# Energy Efficient Non-Cooperative Power Control in Small Cell Networks

## TL;DR

This paper proposes a distributed, energy-efficient power control scheme for small cell networks modeled as a non-cooperative game, transforming a non-convex problem into a convex one to achieve Nash equilibrium with minimal information exchange.

## Contribution

It introduces a novel distributed power control method using fractional programming and penalty functions, ensuring existence and uniqueness of Nash equilibrium in small cell networks.

## Key findings

- Significant improvements in energy efficiency demonstrated in simulations
- The proposed scheme converges to a unique Nash equilibrium
- Reduced information exchange among small base stations

## Abstract

In this paper, energy efficient power control for small cells underlaying a macro cellular network is investigated. We formulate the power control problem in self-organizing small cell networks as a non-cooperative game, and propose a distributed energy efficient power control scheme, which allows the small base stations (SBSs) to take individual decisions for attaining the Nash equilibrium (NE) with minimum information exchange. Specially, in the non-cooperative power control game, a non-convex optimization problem is formulated for each SBS to maximize their energy efficiency (EE). By exploiting the properties of parameter-free fractional programming and the concept of perspective function, the non-convex optimization problem for each SBS is transformed into an equivalent constrained convex optimization problem. Then, the constrained convex optimization problem is converted into an unconstrained convex optimization problem by exploiting the mixed penalty function method. The inequality constraints are eliminated by introducing the logarithmic barrier functions and the equality constraint is eliminated by introducing the quadratic penalty function. We also theoretically show the existence and the uniqueness of the NE in the non-cooperative power control game. Simulation results show remarkable improvements in terms of EE by using the proposed scheme.