ECE 6640 Digital Communications
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1 C 664 Digial Communiaion D. Badley J. Bazuin ian Poeo Depamen o leial and Compue ngineeing College o ngineeing and pplied Siene
2 Chape 4 4. Bandpa Modulaion and Demodulaion/Deeion.. Why Modulae?. Digial Bandpa Modulaion ehnique. 3. Deeion o Signal in Gauian Noie. 4. Coheen Deeion. 5. Nonoheen Deeion. 6. Complex nvelope. 7. o Peomane o Binay Syem. 8. M-ay Signaling and Peomane. 9. Symol o Peomane o M-ay Syem (M>>). C 664
3 Sla Communiaion Syem Noe and igue ae aed on o aen om maeial in he oue exoo: C 664 Benad Sla, Digial Communiaion, Fundamenal and ppliaion, 3 Penie Hall PR, Seond diion,.
4 Signal Poeing Funion C 664 Noe and igue ae aed on o aen om maeial in he oue exoo: Benad Sla, Digial Communiaion, Fundamenal and ppliaion, Penie Hall PR, Seond diion,. 4
5 Bandpa Demodulaion and Deeion Fou on Signal o Symol, Sample, and Deeion In he peene o Gauian Noie and Channel e C 664 5
6 C nalog Bandpa Modulaion Inlude he RF/IF Fequeny M, PM and FM Modulaion p d m m m 3 o o 3 p d m m he ime vaying phae omponen
7 Phao Repeenaion aing he poiive peum omplex epeenaion Reexpj j j hin in em o he analyial ignal epeenaion Complex, poiive equenie only C 664 7
8 xample: Bandpa Phao nalyi o Doule Sideand (DSB) Given a one meage m o m o o m m o o poiive equeny phao an e deined and dawn C po Fi deine he omplex ignal a (o exp) 4 m expj expj m m C m m m m
9 Phao nalyi DSB () poiive equeny phao an e deined and dawn C po 4 m expj expj m m 4 m m m 4 m C 664 9
10 Phao nalyi M Given a one meage o o o m poiive equeny phao an e deined and dawn 4 C expj expj expj po o o o m m m m 4 m m C 664
11 Phao nalyi M () poiive equeny phao an e deined and dawn 4 C expj expj expj po m 4 m 4 m m 4 C 664
12 C 664 Naowand FM & PM Speum Foming he Quadaue Repeenaion and anoming he eie expanded ig union j j exp C j exp j exp j j exp C C j! j j exp Mainaining he ode em j j exp C
13 C Naowand FM & PM Speum () aing he Fouie anom o he ode appoximaion j j exp C j S C C j S C S
14 PM and FM Bai Baed on he peviou analyi, we need o deemine he anom o he phae omponen PM p m FM m 3 d PM p M FM M3 j C 664 4
15 PM Phao v expj j expj m p he aie an e emoved o deie he aeand ignal a a ounded phae vaiaion aou he aie p m o C 664 5
16 C PM Phao v Fo a o wave meage inpu o j j exp C j exp j j exp j j exp m p m p C
17 C FM Phao Fo a o wave meage inpu j j exp C m C d o j j exp in j j exp m C j exp j exp j exp m m C See Figue 4.4, p. 73
18 Why diu phao? We ae aou o deie digial modulaion in em o one, wo, and hee dimenional onellaion poin. mpliude Shi Keying: -D aay o poile poin Phae Shi Keying: -D ile wih poin equally paed on he ile Fequeny Shi Keying: N-D pae wih one poin on eah o he N axi Quadaue mpliude Modulaion: -D M x M aay o poin C 664 8
19 Geneal Noe om BC he ollowing noe ae aed on Calon Chape 4. hee i a noaional dieene eween Sla and Calon in deiing a ymol. Sla moe eaily lend iel o deining /No! C 664 9
20 Binay modulaed waveom a) SK ) FSK ) PSK d) DSB wih aeand pule haping See Figue 4.5 on p. 74
21 mpliude Shi Keying (SK) Digial Symol mpliude Modulaion On-O Keying (OOK) uo-oelaion veage Powe o o 4 o OOK OOK P R P R P P p p
22 mpliude Shi Keying () uo-oelaion R R o Symol Powe Speal Deniy S OOK 8 in in Bandpa Bandwidh Nominally: B =/, i null a B null =/
