# Social-Aware Peer Selection for Device-to-Device Communications in Dense Small-Cell Networks
## 3 System Description
### System Model  
In this paper, we mainly focus on the performance evaluation of our proposed algorithm in small-cell scenarios. However, for comparison with the macro-cell in terms of energy efficiency, we also perform simulations of macro-cell scenarios by changing the coverage area and transmission power. We assume a set of UEs that consists of DUEs and CUEs. Both DUE and CUE have the capability to communicate through the base station. However, we assume DUE as the one that has the desired data/service needed by the requesting UE. Hence, it could be selected as the D2D peer. On the other hand, CUE cannot be selected as the D2D peer because it does not have the desired service/data. The CUEs are allocated with orthogonal sub-channels while the DUEs reuse the same sub-channels for D2D communications. Hence, the CUEs do not interfere with each other. Each D2D pair reusesthe spectrum resource of a CUE. The BS (SCBS/MCBS) ensures that the resource of a CUE is reused by exactly one D2D pair to mitigate the interference among DUEs. However, interference can occur between CUEs and DUEs because they share the same spectrum resource. In addition, a Rayleigh fading channel model is assumed for the proposed system [13].  
We assume that the BS (SCBS/MCBS) can get the social attributes of UEs while it knows their physical locations. When it receives a request for D2D communications from a UE, it constructs a separate decision matrix for the social attributes of the UEs denoted by M\({}_{DS}\), and physical attributes denoted by M\({}_{DP}\), as presented generically in (5). Before applying the TOPSIS algorithm, the UEs with no social friendships are excluded from the M\({}_{DS}\). Similarly, UEs whose distance from the requesting UE is greater than the minimum D2D distance threshold (i.e., 50 m) are omitted from the M\({}_{DP}\). These significantly simplify the peer selection task. A modified version of the TOPSIS algorithm is then applied to both the M\({}_{DS}\) and M\({}_{DP}\) to compute the closeness coefficient for social and physical attributes denoted by \(\delta_{s}\) and \(\delta_{p}\), respectively. The two closeness coefficients are added together to get the cumulative closeness coefficient denoted by \(\Delta\), which is then used to calculate the signal-to-noise ratio and the data rate for the D2D communications as given in (15) and (16), respectively. Finally, we use the calculated data rate to compute the throughput and energy efficiency for D2D communications as given in (17) and (18) respectively. The BS probes the candidate's UEs for D2D communications. It shares the information of those who are ready for D2D communications with the requesting UE. Moreover, it also shares the information of the requesting UE with its D2D peer, and hence, they establish a direct link for D2D communications. If there is no UE with social friendship in the M\({}_{DS}\), the proposed method selects D2D peers based on the similarity in their interests.  
As social-aware D2D communications exploit the attributes of users in both social and physical domains. Therefore, we divided our system model into two layers--a social proximity layer (SPL) and a physical proximity layer (PPL)--(as shown in Figure 1) to model their social relationships and physical constraints. The next subsection briefly discusses both the layers of our model and the way the model reflects the corresponding attributes.