ECE 6640 Digital Communications

Transcription

1 C 664 Digial Communiaion Dr. Bradley J. Bazuin Aian Proeor Deparmen o lerial and Compuer ngineering College o ngineering and Applied Siene

2 Chaper 4 4. Bandpa Modulaion and Demodulaion/Deeion.. Why Modulae?. Digial Bandpa Modulaion ehnique. 3. Deeion o Signal in Gauian Noie. 4. Coheren Deeion. 5. Nonoheren Deeion. 6. Complex nvelope. 7. rror Perormane or Binary Syem. 8. M-ary Signaling and Perormane. 9. Symol rror Perormane or M-ary Syem (M>>). C 664

3 Slar Communiaion Syem Noe and igure are aed on or aen rom maerial in he oure exoo: C 664 Bernard Slar, Digial Communiaion, Fundamenal and Appliaion, 3 Prenie Hall PR, Seond diion,.

4 Signal Proeing Funion C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: Bernard Slar, Digial Communiaion, Fundamenal and Appliaion, Prenie Hall PR, Seond diion,. 4

5 Bandpa Demodulaion and Deeion Fou on Signal o Symol, Sample, and Deeion In he preene o Gauian Noie and Channel e C 664 5

6 C Analog Bandpa Modulaion Inlude he RF/IF Frequeny AM, PM and FM Modulaion p d m m m A A 3 o o 3 p d m m he ime varying phae omponen

7 Phaor Repreenaion aing he poiive perum omplex repreenaion AReexpj j j hin in erm o he analyial ignal repreenaion Complex, poiive requenie only C 664 7

8 xample: Bandpa Phaor Analyi o Doule Sideand (DSB) Given a one meage m A A o m A A o o A m m o o A poiive requeny phaor an e deined and drawn C po Fir deine he omplex ignal a (o exp) A A 4 m expj expj m m C m m m m

9 Phaor Analyi DSB () A poiive requeny phaor an e deined and drawn C po A A 4 m expj expj m m A 4 A m m m A 4 A m C 664 9

10 Phaor Analyi AM Given a one meage A o A o o m A poiive requeny phaor an e deined and drawn A A 4 C expj expj expj po A o o o A m m m m A A 4 m m C 664

11 Phaor Analyi AM () A poiive requeny phaor an e deined and drawn A A 4 C expj expj expj po m A 4 m A 4 A m m A 4 C 664

12 C 664 Narrowand FM & PM Sperum Forming he Quadraure Repreenaion and ranorming he erie expanded rig union j j exp A C j exp j exp A j j exp A C C j! j j exp A Mainaining he order erm j j exp A C

13 C Narrowand FM & PM Sperum () aing he Fourier ranorm o he order approximaion j j exp A C j A S C C j A S C A S

14 PM and FM Bai Baed on he previou analyi, we need o deermine he ranorm o he phae omponen PM p m FM m 3 d PM p M FM M3 j C 664 4

15 PM Phaor v A expj j expj m p he arrier an e removed o derie he aeand ignal a a ounded phae variaion aou he arrier p m A o C 664 5

16 C PM Phaor v For a o wave meage inpu A o j j exp A C j exp j j exp j j exp A m p m p C

17 C FM Phaor For a o wave meage inpu j j exp A C m C d o j j exp A in j j exp A m C j exp j exp j exp A m m C See Figure 4.4, p. 73

18 Why diu phaor? We are aou o derie digial modulaion in erm o one, wo, and hree dimenional onellaion poin. Ampliude Shi Keying: -D array o poile poin Phae Shi Keying: -D irle wih poin equally paed on he irle Frequeny Shi Keying: N-D pae wih one poin on eah o he N axi Quadraure Ampliude Modulaion: -D M x M array o poin C 664 8

19 General Noe rom ABC he ollowing noe are aed on Carlon Chaper 4. here i a noaional dierene eween Slar and Carlon in deriing a ymol. Slar more eaily lend iel o deining /No! C 664 9

20 Binary modulaed waveorm a) ASK ) FSK ) PSK d) DSB wih aeand pule haping See Figure 4.5 on p. 74

21 Ampliude Shi Keying (ASK) Digial Symol Ampliude Modulaion On-O Keying (OOK) Auo-orrelaion Average Power A o A o 4 o OOK OOK A A P R P R P P p p A

22 Ampliude Shi Keying () Auo-orrelaion R R o Symol Power Speral Deniy A A S OOK A 8 in in Bandpa Bandwidh Nominally: B =/, ir null a B null =/

