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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:


D.Sekhar,ECE Department, SCET(e-mail:


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.

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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)

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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.


frequency.


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,

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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 : 4.2(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

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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.

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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

http://en.wikipedia.org/wiki/B-2_Spirit

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Frequency is 3GHz ; Scatter spacing is 0.5 m

Fig:7.1 Aspect Angle Vs RCS in dBsm


Frequency is 10GHz ;Scatter spacing is 0.5 m



Frequency is 10GHz ;Scatter spacing is 1.0 m


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

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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


11. Truncated Cone (Frustum)

r1= 2; r2= 4; h= 8; freq= 9.5GHz ; indicator = 0


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.

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[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


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


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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