## 3 System Model and Proposed Scheme
### The Proposed Interference Mitigation Scheme  
We propose a hybrid scheme of FFR and almost blank sub-frame (ABS) to mitigate the inter-cell and inter-sector interferences. The proposed scheme firstly adopts soft FFR for efficient frequency reuse and interference avoidance between cellular and D2D links. The proposed scheme also exploits the ABS method to mitigate the inter-sector interference that can not be efficiently managed by only soft FFR.  
The overall operational flow of the proposed scheme is described in Algorithm 1. The proposed scheme consists of three phases: soft FFR, ABS, and data transmission. In phase 1, an eNB operates soft FFR. The eNB divides its own cell into four different sectors like \(S_{0}\), \(S_{1}\), \(S_{2}\), and \(S_{3}\). Then, it checks the locations of CUEs and allocates frequency to CUEs through the soft FFR method. The details of soft FFR are described in the next section. Phase 2 is an ABS configuration by the eNB. If the eNB receives  
Figure 3: System model and resource allocation for soft fractional frequency reuse (FFR).  
a D2D connection request from DUE-Tx \(i\) to DUE-Rx \(j\), it lists CUEs whose distance to the DUE-Rx \(j\) is less than \(D_{max}^{ABS}\). The list is a set \(\mathcal{ABS}_{j}^{CUE}\) of CUEs that should be silent on ABS sub-frames for the DUE-pair \(i,j\). The eNB then sends control signals including the ABS pattern for the DUE-pair \(i,j\). The final phase is data transmission by DUEs and CUEs. In this phase, the eNB checks the DUE-pair \(i,j\) and the set \(\mathcal{ABS}_{j}^{CUE}\) for the DUE-pair \(i,j\). The CUEs in the set should be silent during ABS sub-frames. In the proposed scheme, the CUEs that cause severe interference are selectively chosen to be silent in ABS to minimize the throughput loss.  
```
1:Parameters:\(D_{max}^{ABS}\)
2:Input: DUE-Tx \(i\), DUE-Rx \(j\)
```  
**Phase1 - Soft FFR by eNB**  
```
1:sectorize its cell into \(S_{0}\), \(S_{1}\), \(S_{2}\), and \(S_{3}\)
2:check locations of CUEs
3:allocate frequency for CUE with soft FFR
```  
**Phase2 - ABS by eNB**  
```
1:while receive D2D connection request from DUE-Tx \(i\) to DUE-Rx \(j\)do
2:\(\mathcal{ABS}_{j}^{CUE}\) = { CUE \(c\) | distance between CUE \(c\) and DUE-Rx \(j<D_{max}^{ABS}\) }
3:send control signal to DUE-Tx \(i\) including ABS pattern for the DUE-pair \(i,j\)
4:endwhile
```  
**Phase3 - Data transmission by DUEs and CUEs**  
```
1:for DUE-pair \(i,j\) that requested D2D connections do
2:if\(\mathcal{ABS}_{j}^{CUE}\
eq\emptyset\)then
3:for CUE \(c\) in \(\mathcal{ABS}^{CUE}j\)do
4: mutate data transmission of CUE \(c\) on ABS subframes
5:endfor
6:endif
7:endfor
```  
**Algorithm 1** Operations of the Proposed Scheme.  
Figure 4 depicts different interference sources and the sub-frame allocation for DUE-pair and CUE in the proposed FFR-ABS scheme. In the proposed FFR-ABS, ABS is applied only to CUEs whose distance is too close to D2D links. As shown in Figure 4, there are two different interference sources such as outer and inner CUEs. If the distance to the D2D link is longer than \(D_{max}^{ABS}\), the node is called an outer CUE. Since the signal from an outer CUE does not interfere with the D2D link, the ABS method is not applied to an outer CUE. It is defined as a non-ABS (NABS) case in the proposed scheme. In an NABS case, even outer CUEs transmit data on the non-orthogonal frequency with DUEs, and the interference to DUEs can be tolerable. On the other hand, a CUE that is closer to the D2D link than \(D_{max}^{ABS}\) is called an inner CUE. In the proposed scheme, ABS is applied to an inner CUE because it can severely interfere with the D2D link. An eNB broadcasts ABS patterns to the entire cell. In the proposed FFR-ABS scheme, DUE-Tx transmits data on the ABS subframes while inner CUEs should be silent on the ABS subframes to avoid interference with D2D links as shown in Figure 4.