Bandlimited communication systemsPassband channel exampleBandlimited channel exampleInter-Symbol Interference (ISI)Bandlimited communication systemsSymbol-by-symbol detectionVector channel - revisitedISI impactMatched Filter BoundNyquist criterion – 6.011 revisitedRaised-cosine pulsesBasic equalization conceptsLinear equalizationZFE vs. MMSE - LEExample: ZFE vs. MMSE LEFractional equalizersISI channel modelFinite length equalizer formulationZFE and MMSE solutionDecision feedback equalizerMMSE DFEBasic multitone modulationA bit of historyBasic multitone transmissionThe effect of the channelGap reviewExample – simplified multitoneWater-filling derivationWater-filling spectrumWater-fill loading algorithmsRate-adaptive loadingWater-filling example (rate-adaptive)Summary6.973 Communication System Design – Spring 2006Massachusetts Institute of TechnologyCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Bandlimited communication systemsLecture 3Vladimir StojanovićPassband channel example Two-ray wireless channel (multi-path – 1+0.9D) Multi-path creates notching in frequency domain Just slide the frequency window to bb Add single-sided noiseCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design2Bandlimited channel example0 2 4 6 8 10-60-50-40-30-20-100frequency [GHz]Attenuation [dB]0 1 2 300.20.40.60.81nspulse responseTsymbol=160ps Low-pass channel causes pulse attenuation and dispersion Notches cause ripples in time domain Makes it hard to transmit successive messagesCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design3Inter-Symbol Interference (ISI)0 2 4 6 8 10 12 14 16 1800.20.40.60.81Symbol timeAmplitudeError! Middle sample is corrupted by 0.2 trailing ISI (from the previous symbol), and 0.1 leading ISI (from the next symbol) resulting in 0.3 total ISI As a result middle symbol is detected in errorCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design4Bandlimited communication systems Block detector vs. symbol-by-symbol Block of K symbols – MKmessages MAP/ML detector complexity grows exponentially MKbasis functions (branches in the matched filter) Sequence detection can bound that growth Simpler detector is “Symbol-By-Symbol” Optimal for AWGN channelCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design5BlockDetectorRSBSdetectoryp(t)yp(t)φk(KT - t)φ2(KT - t)φ1(KT - t)Xϕp(T - t)t = KTt = kT, k = 0,...,K - 1Xk k = 0,...,K -1yp(t)...Figure by MIT OpenCourseWare.Symbol-by-symbol detection Suffers significantly from Intersymbol-interference (channel memory), so need to remove ISI to get almost AWGN channel Need to adapt basis functions to the particular channel, to avoid ISI Alternatively, use equalization to remove ISICite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design6BandlimitedchannelReceiverx (t)n (t)SamplerEstimate of inputsymbol at time kInput symbolat time kxkykzkxk+MatchedfilterSBSdetectorRmod h(t)Figure by MIT OpenCourseWare.Vector channel - revisitedCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design7x(t)h(t)h(t)xknnp (t)np (t)xp (t)yp (t)yp (t)yp (t)xp (t)xn (t)np (t)pn(t)ϕn(t)xp (t)xkn+++Figure by MIT OpenCourseWare. Mean-distortion Treat ISI as noise Peak-distortion Treat worst-case ISI as constellation offsetCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].ISI impact6.973 Communication System Design8pulse response p(t)sample attimes kTdiscretetimereceiverxkxp,kxp(t)np(t)yp(t)ykxky(t)Sq(t) = jp(t)*jp(-t)||p||jp(t)jp (-t)Figure by MIT OpenCourseWare.Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design9Matched Filter Bound You can’t do better with successive transmissions than with one-shot Matched filter collects the pulse energy ||p||2 Then calculate performance as on AWGN Example – binary transmission Will use MFB to compare different ISI compensation techniques10Nyquist criterion – 6.011 revisited A channel specified by pulse response p(t) is ISI free if Nyquist frequency: w=pi/T or f=1/2TCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System DesignRaised-cosine pulses Can have “excess” bandwidth as long as there is symmetry that “fills” the aliased spectrum flatCite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.973 Communication System Design112Basic equalization concepts Zero-forcing equalization Flattens equalized channel transfer function H(D)=Q(D)*W(D) Wzfe(D)=1/(Q(D)||p||)X=Channel Q(w)Equalizer W(w) Equalized =>Q(D)W(D)kxˆkxkyCite as: Vladimir Stojanovic, course materials for