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In this article, power control of uplink connection in the ultra-dense heterogeneous networks (HetNets), which are studied as different types of access points (APs), is investigated. It is demonstrated that an efficient performance of users during the uplink transmission is limited to the issue of per-user power control. Although the per-user power control allows users to transmit with full power to maintain a stable connection, it also causes a higher outage probability during the uplink transmission. In light of this, we propose a robust distributed energy-efficient scheme for uplink power control in HetNets, which confronts the per-user power control problem and coordination of the multi-user interferences. Therefore, firstly, Jarvic-Patric (JP) algorithm is adopted for the users' clustering. Unlike the traditional JP algorithm, conditions for the formation of users' clustering are extended with a term named the degree of membership in this article. Secondly, the distributed energy efficiency (EE) problem is formulated as the mean-metric of the EE, i.e., a sum of users' cooperative EE functions to address the cooperation problem among clustered interfering users at the local level and coordination of multi-user interferences at a global level. The formulation of the EE problem in this fashion reveals the interdependence of power optimization at local and global levels, which brings about the necessity of joint optimization. Hence, we propose a novel 2-level distributed cooperative learning (DCL) scheme, where users act as self-organized agents and optimize power control at local and global levels jointly. In the 2-level DCL scheme, clustered users are engaged in the cooperative game of power control at the local level to maximize the cooperative EE. Meantime, users communicate with each other to learn an online power control at the global level. Besides, a popular performance metric for a machine learning scheme named regret is demonstrated for the 2-level DCL scheme. Finally, the numerical results demonstrate that the proposed scheme significantly improves the EE compared to existing works.

Users First: A Robust Two-Level Learning of Power Control in Uplink Ultra-Dense HetNets