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Device-to-device (D2D) communications underlaying cellular networks have been recognized as a promising technology to improve the system capacity and spectral efficiency of 5G networks. In this paper, we investigate the problem of designing the joint uplink subcarrier assignment and power allocation scheme to optimize the sum data rate of D2D pairs, under a general “many-to-many” scenario in which a subcarrier could be shared by multiple D2D pairs and a D2D pair could also reuse multiple subcarriers. In particular, the optimization problem is to maximize the sum data rate of all D2D pairs under the constraints of minimum data rate requirements of cellular user equipments (CUEs). The formulated problem falls into a mixed integer nonlinear programming, which is generally NP-hard. To solve the problem, we decompose it into two subproblems: the subcarrier assignment subproblem and the power …