Communication Systems, 5e

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1 Communicaion Sysems, 5e Chae : Baseand Digial ansmission. Buce Calson aul B. Cilly he McGaw-Hill Comanies

2 Chae : Baseand Digial ansmission Digial signals and sysems oise and eos Bandlimied digial M sysems Synchonizaion echniques he McGaw-Hill Comanies

3 Digial Fomaing and ansmission Digial info. souce exual info. nalog info. Samle Foma Quanize Encode ulse modulae ansmi sin nalog info. exual info. Low-ass file Foma Decode Bi seam ulse wavefoms Demodulae/ Deec Channel eceive Digial info. 3

4 BC Binay M fomas Coyigh he McGaw-Hill Comanies, Inc. emission equied fo eoducion o dislay. (a) uniola Z & Z () ola Z & Z (c) iola Z (d) sli-hase Manchese (e) ola quaenay Z: Figue.- 4

5 BC CM Definiions Uniola he signal can e consideed on and off, wih signal levels of and in amliude. ola he signal has oosie olaiy comonens, so ha he signal has a zeo () DC comonen if s and s ae equally liely. Biola he signal also has oosie olaiy comonens, u also inlcudes zeo () as a seudo-inay foma. 5

6 Baseand Binay eceive Coyigh he McGaw-Hill Comanies, Inc. emission equied fo eoducion o dislay. Figue.- x a y a h n h y Synchonous ime samling of maximum file ouu a n in 6

7 Symol Deecion Keys File oiae andwidh o ade-off signal owe and noise owe mached file is oimal! Deecion heshold Wha heshold is used o deec a inay symol? Minimize he oailiy of a i eo Based on hyohesis esing 7

8 8 ola Binay Eo oailiy Hyohesis esing using a volage heshold Hyohesis Hyohesis Fo oise ha is WG e e eo H H y H y Y - Y y H y ex y y H y Y x d ex Q x Q V Q dy y V Y V e Q V Q dy y V Y V e V fo

9 9 elaionshi o signal owe Defining he aveage eceived signal owe Uniola ola Biola In ems of S S,,,, 4 S ola fo S Uniola fo S 4 S,, Biola fo S lim c d x E S

10 S o E/o Fo he Signal o oise aio S elaes he aveage signal owe and aveage noise owe ( is i eiod, W is file andwidh) E/o elaes he enegy e i o he noise enegy (a mulile of he ime-andwidh oduc) W E W E W E S W S W S E

11 elaionshi o E/o Defining he enegy e i o noise owe aio fo a ime-andwidh oduc of Uniola ola Biola E S 4 E S 4 E S W

12 elaionshi o Bi Eo oailiy Defining he inay i eo oailiy fo a ime-andwidh oduc Uniola ola Biola eo E Q Q eo E Q Q eo E Q Q

13 Bi Eo ae lo Classical Bi Eo aes Ohogonal niodal Bi Eo ae Eo=(:)'/; % Q(x)=.5*efc(x/sq()) Oho=.5*efc(sq(Eo)/sq()); niodal=.5*efc(sq(*eo)/sq());.5 semilogx(eo,[oho niodal]). ylael('bi Eo ae') xlael('e/o').5 ile('classical Bi Eo aes') legend('ohogonal','niodal') E/o 3

14 BE efomance, Classical Cuves log-log lo - Classical Bi Eo aes Ohogonal niodal - Bi Eo ae E/o 4

15 niodal and Ohogonal Signals niodal Disance is wice signal volage Only wos fo one-dimensional signals d E fo i j zij si s j d E fo i j Ohogonal Ohogonal symol se Wos fo o dimensional signals d E z ij fo i j si s j d E fo i j 5

16 M-ay Signals Symol eesens is a a ime Symol seleced ased on is M wavefoms may e ansmied M llow fo he adeoff of eo oailiy fo andwidh efficiency Ohogonaliy of -i symols ume of is ha agee=ume of is ha disagee z ij K sum i j i j sum K fo i j fo i j 6

17 Q Funcion nohe defined funcion ha is elaed o he Gaussian (and used) is he Q-funcion.: Q Funcion ale. 858 Q x u x ex u du he Q-funcion is he comlemen of he nomal funcion, : Q x x heefoe noe ha: Q x Qx x X F X x Q 7

18 Using MLB nohe way o find values fo he Gaussian he eo funcion F X x ef x x ex u du u Qx ef x x X x ef ef X he eo funcion (Y = EF(X)) is uil-in o MLB Fom MLB: EF Eo funcion. Y = EF(X) is he eo funcion fo each elemen of X. X mus e eal. he eo funcion is defined as: ef(x) = /sq(i) * inegal fom o x of ex(-^) d. See also efc, efcx, efinv. efeence age in Hel owse doc ef 8

