H(f),G(f),C(f) W OR. H(f) H(f),G(f),C(f) 2W. 101 modulator PB.1 PB.2

Transcription

1 Passand Daa ransmissin In aseand daa ransmissin, a daa sream represened in he frm f a discree pulse-ampliude mdulaed PAM signal is ransmied ver a lw-pass channel. ample: yquis channel Hf,Gf,Cf W OR Gf Hf Cf PB. Passand Daa ransmissin In passand daa ransmissin, he incming daa sream is mdulaed n a carrier wih fied frequency and hen ransmied ver a and-pass channel. ample: Hf,Gf,Cf W mdular Gf Hf Cf cs πf PB.

2 ample Passand daa ransmissin allws mre efficien use f he allcaed RF andwidh, and fleiiliy in accmmdaing differen aseand signal frmas. ample Mile elephne Sysems GSM: Gaussian Minimum Shif Keying GMSK is used a variain f FSK IS-54: π/4-differenial Quaernary Phase Shif Keying DQPSK is used a variain f PSK PB.3 ypes he mdulain prcess making he ransmissin pssile invlves swiching keying he ampliude, frequency, r phase f a sinusidal carrier in accrdance wih he incming daa. here are hree asic signaling schemes: Ampliude-shif keying ASK Frequency-shif keying FSK Phase-shif keying PSK PB.4

3 ASK PSK w wavefrms FSK PB.5 ASK, PSK and FSK Unlike ASK signals, h PSK and FSK signals have a cnsan envelpe. PSK and FSK are preferred ASK signals fr passand daa ransmissin ver nnlinear channel ampliude nnlineariies such as micrwave link and saellie channels. PB.6

4 Classificain f digial mdulain echniques Cheren and ncheren Digial mdulain echniques are classified in cheren and nncheren echniques, depending n wheher he receiver is equipped wih a phase-recvery circui r n. he phase-recvery circui ensures ha he lcal scillar in he receiver is synchrnized he incming carrier wave in h frequency and phase. PB.7 Phase Recvery Carrier Synchrnizain w ways in which a lcal scillar can e synchrnized wih an incming carrier wave ransmi a pil carrier similar he DSB-LC mdulain in analg cmmunicain Pil carrier f Use a carrier-recvery circui such as a phase-lcked lp PPL PB.8

5 M-ary signaling In an M-ary signaling scheme, here are M pssile signals during each signaling inerval f durain. n Usually, M and n where is he i durain. n M is mdular PB.9 M-ary signaling In passand ransmissin, we have M-ary ASK M-ary PSK M-ary FSK We can als cmine differen mehds: M-ary quadraure-ampliude mdulain QAM In aseand daa ransmissin, we have M-ary PAM PB.

6 M-ary signaling M-ary signaling schemes are preferred ver inary signaling schemes fr ransmiing digial infrmain ver and-pass channels when he requiremen is cnserve andwidh a he epense f increased pwer. he use f M-ary signaling enales a reducin in ransmissin andwidh y he facr n lg M ver inary signaling. Bandwidh n M is mdular PB. Cheren PSK he funcinal mdel f passand daa ransmissin sysem is m i Signal ransmissin encder si s i Signal Mdular Channel Deecr ransmissin decder mˆ Carrier signal m i is a sequence f syml emied frm a message surce. he channel is linear, wih a andwidh ha is wide enugh ransmi he mdulaed signal and he channel nise is Gaussian disriued wih zer mean and pwer specral densiy /. PB.

7 Cheren PSK he fllwing parameers are cnsidered fr a signaling scheme: Prailiy f errr A majr gal f passand daa ransmissin sysems is he pimum design f he receiver s as minimize he average prailiy f syml errr in he presence f addiive whie Gaussian nise AWG PB.3 Cheren PSK Pwer specra Use deermine he signal andwidh and c-channel inerference in mulipleed sysems. Mulipleer inerference In pracice, he signalings are linear perain, herefre, i is sufficien evaluae he aseand pwer specral densiy. B B PB.4

8 Bandwidh fficiency Cheren PSK R Bandwidh efficiency ρ is/s/hz B where R is he daa rae and B is he used channel andwidh. ample: yquis channel fr aseand daa ransmissin Bandwidh B W /. W R ρ B / / is/s/hz PB.5 Cheren PSK In a cheren inary PSK sysem, he pair f signals s and s used represen inary symls and, respecively, is defined y s csπf c s csπf c + π csπf c where, and is he ransmied signal energy per i PB.6

9 Cheren PSK ample: [ s ] d cs πf c d ensure ha each ransmied i cnains an inegral numer f cycles f he carrier wave, he carrier frequency f c is chsen equal n / fr sme fied ineger n. / f c PB.7 Cheren PSK he ransmied signal can e wrien as s s and where csπf c < e : csπf c d PB.8

10 Generain f cheren inary PSK signals generae a inary PSK signal, he firs sep is represening he inpu inary sequence in plar frm wih symls and represened y cnsan ampliude levels f and, respecively. his signal ransmissin encder is perfrmed y a plar nnreurn--zer RZ encder. s i + inpu syml is inpu syml is Signal ransmissin si encder PB.9 Generain f cheren inary PSK signals he secnd sep is muliplying he carrier encder upu wih he carrier s csπf c if si si s csπf c if si f n / c s i Prduc Mdular csπf c s i PB.

