The approach of factor-graphs (FGs) is applied in the context of power control and user pairing in Device-to-Device (D2D) communications as an effective underlay concept in wireless cellular networks. D2D communications can increase the spectral efficiency of wireless cellular networks by establishing a direct link between devices with limited help from the evolved node base stations (eNBs). A well-designed user pairing and power allocation scheme with low complexity can remarkably improve the system's performance. In this paper, a simple and distributed FG based approach is utilized for power control and user pairing implementation in an underlay cellular network with D2D communications. A max-min criterion is proposed to maximize the minimum rate of all active users in the network, including the cellular and multiple D2D co-channel links in the uplink direction. An associated message-passing (MP) algorithm is presented to distributedly solve the resultant NP-hard maximization problem, with a guaranteed convergence compared to game theoretic and Q-learning based methods. The complexity and convergence of the proposed method is analyzed and numerical results confirm that the proposed scheme outperforms alternative algorithms in terms of complexity, while keeping the sum-rate of users nearly the same as centralized counterpart methods.

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Device-to-device (D2D) communication is a proximity-based data transmission technique where users communicate directly with each other, when bypassing evolved node base station. The most common assumption in the literature is that every D2D user connects to its nearest node. However, in many situations connection to the first nearest node for a D2D user is not possible due to the channel conditions or user's decline in joining in a D2D connection. The impact of connecting to the nth nearest node in a dedicated D2D enabled network is investigated. The coverage probability and average data rate of a typical D2D link in the network, where users connect to their nth nearest node are studied. The results show that considering the first nearest node is an ideal assumption and investigating the connection to the other farther nodes is of great importance.

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