19 Using MLB () he comlemenay eo funcion Q x efc x efc x ef x he eo funcion (Y = EFC(X)) is uil-in o MLB.. Fom MLB: EFC Comlemenay eo funcion. Y = EFC(X) is he comlemenay eo funcion fo each elemen of X. X mus e eal. he comlemenay eo funcion is defined as: efc(x) = /sq(i) * inegal fom x o inf of ex(-^) d. = - ef(x). Class suo fo inu X: floa: doule, single See also ef, efcx, efinv. efeence age in Hel owse doc efc 9

20 Qfn and Qfninv hese funcion ae now in he Misc_Mala zi file on he we sie funcion [Qou]=Qfn(x) % Qfn(x) =.5 * efc(x/sq()); Qou =.5 * efc(x/sq()); funcion [x]=qfninv(e) % Fo Qfn(x) =.5 * efc(x/sq()); % he invese can e found as x=sq()*efcinv(*e);

21 Mached File CM () mached file is he ime evesed vesion of he ansmied signal () a x K h d K a K a y ' ' ' d K a y ' ' ' d K a K a y By definiion, he maximum of he auocoelaion occus a =. heefoe, he ouu is maximized a y().

22 Mached File CM () If we define he consan K as K eq d y a a d d he maximum a = ecomes y a nd susequen samles a ime x ae y a

23 Mached File CM (3) he noise owe fo a mached file is n n h n K d n E n K d n E K n E K n n d d E h K d n K En n E d d n K E d d 3

24 4 Mached File CM (4) he noise owe ouu ecomes Using he definiion of K Fo eq =/ eq, his is he minimum andwidh; heefoe, he ouu achieves he maximum S K h eq d K n E eq eq eq d n E

25 Mached fileing wih ecangula ulses Coyigh he McGaw-Hill Comanies, Inc. emission equied fo eoducion o dislay. (a) eceived ulse () imulse esonse (c) ouu ulse: Figue.-6 5

26 Mached File fo Z n inegae and dum cicui can ovide he oimal mached file ouu a imes x Sync C +Vdc Vin V- Vou V+ -Vdc 6

27 oeies of Mached and Wiene Files See ECE38 oes eview fom Chae 9 7

28 Mala ulsedeec.m See simulaion 8

29 Defining a File fo ulses y a We wan o minimize o zeo ine-symol inefeence (ISI) We wan a fequency and limied file whee B f, wih llowale signal aes wih as he excess andwidh d,, B f and B, fo B B B B 9

30 Defining a File fo ulses ossile soluions f,, B f sinc f fo f heefoe we selec f f df f ec f hese ae consideed he yquis condiions fo he file 3

31 Cosine Secal Shaing aised cosine ulse. (a) Wavefom () Deivaives (c) mliude secum Figue.5-7 Fom Cha aised cosine ulse candidae file is (wih wih as he excess BW) f f cos 4 4 f ec 3

32 Convolving aised Cosine Convoluion wih Bandlimied Secum f whee cos B f 4, f cos f wih ec 4 f sinc f f and B ansfoming o he ime domain file f B 3

33 yquis/aised Cosine ulse Shaing h://en.wiiedia.og/wii/aised-cosine_file BC GU FDL:Oli Filh, aised Cosine File esonse, en.wiiedia.og, 3 oveme 5, Oli Filh BC GU FDL:Oli Filh, aised Cosine File, Imulse esonse, en.wiiedia.og, 3 oveme 5, Oli Filh 33

34 yquis File cos 4 cos n f s n M sinc fs M sinc n n cos M n sinc, n M M fo M n M % funcion hnyq=nyquisfil(alha,m) % o % funcion hnyq=nyquisfil(alha,fsymol,fsamle,) % % alha oll-off % fsamle ae % fsymol ae % M = fsamle/fsymol (an inege value) % is / he nume of symols in he file % he file lengh is euqal o *ceil(*m)+ % % discee ime cosine aed yquis file % Based on fedeic hais, Muliae Signal ocessing fo Communicaions % enice-hall,,

35 MLB aised Cosine Files cosine [UM, DE] = COSIE(Fd, Fs, fi, ) FI aised cosine file o file a digial signal wih he digial ansfe samling fequency Fd. he file samling fequency is Fs. Fs/Fd mus e a osiive inege. secifies he olloff faco which is a eal nume in he ange [, ]. cosfi B = COSFI(, _, E, ) aised cosine FI file. is he inu signal samling eiod, in seconds. E is he ovesamling ae fo he file (o he nume of ouu samles e inu samle). he olloff faco,, deemines he widh of he ansiion and. _ is a scala o a veco of lengh. If _ is secified as a scala, hen he file lengh is * _ + inu samles. 35

Low-complexity Algorithms for MIMO Multiplexing Systems

Low-complexity Algorithms for MIMO Multiplexing Systems Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :