## 1 Introduction
The authors in [11] have proposed an optimal channel assignment technique for D2D communications underlaying cellular networks. In this study, a channel assignment algorithm was first proposed based on a dynamic programming method. This algorithm reduced the computational complexity of the study. Furthermore, the authors studied a cluster-based channel assignment problem to achieve a high successful transmission probability. Unfortunately, in the schemes in [6; 7; 8; 9; 10; 11], the network models cannot precisely mitigate interference, and the available frequency is not fully utilized; thus, the systems are not spectrally efficient. To attain a massive number of connected devices with minimal interference in D2D communications, we propose a resource management and power control scheme for an underlaying D2D communications using a fractional frequency reuse (FFR) scheme. Aiming for high spectrum efficiency, in our study, a network-assisted D2D communications scenario is considered. In this paper, we not only consider an FFR scheme but also consider a scalable frequency reuse method to achieve the best system performance. The primary contributions of this paper are as follows:  
* First, we define a system architecture that allows multiple DPs to simultaneously reuse the same uplink cellular resource, enabling maximum spectrum utilization. * We propose an optimal resource management and power control scheme for underlay D2D communications in cellular networks based on the FFR scheme with a scalable frequency reuse factor to mitigate interference induced by DPs to CUs. Statistical channel information for both CUs and DPs is assumed to evaluate the SINR. Then, we formulate the sum throughput maximization problem by introducing the SINR and power bound constraints. * The major limitation in sum throughput optimization is the high computational complexity that results from an exhaustive search. Thus, the throughput maximization problem can be solved by using two methods, namely, a greedy heuristic method and a binary power control method. The greedy heuristic search algorithm can provide a suboptimal solution by performing a local search. This algorithm minimizes interference by assigning a matching subcarrier to DPs. Then, a binary power control scheme is introduced to maximize the system throughput by achieving a near-optimal solution. The main benefit of the binary power control scheme is that it does not require continuous channel state information (CSI) updates, thus reducing the computational complexity. * We perform rigorous numerical analysis and simulations, and the results demonstrate that the proposed resource management and binary power control scheme outperforms the traditional D2D communications underlaying uplink cellular networks. To our knowledge, this is the first approach to introduce both a greedy heuristic search algorithm and a binary power control scheme using the FFR technique to handle the sum throughput optimization problem for D2D communications in cellular networks. The remainder of this paper is presented as follows: Section 2 explains the related works. In Section 3, we present the system model and problem formulation. Section 4 presents the proposed resource management and power control scheme. The resource management method is analyzed using a greedy heuristic search algorithm and a binary power control scheme. The results of performance analysis are provided in Section 5, and this paper is concluded in Section 6.