23 SK Powe Speum Fom BC Chape S vv Baeand o LPF analyi RF nalyi P m Pn n a, a n a n S vv G 4 a in n 4 P p e S S 4 vv vv in 3
24 4 Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.- SK Powe Speum () S vv 4 in 4 vv vv S S G 4
25 SK MLB Simulaion Symol Sequen in ime Symol Sequene Ciula uo-oelaion.5-5 mpliude -.5 Magniude (db) ime x -5 OOK Demodulaion ye Diagam -5 3 Fequeny x 8 Symol Sequene Ciula uo-oelaion - mpliude.5.5 Magniude (db) ime x Fequeny x 7 5
26 SK anmiion Capailiy Compaing he aio o he i ae o he equied ignal andwidh P B Fom he peviou lide o he andwidh heeoe, he anmiion apailiy i B P B i pe eond Hz 6
27 M-ay SK Ue muliple ampliude level o epeen moe han one i pe ymol MSK M- one ae and he o ae ll poiive ampliude (no phae eveal) 7 M m a M a m a n a n a M M S vv 4 in vv vv S S G
28 M-ay SK anmiion Capailiy Compaing he aio o he i ae o he equied ignal andwidh Fo m-ay, he i ae i i ae log he ymol andwidh emain B heeoe, he anmiion apailiy i P log B M log Noe ha o m-ay SK, he OOK yem ha he malle peal eiieny M M i pe eond Hz 8
29 Binay QM Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. (a) anmie () ignal onellaion : Figue 4.-3 x x q i a p a p m a a a x n a n x x i q o in 9
30 Quadaue M (QM) n M-ay Signal 4 omplex ymol Quadaue p p p p 3 i i o i o o i o uo-oelaion, Single Pule Peiod * o 3 veage Powe QM o 3
31 3 QM Symol Co Coelaion No ha adjaen ymol aveage oelaion i zeo o equal poailiy ymol i C C,, i C C,3, o i i i C P C P C P C P
32 3 Quadaue M Powe Speum P in p e e vv vv S S G in vv S Noe ha he ymol ae i one-hal he i ae. n a a vv n n P m P S in vv S in 4 vv S
33 QM anmiion Capailiy Compaing he aio o he ymol ae o he equied ignal andwidh log B P heeoe, he anmiion apailiy i M P i pe eond Hz 33
34 34 Phae Modulaion Mehod Phae hi eying (PSK) i digial PM Poin on a uni ile o a onellaion plo 4-QM a peviouly deied i uing phae o epeen ymol. he magniude i he ame, u ueive ymol die y 9 degee in phae. Fequeny hi eying (FSK) i digial FM Muliple diee equenie D p x o D d p a x o
35 PSK Signal Conellaion hi i QM, oaed y pi/4 o 4-PSK M=4 4-PSK M=8 8-PSK 35
36 36 M-PSK n M-ay Signal M omplex ymol Quadaue ( poile epeenaion) uo-oelaion, ingle ymol Peiod veage Powe, mpliude o negy M o o, M o * o o QM P M o o, M,in M o,q I p
37 Binay PSK Signal Symol o o o o uooelaion * o Co Coelaion (he deiniion o anipodal) * o R R 37
38 Binay PSK Signal Symol o o o o uooelaion * o Co Coelaion (he deiniion o anipodal) * o R R 38
39 BPSK Powe Speum Fom Chape S vv Baeand o LPF analyi RF nalyi P m Pn n a, a n a n G S vv a in n P p e S S vv vv in 39
40 BPSK MLB Simulaion mpliude ime x -6 BPSK Demodulaion ye Diagam.5 Magniude (db) Fequeny x mpliude Magniude (db) ime x Fequeny x 7 4
41 Ohe Fom o PSK Dieenial PSK he ymol ae he enoding o wo adjaen i noding he i hange no he i value ypially an exluive-o o xluive NOR QPSK leady hown a QM Oe QPSK Oe he I and Q i o QM y one hal he ymol peiod Phae hange a BPSK i ae, i aolue phae hange i now alway pi/ (ohogonal) 4
42 Dieenial noded PSK (DPSK) he inay daa eam i dieenially enoded he logial ominaion o he peviou i en and he nex i o e en. n xluive NOR gae an e ued. Povide an aiay a only phae hange y pi i equied o deode he meage, no he aolue i value! Sample Index Inomaion m() Di. noding () DPSK Phae pi pi pi Dee Di. noding () DPSK Phae pi pi pi pi pi pi pi pi Dee 4
