A hybrid system of cellular mode and device-to-device(D2D)mode is considered in this paper,where the cellular resource is reused by the D2D transmission.With the objective of capacity maximization,the power optimization of D2D sub-system is considered,taking into account quality of service(QoS)requirement.The power optimization problem is divided into two stages:The first stage is the admission control scheme design based on the QoS requirement of D2D users,and the second is power allocation to maximize aggregate throughput of admissible D2D users.For the D2D admission control problem,a heuristic sorting-based algorithm is proposed to index the admissible D2D links,where gain to Interference ratio(GIR)sorting criterion is used.Applying an approximate form of Shannon capacity,the power allocation problem can be solved by convex optimization and geometric programming tools efficiently.Based on the theoretical analysis,a practical algorithm is proposed.The precision can reach a trade-off between complexity and performance.Numerical simulation results confirm that combining with GIR sorting method,the proposed scheme can significantly improve the D2D system’s capacity and fairness. A hybrid system of cellular mode and device-to-device (D2D) mode is considered in this paper, where the cellular resource is reused by the D2D transmission. The objective of capacity maximization, the power optimization of D2D sub-system is , taking into account quality of service (QoS) requirement. The power optimization problem is divided into two stages: The first stage is the admission control scheme design based on the QoS requirement of D2D users, and the second is power allocation to maximize aggregate throughput of admissible D2D users.For the D2D admission control problem, a heuristic sorting-based algorithm is proposed to index the admissible D2D links, where gain to Interference ratio (GIR) sorting criterion is used. Applying an approximate form of Shannon capacity, the power allocation problem can be solved by convex optimization and geometric programming tools efficiently.Based on the theoretical analysis, a practical algorithm is proposed. precision can reach a trade-off between complexity and performance. Numerical simulation results confirm that combining with GIR sorting method, the proposed scheme can significantly improve the D2D system’s capacity and fairness.