142 



THE CALCULATION OF RADAR DETECTION PROBABILITY 



Factors to be considered include the model assumed to represent system 

 operation, the effect of the operator, the effect of the target's closing 

 velocity, and the effect of fluctuations in target size. 



Model of System Operation. The notation which we shall adopt in 

 this paragraph is listed below. 



S /N = signal to noise power ratio 



tsc = scan time 



u = video voltage at pulse inte- 

 grator output 



V = video voltage at square law 

 detector output 



rj = false alarm number 



6 = antenna beamwidth 



r = pulse length 



a = received signal voltage 

 (peak) 



fr = pulse repetition frequency 



A^ = noise power 



n = number of pulses illumi- 

 nating a target during scan 



Ro = idealized range 



R = actual range 



R = range rate 



AR = range decrement between 

 scans 



S = received signal power fpeak) 



The radar system model providing the basis for our analysis of the 

 detection process is shown in Fig. 3-1. The target is assumed to be an 

 aircraft at a range R closing on the radar system at a constant range rate R. 



coc = angular carrier frequency 

 (RF or IF) 



cos = scan speed 



Target 

 (possibly fluctuating) 



Range =R 

 Range Rate =R 



Scanning 

 Antenna^/\ 



Noise 



\JI 



Predetection Square - Law Pulse Deci 



Amplifier " ■ i-h,_x ^..i-H-r, — 



Integrator 



Threshold 



RECEIVER 



TRANSMITTER 



I Pulse Rate = f , 



Pulse Length = r 



Fig. 3-1 Radar System Model Assumed for Analysis of Detection Process. 



Two cases are distinguished: (1) a target of constant size and (2) a target 

 whose size fluctuates in accord with a Rayleigh distribution as is discussed 

 in Paragraphs 4-7 and 4-8. 



A pulse radar with a small duty cycle (on the order of a thousandth or 

 less) is assumed. The target is illuminated periodically by a scanning 



