Pulse Compression - MATLAB Simulations for Radar Systems Design - page 247

Assume a radar system using a stretch processor receiver. The pulsewidth is
and the chirp bandwidth is . Since stretch processing is normally used in
extreme bandwidth cases (i.e., very large ), the receive window over which
radar returns will be processed is typically limited to from a few meters to pos-
sibly less than 100 meters. The compressed pulse range resolution is computed
from Eq. (5.8). Declare the FFT size to be and its frequency resolution to be
. The frequency resolution can be computed using the following procedure:
consider two adjacent point scatterers at range and . The minimum fre-
quency separation, , between those scatterers so that they are resolved can
be computed from Eq. (5.34). More precisely,

τ′ B

B

N

∆ f

R 1 R 2

∆ f

2 B
c τ′

2 B
c τ′

------- ------- ∆ R

∆ f = f 2 – f 1 = ( R 2 – R 1 ) =

(5.38)

Substituting Eq. (5.8) into Eq. (5.38) yields

2 B
c τ′

c
2 B

1
τ′

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

∆ f = = ----

(5.39)

The maximum frequency resolvable by the FFT is limited to the region
. Thus, the maximum resolvable frequency is ± N ∆ f ⁄ 2

2 BR max ( – R min )

2 BR rec
c τ′

N ∆ f
2

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

> = -----------------

(5.40)

c τ′

Using Eqs. (5.30) and (5.39) into Eq. (5.40) and collecting terms yield

N > 2 BT rec

(5.41)

For better implementation of the FFT, choose an FFT of size

2 m

N FFT ≥ N =

(5.42)

m is a nonzero positive integer. The sampling interval is then given by

1
T s N FFT

1
∆ fN FFT

∆ f = ----------------- ⇒ T s = ------------------

(5.43)

MATLAB Function Ðstretch.mÑ

The function Ðstretch.mÑ presents a digital implementation of stretch pro-
cessing. It is given in Listing 5.4 in Section 5.5. The syntax is as follows:

[y] = stretch (nscat, taup, f0, b, scat_range, rrec, scat_rcs, win)

where