This work considers the identification of the available whitespace, i.e., the regions that do not contain any existing transmitter 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 rs using a binary sensing model, and their individual decisions are combined to estimate the available whitespace. The limiting behavior of the recovered whitespace as a function of n and rs 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 optimally scale as log(n) as n gets large. The problem of minimizing the sum absolute error in transmitter localization is also analyzed, and the corresponding optimal scaling of the radio range and the necessary minimum transmitter separation is determined.
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