162 THE CALCULATION OF RADAR DETECTION PROBABILITY 



the effective number of pulses integrated n are those contained within the 



antenna beamwidth. The optimum number of pulses to integrate will differ 



slightly from this.^^ 



The effective power within the antenna beamwidth will be proportional 



to the following integral. 



re/2 



Total received power = / d'-^'/o.ise' ^^ == 0.686. (3-46) 



7 -e/2 



Thus, where the maximum power of the pulses in a Gaussian beam is unity, 

 the equivalent power of uniform pulses is only 0.68, giving a scan loss of 

 1.7db.i« 



A second problem concerns the number of pulses integrated when the 

 scan is complex. Where it is probable that there is a substantial non- 

 uniformity in the pulse distribution, a pulse count should be carried out. 

 That is, the actual number of pulses returned from typical target locations 

 for a sample scan would be determined by counting them. More usually, 

 it is adequate simply to use the average number of pulses per scan as was 

 done in Paragraph 3-3 for the example illustrating the calculation of the 

 single-scan probability of detection. The beam area was divided into the 

 scan area to give the number of beams per scan. This number was in turn 

 divided into the total number of pulses per scan to yield the received pulses 

 per scan. 



3-5 THE CALCULATION OF DETECTION PROBABILITY 

 FOR A PULSED DOPPLER RADAR 



With proper interpretation, the methods developed in Paragraphs 3-3 

 and 3-4 are applicable to a variety of types of radar systems. To illustrate 

 how this can be carried out, we shall develop some of the details of such an 

 application to the gated pulsed doppler radar described in Paragraph 6-6, 

 whose functional block diagram is given in Fig. 6-25. This type of radar 

 transmits pulses at a very high repetition rate in order to avoid doppler 

 frequency ambiguities. The duty ratio is also considerably greater than in 

 a conventional pulse radar. All the possible target ranges (ambiguous) are 

 gated into separate filter banks which cover the spectrum of possible 

 doppler frequencies. The filters respond to the fundamental component of 

 the gated doppler signal which is received. 



Single-Scan Probability of Detection. The idealized range for this 

 type of system is essentially given by Equation 3-9. This is restated in 

 Chapter 6 as Equation 6-39 with the effects of the signal and gating duty 



'^L. V. Blake, "The Number of Pulses per Beamwidth in a Scanning Radar," Proc. IRE, 

 June, 1953. 



'^A scan loss of L6 db was obtained by L. V. Blake in the paper cited in footnote 15. 



