In this paper, we consider device-to-device (D2D) communication underlayinguplink cellular networks with multiple base stations (BSs), where each user canswitch between traditional cellular mode (through BS) and D2D mode (byconnecting proximity user), namely mode selection. We impose load balancingconstraints on BSs to efficient resource usage. The joint problem of modeselection and user association is formulated as a combinatorial problem andNP-complete. We adopt a graph-based approach to solve the problem globallyoptimally in polynomial time. To further reduce complexity, we also propose adistributed algorithm based on dual method. We show that the proposeddistributed algorithm achieves nearly the same performance as the proposedoptimal graph based algorithm.
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