Device-to-device (D2D) communication is a promising option for the fifth generation (5G) mobile communication network to reduce energy consumption and increase throughput, which makes high throughput applications possible. Also, the improvement for energy and spectrum efficiency is critical in such applications. Without occupation of cellular spectrum resources, outband D2D communication is increasingly applied to high throughput applications to increase spectrum supply. However, energy

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... cy is still a key issue that needs to be addressed. Moreover, the overall energy efficiency in cellular networks is severely limited by cell-edge devices. Therefore, in this paper, we apply multi-hop relay-aided outband D2D communication to cellular networks and propose a game-based power adjustment method to address throughput optimization problem. Firstly, we model an interaction relationship of power adjustment for each transmission path as a potential game, where a new utility function is designed for each player (i.e., the receiving end of a transmission path) to evaluate its action gain and to determine whether taking action or not. And then, it is proved that the utility function is an ordinal potential function (OPF) and the game of power adjustment is an ordinal potential game (OPG), which guarantees the convergence of game decision process. Moreover, we propose a new game decision algorithm, which has quicker convergence speed than the existing typical algorithm. In addition, we design a networkassisted distributed processing architecture for solving throughput optimization problem, including receiving mode selection, verification for relay selection, and transmission power adjustment, which can ease the burden of centralized processing. The experimental results show that our scheme is superior to the existing typical work in terms of throughput, delay, energy efficiency, continuous service ability, and convergence performance.