Gaussian pulses for 60GHz

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1、1.Directpulsea.TheidealpulseTheidealpulsecanbederivedfromtheFouriertransformofthefrequencyMASK.TheidealPSDisb.Gaussianseriesgj(t)istheGaussianpulse(j=0)oritsjthderivatives(j>1)whichcanbedescribedas各级导数(1)wheretheamplitudeAisusedtonormalizethepulseamplitude,andαispulseshapingfactor.Φgg(

2、f)isthepowerdensityspectrumofg(t),anditcanbegivenby(2)whereG(f)istheFourierTransform(FT)ofg(t).TheFTsofGaussianpulseseriesareshownas(3)ThenwecangetthePSDoftheGaussianpulseserieswithexpression(2)and(3),(4)Fig1.α=36ps,k=15,i.e.15thderivativeofGaussianpulseFig2.α=36ps,PSDofderivativeofGau

3、ssianpulseFig3.α=45ps,Gaussianderivativepulseseries.Fig4.α=45ps,PSDofderivativeofGaussianpulse.Fig3andFig4showthatthereislittledifferenceinderivativesofGaussianpulseintermsofshapesoftheirPSDandbandwidth.a.Hannwindowpulse,wherefsisthemodulationfrequencythatprimarilyimpactsthebandwidthof

4、thetransmittedsignal,fs=1/Tp.b.Rectangularc.TriangularThecenterfrequencyofHannwindow,RectangularandTriangularpulseis0GHz.Thesedirectpulsescannotmeetthe60GHzspectrumrequirements.d.OrthogonalmodifiedHermitepulseHermitepolynomialscanbemodifiedtobecomeorthogonalas(5)Wheren=0,1,2,…and-∞

5、.Herearesomeexamples:Fig5OrthogonalmodifiedHermitepulseswithdifferentnFig6thePSDofOrthogonalmodifiedHermitepulseswithdifferentn1.Pulsesfor60GHzwithFrequencyshiftA.GaussianpulseseriesAsetofGaussianmonocyclesapproximatelymeetingthespectrumrequirementwastheoriginalproposalforUWBcommunicat

6、ionsystemsandhasbeenwidelyadoptedintheinvestigationofUWBapplications.However,thepulsewaveformsfor60GHzsystemsarerequiredforthe7GHzrangeavailableat60GHz.TheGaussianmonocyclesarenotsuited.AmodulatedGaussianpulsecanmeettheserequirementswhichcanbewrittenas(7)wherefcismodulatingfrequencywhi

7、chdecidesthecenterfrequencyofsj(t),gj(t)istheGaussianpulse(j=0)oritsjthderivatives(j>1)whichcanbedescribedas(8)wheretheamplitudeAisusedtonormalizethepulseamplitude,andαispulseshapingfactor.ThePSDofthesignals(t)=p(t)cos(2πfct),Φss(f),followstheform[11,p204](9)whereΦpp(f)isthepowerdens