# Energy-Efficient On-Off Power Control of Femto-Cell Base Stations for Cooperative Cellular Networks
## 3 System Model, Problem Formulation and Proposed Scheme
### Proposed Scheme  
In order to resolve the problem of excessive computations in solving the optimization problem (3), we have proposed a heuristic scheme based on the concept of LOC that indicates the importance of specific FBS in cooperative transmission. In our proposed scheme, the LOC value of FBSs is used to decide which FBS to be turned off. More specifically, the LOC of FBS \(i\) at time \(t\), which we denote as \(\text{LOC}_{i}(t)\), is defined as follows:  
\[\text{LOC}_{i}(t)=1-\frac{R_{i,t}(\mathbb{A}\setminus i)}{\mathbb{E}\left[R_ {i,t}(\mathbb{N})\right]}. \tag{5}\]  
Note that, in Equation (5), \(R_{i,t}(\mathbb{A}\setminus i)\) and \(\mathbb{E}\left[R_{i,t}(\mathbb{N})\right]\) correspond to the achievable throughput without FBS \(i\) and the expected data rate without the shutdown of all FBSs, i.e., all FBSs are activated, respectively. If FBS \(i\) plays a crucial role in cooperative transmission, i.e., the data rate of cooperative transmission decreases severely without the use of the FBS \(i\), \(\text{LOC}_{i}(t)\) will be close to 1. Otherwise, if the role of FBS \(i\) is minor, \(\text{LOC}_{i}(t)\) will be close to 0. In our proposed scheme, FBSs with low LOC value are switched off because the shutdown of those FBSs will not significantly deteriorate the performance of cooperative transmission. Given that the LOC of FBSs is heavily affected by fluctuating channel environment, e.g., \(h_{i,j}(t)\), \(\text{LOC}_{i}(t)\) has to be accumulated in order to properly decide which FBS to switch off. Otherwise, FBS which temporarily undergoes bad channel condition will be switched off accidentally even though this FBS plays a significant role in the transmission. To this end, in our proposed scheme, FBS \(i\) is turned off if the following inequality is satisfied:  
\[\prod\limits_{t-M\leq k\leq t}\text{LOC}_{i}(k)<1-\epsilon, \tag{6}\]  
where \(M\) is the window size and \(\epsilon\) is the controlling parameter which determines the ratio of FBSs to be turned off. If \(\epsilon\) is small, more FBSs will be turned off such that more energy can be saved, but, at the same time, the throughput of cooperative transmission can be deteriorated more severely, as can be seen from our simulation results in the following section. Moreover, in order to satisfy the tolerable performance degradation, the switched off FBS should be immediately turned on if \(\mathbb{E}\left[\sum\limits_{i=1}^{K}R_{i,t}(\mathbb{A})\right]<R_{thr}\). Given that network environment changes over time, the switched off FBS should not be turned off permanently and be awakened at the proper time. To this end, we assume that turned off FBSs should periodically wake up and listen to the uplink pilot transmitted from neighboring MSs. If the average value of accumulated received signal strength indication (RSSI) of uplink pilot is larger than \(\delta\), the FBS gets up and participates in cooperative transmission because large RSSI implies that the MS is closely located such that the switched off FBS can play a significant role in data transmission to that MS. The criterion to turn on the FBS in shutdown state can be written as follows:  
\[ \begin{array}{c}\sum\limits_{\begin{subarray}{c}t-M\leq s\leq t \end{subarray}}|h_{i_{j}}(t)|^{2}G_{i_{j}}P\\ M\end{array} >\delta. \tag{7}\]  
Algorithm 1 and Figure 3 depict the pseudo code and the illustrative procedure of our proposed scheme, respectively. First, the LOC of each FBS is accumulated as shown in Equation (6). If the accumulated LOC of specific FBS is smaller than \(1-e\), the referenced FBS is turned off and shutdown notification message is sent to a central management unit (CMU). After the shutdown of FBS, the CMU monitors the degradation of service quality. If the level of degradation is larger than threshold, it sends an immediate turn-on message to the switched off FBS such that it can be awakened in order to recover the throughput, cf.