Search

A signal (if present) is located somewhere in a band of frequencies characterized by a total of N search bins. The signal occupies an arbitrary set of M_ of these bins, where not only is M_ unknown, but also, the locations of the particular M_ occupied bins are unknown. Also, the signal strength is unknown. A class of processors, called the power‐law processors, is investigated, in which the available data is raised to the ν‐th power prior to summation over all data values. The receiver operating characteristics have been determined for values of power ν=1, 2, 2.5, 3, ∞ for a wide range of values of M_. These results allow for accurate extraction of required signal‐to‐noise ratios to achieve a specified level of performance, as measured by the false alarm and detection probabilities, Pf and Pd. One of the most surprising and useful results of this study is the discovery that the power‐law processor with ν=2.4 performs near the absolute optimum, even without any knowledge of the number of occupied bins M_ or the signal‐to‐noise ratio.