23 ASK Power Sperum From ABC Chaper S vv Baeand or LPF analyi RF Analyi r P m r Pn r nr A a, a n a A n S vv G A 4r a in r n A 4 P p re r S S 4 vv vv r in r 3

24 4 Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.- ASK Power Sperum () A r r A S vv 4 in 4 vv vv S S G 4 r

25 ASK MALAB Simulaion Symol Sequen in ime Symol Sequene Cirular Auo-orrelaion.5-5 Ampliude -.5 Magniude (db) ime x -5 OOK Demodulaion ye Diagram -5 3 Frequeny x 8 Symol Sequene Cirular Auo-orrelaion - Ampliude.5.5 Magniude (db) ime x Frequeny x 7 5

26 ASK ranmiion Capailiy Comparing he raio o he i rae o he required ignal andwidh r P B From he previou lide or he andwidh hereore, he ranmiion apailiy i B r P r B i per eond Hz 6

27 M-ary ASK - Nonoheren Ue muliple ampliude level o repreen more han one i per ymol MASK M- one ae and he o ae All poiive ampliude (no phae reveral) 7 M m a M a m a n a n a M A r r M A S vv 4 in vv vv S S G

28 M-ary ASK ranmiion Capailiy Comparing he raio o he i rae o he required ignal andwidh For m-ary, he i rae i i rae r log he ymol andwidh remain B r hereore, he ranmiion apailiy i r P log B M log Noe ha or m-ary ASK, he OOK yem ha he malle peral eiieny M M i per eond Hz 8

29 M-ary ASK - Coheren Ue muliple ampliude level MASK M/ poiive value and M/ Negaive value: or =:M/ volage value ould e a (-/)/(M/) Bipolar level (wih phae reveral ) M n n n n n n n n a n M m a a m a n a n M a n a n a in vv r r M A S vv vv S S G Noe ha AC power doen hange, ju DC

30 Binary QAM Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. (a) ranmier () ignal onellaion : Figure 4.-3 x x q i a p a p m a a a x n A a n A x x i q o in 3

31 Quadraure AM (QAM) An M-ary Signal 4 omplex ymol Quadraure p p p p 3 i i A o i A o A o i A o Auo-orrelaion, Single Pule Period * A o 3 Average Power QAM A o A 3

32 3 QAM Symol Cro Correlaion No ha adjaen ymol average orrelaion i zero or equal proailiy ymol i C C,, i C C,3, o A i i i C P C P C P C P

33 33 Quadraure AM Power Sperum r r P in r p re re vv vv S S G in vv r r r A S Noe ha he ymol rae i one-hal he i rae. n a a vv r n r n P r m P r S r r in vv r r A S in 4 vv r r A S

34 QAM ranmiion Capailiy Comparing he raio o he ymol rae o he required ignal andwidh log B P hereore, he ranmiion apailiy i r M P i per eond Hz 34

35 35 Phae Modulaion Mehod Phae hi eying (PSK) i digial PM Poin on a uni irle o a onellaion plo 4-QAM a previouly deried i uing phae o repreen ymol. he magniude i he ame, u ueive ymol dier y 9 degree in phae. Frequeny hi eying (FSK) i digial FM Muliple diree requenie D p A x o D d p a A x o

36 PSK Signal Conellaion hi i QAM, roaed y pi/4 or 4-PSK M=4 4-PSK M=8 8-PSK 36

37 37 M-PSK An M-ary Signal M omplex ymol Quadraure ( poile repreenaion) Auo-orrelaion, ingle ymol Period Average Power, Ampliude o nergy M o or, M o A * o A o QAM A A P M o or, M,in M o,q I p A

38 Binary PSK Signal Symol A o A o A o A o Auoorrelaion * A o Cro Correlaion (he deiniion o anipodal) * A o R R 38

39 Binary PSK Signal Symol A o A o A o A o Auoorrelaion * A o Cro Correlaion (he deiniion o anipodal) * A o R R 39

40 BPSK Power Sperum From Chaper S vv Baeand or LPF analyi RF Analyi r P m r Pn r nr a, a A n a n G S vv a A r in n r P p re r S S vv vv r in r 4

41 BPSK MALAB Simulaion Ampliude ime x -6 BPSK Demodulaion ye Diagram.5 Magniude (db) Frequeny x Ampliude Magniude (db) ime x Frequeny x 7 4

