On the solutions of the minimum energy problem in one dimensional sensor networks

TL;DR

This paper analyzes the minimum energy problem in one-dimensional wireless sensor networks, establishing solutions for various cost functions and showing the equivalence of different problem formulations under certain transmission methods.

Contribution

It provides a comprehensive analysis of the minimum energy problem with general cost functions and proves the equivalence of solutions in specific physical layer transmission scenarios.

Findings

Solutions coincide for point-to-point transmission with power adjustment

Applicable to cost functions with arbitrary exponents a, b and parameter λ

Framework unifies energy optimization approaches in sensor networks

Abstract

We discuss solutions of the minimum energy problem in one dimensional wireless sensor networks for the data transmission cost function $E(x_i,x_j) = d(x_i,x_j)^a + \lambda \;d(x_i,x_j)^b$ with any exponent $a,b\in R$ and $\lambda \geq 0$, where $d(x_i,x_j)$ is a distance between transmitter and receiver. We define the minimum energy problem in terms of sensors signal power, transmission time and capacities of a transmission channels. We prove, that for the point-to-point data transmission method utilized by the sensors in the physical layer, when the transmitter adjust the power of its radio signal to the distance to the receiver, the solutions of the minimum energy problem written in terms of data transmission cost function and in terms of the sensors signal power coincide.