ElectronicallyScannedArraysMATLABModelingandSimulation.PDF

1、ElectronicallyScanned ArraysMATLAB Modeling and SimulationEdited by Arik D.BrownBrownCRC Press is an imprint of theTaylor&Francis Group,an informa businessBoca Raton London New YorkElectronicallyScanned ArraysMATLAB Modeling and SimulationEdited by Arik D.BrownMATLAB is a trademark of The MathWorks,

2、Inc.and is used with permission.The MathWorks does not warrant the accuracy of the text or exercises in this book.This books use or discussion of MAT-LAB software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular us

3、e of the MATLAB software.CRC PressTaylor&Francis Group6000 Broken Sound Parkway NW,Suite 300Boca Raton,FL 33487-2742 2012 by Taylor&Francis Group,LLCCRC Press is an imprint of Taylor&Francis Group,an Informa businessNo claim to original U.S.Government worksVersion Date:20120309International Standard

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8、01923,978-750-8400.CCC is a not-for-profit organization that pro-vides licenses and registration for a variety of users.For organizations that have been granted a pho-tocopy license by the CCC,a separate system of payment has been arranged.Trademark Notice:Product or corporate names may be trademark

9、s or registered trademarks,and are used only for identification and explanation without intent to infringe.Visit the Taylor&Francis Web site athttp:/and the CRC Press Web site athttp:/DedicationI dedicate this to the Lord,who gave me the inspiration to write this book;to my wonderful wife,Nadine,who

10、 has never faltered in her belief in my abilities;and to my two children,Alexis and Joshua,whom I hope this will inspire to fulfill their purpose and destiny in life.vContentsPreface.viiAcknowledgments.ixContributors.xiChapter 1 Electronically Scanned Array FundamentalsPart 1.1Arik D.BrownChapter 2

11、Electronically Scanned Array FundamentalsPart 2.35Arik D.BrownChapter 3 Subarrray Beamforming.81Arik D.BrownChapter 4 Pattern Optimization.109Daniel BoeringerChapter 5 Spaceborne Application of Electronically Scanned Arrays.149Timothy CookeChapter 6 Electronically Scanned Array Reliability.177Jabber

12、ia MillerAppendix.A:.Array.Factor.(AF).Derivation.197Appendix.B:.Instantaneous.Bandwidth.(IBW).Derivation.201Appendix.C:.Triangular.Grating.Lobes.Derivation.203viiPrefaceDuring.the.course.of.my.career.at.Northrop.Grumman,.I.have.had.the.plea-pany.Several.years.ago.one.of.the.things.Ies.from.understa

13、nding.the.fundamentals.I.often.saw.antenna.analy-sis.performed.with.no.real.insight.into.key.concepts.for.understanding.and.students.tackling.more.difficult.problems.with.no.textbook.solution.It.is.widely.known.that.an.electronically.scanned.array.(ESA).pattern.can.be.calculated.by.simply.typing.in.

14、the.fft.function.in.MATLAB,.and,.in.the.blink.of.an.eye.you.have.before.you.a.beautifully.colored.ESA.pattern.However,es.to.analyzing.subarray.architectures,.conformal.arrays,.etc.,.it.is.imperative.that.the.fundamentals.of.an.ESA.are.knownas.opposed.to.how.to.type.the.word.fft.or.fftshift.in.MATLAB

15、.One.of.the.goals.of.this.book.is.to.provide.a.vehicle.whereby.those.who.are.new.to.ESAs.can.get.a.fundamental.understanding.of.how.they.work,.and.also.to.provide.code.to.run.as.an.aid.without.having.to.start.from.scratch.Several.years.ago.I.had.the.honor.and.privilege.of.taking.the.reins.of.an.ESA.

16、course.that.was.being.given.to.customers.who.were.unfamiliar.with.ESA.technology,.and.who.might.not.understand.some.of.the.funda-mental.concepts.One.of.my.mentors,.Bill.Hopwood,.was.the.originator.of.this.course,.and.it.has.proven.quite.beneficial.in.educating.new.customers.on.our.ESA.expertise.at.N

17、orthrop.Grumman.I.also.wanted.this.book.to.be.a.reference.that.I.could.refer.to.those.who.had.an.interest.in.learning.more.about.ESAs.and.wanted.more.than.just.a.cursory.top-level.introduction.Last,.this.book.is.intended.to.serve.as.both.a.textbook.in.a.college/uni-versity.setting.as.well.as.a.refer

