Moving Target Indicator (MTI) and Clutter Mitigation - MATLAB Simulations for Radar Systems Design - page 303

C i = P c

(7.40)

The clutter power at the output of an MTI is

∞
∫

W () H () 2

C o = d f

(7.41)

– ∞

7.7.1. Two-Pulse MTI Case

In this section we will continue the analysis using a single delay line can-
celer . The frequency response for a single delay line canceler is given by Eq.
(7.6). The single canceler power gain is given in Eq. (7.10), which will be
repeated here, in terms of rather than f ω , as Eq. (7.42),

π f
f r

 2

H () 2

 

---- 

= 4 sin (7.42)

 

It follows that

∞
∫

f 2
2σ t 2

P c
2πσ t

 

 2

π f
f r



----  

C o = ------------------- exp – --------- 4 sin d

 

(7.43)

 

 

– ∞

Now, since clutter power will only be significant for small , then the ratio
is very small (i.e., ). Consequently, by using the small angle
approximation, Eq. (7.43) is approximated by

f

f ⁄ f r σ t « f r

∞
∫



f 2
2σ t 2



P c
2πσ t

 2

π f
f r

------------------- --------- ---- 

C o ≈ exp – 4 d

 

(7.44)

 

– ∞

which can be rewritten as

∞
∫

4 P c π 2
f 2

f 2
2σ t 2

 

1

f 2 C o = --------------- ----------------- exp – --------- d

 

(7.45)

2

 

2πσ t

– ∞

The integral part in Eq. (7.45) is the second moment of a zero mean Gaussian
distribution with variance

σ t 2 σ t 2

. Replacing the integral in Eq. (7.45) by

yields

4 P c π 2
f 2

2

--------------- σ t

C o =

(7.46)

Substituting Eqs. (7.46) and (7.40) into Eq. (7.30) produces