E225C Lecture 16OFDM IntroductionEE225C EE225CMultipath can be described in two domains: time and frequencytimetimeSinusoidal signal as inputtimetimeSinusoidal signal as outputfFrequency responseTime domain: Impulse responseFrequency domain: Frequency responsetimeImpulse responsetimetimeModulation techniques: monocarrier vs. multicarrierTo improve the spectral efficiency:To use orthogonal carriers (allowing overlapping)Eliminate band guards between carriers Selective Fading Very short pulses ISI is compartivelylong EQs are then very long Poor spectral efficiencybecause of band guardsDrawbacks It is easy to exploitFrequency diversity Flat Fading per carrier N long pulses ISI is comparatively short N short EQs needed Poor spectral efficiencybecause of band guardsAdvantagesFurthermore It allows to deploy2D coding techniques Dynamic signallingN carriersBPulse length ~ N/BSimilar toFDM technique Data are shared among several carriersand simultaneously transmittedBPulse length ~1/B Data are transmited over only one carrierChannelGuard bandsChannelizationOrthogonal Frequency Division ModulationData coded in frequency domainN carriersBTransformation to time domain:each frequency is a sine wavein time, all added up.fTransmitSymbol:8 periodsof f0Symbol:4 periodsof f0Symbol:2 periodsof f0+ReceivetimeBDecode each frequencybin separatelyChannel frequencyresponseffTime-domain signal Frequency-domain signalOFDM uses multiple carriersto modulate the dataN carriersBModulation techniqueA user utilizes all carriers to transmit its data as coded quantity at each frequency carrier, which can be quadrature-amplitude modulated (QAM).Intercarrier Separation= 1/(symbol duration) No intercarrier guard bands Controlled overlapping of bands Maximum spectral efficiency (Nyquist rate) Very sensitive to freq. synchronization Easy implementation using IFFTsFeaturesDataCarrierT=1/f0Timef0BFrequencyOne OFDM symbolTime-frequency gridOFDM Modulation and Demodulationusing FFTsb0b1b2....bN-1Data coded infrequency domain:one symbol at a timeIFFTInverse fastFourier transformData in time domain:one symbol at a timed0d1d2d3....dN-1timefP/SParallel toserial converterTransmit time-domainsamples of one symbold0, d1, d2, ., dN-1Receive time-domainsamples of one symbold0, d1, ., dN-1S/PSerial toparallel converterd0d1d2....dN-1timeFFTFast Fouriertransformb0b1b2....bN-1fDecode eachfrequency binindependentlyLoss of orthogonality (by frequency offset)k(t) =exp( jk2xt / T)y k +m(t) =exp j2x(k +m)t / Tk+mo(t) =exp j2x(k +m + o) / Tcon o 1/ 2Transmission pulsesReception pulse with offset o 2 4 6 8 10 12 14 16-60-55-50-45-40-35-30-25-20-15-10Total ICI due to loss oforthogonalityCarrier position within the band (N=16)ICI in dBo =0.05o =0.02o =0.01o =0.005o =0.002o =0.001Practical limito assumed r.v.GaussianW=o0-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4Frequency offset: Interference: Im(

)/T en dBLoss for 8 carriersm=1m=3m=5m=7-70-60-50-40-30-20-100Im(o ) = exp jk2xt / Texp j(k + m +o )2xt / Tdt0T=T 1exp( j2xo )j2x(m+ o)Im(o)=T sin xoxm+ oIm2(o)m} To21m2m=1N 1} To2 2314for N ""1 ( N " 5Is enough)Interference betweenchannels k and k+mSumming up V m AsymetricLoss of orthogonality (time)Xi=c0k(t)l*(tX )dtT / 2T / 2+X+ c1k(t)l*(tX )dtT / 2+XT/ 2Let us assumea misadjustment X2 consecutivesymbols0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.081015202530354045Typical deviation for the relative misadjustmentICI in dBN=8N=64ICI due to loss of orthogonaliyX assumed an Uniform r.v.Max. practical limitDoubling N means 3 dB more ICIEXi2T2 | =4XT ' + ' 212+012= 2XT ' + ' 2ICI} 20log 2XT ' + ' , X TPer carrierIn average, the interferingpower in any carrier isXiT}2mxXTmx= 2 XTOr approximately,when X