## 2 Related Works  
The aforementioned works typically focused on resource management methods without employing a spectrum partition technique. The spectrum partition technique is also known as the FFR method, which partitioned the cell coverage into non-overlapping regions using directional antennas [12]. The FFR method can efficiently allocate the available resources among devices based on the channel coefficients of proximate devices. Thus, the FFR method mitigates interference between traditional CUs and DPs, improving the spectrum utilization in the network. A resource allocation scheme based on the FFR scheme was presented in [13]. In their work, the authors assumed a dynamic power control scheme and formulated a throughput maximization problem based on the heuristic search algorithm. In [14], a resource management method was discussed for an underlay D2D communications in cellular networks using an FFR scheme. In this paper, the authors proposed a non-orthogonal resource sharing scheme for an underlay D2D communications. A cell sectorization technique using three 120\({}^{\circ}\) directional antennas was considered to mitigate co-channel interference between users. Finally, a throughput maximization problem was developed based on SINR requirement and the upper and lower bound power levels. However, in their network, the frequency reuse factor is equal to one. In [15], an interference mitigation method for D2D wireless multimedia sensor networks was presented. In their study, an orthogonal frequency assignment technique was applied by dividing the entire cell area into six non-overlapping zones. In addition, a FFR technique was considered to improve the spectrum utilization. But, the optimal power management scenario was not achieved. A distance-constrained resource management method for an underlay D2D communications in cellular networks was proposed in [16]. D2D communications in a cell was categorized depend on the location of users. Moreover, the outage probability was analyzed based on the SINR. However, the methods in [15; 16] cannot support simultaneous D2D connections for simultaneous communications. Therefore, these schemes are not effective for high-density networks. A few studies have considered a frequency reuse factor much higher than one in D2D communications underlaying cellular networks. To accommodate the maximum number of DPs that can simultaneously communicate, a scalable frequency reuse factor for an underlay D2D communications was presented in [17]. In their study, blind admission control, a distributed admission control method and optimal admission control methods were analyzed to achieve the required QoS for both CUs and DPs in a cell. Additionally, an optimization problem was formulated based on the CSI to maximize the network frequency reuse, which results in higher system capacity. However, in their study, the network model could not obtain the optimal interference mitigation scenario due to the absence of an FFR scheme. A spectrum reuse method along with power control scheme was discussed in [18]. In this study, the Stackelberg game approach was analyzed for multi-sharing D2D communications to maximize the independent set of users that simultaneously reused the same subchannels. Therefore, the performance of the proposed scheme increases. In [19], the authors proposed a fast spectrum reuse and power control scheme for D2D communications. A Stackelberg power algorithm was derived, where DPs that are willing to connect are divided into groups. In their study, the analysis was performed in two steps: First, resource assignment was performed based on the maximum independent set to reduce the number of iterations, and second, resource assignment was performed using the Stackelberg power algorithm to reduce the computational complexity of the proposed method. A dynamic FFR scheme to mitigate intercell interference was presented in [20].