Performance analysis of single-cycle detectors with applications to signal presence detection

Use of single-cycle detectors for communication signal interception and feature detection has been shown to be, unlike conventional radiometeric techniques, tolerant to an uncertain noise and interference environment. Work in this dissertation extends the analysis of single-cycle detector (SCD) performance for SCD designs satisfying a certain technical assumption. SCD designs satisfying the technical assumption include carrier feature detectors, but not bit-rate detectors. In particular, methods other than simulation are proposed by which the receiver operating characteristic (ROC) may be evaluated for the case of a cyclostationary signal observed in zero-mean, stationary, white Gaussian noise plus tone interference. An exact, closed form expression is obtained for the single-cycle detector probability of false alarm, {dollar}psb{lcub}fa{rcub}{dollar}. In special cases this expression is easily evaluated. Additional results for {dollar}psb{lcub}fa{rcub}{dollar} are obtained via a generalization of the Gram-Charlier Series. Derivation of the generalized Gram-Charlier Series is included.; The probability of detection, {dollar}psb{lcub}d{rcub}{dollar}, is evaluated using asymptotic arguments. Justification of the use of asymptotic arguments comes directly from work performed in finding {dollar}psb{lcub}fa{rcub}{dollar}. Although the absolute accuracy of this approach is limited by the approximations made, demands on the absolute accuracy of {dollar}psb{lcub}d{rcub}{dollar} are typically minor. A secondary result obtained when finding {dollar}psb{lcub}d{rcub}{dollar} is the asymptotic Gaussianity of the output of narrowband discrete-time linear systems with cyclostationary input signals. The results obtained for {dollar}psb{lcub}d{rcub}{dollar} and {dollar}psb{lcub}fa{rcub}{dollar} are applied to various sample detection problems.