3-5] DETECTION PROBABILITY FOR A PULSED DOPPLER RADAR 167 



^ - '"{Is) - IT-9- (•«5) 



The normalized range decrement is thus 



The resulting cumulative probability is also plotted in Fig 3-14. 



Postdetection Filtering. It is not uncommon in pulsed doppler 

 systems to use a predetection doppler filter which is considerably wider than 

 the reciprocal of the observation time of the signal. Subsequent post- 

 detection filtering is matched to the signal observation time to provide the 

 maximum output signal-to-noise ratio. In this manner the number of 

 doppler filters required can be materially reduced at the expense, of course, 

 of velocity resolution. The filtering or integration is also somewhat less 

 efficient because it is noncoherent representing an operation on the detected 

 signal plus noise. 



An exact analysis of postdetection filtering is not possible in general, and 

 we shall look for reasonable approximations. Postdetection filtering is 

 essentially similar to video pulse integration, whose eff'ect on detection was 

 discussed in some detail in Paragraph 3-3, and it is natural to use this 

 approach in establishing the approximate effect of this operation. What 

 we shall do is to derive an equivalent predetection bandwidth which 

 provides approximately the same detection performance as the combination 

 of pre- and postdetection filters which it represents. It is assumed that the 

 target fluctuates from scan to scan but has a constant size during the 

 observation time. 



The following notation is adopted: 



B = predetection bandwidth (band pass) 

 ^ = postdetection bandwidth (low pass) 

 B' = equivalent predetection bandwidth (band pass) 

 n = equivalent number of signal samples integrated 



The output of the bandpass predetection filter can be represented by a 

 series of samples separated by 1 /B (seconds) as was indicated in Paragraph 

 3-3 where the sampling theorem is quoted. Similarly, the output of the 

 low-pass, postdetection filter can be represented by a series of samples 

 spaced by 1/2^ (seconds). In order to provide signal integration the 

 postdetection sampling time will be longer than that of the predetection 

 signal. The ratio of these sampling times gives the number of predetection 

 samples which are integrated in the postdetection filter: 



Equivalent number of samples integrated = n = Bjlb. (3-57) 



