This thesis provides methods for nonparametric analysis and design of incoherent adaptive CFAR detectors. Adaptive CFAR detectors, both parametric and nonparametric, require a reference sample to learn the statistical properties of the noise. An important issue but one that is often overlooked is the need to choose a reference sample that is representative of the noise in the test cell. An approach to dynamically choose these windows is developed and studied. A powerful test for randomness based on the Mann-Kendall rank test is employed in this approach.
Next the issue of when to use a nonparametric test versus a parametric one is discussed. Bounds for rank detectors operating on square-law data are provided. Neyman-Pearson theory on optimal rank tests is used. The results allow the designer to decide if a rank test is suitable. In addition, a method is developed for real-time implementation of an important class of rank tests. This method solves the difficult and open problem of determining detection thresholds.
In situations for which nonparametric detectors cannot achieve reasonable power, parametric approaches must be considered. The OS-CFAR detector of Rohling is shown to possess unique advantages for design and analysis of robust detectors under which improved P fa control and acceptable P d can be both realized and, most importantly, quantified. The ideas of Nonparametric Tolerance Intervals are used to provide an elegant and simple method for analysis and design of this detector in arbitrary noise.