42 Oher Form o PSK Dierenial PSK he ymol are he enoding o wo adjaen i noding he i hange no he i value ypially an exluive-or or xluive NOR QPSK Already hown a QAM Oe QPSK Oe he I and Q i o QAM y one hal he ymol period Phae hange a BPSK i rae, i aolue phae hange i now alway pi/ (orhogonal) 4

43 Dierenial noded PSK (DPSK) he inary daa ream i dierenially enoded he logial ominaion o he previou i en and he nex i o e en. An xluive NOR gae an e ued. Provide an arirary ar only phae hange y pi i required o deode he meage, no he aolue i value! Sample Index Inormaion m() Di. noding () DPSK Phae pi pi pi Dee Di. noding () DPSK Phae pi pi pi pi pi pi pi pi Dee 43

44 Oe-eyed QPSK ranmier (OQPSK) Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.-6 Inead o hanging I and Q a he ame ime, delay he hange y /. Viualize he phae hange alway o an adjaen ymol! 44

45 Digial Frequeny Modulaion Frequeny Shi Keying (FSK) Coninuou Phae FSK (CPFSK) 45

46 Frequeny Shi Keying Binary FSK A o d A o d M-ary FSK or MFSK A o, or o M ar Deired Condiion (mae he ime ignal oninuou a he ymol ime oundarie) ep m, or m an inerger ep S 46

47 M-FSK An M-ary Signal M omplex ymol A o, or o M ar Deired Condiion (normally) Croorrelaion ep m, or m an inerger ep * A o ar ep Can mae expeed value zero ep Auoorrelaion * A o ar ep 47

48 BFSK Signal Symol Auoorrelaion A o d A o d Cro Correlaion * A o * A o o d * A o d d orhogonal or x d x= d d 48

49 BFSK Quadraure Repreenaion () A o a he ign erm or odd i eome d A o o a A in in a d A o o a A in in d A o o r a A in in r d r d A o o r a A in in r I, Q o r, a in r a d 49

50 5 BFSK Quadraure Repreenaion () r a r Q I in, o, 4 q i lp Q r r r G G G he aeand perum G lp in in 4 r r r r r Q o 4 r r r Q o 4 4 q i lp r r r r r G G G

51 5 Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.-8 Power perum o BFSK d r d r o 4 4 q i lp r r r r r G G G

52 BFSK MALAB Simulaion No readily oervale he hange in requeny i oo mall Magniude (db) BFSK Demodulaion ye Diagram Frequeny x 8 - Ampliude Magniude (db) ime x Frequeny x 7 5

53 Sperum o M-FSK A one wih equal paing are required, MFSK require addiional andwidh or addiional ymol one. he andwidh mu grow a a muliple o M, wherea or M-PSK he andwidh i aed on he ymol period. M-FSK i inherenly wideand modulaion. More i per ymol require more andwidh 53

54 54 Speial Verion o FSK Coninuou Phae FSK (CPFSK) d d x A x o a a a a a d x j j,,, Minimum-Shi Keying (MSK) he inary verion o CPFSK Alo alled a FSK Capale o uing an r / andwidh

55 55 CPFSK Coninuou Phae FSK (CPFSK) he phae i oninuou a he raniion eween i. hi i mo eaily aomplihed i he phae i π or a muliple o π a he ar and end o eah i period. d d x A x o a a a a a d x j j,,,

56 Binary CPFSK he inary verion o CPFSK i alled Minimum-Shi Keying (MSK) Alo alled a FSK Capale o uing an r/ andwidh 56

57 57 MSK Baeand (Slar Chap 9) Frequeny and phae (hiory) modulaion he previou/urren phae deermine he nex phae poin phae x daa ummaion in ime Q I, p a x i o p a x q in r odd or even or,,

58 Illuraion o MSK. Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. (a) phae pah () i and q waveorm: Figure 4.- MSK inlude he phae hiory wih he requeny lope in ime o he new i. hereore he phae plo in ime an appear a hown, wih he orreponding quadraure omponen. 58

59 Minimum Shi Keying (MSK) MSK power perum: Figure 4.-9 ep Ue.5 in BFSK Sim 59

60 Slar Repreenaion Ampliude Shi Keying Phae Shi Keying Frequeny Shi Keying C i i o o o M o or M o o o min M o or ep ep ep o o

61 exoo Waveorm nergy Waveorm nergy (Symol Auoorrelaion) Mahed Filer C i i d d h r h r z u h * d z * d d d z * * Correlaion

62 Signal Power v. Bi nergy For oninuou ime ignal, power i a normal way o derie he ignal. For a diree ymol, he power i u he energy i non-zero hereore, we would lie o derie ymol in erm o energy no power For digial ranmiion how o we go rom power o energy? Power i energy per ime, u we now he ime duraion o a i. Noie ha a andwidh. S R 6

63 nergy and Power For he average power and energy per i eome C d d d d o o o o A P

64 64 SNR o /N o Reminder For he Signal o Noie Raio SNR relae he average ignal power and average noie power ( i i period, W i iler andwidh) /N o relae he energy per i o he noie energy (equal o S/N ime a ime-andwidh produ) W N W N N S W N S R W N S N I you wan a higher /N o, inreae. (Changing W hange he SNR oo!)

