CALCULATING RADAR DETECTION PROBABILITIES BY CONTOUR INTEGRATION (MOMENT GENERATING FUNCTION, MTI RADAR, ORDER STATISTICS, CFAR DETECTION, ROBUST)

Evaluating the performance of signal processing schemes often reduces to computing the error probability in a related hypothesis test. The main theme of this dissertation is to numerically evaluate radar signal processing schemes from contour integrals for error or tail probabilities. The tail probabilities are written as contour integrals that involve the moment generating function (m.g.f.) of the test statistic which obviates the evaluation of an indefinite integral of the density function. Since we are interested in decision thresholds far out on the tails of the distribution and test statistics which are the sum of a large number of processed pulse returns, an efficient numerical procedure is required.; We describe a numerical procedure, saddlepoint integration, that is based on the method of steepest descent and consists of numerical contour integration in the complex plane. After tracing the history of the algorithm, we describe the numerical integration. The trapezoidal rule is employed and we obtain explicit bounds for the truncation error. A generic m.g.f. is used which is applicable in many detection problems.; We evaluate some classical radar detectors for both nonfluctuating and chi-squared fluctuating targets using saddlepoint integration. The method is used with both fixed-threshold and mean-level detectors in which a linear prefilter for moving target detection is employed. The performance analysis of these classical detectors is extended to include some robust constant false-alarm rate detectors that use censoring of the reference samples to mitigate the effect of multiple-target interference. We obtain exact analytical results for systems in which either a single order statistic or a linear combination of order statistics is used to estimate the unknown noise level. The order statistics are drawn from an independent but non-identically distributed population. Although the method of residues suffices for the evaluation of the detection probability, extensions of these problems to ones involving more general target models would require saddlepoint integration.