Radar Detection - MATLAB Simulations for Radar Systems Design - page 108

2.9.1. Cell-Averaging CFAR (Single Pulse)

The CA-CFAR processor is shown in Fig. 2.18 . Cell averaging is performed
on a series of range and/or Doppler bins (cells). The echo return for each pulse
is detected by a square law detector. In analog implementation these cells are
obtained from a tapped delay line. The Cell Under Test (CUT) is the central
cell. The immediate neighbors of the CUT are excluded from the averaging
process due to a possible spillover from the CUT. The output of reference
cells ( on each side of the CUT) is averaged. The threshold value is
obtained by multiplying the averaged estimate from all reference cells by a
constant

M

M ⁄ 2

K 0 (used for scaling). A detection is declared in the CUT if

Y 1 ≥ K 0 Z

(2.101)

Cell-averaging CFAR assumes that the target of interest is in the CUT and all
reference cells contain zero mean independent Gaussian noise of variance .
Therefore, the output of the reference cells, , represents a random variable
with gamma probability density function (special case of the Chi-square) with
degrees of freedom. In this case, the gamma pdf is

ψ 2

Z

2 M

2ψ 2 ( – z ⁄ )

( M ⁄ 2 ) – 1

z e

f () = -------------------------------------------- ; z > 0

(2.102)

2 M

⁄ 2

ψ M Γ M

( ⁄ 2 )

reference
cells

guard
cells

guard reference

cells

CUT

cells

… …

input

square law
detector

M ⁄ 2

M

⁄ 2

…

Σ Σ

Σ

Y 1

Z

K 0 Z

K 0

comparator

threshold

output

Figure 2.18. Conventional CA-CFAR.

The probability of false alarm corresponding to a fixed threshold was
derived earlier. When CA-CFAR is implemented, then the probability of false