140 THE CALCULATION OF RADAR DETECTION PROBABILITY 



An extensive discussion of target cross section is given in Chap. 4. The 

 radar cross section of aircraft targets is discussed in Paragraph 4-7 and some 

 typical examples are shown in Figs. 4-20, 4-21, and 4-22. The effective 

 cross sections of sea and ground surface reflections are discussed in Para- 

 graphs 4-10 through 4-13. In this connection, a normahzed cross section 

 is defined as the radar cross-sectional area per unit surface area. This 

 quantity is denoted by o-" and is usually referred to as sigtna zero. With the 

 illuminated surface area denoted by A, the radar cross section and sigma 

 zero are related by 



ex = a'A. (3-6) 



The area of the resolution element on the ground is a function of the pulse 

 length, depression angle, and antenna beamwidths and is given by Eq. 

 4-60a and b. Examples showing the variation of sigma zero with environ- 

 mental conditions and radar frequency are given in Figs. 4-34 through 4-43. 

 The radar range equation is often expressed as the ratio of the received 

 power reflected from the target to the power of some interfering signal. 

 Most commonly, the interfering signal is random noise generated within 

 the receiver; it might also be ground or sea clutter, atmospheric reflections 

 or anomalies, or some sort of jamming. Internal receiver noise is often 

 referred to as thermal noise, not necessarily because it arises physically from 

 electronic agitation but because in characterizing it a comparison is made 

 with noise which does arise from this source. Normally, internal receiver 

 noise determines the maximum range of the radar system; and even when 

 other sources of interference predominate, it provides a useful reference 

 point. The equivalent input noise power of a receiver is normally expressed 

 in the following form.^ 



Equivalent input noise power = A^ = FkTB watts 



= 4 X \0--'FB watts 



where F = noise figure — the factor by which the equivalent input noise 

 of the actual receiver exceeds that of an ideal reference 



k = 1.37 X 10-23 joule /°K = Boltzmann's constant 



T = absolute temperature of noise source — arbitrarily, 290° K 



B = equivalent rectangular bandwidth of the receiver in cycles per 

 second. 



The ratio of the signal and noise powers as given by Equations 3-5 and 

 3-7 yields the signal-to-noise ratio, S /N. 



Signal-to-noise ratio = S/N' = . )3pkRTR'^ ^'^'^■^ 



^See Paragraph 7-3 for a further discussion of receiver noise and the origin of this expression. 



