R. S. RAVEN 



CHAPTER 3 



THE CALCULATION OF RADAR DETECTION 

 PROBABILITY AND ANGULAR RESOLUTION 



3-1 GENERAL REMARKS 



In establishing the preliminary design of a radar subsystem to meet 

 overall weapons system requirements, the designer must first choose the 

 basic radar organization or configuration. He then endeavors to select the 

 radar parameters so as to provide the required performance with practical 

 equipments. In order to do this rationally, he must have reliable methods 

 for estimating the performance of hypothetical systems. In this chapter, 

 calculations in the critical areas of detection performance and angular 

 resolution will be discussed. The former is a particularly complicated area 

 of analysis because of the statistical problems introduced by receiver noise 

 and target fluctuations. The effects of multiple looks at a target and 

 operator performance further complicate the situation. Techniques for 

 taking these factors into account for a conventional pulse radar and a pulsed 

 doppler radar will be developed. 



The definition of angular resolution and the factors which might act to 

 degrade it will be discussed briefly. These factors include the effects of 

 unequal target sizes, signal-to-noise ratio, receiver saturation, pulsing, and 

 system bandwidth. 



3-2 THE RADAR RANGE EQUATION 



A primary basis for the choice of radar system parameters is the radar 

 range equation. In one form or another, this relation gives the power 

 received from a radar target or the ratio of this signal power to the power 

 of competing noise or other interference from which the signal must be 

 distinguished. We shall briefly consider the origin of the range equation. 



We suppose that a radar transmitter radiates power denoted by Pt 

 isotropically (uniformly in all directions). At a range R, then, the power 

 density or power per unit area will be 



p 



Power density of an isotropic radiator = T~U2' (^-1) 



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