11 Deecin f cheren inary PSK signals deec he riginal inary sequence f s and s, we apply he nisy PSK signal a crrelar. he crrelar upu is cmpared wih a hreshld f zer vls. X Decisin device if if > < Crrelar PB. Deecin f cheren inary PSK signals ample If he ransmied syml is, and he crrelar upu is d csπf c c csπf c cs πf d c csπf d Similarly, if he ransmied syml is,. PB.

12 rrr prailiy f inary PSK We can represen a cheren inary sysem wih a signal cnsellain cnsising f w message pins. he crdinaes f he message pins are all he pssile crrelar upu under a niseless cndiin. he crdinaes fr BPSK are Decisin undary and. PB.3 rrr prailiy f inary PSK here are w pssile kinds f errneus decisin: s Signal is ransmied, u he nise is such ha he received signal pin inside regin wih > and s he receiver decides in favr f signal. s s Signal is ransmied, u he nise is such ha he received signal pin inside regin wih < and s he receiver decides in favr f signal s. s i + w X Decisin device if if > < PB.4

13 PB.5 rrr prailiy f inary PSK Fr he firs case, he servale elemen is relaed he received signal y is a Gaussian prcess wih mean : [ ] + + i d w d w s d i i d w + ] [ ] [ PB.6 rrr prailiy f inary PSK Variance is ] [ ] [ i i d ddu u u ddu u w u w ddu u w u w d w δ σ

14 PB.7 rrr prailiy f inary PSK herefre, he cndiinal prailiy densiy funcin f, given ha syml was ransmied is + f ep ep π σ πσ PB.8 rrr prailiy f inary PSK and he prailiy f errr is + ep d d f p π Puing z +, we have [ ] dz z p erfc ep / π

15 rrr prailiy f inary PSK Similarly, he errr f he secnd kind p p erfc and hence p e erfc PB.9 Quadriphase-shif keying QPSK QPSK has wice he andwih efficiency f BPSK, since is are ransmied in a single mdulain syml. he daa inpu d k is divided in an in-phase sream d I, and a quadraure sream d Q. d k d I d Q : : : PB.3

16 QPSK d k d I d Q PB.3 QPSK he phase f he carrier akes n ne f fur equally spaced values, such as π/4, 3π/4, 5π/4, and 7π/4. si where i,,3,4. cs[πf c + i π / 4] elsewhere is he ransmied signal energy per syml; is he syml durain; f c n / ; e : PB.3

17 QPSK ach pssile value f he phase crrespnds a unique dii. Fr eample, fr i, fr i, fr i3 and fr i4. nly a single i is change frm ne dii he ne PB.33 QPSK he ransmied signal can e wrien as si cs[πf c + i π / 4] cs[πf c]cs[i π / 4] sin[πf c]sin[i π / 4] si + si where cs[πf c]; sin[πf c] PB.34

18 QPSK Inpu dii Phase f QPSK si s i π/4 / / 3π/4 / / 5π/4 / / 7π/4 / / / / PB.35 PB.36

19 Generain f cheren QPSK signals he incming inary daa sequence is firs ransfrmed in plar frm y a nnreurn--zer level encder. he inary wave is ne divided y means f a demulipleer in w separae inary sequences. he resul can e regarded as a pair f inary PSK signals, which may e deeced independenly due he rhgnaliy f and. PB.37 csπf c s i X si Plar RZ Demulipleer + s s i X sinπf c PB.38

20 Deecin f cheren QPSK signals X Decisin device if if > < In-phase channel mulipleer Quadraure channel X Decisin device if if > < PB.39 rrr prailiy f QPSK he received signal is si + w and he servain elemens are d ± / + w d ± d / + w d PB.4

21 PB.4 As a cheren QPSK is equivalen w cheren inary PSK sysems wrking in parallel and using w carriers ha are in phase quadraure. Hence, he average prailiy f i errr in each channel f he cheren QPSK sysem is p erfc / erfc PB.4 rrr prailiy f QPSK As he i errr in he in-phase and quadraure channels f he cheren QPSK sysem are saisically independen, he average prailiy f a crrec decisin resuling frm he cmined acin f he w channels is + c p p erfc 4 erfc erfc

22 he average prailiy f syml errr fr cheren QPSK is herefre p p e c erfc erfc erfc 4 if / >> PB.43 In a QPSK sysem, since here are w is per syml, he ransmied signal energy per syml is wice he signal energy per i, and hen pe erfc d k d I d Q PB.44

23 Wih Gray encding, he i errr rae f QPSK is BR erfc herefre, a cheren QPSK sysem achieves he same average prailiy f i errr as a cheren inary PSK sysem fr he same i rae and he same / u uses nly half he channel andwidh. PB.45 M-ary PSK During each signaling inerval f durain, ne f he M pssile signals is sen. π si csπf c + i i,,..., M PB.46

24 M-ary PSK he signal cnsellain f M-ary PSK cnsiss f M message pins which are equally spaced n a circle f radius. Fr eample, he cnsellain f caphase-shif keying is P e π erfc sin M 4 M PB.47 Pwer specra f M-ary PSK signals he syml funcin is g herwise where lg M and is he i durain. As he energy specral densiy is he magniude f he signal s Furier ransfrm, he aseand pwer specral densiy is sin πf S f πf lg M sinc f lg M PB.48

25 rmalized f PB.49 Bandwidh efficiency he andwidh required pass M-ary signal main le is given y B Qsinc lg M R lg M herefre, he andwidh efficiency is R ρ B lg M PB.5