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EE5713 : Advanced Digital Communications

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EE5713 : Advanced Digital Communications EE5713 : Advanced Digital Communications Week 4, 5: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and Raised-Cosine Filter Eye Pattern Error Performance Degradation (On Board) Demodulation and Detection (On Board) Eb/No and Error Probability (On Board) Matched Filter and Correlator Receiver (On Board) Equalization (On Board) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 1 Baseband Communication System . We have been considering the following baseband system The transmitted signal is created by the line coder according to s(t) a g(t nT ) n b n where an is the symbol mapping and g(t) is the pulse shape Problems with Line Codes One big problem with the line codes is that they are not bandlimited The absolute bandwidth is infinite The power outside the 1st null bandwidth is not negligible. That is, the power in the sidelobes can be quite high 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 2 Intersymbol Interference (ISI) . If the transmission channel is bandlimited, then high frequency components will be cut off – Hence, the pulses will spread out – If the pulse spread out into the adjacent symbol periods, then it is said that intersymbol interference (ISI) has occurred Intersymbol Interference (ISI) . Intersymbol interference (ISI) occurs when a pulse spreads out in such a way that it interferes with adjacent pulses at the sample instant . Causes – Channel induced distortion which spreads or disperses the pulses – Multipath effects (echo) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 3 Pulse spreading – Due to improper filtering (@ Tx and/or Rx), the received pulses overlap one another thus making detection difficult . Example of ISI – Assume polar NRZ line code 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 4 Inter Symbol Interference – Input data stream and bit superposition . The channel output is the sum of the contributions from each bit 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 5 ISI Note: . ISI can occur whenever a non-bandlimited line code is used over a bandlimited channel . ISI can occur only at the sampling instants . Overlapping pulses will not cause ISI if they have zero amplitude at the time the signal is sampled 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 6 ISI Baseband Communication System Model where hT (t) Impulseresponseof the transmitter, hC (t) Impulseresponseof the channel, hR (t) Impulseresponseof the receiver s(t) anhT (t nT), n r(t) an gT (t nT) n(t), where g(t) hT (t)*hC (t), T 1/ fs n y(t) anhe (t nT) ne (t) where he (t) hT (t)*hC (t)*hR (t), n ne (t) n(t)*hC (t)*hR (t) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 7 ISI Baseband Communication System Model . Note that he(t) is the equivalent impulse response of the receiving filter . To recover the information sequence {an}, the output y(t) is sampled at t = kT, k = 0, 1, 2, … . The sampled sequence is y(kT) anhe (kT nT) ne (kT) n AWGN term or equivalently yk anhkn nk h0ak anhkn nk n n,nk Desired symbol scaled by gain parameters h0 Effect of other symbols at the sampling instants t=kT where hk he (kT), nk ne (kT), k 0,1,2,.. – h0 is an arbitrary constant 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 8 Signal Design for Bandlimited Channel Zero ISI y(kT) h0ak anhe (kT nT) ne (kT) n,nk . To remove ISI, it is necessary and sufficient to make the term he (kT nT) 0, for n k and h0 0 . Nyquist Criterion – Pulse amplitudes can be detected correctly despite pulse spreading or overlapping, if there is no ISI at the decision- making instants 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 9 Nyquist Criterion: Time domain p(t): impulse response of a transmission system (infinite length) Suppose 1/T is the sample rate The necessary and sufficient condition for p(t) to satisfy Nyquist Criterion is 1,n 0 pnT 0,n 0 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 10 1st Nyquist Criterion: Time domain . Pulse shape that satisfy this criteria is Sinc(.) function, e.g., t he (t) or p(t) sin c sin c(2Wt) T . The smallest value of T for which transmission with zero ISI is possible is 1 T . Problems with Sinc(.) function 2W – It is not possible to create Sinc pulses due to – Infinite time duration – Sharp transition band in the frequency domain – Sinc(.) pulse shape can cause ISI in the presence of timing errors • If the received signal is not sampled at exactly the bit instant, then