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Device-to-device (D2D) communication underlaid with cellular networks is anew paradigm, proposed to enhance the performance of cellular networks. Byallowing a pair of D2D users to communicate directly and share the samespectral resources with the cellular users, D2D communication can achievehigher spectral efficiency, improve the energy efficiency, and lower thetraffic delay. In this paper, we propose a novel joint mode selection andchannel resource allocation algorithm via the vertex coloring approach. Wedecompose the problem into three subproblems and design algorithms for each ofthem. In the first step, we divide the users into groups using a vertexcoloring algorithm. In the second step, we solve the power optimization problemusing the interior-point method for each group and conduct mode selectionbetween the cellular mode and D2D mode for D2D users, and we assign channelresources to these groups in the final step. Numerical results show that ouralgorithm achieves higher sum rate and serves more users with relatively smalltime consumption compared with other algorithms. Also, the influence of systemparameters and the tradeoff between sum rate and the number of served users arestudied through simulation results.

Joint Mode Selection and Resource Allocation for D2D Communications via Vertex Coloring