# A Comparative Analysis of Wi-Fi Offloading and Cooperation in Small-Cell Network
## 3 System Model
### Transmission Model for Cooperative Small-Cell Network  
Figure 1 shows the transmission scenario for cooperative SC network. In this network, each user can be served by more than one small-cell BSs to enhance its quality-of-service (QoS). As shown in Figure 1, three SCs bounded with dashed lines are present in a MC. User \(j\) is served cooperatively by SBS \(i\) and \(i+2\) through multiple links as illustrated with solid lines. However, SBS \(i+1\) creates interference for UE \(j\). In this paper, we consider achievable data rate as a measure of QoS for a user. In the case of cooperative communication, a joint problem of user association with multiple SCs, RB allocation and  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notations** & **Explanation** \\ \hline \(I\) & Set of SCs in a MC \\ \(J\) & Set of UEs in SCs \\ \(P_{ij}^{k}\) & Power in downlink from a SBS \(i\) to a UE \(j\) on a RB \(k\) \\ \(G_{ij}\) & Gain directed from a SBS \(i\) to a UE \(j\) \\ \(K\) & Vector with RBs \\ \(x_{ij}^{k}\) & Association of a UE \(j\) to a SBS \(i\) on a RB \(k\) \\ \(y_{ij}^{k}\) & Association of a UE \(j\) to a LTE SBS \(i\) on a RB \(k\) \\ \(z_{ij}\) & Association of a UE \(j\) to a LTE-U SBS \(i\) \\ \(\sigma^{2}\) & Noise power \\ \(\gamma_{ij}^{k}\) & Signal-to-interference plus noise of a UE \(j\) using a RB \(k\) of a SBS \(j\) \\ \(R_{ij}^{k}\) & Achievable data rate to a UE \(j\) using a RB \(k\) of a SBS \(i\) \\ \(R_{i}^{\sigma}\) & Achievable data rate to a UE \(j\) using Cooperation \\ \(R_{j}^{\sigma}\) & Achievable data rate to a UE \(j\) using Wi-Fi offloading \\ \(R_{AP_{i}}\) & Total rate of a LTE-U SBS \(i\) \\ \(R_{j}^{th}\) & Threshold Data rate for a UE \(j\) \\ \(M_{j}\) & Threshold number of SBSs can serve a UE \(j\) \\ \(N_{i}\) & Threshold number for UEs associated with a SBS \(i\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Explanation of Notations.  
Figure 1: Transmission scenarios for data rate enhancement in SC network.  
power allocation is studied. Here central BS (macro BS in this case) knows all the channel conditions. The optimization/control variable considered are as follows:  
\[x_{ij}^{k}=\begin{cases}1,&\text{if a UE $j$ is associated with a SBS $i$ on a RB $k$},\\ 0,&\text{otherwise}\end{cases} \tag{1}\]  
and power allocation variable \(P_{ij}^{k}\) which can be allocated a value in range of \(0\leq P_{ij}^{k}\leq P_{i}^{max}\). Dimensions of association matrix and power allocation are \(\mathbf{X}[M\times N\times K]\) and \(\mathbf{P}[M\times N\times K]\) respectively. The signal-to-interference plus noise (SINR) ratio of a UE \(j\) associated with a SBS \(i\) on a RB \(k\) is given as:  
\[\gamma_{ij}^{k}=\frac{P_{ij}^{k}G_{ij}}{\sigma^{2}+\sum_{i^{\prime}\in I,i^{ \prime}\
eq i}P_{i^{\prime}j}^{k}G_{i^{\prime}j}}, \tag{2}\]  
where \(P_{ij}^{k}\) is the power transmitted from a SBS \(i\) to a UE \(j\) on a RB \(k\), \(G_{ij}\) is the channel gain experienced by a UE \(j\) from a SBS \(i\), \(\sum_{i^{\prime}\in I,i^{\prime}\
eq i}P_{ij}^{k}G_{ij}\) is the interference power received from all the remaining cells in set \(I\) and \(\sigma^{2}\) is the additive white Gaussian Noise. A physical interference model is considered to be presented in [31]. According to this model, two users cannot share the same resources if the SINR between the two is above a certain threshold. We use normalized data rates expressed as,  
\[R_{ij}^{k}=\log_{2}(1+\gamma_{ij}^{k}). \tag{3}\]  
Equation (3) represents the achievable data rate of a UE \(j\) from a SBS \(i\) on a RB \(k\). The achievable data rate of a UE over all SBS and all RBs using cooperative communication is represented as follows:  
\[R_{j}^{c}=\sum_{i\in I}\sum_{k\in K}x_{ij}^{k}R_{ij}^{k}, \tag{4}\]  
where \(x_{ij}^{k}\) is an association and RB allocation indicator and which is equal to 1 when a UE \(j\) is associated with a SBS \(i\) on a RB \(k\) and is 0 otherwise. \(R_{j}^{c}\) represents the achievable rate to a UE \(j\) using cooperative communication.