determined subsets $\mathcal{U}_l^0$ and $\mathcal{U}_l^1$.

The computational complexity of this algorithm is $\mathcal{O}(L)$.

  ----- ---------------------------------------------------------------------------------------
  1:    Initialize all $c_l^0$, $c_l^1$, $Q_{L+1}^0$ and $Q_{L+1}^1$ to zero;
  2:    FOR $l=1$ TO $L$
  3:    $\;\;$ IF ($\Gamma_0(1+\Gamma_0)^{c_l^0}G_l^0 \le \Gamma_1(1+\Gamma_1)^{c_l^1}G_l^0$)
  4:    $\;\;\;\;$ Set $\mathcal{U}_l^0=\mathcal{U}_l$ and $\mathcal{U}_l^1=\emptyset$;
  5:    $\;\;\;\;$ $c_l^0=c_l^0+1$;
  6:    $\;\;$ ELSE
  7:    $\;\;\;\;$ Set $\mathcal{U}_l^0=\emptyset$ and $\mathcal{U}_l^1=\mathcal{U}_l$;
  8:    $\;\;\;\;$ $c_l^1=c_l^1+1$;
  9:    $\;\;$ END IF
  10:   END FOR
  11:   FOR $l=L$ TO $1$
  12:   $\;\;$ $Q_l^0=F_0(Q_{l+1}^0,\mathcal{U}_l^0)$ and $P_l^0=Q_l^0-Q_{l+1}^0$;
  13:   $\;\;$ $Q_l^1=F_1(Q_{l+1}^1,\mathcal{U}_l^1)$ and $P_l^1=Q_l^1-Q_{l+1}^1$;
  14:   END FOR
  ----- ---------------------------------------------------------------------------------------

  : Power Allocation Algorithm For Case II

\[tab:Case2Algo\]

#### Case III–MBS and Multiple FBS’s \[subsubsec:case3\]

Finally, we consider the general case with one MBS and multiple FBS’s in the network. Each user is able to connect to the MBS or a nearby FBS. Recall that we define $\mathcal{U}_l$ as the set of users requesting the level $l$ packet, and $\mathcal{U}_l^m$ as the subset of users in $\mathcal{U}_l$ that [*connect*]{} to BS $m$. These sets have the following properties. $$\label{eq:SetProp1}
\left\{ \begin{array}{l}
  \bigcup_{m=0}^M \mathcal{U}_l^m = \mathcal{U}_l  \nonumber \\
  \mathcal{U}_l^m \bigcap \mathcal{U}_l^{m'} = \emptyset, \; \mbox{ for all } m' \neq m. \nonumber
        \end{array} \right.$$ The first property is due to the fact that each user must connect 