APPLICATIONS INVOLVING CHANGES IN ENERGY 



When employing a two-stage procedure with any particular radar, the full 

 power of the radar must, of course, be used in both stages if the best possible 

 detection probability is to be achieved. This policy generally results in using 

 the same per-pulse energy in both stages if the radar is average-power limited 

 but is not (for the waveforms used) peak-power limited. If continual operation 

 at maximum power is impractical, as when the source of energy is so limited by 

 its cost or weight that only a certain average energy can be transmitted per beam 

 position, then the optimum division of energy between the two stages (equivalently, 

 the optimum per-pulse energy for each stage) must be determined for each detec- 

 tion situation under consideration. The determination of these optimum energy 

 levels may involve boundary conditions imposed by peak-power and/or average- 

 power limitations. 



CONCLUDING REMARKS 



Two-stage procedures promise considerable saving over conventional 

 procedures when the target density is low and the radar video is clutter-free. In 

 other environments, two-stage detection systems, like all sequential detection 

 systems, spend too much time in too many sectors. This can be alleviated to 

 some extent by automatically switching to a fixed dwell-time mode in cluttered 

 or jammed sectors. 



For cases where the average number of pulses per beam position is less 

 than about two and a single range-bin is examined in the first stage, calculations 

 showed that the detector with a sequential first stage has a slightly higher de- 

 tection probability than the detector with fixed-sample stages; however, this 

 saving hardly seems enough to compensate for the more complex implementation 

 required by the sequential system and for its slowness in clutter situations. For 

 applications which call for a large average number of pulses per beam position, 

 it seems likely that a detector employing a carefully designed sequential test in 

 the first stage would have a substantially better detection capability than a de- 

 tector with fixed-sample stages, especially if only one or a very few range bins 

 are used in the first stage. The sequential test becomes less suitable as the 

 number of first-stage range bins increases since, as a number of people have 

 demonstrated for a variety of multiple-resolution-element sequential tests, the 

 saving of sequential tests over fixed-sampl^size tests decreases as the number 

 of resolution elements increase. This latter property of sequential tests is the 

 reason for considering their incorporation into two-stage detection procedures 

 when high resolution is required; the benefits of sequential detection may be 

 realized in the detection function of the coarse-resolution first stage, while the 

 fine-resolution requirements are fulfilled in the second stage. 



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