In order to meet the increasing data rate demand of fifth-generation (5G) and sixth generation (6G) wireless networks and by considering the dense deployment of transmitting nodes in future wireless networks, it is critical to design and develop new data transmission techniques. Device-to-device (D2D) communications that enable direct data transmission between proximally situated user equipments (UEs) has been proposed recently to meet the exponentially increasing data rate demands and to increase the spectral efficiency of future cellular networks beyond 5G (B5G) networks. SE improvement is one of the advantages of D2D communications if interference is addressed effectively. Due to the dense deployment of transmitting nodes in future wireless networks, D2D communications can be an effective tool in such networks. Therefore, the resource allocation problem which is the main challenging issue of D2D communications should be investigated. In this research, the resource allocation problem is investigated using a centralized and a distributed approach. Centralized schemes usually have higher performances compared to distributed ones. It is usually assumed in centralized schemes that at most one D2D pair can reuse each cellular link (CL) which simplifies the optimization problem. In this research, we assume that multiple D2D pairs can reuse each CL which can increase the SE of the network dramatically but cause the resource allocation problem to be highly complex. The sum-rate maximization problem constrained to the quality-of-service (QoS) of cellular UEs (CUEs) and D2D pairs is modeled as a mixed-integer non-convex non-linear optimization problem which is NP-hard to be solved. In this research, we propose a low-complexity sub-optimal resource allocation algorithm using the spatial reuse gain of the cell in four steps. The first step is priority assignment to CUE. The D2D pairs are selected using an innovative and effective D2D selection procedure which is the second step. The first two steps result in a CUE-D2D matching. The third step is a fast, effective, analytically proven, and closed-form feasibility check theorem that eva‎luates the feasibility of the resource allocation problem corresponding to the CUE-D2D matching. Using the difference of concave functions property of the objective function, we propose an optimal power allocation using the majorization-minimization (MaMi) technique. The innovative matching procedure, the closed-form feasibility check theorem, and the optimal power allocation cause the proposed scheme to outperform existing methods in dense cellular networks. The performance of the proposed scheme is acceptable but lower than competitive approaches in low-density schemes. We have also investigated distributed schemes in this research. Considering the powerful tool of game theory, we have modeled the optimization problem as a pricing game. In the proposed scheme, a price is set by the base station (BS) for each CL. In the first phase, each CUE and D2D pair tries to maximize its own utility function as a player of the game. At the second phase, the network adjusts the prices of CLs based on the QoS constraints of CUEs and D2D pairs. The repetition of the mentioned phases maximizes the SE of the network in a distributed manner. The reward term of the utility function of each of the UEs is defined based on the achievable data rate of that UE while the penalty term is defined based on the interference that the UE imposes on other UEs. The defined reward and penalty terms cause the proposed scheme to have higher performance and to be more effective compared to other existing methods. The strategy of CUEs is to adjust their transmission powers while the strategy of D2D pairs is to adjust their transmission powers and CLs.

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