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International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 5, July 2012

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 3. RADAR CROSS SECTION (RCS)
In this Paper, the phenomenon of target
3.1. Introduction
scattering and methods of RCS calculation are
examined. Target RCS fluctuations due to aspect The term Radar cross section (RCS) is a measure
angle, frequency, and polarization are presented. of power scattered in a given direction when a
Target scattering matrix is developed. Radar cross target is illuminated by an incident wave from
section characteristics of some simple and complex Radar More precisely it is the limit of that ratio as
targets are also introduced. the distance from scatterer to point where the
scattered power is measured approaches infinity.
2. RADAR FUNDAMENTALS 2
lim E scat
 
RADAR is a contraction of the words RAdio R   E inc
Detection And Ranging. E scat
2
H scat
2

RADAR is an Electromagnetic system for the   4 R 2 2
 4 R 2 2
detection and location of objects. Radar operates by E inc H inc
transmitting a particular type of waveform and
detecting the nature of the signals reflected back
from objects Where σ is Radar Cross Section in sq. meters
The Radar Range Equation- The radar range
equation relates the range of the radar to the E scat is scattered electric field
characteristics of the transmitter, receiver, antenna,
target and the environment. 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.
Manuscript received June 15, 2012.
- EM diffracted field: is the total field in the
Radha Krishna Rapaka, Assoc.Prof. in ECE
Department,Swarnandhra College of Engineering presence of the object.
2 .a
&Technology., (e-mail: radhakrishnarapaka@gamil.com).
Narsapur,India, 9490346661. -when  1 (the Rayleigh region), the
Murali Krishna Rapaka, ECE Department,SCET (e-mail: 
muralirapaka@gamil.com).Narsapur,India, 8790837227.
Gopi Krishna Rapaka, ECE Department, JITS(e-mail: scattering from a sphere can be used for modeling
gopi.ece123@gamil.com).Narsapur,India, 9963438298.
D.Sekhar,ECE Department, SCET(e-mail: raindrops.
sekhoo007@gamil.com).Narsapur,India, 9491018701.

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ISSN: 2277 – 9043

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
Fig:3.1(a) Radar cross section of the sphere aspect angle is then changed from zero to 180
a= radius, λ = wavelength degrees, and the composite RCS of the two
2 .a
-when  1 the σ approaches the optical scatterers measured by the radar is computed.

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 Figure: 3.1(b) RCS dependency on aspect angle.
 Angular orientation of target relative to (a) Zero aspect angle, zero electrical spacing.
transmitter and receiver (b) Aspect angle, electrical spacing.
 Frequency or wavelength
 Transmitter polarization
 Receiver polarization.
Having gone through the introductory part of Radar Fig. 3.2 shows the composite RCS
Cross Section, let us, now discuss the importance corresponding to this experiment. This plot can be
of Radar Cross Section for Naval Targets. reproduced using MATLAB function
“rcs_aspect.m”. As indicated by Fig. 3.1(b), RCS
3.2. Importance of Radar Cross-Section Prediction
for Naval Targets is dependent on the radar aspect angle
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.
Figure: 3.2. Illustration of RCS dependency on
3.3. Methods of RCS prediction aspect angle.
Two categories of RCS prediction methods are
MATLAB Function “rcs_aspect.m”
available: exact and approximate.
Exact methods of RCS prediction are very Its syntax is as follows: [rcs] = rcs_aspect
complex even for simple shape objects associated (scat_spacing, freq)
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),

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The material in this section covers two
Next, to demonstrate RCS dependency on topics. First, a review of polarization fundamentals
is presented. Second, the concept of target
frequency, consider the experiment shown in Fig: scattering matrix is introduced.
3.3. Fig: 3.4 and Fig: 3.5 show the composite RCS
4. RCS OF SIMPLE OBJECTS
versus frequency for scatterer spacing of 0.1 and 4.1. Introduction
0.7 meters. 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: 3.3. Experiment setup which demonstrates
RCS dependency on frequency; dist = 0.1, or 0.7 m.

Figure: 4.1. Direction of antenna receiving
backscattered waves.

4.2. Sphere
Figure: 3.4. Illustration of RCS dependency on The PP backscattered waves from a sphere are
frequency. 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
Figure: 3.5. Illustration of RCS dependency on
of order n, and is given by
frequency.

