  Device-to-device (D2D) communication underlaid with cellular networks is a
new paradigm, proposed to enhance the performance of cellular networks. By
allowing a pair of D2D users to communicate directly and share the same
spectral resources with the cellular users, D2D communication can achieve
higher spectral efficiency, improve the energy efficiency, and lower the
traffic delay. In this paper, we propose a novel joint mode selection and
channel resource allocation algorithm via the vertex coloring approach. We
decompose the problem into three subproblems and design algorithms for each of
them. In the first step, we divide the users into groups using a vertex
coloring algorithm. In the second step, we solve the power optimization problem
using the interior-point method for each group and conduct mode selection
between the cellular mode and D2D mode for D2D users, and we assign channel
resources to these groups in the final step. Numerical results show that our
algorithm achieves higher sum rate and serves more users with relatively small
time consumption compared with other algorithms. Also, the influence of system
parameters and the tradeoff between sum rate and the number of served users are
studied through simulation results.
