3-3] DETECTION PROBABILITY FOR A PULSE RADAR 141 



This expression is also referred to as the radar range equation. The receiver 

 bandwidth B is normally determined by the IF amplifier in pulse radar 

 systems, although in some cases subsequent filtering or integration is 

 interpreted as equivalent to a narrowing of the noise bandwidth. 



Another convention is to solve Equation 3-8 for the range when the 

 signal-to-noise ratio is unity. This range is called the idealized radar range 

 and will be denoted by i?o: 



Idealized radar range = Ro = yj ^^^yj^jpp (3-9) 



With this definition, the expression for the signal-to-noise ratio given in 

 Equation 3-8 takes the following simple and useful form: 



Signal-to-noise ratio = S/N = (Ro/R)'. (3-10) 



To provide an illustration of the use of Equation 3-9, let us suppose that 

 an airborne radar system possesses the following parameter values: 



Pt = peak power = 200 kw a = target cross section = 1.0 m^ 



G = antenna gain = 1000 = 30 db F = noise figure = 10 db 



X = wavelength = 3 cm — 0.03 m 5 = IF bandwidth = 1 Mc/sec 



It is convenient to express each parameter in decibels relative to a con- 

 venient set of units and then simply to add these figures with appropriate 

 signs to obtain the logarithm of the idealized range, thus: 



Pt = 83.0 db (milliwatts) F = -10.0 db (unity) 



C = 60.0 db (unity) kTB = 114.0 db (milliwatts) 



X2 = -30.5 db (meters^) Ro* = 183.6 db (meters^) 



(T = db (meters^) i?o = 45.0 db (meters) = 3.89 X 



(4ir)3 = -32.9 db (unity) 10* meters 



= 20.4 n. mi. 



3-3 THE CALCULATION OF DETECTION PROBABILITY 

 FOR A PULSE RADAR 



Target detection is a radar function of primary importance and a 

 necessary preliminary to other important functions such as tracking, 

 resolution, and discrimination. In this paragraph, we shall discuss the 

 detection process and describe methods for estimating its reliability as a 

 function of the radar system and target parameters. Although the develop- 

 ments in this paragraph will relate primarily to pulse radar systems, the 

 principles apply generally to any type of radar system used for detection. 