43 Oe-eyed QPSK anmie (OQPSK) Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 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! 43
44 Digial Fequeny Modulaion Fequeny Shi Keying (FSK) Coninuou Phae FSK (CPFSK) 44
45 Fequeny Shi Keying Binay FSK o d o d M-ay FSK o MFSK o, o o M a Deied Condiion (mae he ime ignal oninuou a he ymol ime oundaie) ep m, o m an inege ep S 45
46 M-FSK n M-ay Signal M omplex ymol o, o o M a Deied Condiion (nomally) Cooelaion ep m, o m an inege ep * o a ep Can mae expeed value zeo ep uooelaion * o a ep 46
47 BFSK Signal Symol uooelaion o d o d Co Coelaion * o * o o d * o d d ohogonal o x d x= d d 47
48 BFSK Quadaue Repeenaion () o a he ign em o odd i eome d o o a in in a d o o a in in d o o a in in d d o o a in in I, Q o, a in a d 48
49 49 BFSK Quadaue Repeenaion () a Q I in, o, 4 q i lp Q G G G he aeand peum G lp in in 4 Q o 4 Q o 4 4 q i lp G G G
50 5 Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.-8 Powe peum o BFSK d d o 4 4 q i lp G G G
51 BFSK MLB Simulaion No eadily oevale he hange in equeny i oo mall Magniude (db) BFSK Demodulaion ye Diagam Fequeny x 8 - mpliude Magniude (db) ime x Fequeny x 7 5
52 Speum o M-FSK one wih equal paing ae equied, MFSK equie addiional andwidh o addiional ymol one. he andwidh mu gow a a muliple o M, wheea o M-PSK he andwidh i aed on he ymol peiod. M-FSK i inheenly wideand modulaion. Moe i pe ymol equie moe andwidh 5
53 53 Speial Veion o FSK Coninuou Phae FSK (CPFSK) d d x x o a a a a a d x j j,,, Minimum-Shi Keying (MSK) he inay veion o CPFSK lo alled a FSK Capale o uing an / andwidh
54 54 CPFSK Coninuou Phae FSK (CPFSK) he phae i oninuou a he aniion eween i. hi i mo eaily aomplihed i he phae i π o a muliple o π a he a and end o eah i peiod. d d x x o a a a a a d x j j,,,
55 Binay CPFSK he inay veion o CPFSK i alled Minimum-Shi Keying (MSK) lo alled a FSK Capale o uing an / andwidh 55
56 56 MSK Baeand Fequeny and phae (hioy) modulaion Q I, p a x i o p a x q in odd o n even o m,,
57 Illuaion o MSK. Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. (a) phae pah () i and q waveom: Figue 4.- MSK inlude he phae hioy wih he equeny lope in ime o he new i. heeoe he phae plo in ime an appea a hown, wih he oeponding quadaue omponen. 57
58 Minimum Shi Keying (MSK) MSK powe peum: Figue 4.-9 ep Ue.5 in BFSK Sim 58
59 Sla Repeenaion mpliude Shi Keying Phae Shi Keying Fequeny Shi Keying C i i o o o M o o M o o o min M o o ep ep ep o o
60 exoo Waveom negy Waveom negy (Symol uooelaion) Mahed File C i i d d h h z u h * d z * d d d z * * Coelaion
61 Signal Powe v. Bi negy Fo oninuou ime ignal, powe i a nomal way o deie he ignal. Fo a diee ymol, he powe i u he enegy i non-zeo heeoe, we would lie o deie ymol in em o enegy no powe Fo digial anmiion how o we go om powe o enegy? Powe i enegy pe ime, u we now he ime duaion o a i. Noie ha a andwidh. S R 6
62 negy and Powe Fo he aveage powe and enegy pe i eome C d d d d o o o o P
63 63 SNR o /N o Reminde Fo he Signal o Noie Raio SNR elae he aveage ignal powe and aveage noie powe ( i i peiod, W i ile andwidh) /N o elae he enegy pe i o he noie enegy (equal o S/N ime a ime-andwidh podu) W N W N N S W N S R W N S N I you wan a highe /N o, ineae. (Changing W hange he SNR oo!)
