Example What is the minimum bandwidth for transmitting data at a rate of 33.6 kbps without ISI?

Transcription

1 Emple Wh is he minimum ndwidh for rnsmiing d re of 33.6 kps wihou ISI? Answer: he minimum ndwidh is equl o he yquis ndwidh. herefore, BW min W R / 33.6/ 6.8 khz oe: If % roll-off chrcerisic is used, ndwidh Wα 33.6 khz B.67 Emple Bndwidh requiremen of he sysem sysem muliple 4 voice inpus, sed on n 8-i PC word. ndwidh of ech voice inpu B 3. khz For convering he voice signl ino inry sequence, he minimum smpling re B 6. khz Smpling re used in elephone sysem 8 khz B.68

2 Emple Wih smpling re of 8 khz, ech frme of he mulipleed signl occupies period of 5µs. : : o. of is i from s inpu 8 i from nd inpu. 8 i from 4h inpu i for Synchronizion 5 µs B.69 Emple Correspondingly, he i durion is 5 µs/ µs. For elimining ISI, he minimum rnsmission ndwidh is / 77kHz B.7

3 Eye digrms his is simple wy o give mesure of how severe he ISI s well s noise is. his pern is genered y overlpping he incoming signl elemens. Emple: ipolr RZ PA B.7 Eye digrms Eye pern is ofen used o monioring he performnce of send signl. he es ime o smple he received wveform is when he eye opening is lrges. Effecs of noise re ignored B.7

4 Eye digrms he mimum disorion nd ISI re indiced y he vericl widh of he wo rnches smpling ime. B.73 Eye digrms he noise mrgin or immuniy o noise is proporionl o he widh of he eye opening. 3 B.74

5 Eye digrms he sensiiviy of he sysem o iming errors is deermined y he re of closure of he eye s he smpling ime is vried. 4 B.75 Equlizion In preceding secions, rised-cosine filers were used o elimine ISI. In mny sysems, however, eiher he chnnel chrcerisics re no known or hey vry. Emple he chrcerisics of elephone chnnel my vry s funcion of priculr connecion nd line used. I is dvngeous in such sysems o include filer h cn e djused o compense for imperfec chnnel rnsmission chrcerisics, hese filers re clled equlizers. B.76

6 Before equlizion Afer equlizion B.77 rnsversl filer zero-forcing equlizer k is he i durion. B.78

7 Equlizion he prolem of minimizing ISI is simplified y considering only hose signls correc smple imes. he smpled inpu o he rnsversl equlizer is k k he oupu is y k y k For zero ISI, we require h k y k k * B.79 he oupu cn e epressed s y k n n k n k k k k k here re independen equions in erms of n. his limis us o consrins, nd herefore * mus e modified o y k k k ±, ±,..., ± B.8

8 B.8 Equlizion he equions ecomes o B.8 Emple Deermine he p weighs of hree-p, zero-forcing equlizer for he inpu where..3,.,.,.,, k for > k he hree equions re Solving, we oin ,.779,

9 Equlizion he vlues of he equlized pulse re y., y.356, y y 3., y.36, y., y 3.,.85 his pulse hs he desired zeros o eiher side of he pek, u ISI hs een inroduced smple poins frher from he pek. B.83 B.84

10 Duoinry Signling Inersymol inerference is n undesirle phenomenon h produces degrdion in sysem performnce. However, y dding inersymol inerference o he rnsmied signl in conrolled mnner, i is possile o chieve signling re equl o he yquis re of W symols per second in chnnel of ndwidh W Hz. B.85 Coding nd decoding Consider inry inpu sequence { k } consising of uncorreled inry symols nd, ech hving durion. his sequence is pplied o pulsempliude modulor producing wo-level sequence of shor pulses pproiming uni impulse, whose mpliude is k if symol if symol k k is is B.86

11 his sequence is pplied o duoinry encoder s shown elow: { c k } yquis chnnel { } k Dely c k k k One of he effecs of he duoinry encoding is o chnge he inpu sequence { k } of uncorreled wolevel pulses ino sequence { c k } of correled hreelevel pulses. his correlion eween he djcen pulses my e viewed s inroducing inersymol inerference ino he rnsmied signl in n rificil mnner. B.87 Emple Consider { } k where he firs i is srup i. Encoding: {} k : { k }: c : - {} k { } k { } c k B.88

12 Decoding: Using he equion k ck k, or simply using If c k, decide h k. If c k, decide h k. If c k, decide opposie of he previous decision. B.89 Duoinry Signling: Impulse response nd frequency specrum e us now emine n equivlen model of he duoinry encoder. he Fourier rnsfer of dely cn e descried s e f, herefore, he rnsfer funcion of he encoder is H I f is jf H f e I he rnsfer funcion of he yquis chnnel is f < / H f oherwise B.9

13 B.9 he overll equivlen rnsfer funcion f H of he is hen given y f j f j f j f j f j I f e e e e e f f H f H f H cos / for < Hf hs grdul roll-off cn e esily implemened o he nd edge which B.9 he corresponding impulse response h is found y king he inverse Fourier rnsform of Hf / sin / / sin / / sin / / sin / / sin h

14 oice h here re only wo nonzero smples, -second inervls, give rise o conrolled ISI from he djcen i. he inroduced ISI is elimined y use of he decoding procedure. B.93