Device-to-device (D2D) communication is proposed as a promising technique of future cellular networks which fulfills its potential in terms of high resource utilization. In this paper, in order to improve the achievable rate of D2D communication and the spectrum utilization, we consider the scenario that multiple D2D pairs can share uplink spectrum resources with multiple cellular users (CUs). We aim to maximize the overall system spectrum efficiency while satisfying the rate requirements of all CUs and guaranteeing that the system gain is positive. We formulate the joint optimization problem of subcarrier assignment and power allocation which falls naturally into a mixed integer non-linear programming form that is a difficult problem to solve. Hence, we propose a two-stage resource allocation scheme which comprises a subcarrier assignment by employing a heuristic greedy strategy, as well as a power allocation algorithm based on the Lagrangian dual method. Numerical results demonstrate the advantageous performance of our scheme in greatly increasing the system sum spectrum efficiency.
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