Pulse Compression - MATLAB Simulations for Radar Systems Design - page 237

5.3.1. Correlation Processor

Radar operations (search, track, etc.) are usually carried out over a specified
range window, referred to as the receive window and defined by the difference
between the radar maximum and minimum range. Returns from all targets
within the receive window are collected and passed through matched filter cir-
cuitry to perform pulse compression. One implementation of such analog pro-
cessors is the Surface Acoustic Wave (SAW) devices. Because of the recent
advances in digital computer development, the correlation processor is often
performed digitally using the FFT. This digital implementation is called Fast
Convolution Processing (FCP) and can be implemented at base-band. The fast
convolution process is illustrated in Fig. 5.4

matched filter
outp ut

input
signal

multiplier Inv. FFT

FFT

FFT of

stored
replica

Figure 5.4. Computing the matched filter output using an FFT.

Since the matched filter is a linear time invariant system, its output can be
described mathematically by the convolution between its input and its impulse
response,

y () s () h () = •

(5.9)

where is the input signal, is the matched filter impulse response
(replica), and the operator symbolically represents convolution. From the
Fourier transform properties,

s () h ()

•

FFT s () h () { • } = S () H () ⋅

(5.10)

and when both signals are sampled properly, the compressed signal y () can

be computed from

T 1

–

y = { SH ⋅ }

(5.11)

– 1

where is the inverse FFT. When using pulse compression, it is desir-
able to use modulation schemes that can accomplish a maximum pulse com-
pression ratio, and can significantly reduce the sidelobe levels of the
compressed waveform. For the LFM case the first sidelobe is approximately
below the main peak, and for most radar applications this may not be

FFT

13.4 dB