18、ence.for.practicing.engineers.MATLAB.is.one.of.the.best.tools.available.for.exploring.and.understanding.science.and.engineering.concepts.The.code.provided.within.this.book.is.a.great.vehicle.for.understanding.the.analysis.and.simulation.of.ESAs.Tprised.of.six.chapters.Chapters.1.and.2.deal.pri-maril

19、y.with.the.fundamentals.of.ESA.theory.that.should.be.a.part.of.the.knowledge.base.of.anyone.who.is.serious.about.ESAs.Concepts.such.as.beamwidth,.grating.lobes,.instantaneous.bandwidth,.etc.,.are.covered.in.viiiPrefacedetail.Chapter.1.focuses.solely.on.one-dimensional.ESAs,.while.Chapter.2.delves.in

20、to.two-dimensional.ESA.analysis.and.includes.coordinate.definitions,.sine.space,.and.pattern.analysis.Chapters.3.and.4.build.upon.the.fundamental.ESA.topics.covered.in.Chapters.1.and.2,.and.advances.to.subarrays.and.pattern.optimi-zation.Chapter.3.focuses.on.subarray.architectures.and.the.nuances.in

21、volved.with.subarrayed.architectures,.such.as.phase.vs.time.delay.steering,.instantaneous.bandwidth.considerations,.and.the.utility.of.digital.beamforming.The.chapter.concludes.with.the.analysis.of.over-lapped.subarrays.Chapter.4.was.written.by.my.colleague,.Dr.Daniel.Boeringer.It.focuses.on.pattern

22、.optimization.Developing.methodologies.for.optimiz-ing.the.spatial.distribution.of.sidelobes.is.of.great.importance,.and.this.chapter.provides.an.introduction.to.pattern.optimization.and.the.added.capability.it.provides.Chapters.5.and.6.cover.topics.that.have.not.been.explored.as.thor-oughly,.if.at.

23、all,.by.other.books.in.regard.to.ESAs.Presenting.this.infor-mation.is.extremely.exciting.and.I.think.it.will.be.of.great.benefit.to.the.reader.Chapter.5.focuses.on.the.application.of.ESAs.in.a.space.environ-ment.This.chapter.was.written.by.an.extremely.talented.system.engineer,.Timothy.Cooke.The.cha

24、pter.focuses.on.pattern.projections,.translation.of.sine.space.to.latitude/longitude.coordinates.for.ESAs.operating.in.an.orbital.regime,.and.covers.some.basic.astrodynamics.principles.that.are.necessary.to.understand.when.analyzing.space-based.applications.for.ESAs.Chapter.6.concludes.with.reliabil

25、ity.aspects,.which.are.quite.frankly,es.to.analyzing.ESAs.The.material.in.this.chapter.is.based.primarily.on.a.technical.memo.authored.by.one.of.Northrops.retired.senior.system.architects,.Bill.Hopwood.My.colleague.Dr.Jabberia.Miller.formalized.the.notes.and.has.provided.a.most.useful.chapter.on.rel

26、iability.analysis.and.its.impact.on.ESA.performance.MATLAB.is.a.registered.trademark.of.The.MathWorks,.Inc.For.pro-duct.information,.please.contact:The.MathWorks,.Inc.3.Apple.Hill.Drive.Natick,.MA.01760-2098.USA.Tel:.508.647.7000.Fax:.508-647-7001.E-mail:.Web:.ixAcknowledgmentsFirst,.I.thank.God.for

27、.giving.me.the.ability,.opportunity,.and.the.inspira-tion.to.create.this.book.Late.on.a.Tuesday.night,.while.driving.from.class.at.Spirit.of.Faith.Bible.Institute.in.Temple.Hills,.Maryland,.the.Lord.gave.me.the.idea.to.write.this.book.I.had.no.intentions.or.previous.aspirations.to.author.a.book,.and

28、.it.has.truly.been.a.God-inspired.journey.I.thank.my.wife.Nadine.for.her.prayers,.support,.and.sacrifice.of.time.while.I.completed.this.book.I.would.not.be.the.man.I.am.today.without.her.I.also.want.to.thank.my.daughter.and.son,.Alexis.and.Joshua,.for.sacrificing.“daddy.time”.when.I.had.to.work.on.t

