In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellu...In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.展开更多
Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric in...Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.展开更多
基金supported by National Natural Science Foundation of China (No.61501028)Beijing Institute of Technology Research Fund Program for Young Scholars
文摘In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.
基金The Doctoral Programs Foundation(20113401110009) of Education Ministry of Chinathe Natural Science Research Project(2012kj11) of Hefei Normal Universitythe NSF(KJ2013A220) of Anhui Province
文摘Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.
