The performance of the graph-based scheduling for device-to-device communications overlaying cellular networks is studied. The graph-based scheduling consists of two stages, the frequency assignment stage and the time slot scheduling stage. For such scheduling, a theoretical method to analyze the average spectrum efficiency of the D2D subsystem is proposed. The method consists of three steps. First, the frequency assignment stage is analyzed and the approximate formula of the average number of the D2D links which are assigned the same frequency is derived. Secondly, the time slot scheduling stage is analyzed and the approximate formula of the average probability of a D2D link being scheduled in a time slot is derived. Thirdly, the average spectrum efficiency of the D2D subsystem is analyzed and the corresponding approximate formula is derived. Analysis results show that the average spectrum efficiency of the D2D subsystem is approximately inversely linearly proportional to the second- order origin moment of the normalized broadcast radius of D2D links. Simulation results show that the proposed method can correctly predict the average spectrum efficiency of the D2D subsystem.