29、he.book.To.my.parents,.Rudy.and.Meredith,.thank.you.for.always.believing.in,.and.supporting.me.Your.guidence,.since.my.childhood,.paved.the.way.to.my.education.at.MIT.and.the.University.of.Michigan,.to.my.success.at.Northrop.Grumman.The.sacrifices.you.made.for.me.can.never.repaid.To.my.grandparents,

30、.James.and.Ethel.Mae,.Wesley.and.Lilly,.my.godmother.Ruth,.my.aunt.Deborah,.my.mother-in-law.and.father-in-law.Raymond.and.Kathleen.Stuart,.I.thank.you.for.providing.the.extra.support.and.encouragement.To.my.extended.family.(and.there.are.many),.I.thank.you.as.well.I.must.thank.three.outstanding.gen

31、tlemen.who.each.wrote.a.chap-ter.in.this.book,.Dr.Daniel.Boeringer,.Dr.Jabberia.Miller,.and.Timothy.Cooke.It.has.been.a.pleasure.being.your.colleague.You.are.truly.some.of.Northrop.Grummans.best.and.brightest.I.also.thank.all.the.individuals.who.have.helped.to.make.this.book.a.reality:.John.Wojtowic

32、z,.Richard.Konapelsky,.Kurt.Ramsey,.Kevin.Idstein,.Urz.Batzel,.Dr.Sumati.Rajan,.Jon.Ulrey,.John.Long,.Kevin.Schmidt,.and.Tom.Harmon.Many.thanks.to.Dr.Joseph.Payne.for.taking.the.time.to.review.this.manuscript,.and.to.my.past.advisor,.Dr.John.L.Volakis,.who.has.always.had.an.open.door.if.I.needed.to.

33、ask.him.questions.Thanks.for.being.an.outstanding.example.of.a.great.work.ethic.Last,.thanks.to.Dr.Leo.Kempel.There.are.three.individuals.who.have.been.both.friends.and.great.mentors.in.my.career.Northrop.Grumman.Mentors.lead.by.example.and.allow.the.mentee.to.follow.and.learn.along.the.way.From.the

34、se.three.people.I.learned.that.intellect.without.experience.and.hard.work.really.doesnt.amount.to.much.To.Bill.Hopwood,.affectionately.known.as.xAcknowledgments“Uncle.Bill”.and.“Mr.ESA,”.I.thank.you.for.being.an.advocate.for.me.You.are.truly.one.of.the.most.innovative.people.I.have.ever.met,.and.it.

35、has.been.a.pleasure.working.with.you.To.Lee.Cole,.thank.you.for.showing.me.the.ropes.in.regard.to.being.a.system.architect,.and.for.your.open-door.policy.You.are.truly.an.amazing.individual.from.whom.I.am.still.learning.To.Dan.Davis,.I.thank.you.for.all.the.one-on-one.tutorials,.and.your.willingness

36、.to.always.talk.about.concepts.whenever.I.visited.your.office.I.learned.from.you.that.many.times,.difficult.problems.can.be.sim-plified.with.short,.elegant.solutions.Early.in.my.career.you.instructed.me.to.keep.the.MATLAB.codes.I.wrote.in.my.own.“toolbox”.to.have.them.ready.to.use.Well,.I.followed.y

37、our.instructions!Finally,.I.would.be.remiss.if.I.didnt.thank.my.pastor.and.spiritual.father,.Dr.Michael.A.Freeman.I.have.learned.from.you.to.lean.on.God.first.and.then.lean.on.my.intellect.second.(which.is.not.always.easy!).Thank.you.for.your.leadership,.exemplary.lifestyle,.and.pushing.me.to.never.

38、settle.for.being.average.xiContributorsDaniel Boeringer,PhDNorthrop.Grumman.Electronic.SystemsBaltimore,.MarylandArik D.Brown,PhDNorthrop.Grumman.Electronic.SystemsBaltimore,.MarylandTimothy CookeNorthrop.Grumman.Electronic.SystemsBaltimore,.MarylandJabberia Miller,PhDNorthrop.Grumman.Electronic.Sys

39、temsBaltimore,.Maryland1chapter oneElectronically Scanned Array FundamentalsPart 1Arik D.BrownNorthrop Grumman Electronic SystemsContents1.1.Introduction.21.2.General.One-Dimensional.Formulation.31.2.1.Pattern.Expression.without.Electronic.Scanning.31.2.2.Pattern.Expression.with.Electronic.Scanning.

