Inter Symbol Interference-Digital Communication Systems-Lecture Slides, Slides of Digital Communication Systems

Download Inter Symbol Interference-Digital Communication Systems-Lecture Slides and more Slides Digital Communication Systems in PDF only on Docsity! 1 1 Digital Communication Systems Dr. Shurjeel Wyne Lecture 7 Inter-Symbol Interference (CH 3: Baseband Demodulation/Detection) 2 Last time we talked about:  Signal detection in AWGN channels  Maximum likelihood  Minimum distance detector  Average probability of symbol error  Unipolar and Bipolar signalling 2 3 Today we are going to talk about:  Another source of error:  Inter-symbol interference (ISI)  Nyquist Bandwidth Constraint for zero ISI  The techniques to reduce ISI  Pulse shaping  Equalization 4 Inter-Symbol Interference (ISI)  ISI in the detection process is due to filtering effects of the system  Overall equivalent system transfer function  creates echoes and hence time dispersion  causes ISI at sampling time )()()()( fHfHfHfH rct i ki ikkk snsz     5 9 The raised cosine roll-off filter  Raised-Cosine roll-off Filter  Nyquist filter (pulse) having No ISI at sampling time                  Wf WfWW WW WWf WWf fH ||for0 ||2for2|| 4 cos 2||for1 )( 0 0 02 0  Excess bandwidth: 0WW  Roll-off factor 0 0 W WWr  10  r 2 0 0 00 ])(4[1 ])(2cos[))2(sinc(2)( tWW tWWtWWth     W = absolute bandwidth , W0=1/(2T) is minimum Nyquist Bandwidth RC RC 10 The Raised cosine filter – cont’d 2 )1(Baseband sSB s RrW  |)(||)(| fHfH RC 0r 5.0r 1r 1r 5.0r 0r )()( thth RC T2 1 T4 3 T 1 T4 3 T2 1 T 1 1 0.5 0 1 0.5 0 T T2 T3TT2T3 sRrW )1(Passband DSB  Roll-off factor 0 0 W WWr  10  r Adjust r according to trade-off between Excess bandwidth and sensitivity to timing error 6 11 Pulse shaping and equalization to remove ISI  Square-Root Raised Cosine (SRRC) filter and Equalizer )()()()()(RC fHfHfHfHfH erct No ISI at the sampling time )()()()( )()()( SRRCRC RC fHfHfHfH fHfHfH tr rt   Taking care of ISI caused by tr. filter )( 1)( fH fH c e  Taking care of ISI caused by channel 12 Example of pulse shaping  Square-root Raised-Cosine (SRRC) pulse shaping t/T Amp. [V] Baseband tr. Waveform Data symbol First pulse Second pulse Third pulse 7 13 Example of pulse shaping …  Raised Cosine pulse at the output of matched filter t/T Amp. [V] Baseband received waveform at the matched filter output (zero ISI) 14 Eye pattern  Eye pattern:Display on an oscilloscope which sweeps the system response to a baseband signal at the rate 1/T (T = symbol duration) time scale am pl itu de sc al e Noise margin Sensitivity to timing error Distortion due to ISI Timing jitter 10 19 Equalization – cont’d Frequency down-conversion Receiving filter Equalizing filter Threshold comparison For bandpass signals Compensation for channel induced ISI Baseband pulse (possibly distored) Sample(test statistic) Baseband pulseReceived waveform Step 1 – waveform to sample transformation Step 2 – decision making )(tr )(Tz im̂ Demodulate & Sample Detect 20 Example of eye pattern with ISI: Binary-PAM, SRRC pulse  Non-ideal channel and no noise )(7.0)()( Tttthc   11 21 Example of eye pattern with ISI: Binary-PAM, SRRC pulse …  AWGN (Eb/N0=20 dB) and ISI )(7.0)()( Tttthc   22 Example of eye pattern with ISI: Binary-PAM, SRRC pulse …  AWGN (Eb/N0=10 dB) and ISI )(7.0)()( Tttthc   12 23 Equalizer block in Rx  Baseband system model  Equivalent model Tx filter Channel )(tn )(tr Rx. filter Detector kz kTt   kâ 1a 2a 3a T )( )( fH th t t )( )( fH th r r )( )( fH th c c Equivalent system )(ˆ tn )(tz Detector kz kTt  )( )( fH th filtered noise )()()()( fHfHfHfH rct   k k kTta )( Equalizer )( )( fH th e e 1a 2a 3a T   k k kTta )( )(tx Equalizer )( )( fH th e e )()()(ˆ thtntn r  kâ)(tz )(tz 24 Equalizer Types  Filter based  Linear Filtering  Zero-forcing equalizer  Minimum mean square error (MMSE) equalizer  Non-linear filtering  Decision feedback equalizer Using the past decisions to remove the ISI contributed by them  MLSE (Maximum likelihood sequence estimation) Enable the detector to make good symbol estimates based on the demodulated distorted pulses. The ISI affected pulses are not directly reshaped. In general the channel is time varying, and therefore the tap weights have to be adjusted according to the channel variations resulting in so-called adaptive equalizers.