Device-to-device (D2D) communications allows user equipment (UE) that are in close proximity to communicate with each other directly without using a base station. Relay-assisted D2D (RA-D2D) communications in 5G networks can be applied to support long-distance users and to improve energy efficiency (EE) of the networks. In this paper, we first establish a multi-relay system model where the D2D UEs can communicate with each other by reusing only one cellular uplink resource. Then, we apply an adaptive neuro-fuzzy inference system (ANFIS) architecture to select the best D2D relay to forward D2D source information to the expected D2D destination. Efficient power allocation (PA) in the D2D source and the D2D relay are critical problems for operating such networks, since the data rate of the cellular uplink and the maximum transmission power of the system need to be satisfied. As is known, 5G wireless networks also aim for low energy consumption to better implement the Internet of Things (IoT). Consequently, in this paper, we also formulate a problem to find the optimal solutions for PA of the D2D source and the D2D relay in terms of maximizing the EE of RA-D2D communications to support applications in the emerging IoT. To solve the PA problems of RA-D2D communications, a particle swarm optimization algorithm is employed to maximize the EE of the RA-D2D communications while satisfying the transmission power constraints of the D2D users, minimum data rate of cellular uplink, and minimum signal-to-interference-plus-noise-ratio requirements of the D2D users. Simulation results reveal that the proposed relay selection and PA methods significantly improve EE more than existing schemes.
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