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130 InternatIonal Journalof electronIcs & communIcatIon technology

IJECT Vol. 2, SP-1, DEC. 2011 ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)

w w w . i j e c t . o r g

Abstract

Range resolution for a given radar can be signicantly improved

by using very short pulses. Unfortunately, utilizing short pulses

decreases the average transmitted power, which can hinder the

radars normal modes of operation, particularly for multi-function

and surveillance radars. Since the average transmitted power

is directly linked to the receiver SNR, it is often desirable

to increase the pulse width while simultaneously maintaining

adequate range resolution. This can be made possible by using

pulse compression techniques. Pulse compression allows us

to achieve the average transmitted power of a relatively long

pulse, while obtaining the range resolution corresponding to

a short pulse. In this paper, we shall implement two digital

pulse compression techniques. The rst technique is known as

correlation processing which is predominantly used for narrowband and some medium band radar operations. The second

technique is called stretch processing and is normally used for

extremely wide band radar operations.

Keywords

Range resolution, Pulse compression, Stretch correlation

processing.

I. Introduction

The word radar is an abbreviation for Radio Detection and

Ranging. In general, radar systems use modulated waveforms

and directive antennas to transmit electromagnetic energyinto a specic volume in space to search for targets. Objects

(targets) within a search volume will reect portions of this

energy (radar returns or echoes) back to the radar. These

echoes are then processed by the radar receiver to extract

target information such as range, velocity, and other target

identifying characteristics.

A. Pulse Compression and Range Resolution

Range resolution, denoted as R , is radar metric that describes

its ability to detect targets in close proximity to each other

as distinct objects. Radar systems are normally designed to

operate between a minimum range minR and maximum range

maxR

.

The distance between minR and maxR is divided into M range

bins (gates), each of width R ,

max minR R

MR

=

(1)

Targets separated by at least R will be completely resolved in

range. Targets within the same range bin can be resolved in cross

range (azimuth) utilizing signal processing techniques. Consider

two targets located at ranges 1 and 2R , corresponding to timedelays

1t and 2t , respectively.

In general, radar users and designers alike seek to minimize

R in order to enhance the radar performance. As suggested

by Eq (1), in order to achieve ne range resolution one must

minimize the pulse width. However, this will reduce the average

transmitted power and increase the operating bandwidth.

Achieving ne range resolution while maintaining adequate

average transmitted power can be accomplished by using pulse

compression techniques.

B. Radar Pulse Compression

Pulse compression allows us to achieve the average transmitted

power of a relatively long pulse, while obtaining the range

resolution corresponding to a short pulse. Now, we will analyze

analog and digital pulse compression techniques. The rst

technique is known as correlation processing which is

dominantly used for narrow band and some medium band

radar operations. The second technique is called stretch

processing and is normally used for extremely wide bandradar operations.

C. Radar Equation with Pulse Compression

The radar equation for pulsed radar can be written as

( )

2 2

3 44

t

e

P GSNR

R kT FL

=

(2)

where is tp peak power, is pulse width , G is antenna gain, is target RCS, R is range, is Boltzmans constant,

eT is

effective noise temperature, F is noise gure, and L is total

radar losses. Pulse compression radars transmit relatively long

pulses (with modulation) and process the radar echo into veryshort pulses (compressed). One can view the transmitted pulse

to be composed of a series of very short subpulses (duty is

100%), where the width of each sub pulse is equal to the desired

compressed pulse width. Denote the compressed pulse width

as c . The SNR for the uncompressed pulse is given as

( )

( )

2 2

3 44

t c

e

P n GSNR

R kT FL

==

(3)

where n is the number of subpulses. Eq (3) is denoted as the

radar equation with pulse compression. For a given set of radar

parameters, and as long as the transmitted pulse remains

unchanged, then the SNR is also unchanged regardless of the

signal bandwidth. More precisely, when pulse compressionis used, the detection range is maintained while the range

resolution is drastically improved by keeping the pulse width

unchanged and by increasing the bandwidth. Remember that

range resolution is proportional to the inverse of the signal

bandwidth,

2R c B = (4)

D. LFM Pulse Compression

Linear FM pulse compression is accomplished by adding

frequency modulation to a long pulse at transmission, and by

using a matched lter receiver in order to compress the receivedsignal. As a result, the matched lter output is compressed

by a factor B = , where is the pulsewidth and isthe bandwidth. Thus, by using long pulses and wideband LFM

modulation large compression ratios can be achieved. Figure

Radar Pulse Compression1M. Vamsi Krishna, 2K. Ravi kumar, 3K. Suresh, 4V. Rejesh

1,3 Dept. of ECE, Chaithanya Engineering College, Visakhapatnam, A.P, India2,4 Dept. of ECE, Regency Institute of Technology, YANAM, UT of Pudecherry, India

