Many-to-Many Matching With Externalities for Device-to-Device Communications

In this letter, we aim to solve the resource allocation problem for device-to-device (D2D) communications underlaying cellular networks. Particularly, multiple D2D pairs are allowed to reuse the same resource block (RB), and one D2D pair is allowed to use the spectrum of multiple RBs. Our objective is to maximize the system sum rate by satisfying the signal-to-interference-plus-noise ratio constraints for both D2D and cellular user equipments. In order to solve this non-deterministic polynomial-time hard optimization problem, we propose a novel algorithm for obtaining a sub-optimal solution based on the many-to-many two-sided matching game with externalities. To characterize the properties of the proposed algorithm, we prove that it converges to the two-sided exchange stability within a limited number of iterations. Additionally, simulation results show that the proposed algorithm can achieve the near-optimal system sum rate and significantly outperforms a one-to-one matching algorithm.