Calculating radar detection probabilities by contour integration

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. A numerical procedure is described 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, the numerical integration is described. 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. Some classical radar detectors are evaluated for both nonfluctuating and chi-squared fluctuating targets using saddlepoint integration.