65 Symol Deeion Baeand deeion and BR deined in he previou haper. he ollowing are rom ABC Chap. 4 C

66 Opimum inary deeion Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. (a) parallel mahed iler () orrelaion deeor: Figure

67 Condiional PDF Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure

68 Bandpa inary reeiver Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.- Uing uperpoiion o he parallel mahed iler, he BPF i he dierene o he wo iler. h h h BPF hi reul in an opimal inary deeor 68

69 Binary Reeiver h OOK BPSK BPF BFSK h h h h BPF h BPF h h K K h K o h h h K o BPF h BPF h h K K o o h BPF d in in d d 69

70 Correlaion reeiver or OOK or BPSK Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.-4 Sine oh opimal iler oni o oine waveorm, mix and inegrae inead o iler an opimally ample. Noe ha he inegraor an e a reangular window iler ha i opimally ampled. (Provide unionaliy near ynhronizaion a well.) 7

71 7 Opimal Parallel Mahed Filer Reeiver rror Analyi valuaing he expeed value max N d z z d d d d d max N N z z

72 Opimal Parallel Mahed Filer Reeiver rror Analyi d OOK z z N max PSK z z N max FSK z z N max 7

73 Generalized Proailiy o rror Uing he opimal BPF iler and ampling or eah ymol, he relaionhip will e aed on: z z N N max he BR i hen aed on P e z z Q Q N hereore piing arirary ymol i poile, u he ymol orrelaion oeiien will drive he BR perormane. 73

74 Generalized FSK A o d A o A o A d o d d o o in d in 4 d in 4 d here are muliple orhogonal one eparaion. d ep he orrelaion oeiien an go negaive! he minimum our a approximaely in(.) = -.66 d d d exp d exp d i d i exp i d d i exp i i d d d r 74

75 MALAB Coheren Reeiver BASK example ode BPSK example ode BFSK example ode C

76 Nonoheren Binary Syem Synhronou oheren reeiver an e very diiul o deign. Can nonoheren yem e more eaily deigned wihou giving up igniian BR perormane? For a - db /No perormane lo, YS! 76

77 Nonoheren OOK reeiver Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.3- Uing an envelope deeor, he noie pd or a zero ymol eome Riian and i non-longer Gauian. he noie pd or a one ymol remain Gauian 77

78 78 Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure Condiional PDF or nonoheren OOK op A V op e op e V P V P exp N P e exp N P P P P e e e e

79 Nonoheren deeion o inary FSK Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure

80 Nonoheren FSK Qualiaive ommen Uing envelope deeor on eah ymol oupu, he Riian error diriuion ee he z deeion aii. P e exp N 8

81 Binary error proailiy urve Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. (a) oheren BPSK () DPSK () oheren OOK or FSK (d) nonoheren FSK (e) nonoheren OOK: Figure BR Simulaion or BPSK and BFSK - - BR BPSK imulaion BPSK (heoreial) BFSK imulaion BFSK (heoreial) /N o (db) 8

82 Binary error proailiy urve (a) oheren BPSK () DPSK () oheren OOK or FSK (d) nonoheren FSK (e) nonoheren OOK Figure Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay.

83 Deeion or M-ary Syem Deermine he deeion aii or all ymol Sele he maximum aii Deode he inary value rom he eleed ymol Noe: M-ASK and M-PSK ymol may no longer e orhogonal M-FSK ymol may e orhogonal, u he andwidh W mu inreae o onain he ymol. 83

84 Quadraure-arrier reeiver wih orrelaion deeor Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure 4.4- Appliale or: M-QAM M-PSK 84

85 Carrier ynhronizaion or quad-arrier reeiver Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure

86 Coheren M-ary PSK reeiver Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure PreDeode, /N (db)=9 5 Imag 5 MPSK_Demo.m Fixed N, varying ignal Real

87 Deiion hrehold or M-ary PSK Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. Figure PreDeode, /N (db)=9 5 Imag Real

88 PSK ignal onellaion (a) M=4 () M=8 Figure 4.5- MPSK Symol are ypially Gray-ode enoded prior o ranmiion In he Gray-ode, adjaen ymol are only dieren y i value! 88 Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay.

