Device-to-device (D2D) underlaying communication brings great benefits to the cellular networks from the improvement of coverage and spectral efficiency at the expense of complicated transceiver design. With frequency spectrum sharing mode, the D2D user generates interference to the existing cellular networks either in downlink or uplink. Thus the resource allocation for D2D pairs should be designed properly in order to reduce possible interference, in particular for uplink. In this paper, we introduce a novel bandwidth allocation scheme to maximize the utilities of both D2D users and cellular users. Since the allocation problem is strongly NP-hard, we apply a relaxation to the association indicators. We propose a low-complexity distributed algorithm and prove the convergence in a static environment. The numerical result shows that the proposed scheme can significantly improve the performance in terms of utilities. Our distributed resource allocation scheme is effective for the scenario with large number of D2D users. The performance of D2D communications related to peer locations, the number of D2D users and QoS (Quality of Service) requirement are investigated thoroughly.
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