pulse compression radar

8/12/2019 Pulse Compression Radar

1/23

RADAR SYSTEMS : AN INTRODCTION

( Lecture prepared for the delivery at the C.V.Raman College of Engg.,Bhubaneswar, Orissa on Feb.02,2010 )

B.K.SARKAR.

ISRO CHAIR PROFESSOR

DEPT. OF E & ECE

IIT KHARAGPUR


2/23

12. High Resolution Imaging

Real array imaging radars obtain

Y direction resolution by virtue of the real antenna beam coverage on theground which is determined by the physical size of the antenna.

Finer resolution will require longer antennas

Radar images are composed of many dots or picture elements (Pixel) representing RCS

for that area on ground.

Darker arealow RCS

Brighter areaHigh RCS

Rougher the surface higher the RCS

Vegetation is moderately roughappear as grey or light grey in the radar image.


3/23


4/23

The aircraft flies along the track y-direction at velocity v.

Y- direct ion resolut ion is determined by the beamwid th whi le acros s the track, thex-direct ion resolu t ion is determined by the pulse length.

Resolution considerations:

If sufficient resolution is present in both range and cross-range, it may be possible to

construct a radar map of the target, resolving its individual scatterers

Resolution is the ability to separately detect multiple targets or multiple patterns on the

same target.


5/23

Targets can be resolved in four dimensions:

Range

Azimuth

Cross-range

Elevation cross range and

Doppler

Range resolution is the resolution of the multiple scatterers differing in their distance

from the radar

Crossrange resolution is the separation of the scatterers differing in the dimension

normal to range

Horizontal scatterer separation requires azimuth cross-range resolution, vertical requires

elevation cross-range resolution.

Resolution of scatterers differing in Doppler shift requires Doppler resolution.


6/23

Range resolution:

is the ability to separate multiple targets at the same angular position but at

different ranges.

Radar mapping requires resolution for recognizing outlines, boundaries and detailed

differences of various mapped objects.

The required square resolution cell sizes for variety of objects on given below.

Item Square cell size, meters

Coastlines, Cities, Mountains 150

Major Highways, Large airfields 30

City streets, large buildings 15

Vehicles, Houses, Buildings 3


7/23

Pulse radars measure range by transmitting a pulse and timing the returned pulse from

the target.

Transmitted pulse direction by radar pulse period is T.

Assuming that range gates are of duration T, two adjacent points on the ground A and T

which are Rx apart can be resolved by their scattering two adjacent range gates as

shown

Where Rx is the resolution in the x direction or perpendicular to the track.

x

2R 2(R R)t ; tc c

2 R CTor R

c 2

RFrom the fig R

cos

c

2cos

+ D= + t =

D\ t = D =

DD =

a

t=

a


8/23


9/23

In matched transmit/receive radars, usually, the product of pulse duration and the

receiver bandwidth, B is unity, i.e

In the fig the radar has the max. measurable ranges, Rmax which is a function of

interpulse provide T

Beyond this range, the elapsed time between transmitted pulse and target return pulse

will include multiples of interpulse period T, making the measured range ambiguous.

- As an example of resolution along x-direction, consider a radar with a pulse duration of

seconds with a small look-down angle

x

1B 1 or

B

CR2BCos

t = t =

\ D =a

max

CTR

2=

( )cos 1.0a =7T 10-=


10/23

10 7

x

3 10 10R cm 1500cm 15m

2

- D = = =

Range resolution is a function of the transmitted waveform.

Two related factors determine a word resolving capability: compressed pulse width and

waveform bandwidth.

These factors are the result of a third waveform property.

This property is a waves autocorrelation function and is the actual determinant of its

range resolving capability.

Wave evaluation is accomplished using the ambiguity function.


11/23

Range resolution can thus be defined in three ways:

By compressed pulse width

By signal bandwidth

By signal autocorrelation function

pulse width if there is no compression

Compressed pulse width

B Echo waveforms matched bandwidth Hz

( )

C

CTR2

T R C

2

C R2B

TA R C2

- D

D

D

D

R range resolution in metersD -

t -

ct -


12/23

Width of the echo signals auto-correlation function in seconds

Enhanced range resolution is achieved through pulse compression which eliminates theneed to trade target detection capability for range resolution.

Resolution in the y-director (cross range resolution)

Cross-range is resolved width antenna beamwidths. Cross-range resolution of

any radar is given by

R range from radar to target (in meters)

3dB Beamwidth of the antenna in the direction of the resolution

A circular antenna of diameter D with uniform current distribution will have 3dB

beamwidth in radian as

At -

Ry R (if is in radian)D q q;

radian, wavelengthD

lq l -

y RRD

l\ D ;


13/23

Example: A radar with a transmit wavelength , (f = 20GHz), a range to

ground R=5km and an antenna length of l = 5meters will have cross range resolution

of

Doppler Resolution:

Radar resolution can also refer to the ability of a radar to resolve target radial velocity

The Doppler frequency fDproduced by a single-point scatterer at radial velocity is

Doppler resolution of a radar is fundamentally related to coherent-integration time of the

echo signal or signal gathering time.

5

2

5 10 1.5Ry 15m

5 10

D = =

1.5cml =

t t

D D

2v 2fvf for f f

c= =

l?

tJ

D

1fd

TD


14/23

Where fd- Doppler resolution in Hz

TD- the time spent gathering data for the analysis (seconds)

In sample systems, the data gathering time (look time or dwell time) is the sample period

times the number of pulses gathered. Pulse radars sample targets at PRF ratio

Where NLthe no.of samples in a look.

fsthe sample rate, which in a pulsed radar equals the PRF

Coherent integration can be achieved in several ways.

