This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of OFDMA-based HetNets where a macro-tier is augmented with small cell access points. Each user equipment (UE) in the network is modeled as a rational agent that engages in a non-cooperative game and allocates its available transmit power over the set of assigned subcarriers to maximize its individual utility (defined as the user's throughput per Watt of transmit power) subject to a target rate requirement. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of the concept of Nash equilibrium. Using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters. G. Bacci is with Mediterranean Broadband Infrastructure (MBI) srl, 56121 Pisa, Italy (email: gbacci@mbigroup.it). E. V. Belmega is with ETIS
Focusing on uplink heterogeneous networks (HetNets), the authors in REF adopt the Debreu-type noncooperative game and introduce a distributed power allocation algorithm based on an iterative water-filling best response process.
Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints
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