Radar Detection - MATLAB Simulations for Radar Systems Design - page 107

P D

.5

1

R ⁄ 10

Figure 2.17. Cumulative probability of detection versus normalized range.

2.9. Constant False Alarm Rate (CFAR)

The detection threshold is computed so that the radar receiver maintains a
constant pre-determined probability of false alarm. Eq. (2.19b) gives the rela-
tionship between the threshold value and the probability of false alarm
, and for convenience is repeated here as Eq. (2.100):

V T

P fa

1
P fa



2ψ 2

------ 

V T = ln

(2.100)

ψ 2

If the noise power is assumed to be constant, then a fixed threshold can sat-
isfy Eq. (2.100). However, due to many reasons this condition is rarely true.
Thus, in order to maintain a constant probability of false alarm the threshold
value must be continuously updated based on the estimates of the noise vari-
ance. The process of continuously changing the threshold value to maintain a
constant probability of false alarm is known as Constant False Alarm Rate
(CFAR).

Three different types of CFAR processors are primarily used. They are adap-
tive threshold CFAR, nonparametric CFAR, and nonlinear receiver techniques.
Adaptive CFAR assumes that the interference distribution is known and
approximates the unknown parameters associated with these distributions.
Nonparametric CFAR processors tend to accommodate unknown interference
distributions. Nonlinear receiver techniques attempt to normalize the root
mean square amplitude of the interference. In this topic only analog Cell-Aver-
aging CFAR (CA-CFAR) technique is examined. The analysis presented in this
section closely follows Urkowitz 1 .

1. Urkowitz, H., Decision and Detection Theory , unpublished lecture notes. Lockheed
Martin Co., Moorestown, NJ.