empty, we define 