Network-assisted single-hop device-to-device (D2D) communication can increase the spectral and energy efficiency of cellular networks by taking advantage of the proximity, reuse, and hop gains when radio resources are properly managed between the cellular and D2D layers. In this paper we argue that D2D technology can be used to further increase the spectral and energy efficiency if the key D2D radio resource management algorithms are suitably extended to support network assisted multi-hop D2D communications. Specifically, we propose a novel, distributed utility maximizing D2D power control (PC) scheme that is able to balance spectral and energy efficiency while taking into account mode selection and resource allocation constraints that are important in the integrated cellular-D2D environment. Our analysis and numerical results indicate that multi-hop D2D communications combined with the proposed PC scheme can be useful not only for harvesting the potential gains previously identified in the literature, but also for extending the coverage of cellular networks.
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