A simple bandpass filter tuned to a Doppler shifted signal will coherently integrate the

signal over an integration time that is approximately equal to the reciprocal of the filter

bandwidth.

Now a days, it is common to carry out Doppler filtering of sampled echo data by usingdiscrete Fourier Transform DFT method.

LD

s

NT

f=

E l


15/23

Example:

A radar transmits a 3.5s pulse at 5.70GHz with a bandwidth of 4.0MHz. The PRF is 550

pps and 64 pulses are processed together. The antenna beamwidth is 1.20. Find how far

targets must be spaced from one another at a range of 20km in range, azimuth cross

range and Doppler.

Ans:

The radar uses pulse compression and the BW is much greater than the reciprocal of

the pulsewidth.

The range resolution from eqn is 37.5m. The crossrange resolution at 20km is TheDoppler resolution is Thus two scatterers at 20km range must be separated by at least

37.5m in range or 418.8m in azimuth cross-range or 8.6Hz in Doppler to be resolved.

Pulse Compression:

is the process of transmitting a wide pulse (for energy and detection) andprocessing it to narrow pulse (for range resolution).

The transmitted pulse is called the expanded pulse and the processed pulse is called

the compressed pulse.

The compression ratio is ECR Ct= t

th d d (t itt d) l idth


16/23

= the expanded (transmitted) pulse width

= compressed (processed) pulse width

Two diff primary classes of pulse compression are used in radars:

analog where the transmit wave contains frequency modulation

across the pulse

and

digital where the transmit pulse is phase coded.

Et

Ct

P l i h BW hi h i h t th th i l f th


17/23

Pulse compression wave has BW which is much greater than the reciprocal of the

expanded pulse width and is approx. reciprocal of the compressed pulse width.

The received echoes are compressed either in a filter matched to the transmit wave or

by the process of correlation with a delayed copy of the transmit wave.

Generally, analog pulse compression is done with matched filters and digital is done by

correlation.

Matched Filter:

A filter matched to a given input signal is an optimum filter for signal reception when the

received signal is corrupted by additive white Gaussian noise.

E

C

1B

1B

where B is the BW

t

t

?

Th filt i ti i l


18/23

The filter is optimum in several senses.

These include maximizing the output signalto noise ratio and maximinzing the

accuracy of parameter estimation (for parameters such as delay, Doppler frequency and

signal amplitude)

A matched filter to an input signal Si(t) with spectrum Si(f) is defined in terms of the

matched filter transfer function H(f) and the corresponding impulse response function

h(t) as follows:

Where G is gain (or loss) of the filter. is a fixed delay through the filter. H(f) is the

Fourier transform of h(t). The asterisk refers to the conjugate form.

The basic relationships stated above, assuming unity gain and the fixed time delay of

zero through the filter, are

j2 f H(f ) GSi*(f )e

and h(t) GSi*( t)

- P t=

= t -

H(f ) GSi*(f )

and h(t) GSi*( t)

=

= -

M t h d filt t ll d i d t t h i t i l I t d th t h i


19/23

Matched filters are not normally designed to match an input signal. Instead, the match is

made to the transmitted waveform which remains constant, regardless of the target.

It is possible to design filters matched to very wideband waveforms

A well known type of matched filter for high resolution radar is the pulse-compression

filter.

Ambiguity function

It reveals the range-Doppler position of ambiguous responses and defines the range and

Doppler resolution

The ambiguity function of a waveform Si(t) can be defined as the

cross-correlation of a Doppler shifted version Si(t) exp(j2fDt) of the waveform with the

unshifted waveform.

DX( , f )t

From the definition of cross correlation e can rite


20/23

From the definition of cross-correlation, we can write

It is common to refer to the absolute value of as the ambiguity surface

of the waveform

The shape of the ambiguity surface is entirely dependent upon waveform parameters.

A normalized expression is obtained by requiring that

With this normalization, the magnitude of the ambiguity function has a value at (0,0) of

unity.

( )

( )

D

D

j2 f t

D 1 1

j2 f t

1 1

X( ,f ) S (t)e S * t dt

S (t)S * t e dt

aP

-

P

-

t = - t

= - t

D

X( ,f )t

( )2

1S t dt 1

-

=


21/23

The basic outline of a matched filter pulse compression system is shown below:

The COHO and a short pulse are fed to H(f) the expansion filter where the transmit


22/23

The COHO and a short pulse are fed to H(f), the expansion filter, where the transmit

waveform is generated.

The output of the H(f) has a pulse width equal to the expanded pulse width.

The expanded pulse is frequency shifted and transmitted.

The echoes and interference are received, frequency shifted back to the COHO freq.

(plus the Doppler shift) and fed to the compression filter.

The response of the compression filter is the complex of that of the expansion filter.

If H(f) = the Fourier transform of h(t)

Then H*(f) = the Fourier transform of h(-t)

Thus any phase change introduced into the signal by H(f) (such as a frequency sweep

across the pulse) is undone in H*(f).

If a short burst of the COHO is expanded in H(f) approximately but not exactly the


23/23

If a short burst of the COHO is expanded in H(f), approximately, but not exactly, the

same short burst of COHO is recovered in H*(f)

Because of the finite nature of the signal used, the compressed wave is not exactly the

same as COHO pulse which was expanded

This introduces the undesired characteristic that the compressed pulse leaks into times

other than that occupied by the echo.

This range leakage allows large interfering signals to hide small desired echoes

For this reason, a mismatched must be introduced the result of which is the

compressed pulse (with window).

This mismatch reduces the leakage with the penalty of increasing the compressed pulse

width.

pulse compression radar

Documents