Pulse Compression - MATLAB Simulations for Radar Systems Design - page 244

5.3.2. Stretch Processor

Stretch processing, also known as Ðactive correlation,Ñ is normally used to
process extremely high bandwidth LFM waveforms. This processing technique
consists of the following steps: First, the radar returns are mixed with a replica
(reference signal) of the transmitted waveform. This is followed by Low Pass
Filtering (LPF) and coherent detection. Next, Analog to Digital (A/D) conver-
sion is performed; and finally, a bank of Narrow Band Filters (NBFs) is used in
order to extract the tones that are proportional to target range, since stretch pro-
cessing effectively converts time delay into frequency. All returns from the
same range bin produce the same constant frequency. Fig. 5.10a shows a block
diagram for a stretch processing receiver. The reference signal is an LFM
waveform that has the same LFM slope as the transmitted LFM signal. It exists
over the duration of the radar Ðreceive-window,Ñ which is computed from the
difference between the radar maximum and minimum range. Denote the start
frequency of the reference chirp as

f r .

Consider the case when the radar receives returns from a few close (in time
or range) targets, as illustrated in Fig. 5.10a. Mixing with the reference signal
and performing low pass filtering are effectively equivalent to subtracting the
return frequency chirp from the reference signal. Thus, the LPF output consists
of constant tones corresponding to the targetsÓ positions. The normalized trans-
mitted signal can be expressed by

µ

   

--- t 2

s 1 () = cos 2π f 0 t + 0 ≤≤ t τ′

(5.26)

   

where µ = B τ′ ⁄ is the LFM coefficient and f 0 is the chirp start frequency.

Assume a point scatterer at range R . The signal received by the radar is

µ
--- t ∆τ

 

) 2 s r () a = cos 2π f 0 ( t ∆τ – ) + ( –

(5.27)

 

where is proportional to target RCS, antenna gain, and range attenuation.
The time delay

a

∆τ is

∆τ = 2 Rc ⁄

(5.28)

The reference signal is

µ

 

--- t 2

 

s ref () 2 = cos 2π f r t + 0 ≤≤ tT rec

(5.29)

   

The receive window in seconds is

2 R max ( – R min ) 2 R rec

c

T rec = ------------------------------------ = -------------

(5.30)

c