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PROBLEM 



Apply statistical decision theory to the design of automatic radar detection 

 systems. The specific phase of the problem reported here is the theoretical investi- 

 gation of a system based on a two-stage binomial test which uses low resolution 

 data in the first stage and high resolution data in the infrequently employed 

 second stage. 



RESULTS 



1. Detection probabilities for binomial two-stage detection systems with 

 coarse-fine range resolution have been calculated; they indicate substantial 

 saving over conventional systems. 



2. The use of sequential rather than fixed-sample-size testing in the first 

 stage has been found, in the special cases analyzed, to improve the detection 

 probability only slightly. 



3. In certain clutter-free situations, doubling the number of first-stage range 

 bins used to cover the detection zone (by halving the first-stage pulse length and 

 doubling the instantaneous power) has been shown to cause a loss in detection 

 probability equivalent to roughly 0.3 to 0.5 dB/pulse in signal-to-noise ratio 

 (assuming that the dwell-time, false-alarm rate, and second-stage range resolution 

 are held constant). 



4. The optimum length of the second stage has been shown to vary consider- 

 ably with other design parameters and quantities. 



RECOMMENDATIONS 



1. Extend the analysis of two-stage systems with fixed-sample stages to 

 cases where the radar cross section is slowly fluctuating. 



2. Calculate the cumulative detection probability (the probability that an 

 approaching target is detected before it reaches a given range) for cases of 

 practical interest. 



3. Consider two-stage systems for applications in which the power capability 

 of the radar dictates that the average number of pulses per beam position be large. 



