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With device-to-device (D2D) communications, a user terminal can be used as a relay node to support multi-hop transmission, so that cell-edge or deeply faded users can obtain a better connective experience. In this paper, we investigate energy-efficient mobile association in D2D-enabled heterogeneous networks. We consider joint access point selection, mode switching, D2D relay node (DRN) selection, and power control to maximize the energy efficiency (EE) of uplink transmission while guaranteeing the quality-of-service requirement of users. The optimization problem can be decomposed into three subproblems: access point selection, power control, and joint mode switching and DRN selection. The joint mode switching and DRN selection problem is a 0-1 integer optimization problem, whose optimal solution can be found by the brute-force searching method that is complexity-prohibitive when the number of …