Although coverage and capacity are the key elements of the 5G user experience, a dominant part of the population living in rural areas still experience inferior connectivity. Several solutions have been proposed to address this issue. They include deploying small cells, increasing the number of sectors per eNodeB, and reusing signal repetition. However, most of them require complex deployment and expensive fees. Accordingly, many efforts have been deployed on coverage extension software. Even so, many critical issues related to public safety, relay capacity, and devices power constraints are still challenging. As a contribution, we propose in this paper a spectral and energy-efficient two-hop device to device (D2D) relay selection algorithm. Our main goal is to extend the connectivity to the out-of-coverage (OOC) devices. Contrarily to previous solutions in which the relay is selected centrally or individually, we propose a distributed two-stage algorithm based on the Stackelberg game to involve all the competing devices. In the first stage, the OOC devices (OCDUs) are matched with the relays maximizing their spectral efficiency, and the required bandwidth for each one is determined. Then, a power control stage is investigated to calculate the optimal transmission power. The numerical and simulation analysis shows that the proposed schema outperforms the former solutions in total system capacity, spectral efficiency (SE), and energy efficiency (EE) while reducing the complexity.

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