40、41.3.ESA.Fundamental.Topics.61.3.1.Beamwidth.61.3.2.Instantaneous.Bandwidth.81.3.3.Grating.Lobes.101.4.One-Dimensional.Pattern.Synthesis.121.4.1.Varying.Amplitude.Distribution.141.4.2.Varying.Frequency.171.4.3.Varying.Scan.Angle.171.5.Conformal.Arrays.191.5.1.Formulation.191.5.1.1.Array.Pattern.for.

41、a.Linear.Array.191.5.2.Array.Pattern.for.a.Conformal.Array.211.5.3.Example.221.5.3.1.Conformal.One-Dimensional.Array.221.6.MATLAB.Program.and.Function.Listings.231.6.1.BeamwidthCalculator.m.231.6.2.Compute_1D_AF.m.(Function).231.6.3.Compute_1D_EP.m.(Function).241.6.4.Compute_1D_PAT.(Function).241.6.

42、5.process_vector.m.(Function).241.6.6.Pattern1D.m.241.6.7.Pattern1D_GLs.m.271.6.8.Pattern1D_IBW.m.292Electronically Scanned Arrays:MATLAB Modeling and Simulation1.1 IntroductionElectronically.scanned.arrays.(ESAs)mand-able,.agile,.high-gain.beams,.which.is.advantageous.for.applications.such.as.radar

43、,.weather.surveillance,.and.imaging.In.contrast.to.reflector.anten-nas,.which.require.a.gimbal.for.steering.the.array.beam,.ESAs.electroni-cally.scan.the.array.beam.in.space.without.physical.movement.of.the.array.(see.Figure1.1).Scanning.the.beam.with.an.ESA.can.be.performed.on.the.order.of.microsec

44、onds.as.opposed.to.milliseconds.for.a.reflector.Tmand.the.array.beams.position.in.space.for.tailored.modes.of.operation.When.designing.ESAs,.there.are.basic.fundamentals.that.need.to.be.understood.for.a.successful.design.(i.e.,.grating.lobes,.beamwidth,.instan-taneous.bandwidth,.etc.).Additionally,.

45、a.fundamental.understanding.of.the.application.of.ESAs.is.necessary.(i.e.,.pattern.optimization,.subarrays,.digital.beamforming.(DBF),.etc.).After.these.foundations.are.set,.then.an.understanding.of.practical.aspects.of.ESAs,.such.as.reliability,.should.1.6.9.Taylor.m.(Function).311.6.10.AmpWeightsC

46、ompare.m.321.6.11.Pattern1D_ConformalArray.m.33References.34PhaseshiftersESA ElectronicallySteers the AntennaBeamReflector AntennaRequires a Gimbalto MechanicallySteer the AntennaBeamFigure 1.1 Reflector.vs.ESA.steering.(From.Walsh,.T.,.et.al.,.Active Electronically Scanned Antennas(AESA),.Radar.Sys

47、tems.Engineering.Course,.Northrop.Grumman.Electronic.Systems,.Baltimore,.MD,.December.2003.)3Chapter one:Electronically Scanned Array FundamentalsPart 1provide.a.well-rounded.understanding.of.designing.ESAs.The.remainder.of.this.chapter.will.focus.on.basic.ESA.fundamentals.1.2 General One-Dimensiona

48、l Formulation1.2.1 Pattern Expression without Electronic ScanningConsider.a.one-dimensional.array.of.M.elements.as.shown.in.Figure1.2.The.elements.are.uniformly.spaced.with.a.spacing.of.d.The.overall.length.of.the.array,.L,.is.equal.to.Md.The.elements.are.centered.about.x.=.0,.and.their.position.can

49、.be.denoted.as.xmMdmMm(0.5(1),where1,=+=.(1.1)Eplex.voltage.denoted.as.am.Aposite.signal.The.expression.for.the.coherent.sum.of.voltages.is.represented.as.AFA emjxmMmsin12=.(1.2)AF.is.the.array.factor.and.describes.the.spatial.response.of.the.M.array.elements.From.Equation.(1.2),.we.can.see.that.the

50、.AF.is.a.function.of.the.aperture.distribution.(Am),.frequency.(cf=,.c.is.the.speed.of.light.and.f.is.frequency),.element.spacing.(d),.and.angle.().The.AF.in.Equation.(1.2).has.a.maximum.value.when.=.0.This.maximum.value.is.M,.which.is.the.L=N ddNxz1Figure 1.2 Linear.array.of.N elements.4Electronica