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Transcript of 67 75
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
67 All Rights Reserved © 2012 IJARCSEE
RADAR CROSS SECTION PREDICTION FOR DIFFERENT
OBJECTS USING MAT LAB AND RADAR CROSS SECTION
(RCS) REDUCTION R.Radha Krishna, Assoc.Prof, R.Murali Krishna, R.Gopi Krishna, D.Sekhar
_____________________________________________________________________
ABSTRACT----Radar Cross Section (RCS) depends on the characteristic dimensions of the object compared to the
radar wave length. The Radar Cross Section of the target determines the power density returned to the radar for a
particular power density incident on the target. The cross section is more dependent on the target shape than its
physical size. The radar antenna captures a portion of echo energy incident on it. Radar Cross Section fluctuates as a
function of radar aspect angle and frequency.
Using the MAT LAB Programming, Prediction of Radar cross section `σ` for simple shapes of targets like
Sphere, Ellipsoid and Circular Flat Plate. The methods of controlling radar cross section and penalties of
implementing these methods are discussed. The four basic techniques for reducing radar cross section (target
shaping, radar absorbing materials, passive cancellation, and active cancellation) are summarized with their
advantages and disadvantages.
Keywords: Active cancellation, Echo energy, Passive cancellation, Radar Cross Section
1. INTRODUCTION
In this Paper, the phenomenon of target
scattering and methods of RCS calculation are
examined. Target RCS fluctuations due to aspect
angle, frequency, and polarization are presented.
Target scattering matrix is developed. Radar cross
section characteristics of some simple and complex
targets are also introduced.
2. RADAR FUNDAMENTALS
RADAR is a contraction of the words RAdio
Detection And Ranging.
RADAR is an Electromagnetic system for the
detection and location of objects. Radar operates by
transmitting a particular type of waveform and
detecting the nature of the signals reflected back
from objects
The Radar Range Equation- The radar range
equation relates the range of the radar to the
characteristics of the transmitter, receiver, antenna,
target and the environment.
Manuscript received June 15, 2012.
Radha Krishna Rapaka, Assoc.Prof. in ECE
Department,Swarnandhra College of Engineering
&Technology., (e-mail: [email protected]).
Narsapur,India, 9490346661.
Murali Krishna Rapaka, ECE Department,SCET (e-mail:
[email protected]).Narsapur,India, 8790837227.
Gopi Krishna Rapaka, ECE Department, JITS(e-mail:
[email protected]).Narsapur,India, 9963438298.
D.Sekhar,ECE Department, SCET(e-mail:
[email protected]).Narsapur,India, 9491018701.
3. RADAR CROSS SECTION (RCS)
3.1. Introduction
The term Radar cross section (RCS) is a measure
of power scattered in a given direction when a
target is illuminated by an incident wave from
Radar More precisely it is the limit of that ratio as
the distance from scatterer to point where the
scattered power is measured approaches infinity. 2
liminc
scat
E
E
R
2 2
2 2
2 24 4
scat scat
inc inc
E HR R
E H
Where σ is Radar Cross Section in sq. meters
E scat is scattered electric field
E inc is field incident at the target
R is the distance to the target from the Radar
Antenna.
-EM scattered field: is the difference between the
total field in the presence of an object and the field
that would exist if the object were absent.
- EM diffracted field: is the total field in the
presence of the object.
-when 1.2
a(the Rayleigh region), the
scattering from a sphere can be used for modeling
raindrops.
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
68 All Rights Reserved © 2012 IJARCSEE
Fig:3.1(a) Radar cross section of the sphere
a= radius, λ = wavelength
-when 1.2
a the σ approaches the optical
cross section πa2. RCS can be expressed as
Because in the far field either E or H is sufficient to
describe the EM wave.
Radar Cross Section is a function of
Position of transmitter relative to target
Position of receiver relative to target
Target geometry and material composition
Angular orientation of target relative to
transmitter and receiver
Frequency or wavelength
Transmitter polarization
Receiver polarization.
Having gone through the introductory part of Radar
Cross Section, let us, now discuss the importance
of Radar Cross Section for Naval Targets.
3.2. Importance of Radar Cross-Section Prediction
for Naval Targets
There are five basic reasons for why the RCS
measurements are conducted. They give brief
knowledge of the following. They are
Acquire understanding of basic scattering
phenomena
Acquire diagnostic data
Verify the system performance
Build a database
Satisfy a contractual requirement.
Due to the above reasons Radar Cross Section
measurement has gained a lot of importance.
3.3. Methods of RCS prediction
Two categories of RCS prediction methods are
available: exact and approximate.
