On Whitespace Identification Using Randomly Deployed Sensors

TL;DR

This paper analyzes how randomly deployed sensors can identify available whitespace and localize transmitters, revealing optimal scaling laws and deployment strategies for large sensor networks.

Contribution

It provides a comprehensive analysis of whitespace detection and transmitter localization using random sensors, establishing optimal scaling laws and deployment strategies.

Findings

Whitespace recovery scales as log(n)/n with increasing sensors.

Optimal sensor radio range also scales as log(n)/n.

Sensor unreliability does not alter the optimal scaling law.

Abstract

This work considers the identification of the available whitespace, i.e., the regions that are not covered by any of the existing transmitters, within a given geographical area. To this end, $n$ sensors are deployed at random locations within the area. These sensors detect for the presence of a transmitter within their radio range $r_s$, and their individual decisions are combined to estimate the available whitespace. The limiting behavior of the recovered whitespace as a function of $n$ and $r_s$ is analyzed. It is shown that both the fraction of the available whitespace that the nodes fail to recover as well as their radio range both optimally scale as $\log(n)/n$ as $n$ gets large. The analysis is extended to the case of unreliable sensors, and it is shown that, surprisingly, the optimal scaling is still $\log(n)/n$ even in this case. A related problem of estimating the number of transmitters and their locations is also analyzed, with the sum absolute error in localization as performance metric. The optimal scaling of the radio range and the necessary minimum transmitter separation is determined, that ensure that the sum absolute error in transmitter localization is minimized, with high probability, as $n$ gets large. Finally, the optimal distribution of sensor deployment is determined, given the distribution of the transmitters, and the resulting performance benefit is characterized.