  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.
