Cumulative probability of detection for targets approaching a uniformly scanning search radar

This paper deals with the cumulative detection probability of a search radar when it is scanning uniformly. This is the probability that a target, approaching the radar at a constant radial velocity, is detected at least once by the time it reaches a given range, as distinguished from the more common blip-scan ratio (a single-scan detection probability). It is shown that for constant-velocity targets the range for a given cumulative-detection probability varies as the cube root of the power-aperture product, rather than as the fourth root. Curves of cumulative detection probability, as a function of normalized range, are given for three different target scintillation models. Also, curves of optimum (normalized) frame time, are given as a function of the desired cumulative detection probability for each of the three target scintillation characteristics.