Exact methods of RCS prediction are very
complex even for simple shape objects associated
with the exact RCS prediction, approximate
methods become the viable alternative. The
majority of the approximate methods are valid in
the optical region, approximate methods are
Geometrical Optics (GO), Physical Optics (PO),
Geometrical Theory of Diffraction (GTD), Physical
Theory of Diffraction (PTD), and Method of
Equivalent Currents (MEC). Interested readers may
consult Knott or Ruck (see References) for more
details on these and other approximate methods.
3.4. RCS Dependency on Aspect Angle and
Frequency
Radar cross section fluctuates as a function of
radar aspect angle and frequency. The spacing
between the two scatterers is 1 meter. The radar
aspect angle is then changed from zero to 180
degrees, and the composite RCS of the two
scatterers measured by the radar is computed.
Figure: 3.1(b) RCS dependency on aspect angle.
(a) Zero aspect angle, zero electrical spacing.
(b) Aspect angle, electrical spacing.
Fig. 3.2 shows the composite RCS
corresponding to this experiment. This plot can be
reproduced using MATLAB function
“rcs_aspect.m”. As indicated by Fig. 3.1(b), RCS
is dependent on the radar aspect angle
Figure: 3.2. Illustration of RCS dependency on
aspect angle.
MATLAB Function “rcs_aspect.m”
Its syntax is as follows: [rcs] = rcs_aspect
(scat_spacing, freq)
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
69 All Rights Reserved © 2012 IJARCSEE
Next, to demonstrate RCS dependency on
frequency, consider the experiment shown in Fig:
3.3. Fig: 3.4 and Fig: 3.5 show the composite RCS
versus frequency for scatterer spacing of 0.1 and
0.7 meters.
Figure: 3.3. Experiment setup which demonstrates
RCS dependency on frequency; dist = 0.1, or 0.7 m.
Figure: 3.4. Illustration of RCS dependency on
frequency.
Figure: 3.5. Illustration of RCS dependency on
frequency.
From those two figures, RCS fluctuation as a
function of frequency is evident. Little frequency
change can cause serious RCS fluctuation when the
scatterer spacing is large.
MATLAB Function “rcs_frequency.m”
[rcs] = rcs_frequency (scat_spacing, frequ,
freql)
RCS Dependency on Polarization
The material in this section covers two
topics. First, a review of polarization fundamentals
is presented. Second, the concept of target
scattering matrix is introduced.
4. RCS OF SIMPLE OBJECTS
4.1. Introduction
This section presents examples of backscattered
radar cross section for a number of simple shape
objects. When compared to the optical region
approximation, is overwhelming. Most formulas
presented are Physical Optics (PO) approximation
for the backscattered RCS measured by a far field
radar in the direction (θ,φ) as illustrated in Fig.4.1.
Figure: 4.1. Direction of antenna receiving
backscattered waves.
4.2. Sphere
The PP backscattered waves from a sphere are
LCP, while the OP backscattered waves are
negligible. The normalized exact backscattered
RCS for a perfectly conducting sphere is a Mie
series given by
Where r is the radius of the sphere, k = 2π/λ. λ is
the wavelength Jn, is the spherical Bessel of the
first kind of order n, Hn(1)and is the Hankel function
of order n, and is given by
In Fig. 3.9, three regions are identified. First is
the optical region (corresponds to a large sphere).
In this case,
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
70 All Rights Reserved © 2012 IJARCSEE
Second is the Rayleigh region (small sphere). In
this case,
The region between the optical and Rayleigh
regions is oscillatory in nature and is called the Mie
or resonance region.
Figure : 4.2(a) Normalized backscattered RCS for
a perfectly conducting sphere.
Figure: 4.2(b) Normalized backscattered RCS for
a perfectly conducting sphere using semi-log scale.
The backscattered RCS for a perfectly
conducting sphere is constant in the optical region.
For this reason, radar designers typically use
spheres of known cross sections to experimentally.
4.3 Ellipsoid
An ellipsoid centered at (0, 0, 0) is shown
in Fig. 4.3. It is defined by the following equation:
One widely accepted approximation for the
ellipsoid backscattered RCS is given by
Figure 4.3(a) Ellipsoid.
When, the ellipsoid becomes roll symmetric. Thus,
the RCS is independent of φ, and Eq. is reduced
and for the case when a= b= c.
MATLAB Function “rcs_ellipsoid.m”
[rcs] = rcs_ellipsoid (a, b, c, phi)
Where
Figure: 4.3(b) Ellipsoid backscattered RCS versus
aspect angle, φ = 45° .
4.4 Circular Flat Plate
Fig. 4.4(a) shows a circular flat plate of radius,
centered at the origin. Due to the circular
symmetry, the backscattered RCS of a circular flat
plate has no dependency on φ. The RCS is only
aspect angle dependent. For normal incidence (i.e.,
zero aspect angles) the backscattered RCS for a
circular flat plate is
-------4.35
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
71 All Rights Reserved © 2012 IJARCSEE
Figure: 4.4(a) Circular flat plate.
For non-normal incidence, two approximations
for the circular flat plate backscattered RCS for any
linearly polarized incident waves are
----------4.36
--4.37
Where k =2π/λ/, and J1(β) is the first order
spherical Bessel function evaluated at β . The RCS
corresponding to Eqs. 4.37through4.35 is shown in
Fig.4.4 (b) These plots can be reproduced using
MATLAB function “rcs_circ_plate.m” .
MATLAB Function “rcs_circ_plate.m”
[rcs] = rcs_circ_plate (r, freq)
Figure: 4.4(b) Backscattered RCS for a circular
flat plate.
5. RADAR CROSS SECTION REDUCTION
(RCSR) TECHNIQUES
5.1 Introduction
For military RCS reduction is necessary
because of the following reasons:
To make ships / objects less detectable by
the enemy radar
To increase the effectiveness of Chaff
(Counter Measure)
To make classification of Targets difficult
to the Radar
This chapter evaluates methods of controlling
RCS and the penalties in implementing these
methods. There are four basic techniques for
reducing radar cross section: (1) target shaping, (2)
radar absorbing materials, (3) passive cancellation,
and (4) active cancellation.
Reduction methods are generally limited to a small
spatial region. The platform design process must
address how much RCS reduction is required based
on the platform’s mission, and the additional cost
of manufacturing and maintenance.
5.2 The Four Basic Techniques of RCSR
The following sections provide a summary of
each RCSR technique.
5.2.1. Shaping
Traditionally, shaping is considered the first step
of RCS control. The Lockheed F-117A (Figure 5.1)
is an example of heavily applied surface faceting.
Edges are parallel so that the majority of the edge
effects are collectively directed away from
important viewing angles. The Northrop B-2 also
uses some faceting, especially on the trailing edges
of the wing. In planform (Figure 5.2), the straight
edges are dominant.
For more “boxy” structures such as ships and
ground vehicles, dihedral and trihedral corners, and
“top hats” (right circular cylinders with axes
perpendicular to a flat plane) are the major RCS
contributors. The amount of bulkhead tilt is a trade-
off between RCSR performance and cost.
Figure: 5.1. Planform of the Lockheed F-117.
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
72 All Rights Reserved © 2012 IJARCSEE
Figure: 5.2: The B-2 Spirit was one of the first
aircraft to successfully become 'invisible' to radar.
Figure: 5.3. Planform of the Northrop B-2 .
5.2.2. Radar Absorbing Materials
The radar absorbing materials reduce the energy
reflected back to the radar by means of absorption.
Radar energy is absorbed through one or more of
several mechanisms, which may involve the
dielectric or magnetic properties of the materials. In
summary, the requirements of a RAM for use in
RCS reduction are: (1) the absorbing material
should have adequate frequency response, (2) it
should work for two orthogonal polarizations, and
(3) it should work with the specified aspect angle
characteristics [4]. To choose a RAM that
simultaneously satisfies all of these requirements,
and yet is physically realizable is difficult, if not
impossible. Considerations of weight and
environment (e.g., temperature, rain, snow, etc.)
play an important role in deciding the thickness of
any RAM coating.
5.2.3. Passive Cancellation
Passive cancellation refers to RCS reduction by
introducing a secondary scatterer to cancel with the
reflection of the primary target. This method is also
known as impedance loading.
The basic concept is to introduce an echo source
whose amplitude and phase can be adjusted to
cancel another echo source. This can be
accomplished for relatively simple objects,
provided that a loading point can be identified on
the body.
In addition to this, typical weapons platforms
are hundreds of wavelengths in size and have
dozens, if not hundreds of echo sources. Clearly, it
is not practical to devise a passive cancellation
treatment for each of these sources. Note that there
is a gray area between the technologies of
absorbing materials and passive cancellation. For
example, a layer of lossy dielectric coating applied
to a target could fall into either category.
5.2.4. Active Cancellation
Active cancellation involves the process of
modifying and retransmitting the received radar
signal. Obviously, this requires a challenging task
for the system, as the frequency increases the work
becomes much more difficult
There are two levels of cancellation:
1.Fully active: The cancellation network receives,
amplifies, and retransmits the threat signal such
that it is out of phase with the static RCS of the
target. The transmitted signal amplitude, phase,
frequency and polarization can be adjusted to
compensate for changing threat parameters.
2. Semiactive: No boost in threat signal energy is
provided by the cancellation network, but passive
adjustable devices in the network allow the
reradiated signal to compensate for limited changes
in the threat signal parameters.
The demands for a fully active system are
almost always so severe as to make it impractical.
It requires a transmitter and antennas that cover the
anticipated threat angles, frequencies, incident
power densities, and polarization. Knowledge of
the threat direction is required, as well as the
target’s own RCS. A semiactive system is not as
complicated in terms of hardware, but the use of
adjustable devices still requires bias lines,
controller units, and a computer with the
appropriate data bases.
6. THE PENALTIES OF RCSR
The first and unavoidable penalty of RCSR is
the additional cost. The others are: reduced
payload, added weight, required high maintenance,
and reduced range or other operational limitations.
The mission of the platform and the severity of the
threat environment will determine the required
RCSR and drive the trade-off study.
RCSR is just one aspect of the entire platform
design which is affected by other sensors and
signatures (infrared, acoustic, visual, etc.). An
optimum design must be devised in order to
maximize the objectives of the platform.
In this paper the four basic RCSR techniques
were presented. Of the four, the use of shaping and
radar absorbing material design are the most used
to date. 7. RESULTS
MAT LAB Simulated Results
1. Aspect Angle Vs RCS in dBsm
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
73 All Rights Reserved © 2012 IJARCSEE
Frequency is 3GHz ; Scatter spacing is 0.5 m
Fig:7.1 Aspect Angle Vs RCS in dBsm
2. Aspect Angle Vs RCS in dBsm
Frequency is 10GHz ;Scatter spacing is 0.5 m
Fig:7.2 Aspect Angle Vs RCS in dBsm
3. Aspect Angle Vs RCS in dBsm
Frequency is 10GHz ;Scatter spacing is 1.0 m
Fig:7.3 Aspect Angle Vs RCS in dBsm
4. Frequency Vs RCS in dBsm
Frequency is 1GHz; Scatter spacing is 0.1 m
Fig:7.4 Frequency Vs RCS in dBsm
5. Frequency Vs RCS in dBsm
Frequency is 1GHz; Scatter spacing is 1.0 m
Fig:7.5 Frequency Vs RCS in dBsm
6. Sphere: Sphere circumference Vs RCS
Fig: 7.6(a) Sphere circumference Vs RCS
Fig: 7.6(b) Sphere circumference Vs RCS
7. Ellipsoid: RCS versus aspect angle.
a =0 .15; b =0.20; c=0.95
Fig: 7.6(c) RCS and aspect angle
8. Ellipsoid: RCS versus aspect angle.
a = 0.20;b =0.50;c=0.90
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
74 All Rights Reserved © 2012 IJARCSEE
Fig: 7.8 RCS and aspect angle
9. Circular flat plate
RCS of a circular flat plate of radius’ r’
Frequency in X-Band=12GHz;Radius(r ) = 0.5 m
Fig:7.9 RCS and aspect angle
10. Circular flat plate
RCS of a circular flat plate of radius’ r’
Frequency = X-Band=12GHz ;Radius(r ) = 0.25 m
Fig: 7.10 RCS and aspect angle
11. Truncated Cone (Frustum)
r1= 2; r2= 4; h= 8; freq= 9.5GHz ; indicator = 0
Fig: 7.11 RCS and aspect angle
8. CONCLUSIONS
Using the MAT LAB Programming, Prediction
of Radar cross section of some simple shapes of
targets like Sphere, Ellipsoid, Circular Flat Plate
are obtained.
The RCS variation as a function of frequency is
obtained for two scatters and are presented in
Figures when the scattering spacing is more, RCS
is highly oscillatory. While RCS is less oscillatory
for lower scattering spacing.
The RCS fluctuates as a function of frequency is
evident. The importance of radar cross section
reduction was discussed, and the major RCSR
techniques summarized.
.
REFERENCES
[1] G.T. Ruck, D.E.Barrick, W.D.Stuart and
C.K.Krichbaum” Introduction to Radar Cross-
Section Measurements”, Proc.IEEE, vol.53.
[2] H. Ling, R. Chou, and S.W. Lee, “Shooting
and Bouncing Rays: Calculating the RCS of an
arbitrarily shaped cavity,” IEEE Trans. Antennas
Propagation, vol.37, pp.194-205, Feb. 1989.
[3] Hans C.Strifrs and Guillermo
C.Gaunaurd,”Scattering of Electromagnetic Pulses
by Simple-Shaped Targets with Radar Cross
Section Modified by a Dielectric Coating”,IEEE
Tansactions on Antennas and
Propagation,Vol.46,No.9.
[4] Lorant A.Muth, “Calibration Standards and
Uncertainties in Radar Cross Section
Measurements”, National Institute of Standards and
Technology, Boulder,CO80303.
[5]E.F. Knott,”A progression of high-frequency
RCS prediction
techniques,”Proc.IEEE,vol.73,pp.252-264,Feb.
1985.
[6] R.A. Ross,”Radar cross section of rectangular
flat plates as a function of aspect angle,” IEEE
trans. Antennas Propagation.,vol.Ap-14,pp.329-
335, May 1996.
[7] V. H. Weston, “Theory of Absorbers in
Scattering,” IEEE Transactions on Antennas and
Propagation, Vol. AP, No. 4, September 1963.
[11] J.Rheinstein, “Scattering of Electromagnetic
waves from dielectric coated conducting spheres”,
IEEE Trans.Antennas Propagation.,vol.12, pp.334-
340, May1964.
[12] Prof. G.S.N.Raju,” Radar Engineering and
Fundamentals of Navigational Aids”,
I.K.International Publications, New Delhi, 2008.
[13] Radar Systems Analysis and Design Using
MATLAB, Bassem R. Mahafza
[14] MATLAB Simulations for Radar Systems
Design by Bassem R. Mahafza and Atef Z.
Elsherbeni
[15] Eugene F. Knott, John F. Shaeffer, Michael T.
Tuley, Radar crossection (2nd Edition), Artech
House , London, 1992.
[16] Merrill I.Skolnik,”Introduction to Radar
Systems”, Tata Mc Graw-Hill,New Delhi.
ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012
75 All Rights Reserved © 2012 IJARCSEE
[17] Ruck,G.T.,Barrick,D.E.Stuart,W.D., and
Krichbaum,C.K.”Radar Cross Section Hand
Book”,Volume 2.
[18] “Federation of American Scientist Official
Website “(www.fas.org), 22 June 2003.
[19] Asoke Bhattacharyya, D.L. Sengupta, “Radar
Cross Section Analysis & Control”, Artech House,
1991.
[20] B. C. Hoskin, A. A. Baker, “Composite
Materials for Aircraft Structures”, AIAA, 1986.
[21] David C. Jenn, “Radar and Laser Cross
Section Engineering”, AIAA, 1995.
BIOGRAPHIES
R.Radha Krishna received the B.E. and
M.Tech. degrees in electronics and
Communication engineering from
Andhra University, India, in 2003 and
2009 respectively. In 2004, he joined
Swarnandhra College of Engineering
and Technology as a faculty in
Department of Electronics and
communication Engineering, AP, India. His research interests
include antennas, radar, optical communication and
electromagnetics. He has published 3 research papers in
conferences. He is a Associate member of Institution of
Electronics and Telecommunication Engineers (IETE) He is a
GATE-2007 qualified and UGC NET-Dec.2011 qualified.
R.Murali Krishna received the B.Tech.
and M.Tech. degrees in electronics and
Communication engineering from JNT
University, India , in 2007and 2011
respectively. In 2007, he joined
Swarnandhra College of Engineering
and Technology as a faculty in
Department of Electronics and
communication Engineering, AP, India. His research interests
include Electronic Devices, radar, VLSI design. He has
published 1 research papers in conferences. He is a Associate
member of Institution of Electronics and Telecommunication
Engineers (IETE).
R.Gopi Krishna received the B.E. in
electronics and Communication
engineering from Andhra University,
India , in 2009.He joined JITS
Engineering college as a faculty in
Department of Electronics and
communication Engineering, AP, India
In 2009. Now he is pursuing M.Tech
(Embedded systems) at B.V.C Engineering College, From JNT
University, AP, India.His research interests include radar,
Microprocessors and Embedded systems.
.D.Sekhar received the B.E. and
M.Tech. degrees in electronics and
Communication engineering from
Andhra Universit and JNT University,
India , in 2000 and 2010 respectively. In
2007, he joined Swarnandhra College of
Engineering and Technology as a
faculty in Department of Electronics
and communication Engineering, AP, India. His research
interests include antennas, radar, optical communication and
electromagnetics. He is a Associate member of Institution of
Electronics and Telecommunication Engineers (IETE).
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