Performance Degradation by Postdetector Nonlinearities

A computer program was developed that would draw receiver operating characteristic curves for a system using an envelope detector to search for CW signals in narrowband Gaussian noise.1 The program computed the probability that the detector output would exceed a chosen threshold under two circumstances: (i) No signals were present; this result gives the probability of false alarm, PFA. (ii) Signals at various S / N were present; this result gives the probability of detection, PD. S / N is the ratio of the CW signal power to the noise power ac* The X . S. Navy supported this work under contract N600(63133)64940. T 407 408 T H E BELL SYSTEM TECHNICAL J O U R N A L , MARCH 19G8 companying it in the specified narrow band. These probabilities were calculated using formulas which described the appropriate distributions of the detector output. The program also averaged independent samples of the detector output, and produced appropriate receiver operating characteristic curves by deriving a Gram-Charlier A series for the distribution of the sample average. When the program was adapted to take into account the modifications of the detector output caused by various subsequent nonlinear processes, receiver operating characteristic curves were produced for systems in which such processes occurred. The performance degradation was determined as the change in S/N that would be required to make the detectability of a signal, for given probability of false alarm, the same as without the nonlinear process.