# A Practical Resource Management Scheme for Cellular Underlaid D2D Networks
## 3 System and Channel Models  
In this paper, we investigate a cellular underlaid D2D wireless communication network as depicted in Figure 1. The utilization in cellular uplink is much lower than in downlink because of the asymmetry of mobile internet traffic, and thus it is more efficient for the underlaid D2D network to share uplink resources with cellular communications [18; 19]. However, the resource sharing between D2D and cellular communications can cause the quality deterioration in conventional cellular communications, which have higher priority over D2D communications. Thus, a cellular infrastructure such as BS imposes an interference constraint on D2D communications to secure the quality of cellular communications. In our system model, we have \(N\) D2D pairs, a cellular BS, and a cellular user equipment (UE). In this paper, the association process of D2D pairs and cellular uplink resource scheduling are both beyond the scope of the paper. Thus, we assume that each D2D pair has been already associated. A D2D receiver that wants to receive content is associated with one of the D2D transmitters that cache the wanted content and are located in the proximity of the receiver. In addition, a cellular UE is scheduled to transmit its uplink data to the cellular BS based on a scheduling policy. In this paper, we use a statistical channel model, where \(g_{ij}\) denotes the channel coefficient between transmitter \(i\) and receiver \(j\). \(i\in\{1,2,\cdots,N\}\) or \(i=\text{u}\) and \(j\in\{1,2,\cdots,N\}\) or \(j=\text{b}\). \(i=\text{u}\) denotes a cellular UE and \(j=\text{b}\) denotes a cellular BS. We consider a Rayleigh fading model, and thus \(|g_{ij}|^{2}\) is exponentially distributed with mean value \(\lambda_{ij}\)[20]. The effect of path loss can be incorporated into \(\lambda_{ij}\). Quasi-static block fading is also considered and thus all the channel coefficients are constant during one frame for data transmission and randomly vary each frame. We assume that D2D communications adopt a time division duplex (TDD) scheme and thus the D2D channels are reciprocal without loss of generality. \(N_{0}\) denotes the variance of additive white Gaussian noise (AWGN) in D2D receivers. We assume that the transmit power levels of all D2D transmitters and cellular transmitter are fixed at \(P\). The cellular transmitter can immediately transmit its data regardless of the presence of D2D communications, while D2D transmissions should be controlled to protect the quality of cellular uplink communications. Thus, a cellular BS imposes an interference constraint on D2D communications. That is, the total interference power that all D2D transmissions cause to the cellular BS should be less than \(I_{\text{th}}\) at any moment. \(I_{\text{th}}\) is a parameter that the cellular BS can determine by considering both the quality of cellular communications and the performance of D2D communications. Because D2D transmitters use a  
If we define \(\mathcal{I}\triangleq\{I_{1},\cdots,I_{N}\}\), D2D communications should comply with the following interference constraint imposed by the BS;  
\[\sum_{i=1}^{N}I_{i}P|g_{\mathcal{R}\mathcal{R}}|^{2}\leq I_{\text{th}} \tag{2}\]  
to protect the cellular uplink communications securely. If normalized by \(N_{0}\), Equation (2) can be rewritten as  
\[\sum_{i=1}^{N}I_{i}\rho|g_{\mathcal{R}\mathcal{R}}|^{2}\leq\frac{I_{\text{th}} }{N_{0}}\triangleq I_{\text{th}}^{\prime}, \tag{3}\]  
where \(\rho\) is a transmit power-to-noise ratio of D2D transmitters, hereafter simply called SNR. Then, the signal to noise plus interference (SINR) received at a D2D receiver \(i\), denoted by \(\gamma_{i}\), can be calculated as  
\[\gamma_{i}(\mathcal{I}) = \frac{I_{i}P|g_{ii}|^{2}}{\sum_{k=1,k\
eq i}^{N}I_{k}P|g_{ki}|^{2}+ P|g_{\mathcal{R}\mathcal{R}}|^{2}+N_{0}} \tag{4}\] \[= \frac{I_{i}\rho|g_{ii}|^{2}}{\sum_{k=1,k\
eq i}^{N}I_{k}\rho|g_{ki} |^{2}+\rho|g_{\mathcal{R}\mathcal{R}}|^{2}+1},\]  
for a given \(\mathcal{I}\).