Digital Transmission Through Bandlimited Channels -The Power Spectrum of Digital PAM Signal -Characterization of Bandlimited Channels and Channel Distortion Characterization of Intersymbol Interface -Communication System Design for Bandlimited Channels Linear Equalizer
Digital Transmission Through Bandlimited Channels ◼The Power Spectrum of Digital PAM Signal ◼Characterization of Bandlimited Channels and Channel Distortion ◼Characterization of Intersymbol Interface ◼Communication System Design for Bandlimited Channels ◼Linear Equalizer
Power spectrum of Digital PAM signal The power spectrum of PAM is function of Power spectrum of information ■Spectrum of pulse g()t If information is uncorrelated Then power spectrum of PAM is dependent only on the spectrum of g(t) We have to consider the spectrum of g(t)if channel is bandlimited
Power spectrum of Digital PAM signal ◼ The power spectrum of PAM is function of ◼ Power spectrum of information ◼ Spectrum of pulse g(t) ◼ If information is uncorrelated ◼ Then power spectrum of PAM is dependent only on the spectrum of g(t) ◼ We have to consider the spectrum of g(t) if channel is bandlimited
Characterization of Bandlimited Channel and Channel Distortion Communication channel can be modeled as s Bandlimited Linear Filter Amplitude response Phase response Distortion caused by channel Amplitude distortion Delay distortion ISI(Inter Symbol Interference)caused by delay At Radio channel lonospheric/Tropospheric/multipath
Characterization of Bandlimited Channel and Channel Distortion ◼ Communication channel can be modeled as ◼ Bandlimited Linear Filter ◼ Amplitude response ◼ Phase response ◼ Distortion caused by channel ◼ Amplitude distortion ◼ Delay distortion ◼ ISI(Inter Symbol Interference) caused by delay ◼ At Radio channel ◼ Ionospheric/Tropospheric/multipath
Characterization of ISl The amount of ISl and noise in digital communication system can be viewed on an oscilloscope Eye pattern Large ISI close the eye Small ISI open the eye
Characterization of ISI ◼ The amount of ISI and noise in digital communication system can be viewed on an oscilloscope ◼ Eye pattern ◼ Large ISI close the eye ◼ Small ISI open the eye
Communication system design for Bandlimited Channel Two approaches Design is based on transmitter and receiver filter that result in zero ISI Design is based on transmitter and receiver filter that has predetermined amount of ISl Controlled amount of ISI
Communication system design for Bandlimited Channel ◼ Two approaches ◼ Design is based on transmitter and receiver filter that result in zero ISI ◼ Design is based on transmitter and receiver filter that has predetermined amount of ISI ◼ Controlled amount of ISI
Signal design for Zero ISI Nyquist considered this problem 70 years ago Raised cosine frequency response satisfies zero ISI Add transmitter filter G(f)and receiver filter GR(f) which yield zero ISI G(f)GR(f)=XRc(f)=raised cosine frequency response
Signal design for Zero ISI ◼ Nyquist considered this problem 70 years ago ◼ Raised cosine frequency response satisfies zero ISI ◼ Add transmitter filter GT (f) and receiver filter GR (f) which yield zero ISI ◼ GT (f)GR (f) = XRC(f) = raised cosine frequency response
Signal Design for Controlled ISI Since raised cosine use excess bandwidth ▣frol-off factor≠0 ■Controller ISI uses Duobinary signal pulse Or Modified Duobinary signal pulse Physically realizable filter that approximate spectrum very closely with symbol rate 2W Greater bandwidth efficiency than raise cosine signal pulses
Signal Design for Controlled ISI ◼ Since raised cosine use excess bandwidth ◼ If roll-off factor 0 ◼ Controller ISI uses ◼ Duobinary signal pulse ◼ Or Modified Duobinary signal pulse ◼ Physically realizable filter that approximate spectrum very closely with symbol rate 2W ◼ Greater bandwidth efficiency than raise cosine signal pulses
Precoding for Detection of Partial Response signals ■Using controlled ISI Error arising from additive noise tend to propagate The error of(k-1)affects the error of k Predecoding prevents error propagation
Precoding for Detection of Partial Response signals ◼ Using controlled ISI ◼ Error arising from additive noise tend to propagate ◼ The error of (k-1) affects the error of k ◼ Predecoding prevents error propagation
Linear Equalizer ■Reduce ISI Type of Linear Equalizer Linear FIR filter ■Preset Equalizer Fixed parameter Adaptive Equalizer can track a slowly time-varying channel response
Linear Equalizer ◼ Reduce ISI ◼ Type of Linear Equalizer ◼ Linear FIR filter ◼ Preset Equalizer ◼ Fixed parameter ◼ Adaptive Equalizer ◼ can track a slowly time-varying channel response
Nonlinear Equalizer Linear Equalizer performs poorly for mobile radio channel or Cellular DFE(Decision Feedback Equalizer)= Feedforward Filter Feedback Filter Outperforms a Linear Equalizer Not optimal because it does not minimize Pe MLSD(Maximum Likelihood Sequence Detector) Viterbi algorithm Effective but Computational complexity
Nonlinear Equalizer ◼ Linear Equalizer performs poorly for mobile radio channel or Cellular ◼ DFE(Decision Feedback Equalizer) = Feedforward Filter + Feedback Filter ◼ Outperforms a Linear Equalizer ◼ Not optimal because it does not minimize Pe ◼ MLSD(Maximum Likelihood Sequence Detector) ◼ Viterbi algorithm ◼ Effective but Computational complexity