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InternatIonal Journalof electronIcs & communIcatIontechnology 131

IJECT Vol. 2, SP-1, DEC. 2011ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)


1 shows an ideal LFM pulse compression process. Part (a)

shows the envelope for a wide pulse 2 1B f f= , part (b) shows

the frequency modulation with bandwidth. Part (c) shows the

matched lter time-delay characteristic, while part (d) shows

the compressed pulse envelope. Finally part (e) shows the

Matched lter input/output Waveforms.

Fig. 1: Ideal LFM pulse compression

II. Correlation Processor

Radar operations (search, track, etc.) are usually carried out

over a specied range window, referred to as the receive window

and dened by the difference between the radar maximum and

minimum range. Returns from all targets within the receive

window are collected and passed through a matched lter

circuitry to perform pulse compression. One implementation

of such analog processors 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. Since the matched lter is a linear time invariant system,

its output can be described as the convolution between its input

and its impulse response. When using pulse compression, it is

desirable to use modulation schemes that can accomplish a

maximum pulse compression ratio, and can signicantly reduce

the side lobe levels of the compressed waveform. For the LFM

case the rst side lobe is approximately 13.5 dB below the main

peak, and for most radar applications this may not be sufcient.

In practice, high side lobe levels are not preferable because

noise and/or jammers located at the side lobes may interferewith target returns in the main lobe. Weighting functions

(windows) can be used on the compressed pulse spectrum in

order to reduce the side lobe levels. However, this approach

is rarely used, since amplitude modulating the transmitted

waveform introduces extra burdens on the transmitter.

III. Stretch Processor

Stretch processing, also known as active correlation,

is normally used to process extremely high and width 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 PassFiltering (LPF) and coherent detection. Next, Analog to Digital

(A/D) conversion is performed; and nally, a bank of Narrow

Band Filters (NBFs) is used in order to extract the tones that are

proportional to target range, since stretch processing effectively

converts time delay into frequency. All returns from the same

range bin produce the same constant frequency. 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 receive-window, which is computed from the difference

between the radar maximum and minimum range. Denote the

start frequency of the reference chirp as r . Consider the case

when the radar receives returns from a few close (in time or

range) targets. Mixing with the reference signal and performing

low pass ltering are effectively equivalent to subtracting the

return frequency chirp from the reference signal.

And hence, target returns appear at constant frequency tones

that can be resolved using the FFT. Consequently, determining

the proper sampling rate and FFT size is very critical. The rest of

this section presents a methodology for computing the proper

FFT parameters required for stretch processing. Assume a

radar system using a stretch processor receiver. The pulse width

is and the chirp bandwidth is B . Since stretch processingis normally used in extreme bandwidth cases (i.e., very large),

the receive window over which radar returns will be processed

is typically limited to few meters to possibly less than 100meters. Declare the FFT size by and its frequency resolution

by . The frequency resolution can be computed using the

following procedure: consider two adjacent point scatterers at

range1

R &2

R . The minimum frequency separation, between

those scatterers so that they are resolved can be computed.

More precisely, the maximum resolvable frequency by the FFT

is limited to the region 2N f . Thus, the maximum resolvable

frequency is

( )max min2 22

recB R R BRN f

c c

> =

(5)

Collecting terms from Eq (5) yields

2

recN BT>

(6)

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

2

m

FFTN N =

(7)m is a nonzero positive integer. The sampling interval is then

given by

1 1

s

s FFT FFT

f TT N fN

= =

(8)

IV. Implementation And Results

The implementation of the paper is carried out in threephases. In the rst phase the suitability of various waveforms

for pulse compression is evaluated by computing and plotting

the ambiguity function of various waveforms viz Rectangular

Pulse, Linear Frequency Modulation (LFM), Pulse Train, Barker

Sequence. In the second phase, system level implementation

of Correlation Processor used in low bandwidth radar receiver

applications is done using MATLAB and results are obtained for

various target congurations. In the third phase, system level

implementation of Stretch Processor using for wide bandwidth

radar receiver applications is done using MATLAB and results

are obtained for various target congurations.

