## 2 Related Work  
Nowadays, the concern of the interference caused by the D2D communication underlaying uplink cellular network has been the target of many researchers. Some of the related works are mentioned in this section. The problem of interference mitigation in a D2D communication underlaying uplink cellular networks has been discussed in [14]. In this paper, an optimization problem is analyzed to minimize the total interference of the cellular network. The optimization problem is formulated in two steps: at the first step the resources are allocated with a fixed power level, and at the second step interference minimization is addressed into multiple interference minimization problems per available resources. The results showed that their proposed scheme reduces the total interference significantly as compared to random resource allocation (RRA) scheme. However, the proposed system model is equipped with a single omni-directional antenna. Therefore, this scheme is not spectral efficient. The authors of [15] proposed a novel scheme to find the optimal solution for D2D users by defining two types of constraints, namely the peak interference and average interference caused by the D2D communication. However, since both the cellular users and D2D pairs employed the resources non-orthogonally, intra-cell interference becomes severe. In order to mitigate intra-cell interference, a FFR scheme for D2D communications has been discussed in [16]. In the paper, the authors proposed a resource allocation (RA) scheme for D2D communications for a multi-cell cellular network with FRF of 1. In this work, the optimization problem was formulated to reduce the outage probability and increase the overall network throughput. Also, the advantages of limited co-channel power control, fractional frequency power control, and fractional frequency adaptive power control schemes were analyzed. However, the available frequency band was not fully allocated to the whole cell area. In [17], an optimization problem was formulated to maximize the overall system throughput. The demerit of this proposed scheme is that it only focused on the performance improvement of conventional cellular users. The work in [18] presented a thorough survey on the various fairness models in wireless networks. In this context, the authors discussed different fairness models and compared in terms of the energy consumption, power consumption, scheduling phenomenon, utility management, and resource allocation scenario. An optimal trade-off between system efficiency and Jain's fairness index (JFI) for multiple D2D users has been studied in [19]. An admissible utilization method is presented by considering the trade-off policy between system efficiency and fairness index. However, complexity of the proposed method is very high. In [20], a joint power control and fairness scheduling for D2D communication have been proposed. The Hungarian algorithm is considered to maximize the overall throughput while ensuring signal-to-interference-noise ratio (SINR) requirement. However, this method does not provide significant performance improvement as it only assumed the present time slot. The work in [21] proposed a scheme which analyzes outage probability by jointly considering the effect of interference, noise, and Rayleigh multipath fading phenomenon. Also, the outage probability model is analyzed using additive white Gaussian noise based on stochastic geometry, Laplace transforms, and probability density function. Moreover, an analytical expression under realistic interference scenarios was derived. In [22], the authors introduced exact and approximate formulas for calculating outage probability. The results showed that their proposed scheme significantly improves the system throughput. The limitation of this scheme is that the system model does not accommodate large capacity of users.