89 MPSK /N xample PreDeode, /N (db)= PreDeode, /N (db)= Imag Imag PreDeode, /N (db)=9 Real Symol rror Rae, M=8 Real Bi rror Rae, M= BR SR Imag Real /No (db) - /No (db) 89

90 Simulaed Perormane MPSK MPSK_Ber and MPSK_PP_Plo MPSK Symol rror Rae MPSK Bi rror Rae SR M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound /N (db) BR M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound /N (db) 9

91 Simulaed Perormane MFSK MFSK_Ber and MFSK_PP_Plo MFSK Symol rror Rae MFSK Bi rror Rae SR M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound /N (db) BR M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound /N (db) 9

92 Comparing MPSK and MFSK MPSK More /N required or higher M or ymol error rae - and 4-PSK have he ame BR Oherwie higher BR or higher M MFSK More /N required or higher M or ymol error rae, BU i doe no inreae a a a MPSK Le /N required or higher M or BR! How ould hi e? he ymol are all orhogonal! Bu he ymol andwidh (ilering) mu e inreaing. 9

93 M-ary QAM yem Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay. (a) ranmier () reeiver () quare ignal onellaion and hrehold wih M=6 Figure

94 Perormane omparion o M-ary modulaion yem P e 4 94 Copyrigh he MGraw-Hill Companie, In. Permiion required or reproduion or diplay.

95 MALAB Coheren Reeiver MPSK example ode MFSK example ode QAM example ode C

96 Noe on BR For MPSK and QAM Slar QAM p. 565 MPSK p. 9-3 J.G. Proai & M. Salehi, Digial Communiaion, 5 h ed. QAM p. 96- MPSK p Jianhua Lu; Leaie, K.B.; Chuang, J. C-I; Liou, M.-L., "M-PSK and M-QAM BR ompuaion uing ignal-pae onep," Communiaion, I ranaion on, vol.47, no., pp.8,84, Fe 999. C

97 QAM BR Compuaion % Slar (i error rae) PB(:,ii) = *((-L^-)/log(L))*Q_n(qr(3*log(L)**_No/((M-)*iperym)) ); % Proai (ymol error rae) PB(:,ii) = *(-L^-)*Q_n(qr(3*log(M)*_No/((M-)*iperym))); PB(:,ii) = *PB(:,ii).*(-.5*PB(:,ii)); PB(:,ii) = PB(:,ii)/iperym; % Lu, Laaie, Chuang, and Liou (i error rae) Qum = ; or jj=:l/ Qum=Qum+Q_n((*jj-)*qr(3*log(M)*_No/((M-)*iperym))); end PB3(:,ii) = 4*((-L^-)/log(M))*Qum; C

98 QAM BR Curve BR Compoie Plo QMA 6 QAM 64 QAM 56 QAM Bi rror Rae /No (db) C

99 QAM BR Curve Deail/Dierene BR Compoie Plo 4 QMA 6 QAM 64 QAM 56 QAM Bi rror Rae /No (db) C

100 MPSK Nyqui Filer BR SR v SNR Slar heory Plo MPSK Simulaion: heory v. Simulaion - - Symol rror Rae S4 8 S8 6 S6 3 S3 64 S64 8 S8 56 S SNR (db) C 664

101 MPSK Nyqui Filer BR BR v /No Slar heory Plo - MPSK Simulaion: heory v. Simulaion - Bi rror Rae S4 8 S8 6 S6 3 S3 64 S64 8 S8 56 S No (db) C 664

102 QAM Nyqui Filer BR SR v. SNR Slar heory Plo QAM Simulaion: heory v. Simulaion - Symol rror Rae S4 6 S6 64 S64 56 S C 664 SNR (db)

103 QAM Nyqui Filer BR BR v /No Slar heory Plo - QAM Simulaion: heory v. Simulaion - Bi rror Rae S4 6 S6 64 S64 56 S C 664 No (db) 3

104 M-ary Signaling Doe M-ary ignaling improve or degrade error perormane? hi i a loaded queion! For oheren orhogonal ignaling here appear o e an improvemen. However, he andwidh mu e inreaing i he ame ymol rae i mainained. For oheren phae aed ignaling here appear o e a degradaion. However, or he ample ymol ime, he daa rae i inreaing. I may e dereaed when more i-per-ymol are ranmied. M-ary ignaling provide a mehod o provide yem radeo. rror perormane an e raded o wih ymol ime and andwidh. radeo o e diued in Chap. 9. C 664 4