From those two figures, RCS fluctuation as a
function of frequency is evident. Little frequency
change can cause serious RCS fluctuation when the In Fig. 3.9, three regions are identified. First is
scatterer spacing is large.
MATLAB Function “rcs_frequency.m” the optical region (corresponds to a large sphere).
[rcs] = rcs_frequency (scat_spacing, frequ, In this case,
freql)

RCS Dependency on Polarization

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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 4.3(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”
Figure : 4.2(a) Normalized backscattered RCS for [rcs] = rcs_ellipsoid (a, b, c, phi)
a perfectly conducting sphere. Where

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 Figure: 4.3(b) Ellipsoid backscattered RCS versus
spheres of known cross sections to experimentally. aspect angle, φ = 45° .
4.3 Ellipsoid 4.4 Circular Flat Plate
An ellipsoid centered at (0, 0, 0) is shown Fig. 4.4(a) shows a circular flat plate of radius,
in Fig. 4.3. It is defined by the following equation: 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
One widely accepted approximation for the
ellipsoid backscattered RCS is given by
-------4.35

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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
Figure: 4.4(a) Circular flat plate.
on the platform’s mission, and the additional cost
For non-normal incidence, two approximations
of manufacturing and maintenance.
for the circular flat plate backscattered RCS for any
linearly polarized incident waves are
5.2 The Four Basic Techniques of RCSR

The following sections provide a summary of
----------4.36
each RCSR technique.
5.2.1. Shaping
Traditionally, shaping is considered the first step
of RCS control. The Lockheed F-117A (Figure 5.1)
--4.37 is an example of heavily applied surface faceting.
Where k =2π/λ/, and J1(β) is the first order Edges are parallel so that the majority of the edge
spherical Bessel function evaluated at β . The RCS effects are collectively directed away from
corresponding to Eqs. 4.37through4.35 is shown in important viewing angles. The Northrop B-2 also
Fig.4.4 (b) These plots can be reproduced using uses some faceting, especially on the trailing edges
MATLAB function “rcs_circ_plate.m” . of the wing. In planform (Figure 5.2), the straight
edges are dominant.
MATLAB Function “rcs_circ_plate.m” For more “boxy” structures such as ships and
ground vehicles, dihedral and trihedral corners, and
[rcs] = rcs_circ_plate (r, freq)
“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: 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 Figure: 5.1. Planform of the Lockheed F-117.
(Counter Measure)
 To make classification of Targets difficult
to the Radar

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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
Figure: 5.2: The B-2 Spirit was one of the first becomes much more difficult
aircraft to successfully become 'invisible' to radar. 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
Figure: 5.3. Planform of the Northrop B-2 . in the threat signal parameters.
5.2.2. Radar Absorbing Materials The demands for a fully active system are
almost always so severe as to make it impractical.
The radar absorbing materials reduce the energy It requires a transmitter and antennas that cover the
reflected back to the radar by means of absorption. anticipated threat angles, frequencies, incident
Radar energy is absorbed through one or more of power densities, and polarization. Knowledge of
several mechanisms, which may involve the the threat direction is required, as well as the
dielectric or magnetic properties of the materials. In target’s own RCS. A semiactive system is not as
summary, the requirements of a RAM for use in complicated in terms of hardware, but the use of
RCS reduction are: (1) the absorbing material adjustable devices still requires bias lines,
should have adequate frequency response, (2) it controller units, and a computer with the
should work for two orthogonal polarizations, and appropriate data bases.
(3) it should work with the specified aspect angle
characteristics [4]. To choose a RAM that
simultaneously satisfies all of these requirements, 6. THE PENALTIES OF RCSR
and yet is physically realizable is difficult, if not The first and unavoidable penalty of RCSR is
impossible. Considerations of weight and the additional cost. The others are: reduced
environment (e.g., temperature, rain, snow, etc.) payload, added weight, required high maintenance,
play an important role in deciding the thickness of and reduced range or other operational limitations.
any RAM coating. The mission of the platform and the severity of the
5.2.3. Passive Cancellation threat environment will determine the required
RCSR and drive the trade-off study.
Passive cancellation refers to RCS reduction by RCSR is just one aspect of the entire platform
introducing a secondary scatterer to cancel with the design which is affected by other sensors and
reflection of the primary target. This method is also signatures (infrared, acoustic, visual, etc.). An
known as impedance loading. optimum design must be devised in order to
The basic concept is to introduce an echo source maximize the objectives of the platform.
whose amplitude and phase can be adjusted to In this paper the four basic RCSR techniques
cancel another echo source. This can be were presented. Of the four, the use of shaping and
accomplished for relatively simple objects, radar absorbing material design are the most used
provided that a loading point can be identified on to date.
the body. 7. RESULTS
In addition to this, typical weapons platforms
are hundreds of wavelengths in size and have MAT LAB Simulated Results
dozens, if not hundreds of echo sources. Clearly, it 1. Aspect Angle Vs RCS in dBsm

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Frequency is 3GHz ; Scatter spacing is 0.5 m

