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The continuous development of fifth generation (5G) communication and Internet of Thing (IoT) inevitably necessitates more advanced systems that can satisfy the growing wireless data rate demand of future equipment. Device-to-Device (D2D) communication, whose performance is evaluated in terms of the overall throughput, energy efficiency (EE) and spectral efficiency (SE), is considered a promising solution for the aforementioned problem. Thereby, this paper aims at improving the performance of the D2D communication underlaying cellular networks operating on multiple bands by maximizing the EE in its uplink. Thanks to the stochastic geometry theory, it is possible to derive the closed-form expressions for the successful transmission probability (STP), the total average transmission rate (TATR), and the total average energy efficiency (TAEE) of cellular and D2D users in different time slot setting. Particularly investigated and compared in this study, there are one-hop, direct, D2D communication in two time slots (2TS), and multi-hop, indirect, D2D communication in three time slots (3TS) with an additional D2D user acting as a two-way relay to assist the communication. Moreover, an optimization problem is formulated to calculate the maximum TAEE of D2D users and the optimum transmission power of both the cellular and D2D users. Herein this optimization study, which is proven to be non-convex, the Quality of Service (QoS) is ensured as the STP on every link is considered. The herein approach is referred to as relay-assisted D2D communication which is capable of delivering a notably better QoS and lower transmission power for communication among distant D2D users.

Energy Efficiency Maximization of Two-Time-Slot and Three-Time-Slot Two-Way Relay-Assisted Device-to-Device Underlaying Cellular Networks