105 Symol v Bi rror Rae SNR and /No are relaed or M-ary ymol ranmiion. o derive /No, or a nown numer o ymol i log M ymol log M ymol i R log M ymol N S N W R S N W In every MALAB Simulaion I ry o e very areul in deining SR v BR and /No v /No. C 664 5

106 Noe rom Proai Noe and igure are aed on or aen rom maerial in he previou oure exoo J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8. C 664 6

107 4.3 Opimal Deeion and rror Proailiy or Band-Limied Signaling hee are or lower andwidh, low dimenionaliy ignaling ype. hi eion i an exellen reerene or ome o he primary ignal ype diued. xplii BR v. /No equaion are derived aed on he previou maerial preened. An aumpion o equally liely ymol i made or eah derivaion Derive ASK or PAM 4.3- Derive MPSK Derive QAM C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 7 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

108 MASK Summary C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 8 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

109 MASK C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 9 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

110 MASK Perormane C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

111 MPSK he marginal proailiy deniy union or a ymol an e deined a he pd i a union o he average ymol energy he higher he numer o ymol, he igher he ymol deiion region mu eome and more error an e expeed. C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

112 MPSK In general, he inegral o p(θ) doe no redue o a imple orm and mu e evaluaed numerially, exep or M = and M = 4. For M= For M=4 For oher M (M large and SNR large) C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

113 MPSK M= M=4 M oher C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 3 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

114 QAM QAM i dependen upon he ymol onellaion eleed. Deaul o quare onellaion o 4, 6, 64, & 56 Numerou oher are poile wih poenially eer yem perormane he opimal deeor ue ai ymol o reolve he in-phae and quadraure omponen C Noe and igure are aed on or aen rom maerial in he oure exoo: J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

115 Square Conellaion QAM hi ae appear a wo dimenional ASK/PAM C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 5 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

116 Square Conellaion QAM C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 6 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

117 Comparing QAM and MPSK Looing a he raio o he Q(x) argumen A M=4 he yem are equivalen, u or higher M QAM ha eer perormane. C 664 Noe and igure are aed on or aen rom maerial in he oure exoo: 7 J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

118 Demodulaion and Deeion o Band- Limied Signal Mahed iler involve he ai orm o he ignal. Noe: Filer are mahed o ai, no mahed o ymol! C Noe and igure are aed on or aen rom maerial in he oure exoo: J.G. Proai and M.Salehi, Digial Communiaion, 5h ed., MGraw-Hill, 8.

119 4.4 Opimal Deeion and rror Proailiy or Power-Limied Signaling hee are or wider andwidh, higher dimenionaliy ignaling ype. BR v. /No equaion are derived aed on he previou maerial preened. An aumpion o equally liely ymol i made or eah derivaion Orhogonal FSK 4.4- Biorhogonal Simplex C 664 9

120 Orhogonal Signal - MFSK For equiproale, equal-energy orhogonal ignal, he opimum deeor ele he ignal reuling in he large ro-orrelaion eween he reeived veor r and eah o he M poile ranmied ignal veor { m }, i.e., d min C 664

121 Orhogonal Signal (on) he proailiy o orre ymol deeion an e deried a auming Gauian noie elemen where he elemen are independen and idenially diriued (IID) wih an individual dimenion repreened a C 664

122 Orhogonal Signal (on) he inegral eome he error i he omplemen, hereore In general, quaion 4.4 anno e made impler, and he error proailiy an e ound numerially or dieren value o he SNR. o deermine i error, le u aume ha orrepond o a daa equene o lengh wih a a he ir omponen. he proailiy o an error a hi omponen i he proailiy o deeing an m orreponding o a equene wih a a he ir omponen. Sine here are uh equene, we have C 664

123 FSK Signaling Anoher Union Bound he orhogonal ae i eaier han he previou derivaion a all ymol have he minimum diane. aing he reul For orhogonal ignaling d min Uing M = and = /, we have Noe ha i Noe: a neeary and uiien ondiion or reliale omm. ha i lighly lower i derived in Chap. 6. I i alled he Shannon limi. hen P e a (no P e ininie lie he ex ay!!) C 664 3

124 Orhogonal Signaling C 664 4

125 4.4- Biorhogonal Signaling d min d oher C 664 5

126 Biorhogonal Signaling C 664 6