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    • ISSN: 2277 – 9043 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 theradar wave length. The Radar Cross Section of the target determines the power density returned to the radar for aparticular power density incident on the target. The cross section is more dependent on the target shape than itsphysical size. The radar antenna captures a portion of echo energy incident on it. Radar Cross Section fluctuates as afunction of radar aspect angle and frequency. Using the MAT LAB Programming, Prediction of Radar cross section `σ` for simple shapes of targets likeSphere, Ellipsoid and Circular Flat Plate. The methods of controlling radar cross section and penalties ofimplementing these methods are discussed. The four basic techniques for reducing radar cross section (targetshaping, radar absorbing materials, passive cancellation, and active cancellation) are summarized with theiradvantages 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. Introductionscattering and methods of RCS calculation areexamined. Target RCS fluctuations due to aspect The term Radar cross section (RCS) is a measureangle, frequency, and polarization are presented. of power scattered in a given direction when aTarget scattering matrix is developed. Radar cross target is illuminated by an incident wave fromsection characteristics of some simple and complex Radar More precisely it is the limit of that ratio astargets 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 incDetection And Ranging. E scat 2 H scat 2 RADAR is an Electromagnetic system for the   4 R 2 2  4 R 2 2detection and location of objects. Radar operates by E inc H inctransmitting a particular type of waveform anddetecting the nature of the signals reflected backfrom objects Where σ is Radar Cross Section in sq. metersThe Radar Range Equation- The radar rangeequation relates the range of the radar to the E scat is scattered electric fieldcharacteristics 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 ECEDepartment,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 modelinggopi.ece123@gamil.com).Narsapur,India, 9963438298. D.Sekhar,ECE Department, SCET(e-mail: raindrops.sekhoo007@gamil.com).Narsapur,India, 9491018701. 67 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 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 asBecause in the far field either E or H is sufficient todescribe 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 RCSCross Section, let us, now discuss the importance corresponding to this experiment. This plot can beof Radar Cross Section for Naval Targets. reproduced using MATLAB function “rcs_aspect.m”. As indicated by Fig. 3.1(b), RCS3.2. Importance of Radar Cross-Section Prediction for Naval Targets is dependent on the radar aspect angle There are five basic reasons for why the RCSmeasurements are conducted. They give briefknowledge 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 Sectionmeasurement has gained a lot of importance. Figure: 3.2. Illustration of RCS dependency on3.3. 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_aspectcomplex even for simple shape objects associated (scat_spacing, freq)with the exact RCS prediction, approximatemethods become the viable alternative. Themajority of the approximate methods are valid inthe optical region, approximate methods areGeometrical Optics (GO), Physical Optics (PO), 68 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 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 targetfrequency, 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 OBJECTSversus frequency for scatterer spacing of 0.1 and 4.1. Introduction0.7 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 demonstratesRCS 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 afunction of frequency is evident. Little frequencychange can cause serious RCS fluctuation when the In Fig. 3.9, three regions are identified. First isscatterer 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 69 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012Second is the Rayleigh region (small sphere). Inthis case, The region between the optical and Rayleighregions is oscillatory in nature and is called the Mieor 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. WhereFigure: 4.2(b) Normalized backscattered RCS fora perfectly conducting sphere using semi-log scale. The backscattered RCS for a perfectlyconducting sphere is constant in the optical region.For this reason, radar designers typically use Figure: 4.3(b) Ellipsoid backscattered RCS versusspheres 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 isOne widely accepted approximation for theellipsoid backscattered RCS is given by -------4.35 70 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 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 anylinearly 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 edgespherical Bessel function evaluated at β . The RCS effects are collectively directed away fromcorresponding to Eqs. 4.37through4.35 is shown in important viewing angles. The Northrop B-2 alsoFig.4.4 (b) These plots can be reproduced using uses some faceting, especially on the trailing edgesMATLAB 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) TECHNIQUES5.1 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 71 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 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 workFigure: 5.2: The B-2 Spirit was one of the first becomes much more difficultaircraft 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 changesFigure: 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 thereflected back to the radar by means of absorption. anticipated threat angles, frequencies, incidentRadar energy is absorbed through one or more of power densities, and polarization. Knowledge ofseveral mechanisms, which may involve the the threat direction is required, as well as thedielectric or magnetic properties of the materials. In target’s own RCS. A semiactive system is not assummary, the requirements of a RAM for use in complicated in terms of hardware, but the use ofRCS 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 theshould work for two orthogonal polarizations, and appropriate data bases.(3) it should work with the specified aspect anglecharacteristics [4]. To choose a RAM thatsimultaneously satisfies all of these requirements, 6. THE PENALTIES OF RCSRand yet is physically realizable is difficult, if not The first and unavoidable penalty of RCSR isimpossible. Considerations of weight and the additional cost. The others are: reducedenvironment (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 the5.2.3. 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 platformintroducing a secondary scatterer to cancel with the design which is affected by other sensors andreflection of the primary target. This method is also signatures (infrared, acoustic, visual, etc.). Anknown 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 techniquescancel another echo source. This can be were presented. Of the four, the use of shaping andaccomplished for relatively simple objects, radar absorbing material design are the most usedprovided that a loading point can be identified on to date.the body. 7. RESULTS In addition to this, typical weapons platformsare hundreds of wavelengths in size and have MAT LAB Simulated Resultsdozens, if not hundreds of echo sources. Clearly, it 1. Aspect Angle Vs RCS in dBsm 72 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012Frequency is 3GHz ; Scatter spacing is 0.5 m Fig:7.1 Aspect Angle Vs RCS in dBsm Fig:7.5 Frequency Vs RCS in dBsm2. Aspect Angle Vs RCS in dBsm 6. Sphere: Sphere circumference Vs RCSFrequency is 10GHz ;Scatter spacing is 0.5 m Fig: 7.6(a) Sphere circumference Vs RCS Fig:7.2 Aspect Angle Vs RCS in dBsm3. Aspect Angle Vs RCS in dBsmFrequency is 10GHz ;Scatter spacing is 1.0 m Fig: 7.6(b) Sphere circumference Vs RCSFig:7.3 Aspect Angle Vs RCS in dBsm4. 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=0.95Fig:7.4 Frequency Vs RCS in dBsm Fig: 7.6(c) RCS and aspect angle5. 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 73 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012 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 REFERENCESRCS 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 and10. 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 SectionFrequency = 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 and11. Truncated Cone (Frustum) Propagation, Vol. AP, No. 4, September 1963. [11] J.Rheinstein, “Scattering of Electromagneticr1= 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 Radarof Radar cross section of some simple shapes of Systems”, Tata Mc Graw-Hill,New Delhi. 74 All Rights Reserved © 2012 IJARCSEE
    • ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering Volume 1, Issue 5, July 2012[17] Ruck,G.T.,Barrick,D.E.Stuart,W.D., and R.Gopi Krishna received the B.E. in electronics and CommunicationKrichbaum,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 inWebsite “(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.TechCross Section Analysis & Control”, Artech House, (Embedded systems) at B.V.C Engineering College, From JNT1991. 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 andSection 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 andcommunication Engineering, AP, India. His research interestsinclude antennas, radar, optical communication and Photo Photoelectromagnetics. He has published 3 research papers inconferences. He is a Associate member of Institution ofElectronics and Telecommunication Engineers (IETE) He is aGATE-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 andcommunication Engineering, AP, India. His research interestsinclude Electronic Devices, radar, VLSI design. He has Photopublished 1 research papers in conferences. He is a Associatemember of Institution of Electronics and TelecommunicationEngineers (IETE). 75 All Rights Reserved © 2012 IJARCSEE