Fig:7.1 Aspect Angle Vs RCS in dBsm
Fig:7.5 Frequency Vs RCS in dBsm
2. Aspect Angle Vs RCS in dBsm
6. Sphere: Sphere circumference Vs RCS
Frequency is 10GHz ;Scatter spacing is 0.5 m

Fig: 7.6(a) Sphere circumference Vs RCS

3. Aspect Angle Vs RCS in dBsm
Frequency is 10GHz ;Scatter spacing is 1.0 m

Fig: 7.6(b) Sphere circumference Vs RCS

4. Frequency Vs RCS in dBsm 7. Ellipsoid: RCS versus aspect angle.
Frequency is 1GHz; Scatter spacing is 0.1 m a =0 .15; b =0.20; c=0.95

Fig:7.4 Frequency Vs RCS in dBsm Fig: 7.6(c) RCS and aspect angle

5. Frequency Vs RCS in dBsm 8. Ellipsoid: RCS versus aspect angle.
Frequency is 1GHz; Scatter spacing is 1.0 m a = 0.20;b =0.50;c=0.90

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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
Fig: 7.8 RCS and aspect angle techniques summarized.
.
9. Circular flat plate
REFERENCES
RCS of a circular flat plate of radius’ r’
[1] G.T. Ruck, D.E.Barrick, W.D.Stuart and
Frequency in X-Band=12GHz;Radius(r ) = 0.5 m
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
Fig:7.9 RCS and aspect angle
Section Modified by a Dielectric Coating”,IEEE
Tansactions on Antennas and
10. Circular flat plate
Propagation,Vol.46,No.9.
RCS of a circular flat plate of radius’ r’ [4] Lorant A.Muth, “Calibration Standards and
Uncertainties in Radar Cross Section
Frequency = X-Band=12GHz ;Radius(r ) = 0.25 m
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-
Fig: 7.10 RCS and aspect angle 335, May 1996.
[7] V. H. Weston, “Theory of Absorbers in
Scattering,” IEEE Transactions on Antennas and
11. Truncated Cone (Frustum) Propagation, Vol. AP, No. 4, September 1963.
[11] J.Rheinstein, “Scattering of Electromagnetic
r1= 2; r2= 4; h= 8; freq= 9.5GHz ; indicator = 0 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.
Fig: 7.11 RCS and aspect angle Elsherbeni
[15] Eugene F. Knott, John F. Shaeffer, Michael T.
8. CONCLUSIONS Tuley, Radar crossection (2nd Edition), Artech
House , London, 1992.
Using the MAT LAB Programming, Prediction [16] Merrill I.Skolnik,”Introduction to Radar
of Radar cross section of some simple shapes of Systems”, Tata Mc Graw-Hill,New Delhi.

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[17] Ruck,G.T.,Barrick,D.E.Stuart,W.D., and R.Gopi Krishna received the B.E. in
electronics and Communication
Krichbaum,C.K.”Radar Cross Section Hand engineering from Andhra University,
Book”,Volume 2. India , in 2009.He joined JITS
[18] “Federation of American Scientist Official Engineering college as a faculty in
Website “(www.fas.org), 22 June 2003. Department of Electronics and
communication Engineering, AP, India
[19] Asoke Bhattacharyya, D.L. Sengupta, “Radar In 2009. Now he is pursuing M.Tech
Cross Section Analysis & Control”, Artech House, (Embedded systems) at B.V.C Engineering College, From JNT
1991. University, AP, India.His research interests include radar,
[20] B. C. Hoskin, A. A. Baker, “Composite Microprocessors and Embedded systems.
Materials for Aircraft Structures”, AIAA, 1986. .D.Sekhar received the B.E. and
[21] David C. Jenn, “Radar and Laser Cross M.Tech. degrees in electronics and
Section Engineering”, AIAA, 1995. or’s Communication engineering from
Andhra Universit and JNT University,
India , in 2000 and 2010 respectively. In
Photo 2007, he joined Swarnandhra College of
BIOGRAPHIES Engineering and Technology as a
faculty in Department of Electronics
R.Radha Krishna received the B.E. and and communication Engineering, AP, India. His research
M.Tech. degrees in electronics and interests include antennas, radar, optical communication and
Communication engineering from electromagnetics. He is a Associate member of Institution of
Andhra University, India, in 2003 and Electronics and Telecommunication Engineers (IETE).
2009 respectively. In 2004, he joined
Swarnandhra College of Engineering
and Technology as a faculty in
or’s
or’s Department of Electronics and
communication Engineering, AP, India. His research interests
include antennas, radar, optical communication and Photo
Photo
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
or’s Department of Electronics and
communication Engineering, AP, India. His research interests
include Electronic Devices, radar, VLSI design. He has
Photo
published 1 research papers in conferences. He is a Associate
member of Institution of Electronics and Telecommunication
Engineers (IETE).

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