An examination of the use of signal excess as a broadband detection performance model

Many modern sonar systems are developed with signal excess as the performance criteria for detection optimization. For narrowband signals, signal excess is well defined and is directly related to the receiver operating characteristic (ROC) performance. In the case of colored signal or noise, however, signal excess is no longer directly related to the ROC performance and may mislead the sonar control system. We examine the use of signal excess for modeling broadband sonar detection performance of the quadratic detector in the case of colored Gaussian signal and noise. We derive the spectral weighting function twice; once to maximize signal excess and again to maximize ROC performance. We then compare the performance of the two weighting functions. Also presented is a simulation of the optimization of the center frequency and bandwidth with a total transducer output power constraint of the transducer for a fixed range. In the appendix, we review three methods of computing signal excess and validate by Monte Carlo simulation