# Speed Based Optimal Power Control in Small Cell Networks

## TL;DR

This paper proposes a linear power control strategy based on user speed to improve small cell network performance, addressing challenges of high-speed users and frequent handovers.

## Contribution

It introduces a novel speed-based power control law derived from Hamiltonian Jacobi equations, optimizing load and handover performance in small cell networks.

## Key findings

- Significant performance improvements with linear power law.
- Up to 89% enhancement over equal power systems.
- Effective even under random interference and non-ideal conditions.

## Abstract

Small cell networks promise good quality of service (QoS) even for cell edge users, however pose challenges to cater to the high-speed users. The major difficulty being that of frequent handovers and the corresponding handover losses, which significantly depend upon the speed of the user. It was shown previously that the optimal cell size increases with speed. Thus, in scenarios with diverse users (speeds spanning over large ranges), it would be inefficient to serve all users using common cell radius and it is practically infeasible to design different cell sizes for different speeds. Alternatively, we propose to allocate power to a user based on its speed, e.g., higher power virtually increases the cell size. We solve well known Hamiltonian Jacobi equations under certain assumptions to obtain a power law, optimal for load factor and busy probability, for any given average power constraint and cell size. The optimal power control turns out to be linear in speed. We build a system level simulator for small cell network, using elaborate Monte-Carlo simulations, and show that the performance of the system improves significantly with linear power law. The power law is tested even for the cases, for which the system does not satisfy the assumptions required by the theory. For example, the linear power law has significant improvement in comparison with the 'equal power' system, even in presence of time varying and random interference. We observe good improvement in almost all cases with improvements up to 89\% for certain configurations.