EE5713 : Advanced Digital Communications
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1 EE573 : 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) E b /N o and Error Probability (On Board) Matched Filter and Correlator Receiver (On Board) Equalization (On Board) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573)
2 Baseband Communication System We have been considering the following baseband system he transmitted signal is created by the line coder according to s ( t) a g( t ) n where a n is the symbol mapping and g(t) is the pulse shape Problems with Line Codes n n b One big problem with the line codes is that they are not bandlimited he absolute bandwidth is infinite he power outside the st null bandwidth is not negligible. hat is, the power in the sidelobes can be quite high 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 2
3 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 Intersymbol Interference (ISI) Channel induced distortion which spreads or disperses the pulses Multipath effects (echo) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 3
4 Pulse spreading Due to improper filtering x and/or Rx), the received pulses overlap one another thus making detection difficult Example of ISI Assume polar NRZ line code 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 4
5 Inter Symbol Interference Input data stream and bit superposition he channel output is the sum of the contributions from each bit 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 5
6 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 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 6
7 ISI Baseband Communication System Model where h h h C R ( t) Impulse responseof the transmitter, ( t) Impulse responseof the channel, ( t) Impulse responseof the receiver s ( t) anh ( t n ), n r( t) an n anhe n g y t) ( t n) n ( t) ( t n) n( t), where e g( t) h ( t)* h C ( t), / ( where h ( t) h ( t)* h ( t)* h ( t), n e e ( t) n( t)* h ( t)* h ( t) C C R R f s 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 7
8 ISI Baseband Communication System Model Note that h e (t) is the equivalent impulse response of the receiving filter o recover the information sequence {a n }, the output y(t) is sampled at t = k, k = 0,, 2, he sampled sequence is or equivalently n y ( k) a h ( k n) n ( k) n e e AWGN term y k n a n h kn n k h 0 a k a n n, nk h kn n k where h k Desired symbol scaled by gain parameters h 0 h e ( k), n n h 0 is an arbitrary constant k e ( k), k 0,, 2,.. Effect of other symbols at the sampling instants t=k 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 8
9 Signal Design for Bandlimited Channel Zero ISI y( k) h o remove ISI, it is necessary and sufficient to make the term h e Nyquist Criterion 0 ak anhe ( k n) ne ( k) n, nk ( k n ) 0, for n k and h 0 Pulse amplitudes can be detected correctly despite pulse spreading or overlapping, if there is no ISI at the decisionmaking instants 0 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 9
10 Nyquist Criterion: ime domain p(t): impulse response of a transmission system (infinite length) Suppose / is the sample rate he necessary and sufficient condition for p(t) to satisfy Nyquist Criterion is p n, n 0 0, n 0 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 0
11 st Nyquist Criterion: ime domain Pulse shape that satisfy this criteria is Sinc(.) function, e.g., h e t ( t) or p( t) sin c sin c(2wt) he smallest value of for which transmission with zero ISI is possible is Problems with Sinc(.) function It is not possible to create Sinc pulses due to 2W 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 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573)
12 st Nyquist Criterion: ime domain p(t) shaping function 0 2 f s t 0 2t 0 t no ISI! - Equally spaced zeros, interval 2 f s 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 2
13 Sample rate vs. bandwidth W is the channel bandwidth for P(f) When / > 2W, there is no way, we can design a system with no ISI P(f) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 3
14 Sample rate vs. bandwidth When / = 2W (he Nyquist Rate), rectangular function satisfy Nyquist condition sin t t, f W pt sinc ; P f t P 2W f 2W f rect rect f ; 0, otherwise, W 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 4
15 Sample rate vs. bandwidth When / < 2W, numbers of choices to satisfy Nyquist condition Raised Cosine Filter Duobinary Signaling (Partial Response Signals) Gaussian Filter Approximation he most typical one is the raised cosine function 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 5
16 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 6 Raised Cosine Pulse he following pulse shape satisfies Nyquist s method for zero ISI he Fourier ransform of this pulse shape is where r is the roll-off factor that determines the bandwidth cos sinc 4 cos sin ) ( t r t r t t r t r t r t r t p r f r f r r f r r f f P 2 0, 2 2, 2 cos 2 / 2 0, ) (
17 Raised cosine shaping radeoff: higher r, higher bandwidth, but smoother in time. P(ω) p(t) W W 2w r=0 r = 0.25 r = 0.50 r = 0.75 r =.00 ω 0 π W π W 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 7 0 t
18 Bandwidth occupied beyond /2 is called the excess bandwidth (EB) EB is usually expressed as a %tage of the Nyquist frequency, e.g., Rolloff factor, r = /2 ===> excess bandwidth is 50 % Rolloff factor, r = ===> excess bandwidth is 00 % RC filter is used to realized Nyquist filter since the transition band can be changed using the roll-off factor he 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 B 2 So the bandwidth becomes: s Rolloff and bandwidth min B B r 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 8 min
19 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 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 9
20 Partial Response Signals o 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) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 20
21 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 ( s and 0 s) Actual eye patterns are used to estimate the bit error rate and the signal to- noise ratio 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 2
22 Eye Patterns Concept of the eye pattern 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 22
23 Eye Patterns Concept of Eye diagram Mask. Waveform must not intrude into the shaded regions. 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 23
24 Cosine rolloff filter: Eye pattern nd Nyquist st Nyquist: 2nd Nyquist: st Nyquist: 2nd Nyquist: st Nyquist st Nyquist: 2nd Nyquist: st Nyquist: 2nd Nyquist: 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 24
25 Eye Diagram Examples EYE DIAGRAM ime (sec) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 25
26 Eye Diagram Examples.5 EYE DIAGRAM WIH NOISE (Variance =0.) ime (sec) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 26
27 Eye Diagram Examples 3 EYE DIAGRAM WIH NOISE (Variance =0.5) ime (sec) 3/27/203 Muhammad Ali Jinnah University, Islamabad Advanced Digital Communications (EE573) 27
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