Periodically pulsed sine wave detected with provision for increasing noise

The detection problem arises due to the false-alarm vulnerability of remote unmanned, signal detectors, typical in current wildlife-tracking studies. Some rather old theory is modified to overcome the effects of transient noise sources such as automobile engines or lightning. The resulting equipment is a simple up-down counter, tending to advance in the presence of large signal-to-noise ratio (SNR) and down-count otherwise. Probability of error for various situations is derived, wherein it is shown that false-alarm probability will be upper bounded and then decrease as noise increases above its quiescent level. The cost of the noise protection in terms of probabilities of error versus SNR is indicated by an example.