## 1 Introduction
In D2D communications, heuristic algorithms can achieve an optimal solution by providing best resources' pairing between cellular users and D2D users. An energy-efficient multicast transmission for underlay D2D communications was proposed in [8] and a heuristic algorithm was introduced to incorporate both the energy constraint and social relationship. The multicast cluster formation was analyzed based on the social knowledge of the D2D communication underlaying a cellular network. However, in this scheme, the energy consumption of the conventional cellular users in the system was not analyzed. The work in [9] proposed an energy-efficient cluster-oriented solution for multimedia delivery in an LTE D2D environment. In their work, the performance of the battery lifetime and system energy consumption was evaluated. Energy harvesting with simultaneous wireless information and a power transfer technique with D2D communication was studied in [10], and the results showed that the proposed technique improved the coverage and energy efficiency. Furthermore, the concept of content sharing and content delivery has recently acquired great interest to offload the traffic in the D2D communication system. For efficient content delivery in D2D communications, it is important to analyze the common interests and social relations of the users. In [11], D2D content delivery in a cellular network was proposed based on the dynamic arrival and departure nature of the content. Also, the multicast content delivery strategy was analyzed to improve the utilization rate and delivery efficiency. The authors in [12] designed a technique to efficiently deliver multicast traffic in a 5G network. The single-frequency operation technique was analyzed to improve the overall network energy efficiency. The results showed that their proposed method improved the network energy efficiency with respect to a conventional multicast scheme. However, due to single frequency operation, the network is not spectrally efficient. In this paper, we discuss the problem of throughput optimization for M-D2D communications underlaying uplink cellular networks to achieve high throughput and spectrum efficiency. In particular, the main contributions of our work are summarized as follows:  
* First, we consider a network-assisted M-D2D communications system that allows transmission of the same data to multiple receivers by reusing uplink cellular resources;
* as a promising solution of future cellular networks, we introduce the FFR technique to mitigate inter-cell interference between the cellular users and M-D2D groups, while sharing the resources between the cellular users and M-D2D groups. In the FFR scheme, the entire cell area is divided into two non-overlapping regions and both regions are served by the directional antennas. The FFR scheme can accommodate higher spectrum utilization, thus it can achieve higher throughput;
* we formulate the sum throughput optimization problem by simplifying the resource allocation method. Resource allocation is performed by assuming upper and lower bounds of the power level;
* we propose a low-complexity metaheuristic-tabu search algorithm to locate the most likely cellular users to find the optimal solution. Tabu search is an efficient metaheuristic technique that finds an optimal and near-to-optimal solution of diverse practical applications. In the metaheuristic-tabu search algorithm, a neighborhood function is defined to overcome the possibility of being trapped at a local optimum. The main benefits of proposing the metaheuristic-tabu search algorithm in our work are that it requires less computation time and is efficient for a large problem size network; and
* extensive analysis over various system parameters show that the proposed scheme can achieve the highest success rate, system throughput, and maximum utilization of the available system resources compared with other schemes. The remainder of the paper is organized as follows. Section 2 presents related works. Section 3 provides the proposed scheme.