A distributed cooperation scheme on frequency resource sharing is proposed to improve the quality of service (QoS) in device-to-device (D2D) communications underlaying cellular networks. Specifically, we formulate the resource allocation problem as a coalition formation game with transferable utility, in which all users have the incentive to cooperate with some others and form a competitive group to maximize the probability of obtaining their favorite spectrum resources. Taking the cost for coalition formation into account, such as the path loss for data sharing, we prove that the core of the proposed game is empty, which shows the impossibility of grand coalition. Hence, we propose a distributed merge-and-split based coalition formation algorithm based on a new defined Max-Coalition order to effectively solve the coalition game. Compared with the exhaustive search, our algorithm has much lower computer complexity. In addition, we prove that stability and convergence of the proposed algorithm using the concept of a defection function. Finally, the simulation results show that the proposed scheme achieves a suboptimal performance in terms of network sum rate compared with the centralized optimal resource allocation scheme obtained via exhaustive search.
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