64 Symol Deeion Baeand deeion and BR deined in he peviou hape. he ollowing ae om BC Chap. 4 C
65 Opimum inay deeion Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. (a) paallel mahed ile () oelaion deeo: Figue
66 Condiional PDF Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue
67 Bandpa inay eeive Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.- Uing upepoiion o he paallel mahed ile, he BPF i he dieene o he wo ile. h h h BPF hi eul in an opimal inay deeo 67
68 Binay Reeive 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 68
69 Coelaion eeive o OOK o BPSK Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.-4 Sine oh opimal ile oni o oine waveom, mix and inegae inead o ile an opimally ample. Noe ha he inegao an e a eangula window ile ha i opimally ampled. (Povide unionaliy nea ynhonizaion a well.) 69
70 7 Opimal Paallel Mahed File Reeive o nalyi valuaing he expeed value max N d z z d d d d d max N N z z
71 Opimal Paallel Mahed File Reeive o nalyi d OOK z z N max PSK z z N max FSK z z N max 7
72 Genealized Poailiy o o Uing he opimal BPF ile and ampling o eah ymol, he elaionhip will e aed on: z z N N max he BR i hen aed on P e z z Q Q N heeoe piing aiay ymol i poile, u he ymol oelaion oeiien will dive he BR peomane. 7
73 Genealized FSK o d o o d o d d o o in d in 4 d in 4 d hee ae muliple ohogonal one epaaion. d ep he oelaion oeiien an go negaive! he minimum ou a appoximaely in(.) = -.66 d d d exp d exp d i d i exp i d d i exp i i d d d 73
74 MLB Coheen Reeive BSK example ode BPSK example ode BFSK example ode C
75 Nonoheen Binay Syem Synhonou oheen eeive an e vey diiul o deign. Can nonoheen yem e moe eaily deigned wihou giving up igniian BR peomane? Fo a - db /No peomane lo, YS! 75
76 Nonoheen OOK eeive Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.3- Uing an envelope deeo, he noie pd o a zeo ymol eome Riian and i non-longe Gauian. he noie pd o a one ymol emain Gauian 76
77 77 Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue Condiional PDF o nonoheen OOK op V op e op e V P V P exp N P e exp N P P P P e e e e
78 Nonoheen deeion o inay FSK Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue
79 Nonoheen FSK Qualiaive ommen Uing envelope deeo on eah ymol oupu, he Riian eo diiuion ee he z deeion aii. P e exp N 79
80 Binay eo poailiy uve Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. (a) oheen BPSK () DPSK () oheen OOK o FSK (d) nonoheen FSK (e) nonoheen OOK: Figue BR Simulaion o BPSK and BFSK - - BR BPSK imulaion BPSK (heoeial) BFSK imulaion BFSK (heoeial) /N o (db) 8
81 Binay eo poailiy uve (a) oheen BPSK () DPSK () oheen OOK o FSK (d) nonoheen FSK (e) nonoheen OOK Figue Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay.
82 Deeion o M-ay Syem Deemine he deeion aii o all ymol Sele he maximum aii Deode he inay value om he eleed ymol Noe: M-SK and M-PSK ymol may no longe e ohogonal M-FSK ymol may e ohogonal, u he andwidh W mu ineae o onain he ymol. 8
83 Quadaue-aie eeive wih oelaion deeo Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue 4.4- ppliale o: M-QM M-PSK 83
84 Caie ynhonizaion o quad-aie eeive Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue
85 Coheen M-ay PSK eeive Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue PeDeode, /N (db)=9 5 Imag 5 MPSK_Demo.m Fixed N, vaying ignal Real
86 Deiion hehold o M-ay PSK Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. Figue PeDeode, /N (db)=9 5 Imag Real
87 PSK ignal onellaion (a) M=4 () M=8 Figue 4.5- MPSK Symol ae ypially Gay-ode enoded pio o anmiion In he Gay-ode, adjaen ymol ae only dieen y i value! 87 Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay.