ISI will occur 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 11 1st Nyquist Criterion: Time domain p(t) 1 shaping function 0 no ISI ! t 1 T 2 fs t0 2t0 Equally spaced zeros, 1 -1 interval T 2 fs 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 12 Sample rate vs. bandwidth . W is the channel bandwidth for P(f) . When 1/T > 2W, there is no way, we can design a system with no ISI P(f) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 13 Sample rate vs. bandwidth . When 1/T = 2W (The Nyquist Rate), rectangular function satisfy Nyquist condition sin t T t T, f W p t sinc ; P f , t T 0,otherwise 1 f P f rect T rect fT ; 2W 2W T W 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 14 Sample rate vs. bandwidth . When 1/T < 2W, numbers of choices to satisfy Nyquist condition – Raised Cosine Filter – Duobinary Signaling (Partial Response Signals) – Gaussian Filter Approximation . The most typical one is the raised cosine function 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 15 Raised Cosine Pulse . The following pulse shape satisfies Nyquist’s method for zero ISI rt rt rt sin cos cos T T t T p(t) sinc rt 4r 2t 2 T 4r 2t 2 1 1 T T 2 T 2 . The Fourier Transform of this pulse shape is 1 r T , 0 | f | 2T T 1 r 1 r 1 r P( f ) T / 21 cos | f | , | f | r 2T 2T 2T 1 r 0, | f | 2T . where r is the roll-off factor that determines the bandwidth 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 16 Raised cosine shaping . Tradeoff: higher r, higher bandwidth, but smoother in time. P(ω) W r=0 r = 0.25 r = 0.50 r = 0.75 r = 1.00 2w p(t) W ω π π W 0 W 0 t 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 17 Rolloff and bandwidth . Bandwidth occupied beyond 1/2T is called the excess bandwidth (EB) . EB is usually expressed as a %tage of the Nyquist frequency, e.g., – Rolloff factor, r = 1/2 ===> excess bandwidth is 50 % – Rolloff factor, r = 1 ===> excess bandwidth is 100 % . RC filter is used to realized Nyquist filter since the transition band can be changed using the roll-off factor . The sharpness of the filter is controlled by the parameter r . When r = 0 this corresponds to an ideal rectangular function . Bandwidth B occupied by a RC filtered signal is increased from its minimum value 1 Bmin 2Ts . So the bandwidth becomes: B Bmin 1 r 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 18 Rolloff and bandwidth . Benefits of large roll off factor – Simpler filter – fewer stages (taps) hence easier to implement with less processing delay – Less signal overshoot, resulting in lower peak to mean excursions of the transmitted signal – Less sensitivity to symbol timing accuracy – wider eye opening . r = 0 corresponds to Sinc(.) function 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 19 Partial Response Signals . To improve the bandwidth efficiency – Widen the pulse, the smaller the bandwidth. – But there is ISI. For binary case with two symbols, there is only few possible interference patterns. – By adding ISI in a controlled manner, it is possible to achieve a signaling rate equal to the Nyquist rate i.e. Duobinary and Polibinary Signaling (Covered in the previous lectures) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 20 Eye Patterns . An eye pattern is obtained by superimposing the actual waveforms for large numbers of transmitted or received symbols – Perfect eye pattern for noise-free, bandwidth-limited transmission of an alphabet of two digital waveforms encoding a binary signal (1’s and 0’s) – Actual eye patterns are used to estimate the bit error rate and the signal to- noise ratio 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 21 Eye Patterns Concept of the eye pattern 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 22 Eye Patterns Concept of Eye diagram Mask. Waveform must not intrude into the shaded regions. 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 23 Cosine rolloff filter: Eye pattern 2nd Nyquist 1st Nyquist: 1st Nyquist: 2nd Nyquist: 2nd Nyquist: 1st Nyquist 1st Nyquist: 1st Nyquist: 2nd Nyquist: 2nd Nyquist: 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 24 Eye Diagram Examples EYE DIAGRAM 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 25 Eye Diagram Examples EYE DIAGRAM WITH NOISE (Variance =0.1) 1.5 1 0.5 0 -0.5 -1 -1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 26 Eye Diagram Examples EYE DIAGRAM WITH NOISE (Variance =0.5) 3 2 1 0 -1 -2 -3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) 3/27/2013 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE5713) 27 .
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