## 1 Introduction  
D2D communication is a novel wireless communication technique where devices located nearby can communicate directly and remain controlled by the base station (BS) [1; 2; 3; 4]. It is a crucial technology for LTE-A that remains good backward compatibility with LTE (TDD & FDD), which means the functions in LTE (TDD & FDD) can be available in LTE-A. D2D communication can work within two modes: overlaid and underlaid. The scenario discussed in this paper is underlaid mode where D2D pairs reuse the RBs of cellular users (CUs), greatly enhancing the spectral efficiency and relieve the load of BSs [5], in which energy consumption and clustering are the essential contents of research [6]. Under this communication method, devices transmit the data signals to associated receivers over direct links by reusing the cellular RBs [7] that is different from cellular communication where devices must communicate through a BS [8]. Thus, the spectral efficiency of a direct link is much higher due to resource sharing [9; 10]. D2D communication underlaid cellular network enhances the performance of the network with much lower protocol overhead than existing cellular networks [11], such that D2D pairs with low transmit power reuse RBs of CUs to achieve high throughput and low delays, and decrease energy consumption [12; 13]. Although D2D communication has received incremental attentions in both 4G and 5G networks [14], the performance of system throughput and spectral efficiency can be improved [15]. Meanwhile, the interference to the cellular network is inevitably enhanced due to RBs' sharing [16]. The method adopted to deal with the interference problem when CUs share RBs with D2D pairs is depicted as: the power control procedure is implemented to ensure that the interference from D2D pairs to CUs do not exceed a given threshold, followed by the application of a proper allocation algorithm to optimize the matching of D2D pairs and RBs to achieve a significant system performance increase. One of the effective methods to increase the performance of communication systems is to build more BSs [17]. However, such an act is impractical due to the factors as high cost, limited space, and low utilization ratio. There are several studies in the literature on resource allocation for D2D communication. In [18], authors tried to reduce the uplink interference in two steps for D2D communication, where CUs share RBs with D2D pairs under the condition that the interference between D2D pairs and CUs are permitted. Nevertheless, the proposed resource allocation method based on Kuhn-Munkres (KM) algorithm would not be effective when the number of D2D pairs and CUs is large. As an improvement, authors managed the interference by dynamic graph framework for multi-hop D2D communication, where the communication system consists of multiple nodes and D2D pairs [19]. Presented in [20; 21], the auction-based method was used in resource allocation problems for the D2D network, where the BS is visualized as the auctioneer, the RBs as the goods, and the users as the bidders. This method could solve resource allocation issues well in a cellular network, despite it being a concept of business at the initial stage. A scenario of Orthogonal Frequency Division Multiple Access (OFDMA) network is depicted in [22], where the method of Lagrange decomposition is adapted to manage sub-channels and transmit power in the two-tier uplink network. Power control is one of the effective methods to solve interference caused by D2D pairs to CUs in both uplink and downlink cases [23]. [PERSON] et al. attempt to satisfy the required system throughput with power constraints of BS and minimized the users' transmission power in a scenario of the multi-node wireless network [24]. However, it is difficult for the proposed algorithm to obtain the optimal solution in cases of nonlinear complexity systems.