88 MPSK /N xample PeDeode, /N (db)= PeDeode, /N (db)= Imag Imag PeDeode, /N (db)=9 Real Symol o Rae, M=8 Real Bi o Rae, M= BR SR Imag Real /No (db) - /No (db) 88
89 Simulaed Peomane MPSK MPSK_Be and MPSK_PP_Plo MPSK Symol o Rae MPSK Bi o 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) 89
90 Simulaed Peomane MFSK MFSK_Be and MFSK_PP_Plo MFSK Symol o Rae MFSK Bi o 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 Compaing MPSK and MFSK MPSK Moe /N equied o highe M o ymol eo ae - and 4-PSK have he ame BR Ohewie highe BR o highe M MFSK Moe /N equied o highe M o ymol eo ae, BU i doe no ineae a a a MPSK Le /N equied o highe M o BR! How ould hi e? he ymol ae all ohogonal! 9
92 M-ay QM yem Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay. (a) anmie () eeive () quae ignal onellaion and hehold wih M=6 Figue
93 Peomane ompaion o M-ay modulaion yem P e 4 93 Copyigh he MGaw-Hill Companie, In. Pemiion equied o epoduion o diplay.
94 MLB Coheen Reeive MPSK example ode MFSK example ode QM example ode C
95 Noe on BR Fo MPSK and QM Sla QM p. 565 MPSK p. 9-3 J.G. Poai & M. Salehi, Digial Communiaion, 5 h ed. QM p. 96- MPSK p Jianhua Lu; Leaie, K.B.; Chuang, J. C-I; Liou, M.-L., "M-PSK and M-QM BR ompuaion uing ignal-pae onep," Communiaion, I anaion on, vol.47, no., pp.8,84, Fe 999. C
96 QM BR Compuaion % Sla (i eo ae) PB(:,ii) = *((-L^-)/log(L))*Q_n(q(3*log(L)**_No/((M-)*ipeym)) ); % Poai (ymol eo ae) PB(:,ii) = *(-L^-)*Q_n(q(3*log(M)*_No/((M-)*ipeym))); PB(:,ii) = *PB(:,ii).*(-.5*PB(:,ii)); PB(:,ii) = PB(:,ii)/ipeym; % Lu, Laaie, Chuang, and Liou (i eo ae) Qum = ; o jj=:l/ Qum=Qum+Q_n((*jj-)*q(3*log(M)*_No/((M-)*ipeym))); end PB3(:,ii) = 4*((-L^-)/log(M))*Qum; C
97 QM BR Cuve BR Compoie Plo QM 6 QM 64 QM 56 QM Bi o Rae /No (db) C
98 QM BR Cuve Deail/Dieene BR Compoie Plo 4 QM 6 QM 64 QM 56 QM Bi o Rae /No (db) C
99 MPSK Nyqui File BR SR v SNR Sla heoy Plo MPSK Simulaion: heoy v. Simulaion - - Symol o Rae S4 8 S8 6 S6 3 S3 64 S64 8 S8 56 S SNR (db) C
100 MPSK Nyqui File BR BR v /No Sla heoy Plo - MPSK Simulaion: heoy v. Simulaion - Bi o Rae S4 8 S8 6 S6 3 S3 64 S64 8 S8 56 S No (db) C 664
101 QM Nyqui File BR SR v. SNR Sla heoy Plo QM Simulaion: heoy v. Simulaion - Symol o Rae S4 6 S6 64 S64 56 S C 664 SNR (db)
102 QM Nyqui File BR BR v /No Sla heoy Plo - QM Simulaion: heoy v. Simulaion - Bi o Rae S4 6 S6 64 S64 56 S C 664 No (db)
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