# CFAR Detection

CFAR detection is a classical technique of radar detection. In a radar system, if the detection threshold V_{T} is set as a constant value, the false-alarm rate *P**f _{a}* will rise with the increase of interference

*r:*

In a radar system, there are not only the thermal noise within the receiver, but also the interferences from the clutter and the enemy. These interferences are strong in most situations, and their amplitudes vary in different scenes. In that case, the false-alarm rate will not be constant any more. The method to keep a constant false-alarm rate is called CFAR detection [6].

With the development of radar detection, many CFAR detection methods are invented [7-13]. In practical applications, the specific method must be chosen according to the echo distribution. In a low-resolution SAR system, the amplitude of the echo obeys the Rayleigh distribution, while the amplitude of the echo obeys other distributions such as Swerling model [14], lognormal model [15] and v^{2 }distribution. In most SAR data, the Rayleigh distribution assumption is convincing, so the classical CA-CFAR algorithm in Rayleigh distribution is introduced in this section.

Suppose the probability distribution function of clutter y is expressed as

Let x = rr, *V _{0} =* VT, and substitute them into Eq. 2.4.4, it yields

For the new clutter, the false-alarm rate follows Eq. 2.4.6, which is not related to the clutter. The relationship between the derivation r and the mean i is

The principle of CA-CFAR is illustrated in Fig. 2.8.

**Fig. 2.8 ****Principle of CA-CFAR detection**