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132 InternatIonal Journalof electronIcs & communIcatIon technology

IJECT Vol. 2, SP-1, DEC. 2011 ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)


Fig. 2: Single Pulse

Fig. 3: Linear Frequency Modulation

Fig. 4: Coherent Pulse Train

Fig. 5: Barkar code

V. Conclusion

Two LFM pulse compression techniques are dealt with in thisproject. The rst technique is known as correlation processing.

which is predominantly used for narrow band and some

medium band radar operations. The second technique is

called stretch processing and is normally used for extremely

wide band radar operations. This paper involves system level

implementation of two popular pulse compression techniques

in MATLAB (correlation processing and stretch processing) to

facilitate simulation and design of the system in software.

System level simulation and design helps in evaluating the

performance of the system before implementing the hardware

prototype. The range resolution of the target is enhanced by

using both the techniques. The correlation processor is bestsuited for narrow band applications and is observed during

simulation. The stretch processor is suited for extreme wide

band applications of radar and is also studied in the simulation.

The characteristics of both the processors are being studied.

Software designing for the above processors implemented and

performance of the system can be evaluated.

VI. Future Scope of the Work

Evaluation of more complex codes such as Polyphase,

Quadriphase, and orthogonal codes which have better

waveform/correlation properties. Implementation of new

complex digital receivers and performance comparison with

the present day receivers. Implementation of this MATLAB code

practically by using a DSP processor.

References

1 Barton, D. K., Modern Radar System Analysis, Artech

House, Norwood, MA, 19 88.

2 Blake, L. V., A Guide to Basic Pulse-Radar Maximum

Range Calculation Part- I Equations, Denitions, and

Aids to Calculation, Naval Res. Lab. Report 5868, 1969.

3 Carpentier, M. H., Principles of Modern Radar Systems,

Artech House, Norwood, MA, 1988

4 Costas, J. P., A Study of a Class of Detection Waveforms

Having Nearly Ideal Range-Doppler Ambiguity Properties,Proc. IEEE 72, 1984, pp. 996- 1009.

5 Mahafza, B. R., Sajjadi, M., Three-Dimensional SAR

Imaging Using a Linear Array in Transverse Motion, IEEE

- AES Trans., Vol. 32, No. 1, January 1996, pp. 499-510.

6 Mahafza, B. R., Introduction to Radar Analysis, CRC

Press, Boca Raton, FL, 1998.

7 Rihaczek, A. W., Principles of High Resolution Radars,

McGraw-Hill, New York, 1969.

8 Kerdock,A.M.,R.Mayer, D.Bass longest binary pulse

compression codes with given peak sidelobe levelsProc.

IEEE 74 .

9 Kerdock,A.M.,R.Mayer, D.Bass longest binary pulse

compression codes with given peak sidelobe levelsProc.

IEEE 74 .

10 levenon .N, A .Freedman .ambiguity function of

Quadriphase coded Radar pulse . IEEE Trans IT-9 (JAN-

1963

11 Martin .T.A low side lobe IMCON pulse compression

Proc.1976 ieee Ultrasonic Symposium.

12 Mac Williams, F.J., N.J.A.Sloan pseudo random sequences

and arrays Proc.IEEE.64, Dec -1976

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InternatIonal Journalof electronIcs & communIcatIontechnology 133

IJECT Vol. 2, SP-1, DEC. 2011ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)


Vamsi Krishna Mothiki is at present pursuing

his M.Tech in the eld of Digital Electronics

and Communication Systems at Chaitanya

Engineering College, Visakhapatnam. He

worked as Assistant Professor, ECE in

Adam's Engineering College, Paloncha from

2004-2009. He also published a textbook

along with his father Suryaprakash Rao

Mothiki with the tile "Pulse and Digital

Circuits in 2011 for Tata McGrawHill Publishing Company

Ltd, India. His areas of interest are Digital Signal Processing,

Digital Image Processing, Antennas and Radar Systems."

K. Ravi Kumar, received his M.Tech from

JNTUK, Kainada, A.P. India Currently,

he is working as Assistant Professor

in the Department of ECE, Regency

Institute of Technology, Yanam, U.T

of Puducherry. His area of interest isDigital Image processing, Radar Signal

Processing and wireless networking.

K Suresh, received his M.Tech from

Andhra University College of Engineering.

Currently, he is working as Associate

Professor in the Department of ECE,

Chaitanya Engineering College. His areas

of interests are Radar signal Processing,

Electromagnetics, Radar Cross-Section

studies, Antennas and Image

Processing

V.Rajesh graduated in Electronics

Engineering from the Institution of

Engineers (India)and post graduated

in Instrumentation from SRTM and

currently submitted his PhD Thesis

from ECE dept, Andhra University and

research interests includes measuring

and processing of Bio Electric Signals,

Virtual Instrumentation and Image

processing.

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