Surface and Volume Clutter - MATLAB Simulations for Radar Systems Design - page 271

From Fig. 6.7 the following relations can be derived

θ r = asin ( h r ⁄ R )

(6.12)
(6.13)
(6.14)

θ e =

∆ R g

asin ( ( h t – h r ) ⁄ R )

= ∆ R cos θ r

where ∆ R is the radar range resolution. The slant range ground projection is

R g = R cos θ r

(6.15)

It follows that the main beam and the sidelobe clutter areas are

A MBc = ∆ R g R g θ A

(6.16)
(6.17)

A SLc = ∆ R g π R g

Assume a radar antenna beam G () of the form



2.776θ 2
θ E



G () = exp – ------------------- ⇒ Gaussian

 

(6.18)

2

 

 2

2.78 θ
θ E

 







sin -----

 

 

πθ E
2.78

------------------------------ ----------



  ; θ ≤



 2

sin
x

()



---------------

G () =

2.78 θ
θ E

⇒

(6.19)

   

-----  



   



 

0

; elsewhere

Then the main beam clutter RCS is

σ 0 A MBc G 2 θ e σ 0 ∆ R g θ A G 2 θ e

σ MBc = ( + θ r ) = R g ( + θ r )

(6.20)

and the sidelobe clutter RCS is

σ 0 A SLc ) 2 σ 0 ∆ R g ) 2

σ SLc = ( SL rms = π R g ( SL rms

(6.21)

where the quantity SL rms is the root-mean-square (rms) for the antenna side-

lobe level.

Finally, in order to account for the variation of the clutter RCS versus range,
one can calculate the total clutter RCS as a function of range. It is given by

σ MBc + σ SLc

σ c () = -----------------------------------

(6.22)

) 4

( 1 + ( RR h ⁄ )

where R h is the radar range to the horizon calculated as