Near-optimum detection of random signals of unknown location, structure, extent, and strength

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 (common) signal strength per bin, S, is unknown. The detection performance of the v-th power-law device is determined and compared to that of the optimum processor, which is evaluated by a new bounding procedure. For N=1024 and for false alarm and detection probabilities 1E-3 and 0.5, respectively, the best single power-law device, to cover all values of unknown parameter H, is v=2.4, which loses less than 1.2 dB in signal-to-noise ratio with respect to the optimum processor.