The effects of hardware faults on signal detector performance

Given a data sample of fixed size, a nonsequential detector computes a test statistic, compares it to a threshold, and generates a decision variable d*. If d* = 1, we decide that the signal is present, and if d* = 0 we decide that the signal is absent. Let S be the event that the signal is present and let Sc be the event that the signal is absent. The performance of the detector is generally measured by the probability of detection PD* and the probability of false alarm PFA*, where PD* = P (d*=1|S) PFA* = P(d*=1|Sc). Existing treatments of such detection problems implicitly assume that the detector is implemented on hardware that is never faulty. In reality, the computational hardware used to compute the decision variable is liable to failures. It is therefore reasonable to analyze the effect of possible hardware failures on the detector performance criteria and to ascertain if the possibility of failures can or cannot be neglected.