TABLE OF CONTENTS So far this chapter has concentrated on a single echo pulse, assumed the target has definite fixed RCS so its echo is non-fluctuating with fixed power, and explained probabilities of detection based on the echo power relative to the mean of the fluctuating noise plus clutter. Without noise or clutter, non-fluctuating echoes marginally below threshold would never be detected but echoes marginally above threshold would have P D = 1.0. The target RCS or echo power probability density function (PDF) would be a narrow spike of great (theoretically infinite) height enclosing unit area, coinciding with a cumulative probability (CP) step function from 0 to 1.0. Only noise and clutter would introduce uncertainty to spoil the picture.
At very short range, noise and clutter may be small and the threshold is then set via the swept gain function to reject trivially small echoes from birds and so forth. The CP here does approximate a step function. And a few real-life longer-range 'hard' targets, such as reflectors and racons, discussed later, do indeed have nearly constant echo strength. But, as indicated in Chapter 7, Section 7.10, for point target pairs and Chapter 10 for extended targets, echo strength of most targets fluctuates significantly above and below their means. We avoid the term Fades, which might infer reductions only, fade margin then being the echo in hand above that required to achieve the required P D.
It is not essential here for us to dissect...
