frequency reuse. The annual power bill is a large part of a mobile operator’s costs [@Ulf10]. Minimizing BS power consumption is important to reduce not only the operator’s OPEX, but also the global CO$_2$ emission; an important step towards “green” communications.

![Superposition coding and successive interference cancellation.[]{data-label="fig:sic"}](superposition-coding.eps){width="4.5in"}

Therefore, we focus on BS power allocation in this paper. The objective is to minimize the total power of all the BS’s, while guaranteeing a target rate $R_{tar}$ for each user. Recall that the data file is partitioned into equal-length packets. The target rate $R_{tar}$ ensures that a packet can be transmitted within a time slot, for given modulation and channel coding schemes.

Define binary indicator $I_m^k$, for all $m$ and $k$, as: $$\label{eq:imk}
    I_m^k = \left\{ \begin{array}{ll}
      1, & \mbox{if user $k$ connects to BS $m$} \\
      0, & \mbox{otherwise.}
                  \end{array} \right.$$ Consider a general time slot $t$ when $L$ data packets, or levels, are requested. We formulate the optimal power allocation problem (termed OPT-Power) as follows. $$\begin{aligned}
\mbox{minimize:} && \hspace{-0.2in} \sum_{m=0}^M \sum_{l=1}^L P_l^m \label{eq:ObjFun11} \\
\mbox{subject to:} && \hspace{-0.2in} B_m\log_2(1+\gamma_m^k I_m^k) \ge R_{tar}I_m^k, \mbox{ for all } k \label{eq:cntrate} \\
 && \hspace{-0.2in} \sum_{m=0}^M I_m^k=1, \mbox{for all } k \label{eq:cnttransceiver} \\
 && 