# Game Theory-Based Smart Mobile-Data Offloading Scheme in 5G Cellular Networks
## 3 System Model
### Mobile-Data Offloading Model  
We consider one CNO operating one macrocell with one BS and \(M\) UEs, in which each UE is equipped with a NRF-EH circuit that can harvest non-RF energy, denoted as UE\({}_{m}\), \(m\in\mathcal{M}\),\(\{1,2,\ldots,M\}\), and where UEs can offload cellular traffic to other UEs. Figure 2 show the MDO system model. The CNO serves a set of UEs that are randomly distributed geographically. In this paper, we study the problem of MDO via D2D links. Therefore, we consider D2D links that are available in the network. We assume that D2D links are independent, i.e., UEs that are either the source or destination in one D2D link is not the source or destination UE in another D2D link. For example, we have two D2D links (UE\({}_{m}\)-UE\({}_{n}\) and UE\({}_{m^{\prime}}\)-UE\({}_{n^{\prime}}\)) as shown in Figure 2. Moreover, other UE activities such as transmitting from UE to BS (e.g., UE\({}_{1}\)-BS link) or idle (e.g., UE\({}_{M}\)) will not affect directly to system performance that only interferes to other connections (e.g., UE\({}_{1}\)-BS links interfere to UE\({}_{m}\)-UE\({}_{n}\) and UE\({}_{m^{\prime}}\)-UE\({}_{n^{\prime}}\) links). The traffic generated by a UE can be offloaded to another UE if the following conditions are all satisfied [2]:  
1. UEs are located within the same coverage area. 2. UEs are equipped with the same radio frequency interface and wireless communication protocol. 3. UEs are enabled to offload traffic. In the system, the traffic of a UE can be offloaded to another UE with an offload coefficient. Let \(\Omega\) denote the set of offload coefficients from UE\({}_{m}\) to UE\({}_{n}\) with \(\Omega\stackrel{{\Delta}}{{=}}\left\{\omega_{1n},\ldots,\omega_{mn} \right\};m,n\in\mathcal{M},n\
eq m\), where \(0\leq\omega_{mn}\leq 1\). The BSs are assumed to be aware of each other's channel gains: \(g_{m}\) (the channel gain between UE\({}_{m}\) and the BS), \(g_{n}\) (the channel gain of the link between the BS and UE\({}_{n}\)), and \(g_{mn}\) (the channel gain between UE\({}_{m}\) and UE\({}_{n}\)). Channel gain is calculated as the inverted path loss. Please note that in our case, the path loss of the link between the BS and the UE and the path loss of the link between one UE and another UE are modeled based on the macro-to-UE model, and on A1-type generalized path-loss models in the frequency range 2-6 GHz developed by the 3\({}^{rd}\) Generation Partnership Project (3 GPP) [61] and WINNER II [62], respectively. In the system, the amount of data of UE\({}_{m}\) can be transmitted to UE\({}_{n}\) with \(N_{m}\) packets and bandwidth \(BW\). The amount of data of the link from UE\({}_{m}\) to UE\({}_{n}\) is calculated as total data of the offloaded transmission from UE\({}_{m}\) to UE\({}_{n}\) (\(\lambda_{mn}^{o}\)) and the transmission from UE\({}_{m}\) to UE\({}_{n}\) (\(\lambda_{mn}^{c}\)) via the BS. On the other hand, in no-offload transmission, the amount of data of the link from UE\({}_{m}\) to UE\({}_{n}\) is only calculated as the transmission from UE\({}_{m}\) to UE\({}_{n}\) (\(\lambda_{mn}^{c}\)) via the BS with an offload coefficient equal to zero. Therefore, the amount of data from UE\({}_{m}\) to UE\({}_{n}\) is defined as follows:  
\[\lambda_{mn}=\lambda_{mn}^{o}+\lambda_{mn}^{c} \tag{6}\]  
Figure 2: The MDO system model.