Near-Optimum Detection Performance of Power-Law Processors for Random Signals of Unknown Locations, Structure, Extent, and Arbitrary Strengths,

Abstract : A signal (if present) is located somewhere in a band of frequencies characterized by a total of N search bins with uniform noise normalized to unit power. The signal occupies an arbitrary set of M of these bins, where not only is extent M unknown, but in addition, the locations of the particular M occupied bins are unknown. Also, the average signal strengths per bin, ?S sub m!for 1 <or= m <or= M, are arbitrary and unknown. The optimum (likelihood ratio) processor can be derived but it cannot be constructed or realized, due to all the unknowns and the voluminous amount of searching required for this scenario. These deleterious conditions force adoption of an approximation to the optimum processor, which leads to a suboptimum processing technique, namely, the v-th power law device, which utilizes absolutely no knowledge of extent M, or locations, structure, or signal strengths ?S sub m! of any sort. The performance of this technique has been accurately evaluated quantitatively, both by analytic means and simulation, in terms of its false alarm and detection probabilities, as functions of N, M, the average signal powers per bin, ?S sub m!, and power law v. Additionally, the absolute limiting detection capability in this environment has been determined quantitatively by means of a new bounding procedure employing signal pairing, for any N and arbitrary signal powers ?S sub m!. The performance levels attained by various actual power law processors lie within 0.1 dB of the ultimate level, for any value of M. The best single compromise power law processor, covering all values of N, is the v = 2.4 device, which loses less than 1.2 dB relative to the unrealistic optimum processor, which must know and use both M and ?S sub m!.