Coherent PSK. The functional model of passband data transmission system is. Signal transmission encoder. x Signal. decoder.

Transcription

1 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.9

2 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 P e 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 Cheren PSK ample: Raised csine specrum α.5 Binary Phase shif keying BPSK +αr.5r R PB.

5 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 /. ρ R B / / is/s/hz W PB.3

6 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 per i, and is he ransmied signal energy PB.4

7 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.5

8 Cheren PSK he ransmied signal can e wrien as s φ s φ and where φ csπf c < e : φ csπf c d PB.6

9 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 symlis Signal ransmissin si encder PB.7

10 Generain f cheren inary PSK signals he secnd sep is muliplying he carrier encder upu wih he carrier s i s s f n / c csπf c csπf c if if s i s s i i Prduc Mdular φ csπf c s i PB.8

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 > < φ Crrelar PB.9

12 PB.3 Deecin f cheren inary PSK signals ample If he ransmied syml is, and he crrelar upu is Similarly, if he ransmied syml is,. cs f c π c c c d f d f f d cs cs cs π π π φ

13 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. φ PB.3

14 rrr prailiy f inary PSK here are w pssile kinds f errneus decisin: Signal s 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 > < φ PB.3

15 rrr prailiy f inary PSK Fr he firs case, he servale elemen is relaed he received signal y [ s + w ] i φ d + φ d w φ d is a Gaussian prcess wih mean : i [ i [ ] + w φ d] PB.33

16 PB.34 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 φ φ φ δ φ φ φ φ φ σ

17 PB.35 rrr prailiy f inary PSK herefre, he cndiinal prailiy densiy funcin f, given ha syml was ransmied is + f ep ep π σ πσ

18 rrr prailiy f inary PSK and he prailiy f errr is p f π d + ep Puing z +, we have p π erfc / ep [ z ] dz d PB.36

19 PB.37 rrr prailiy f inary PSK Similarly, he errr f he secnd kind p p erfc and hence e p erfc

20 PB.38 rrr prailiy he prailiy f i errr rae is prprinal he disance eween he clses pins in he cnsellain. BPSK Binary FSK e d erfc erfc P e d erfc erfc P d d

21 ransmissin Bandwidh he pwer specral densiy PSD f he BPSK fr h recangular and raised csine rllff pulse shapes are pled. null--null andwidh R +αr.5r ρ R B R R.5 ps/hz PB.39

22 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.4

23 QPSK d k d I d Q PB.4

24 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. s i 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.4

25 PB.43 QPSK he ransmied signal can e wrien as 4] / ]sin[ sin[ 4] / ]cs[ cs[ 4] / cs[ s s i f i f i f s i i c c c i φ φ π π π π π π + + where ] sin[ ]; cs[ f f c c π φ π φ

26 s / r / i s / r / i QPSK φ / / φ PB.44

27 QPSK ach pssile value f he phase crrespnds a unique dii. Fr eample: Gray cde nly a single i is change frm ne dii he ne PB.45

28 QPSK Differen QPSK ses can e derived y simply raing he cnsellain. PB.46

29 PB.47

30 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 φ and φ. PB.48

31 φ csπf c s i X si Plar RZ Demulipleer + s s i X φ sinπf c PB.49

32 Deecin f cheren QPSK signals X Decisin device if if < > φ In-phase channel mulipleer Quadraure channel X Decisin device if if > < φ PB.5

33 PB.5 rrr prailiy f QPSK he received signal is w s i + and he servain elemens are + ± d w d / φ φ + ± d w d / φ φ

34 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.5

35 PB.53 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

36 PB.54 he average prailiy f syml errr fr cheren QPSK is herefre / if erfc erfc 4 erfc >> c e p p

37 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 d k p e erfc d I d Q PB.55

38 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.56

39 PB.57 e: he prailiy f i errr rae is als prprinal he disance eween he clses pins in he cnsellain. d erfc erfc BR d / /

40 ransmissin Bandwidh Pwer specral densiy PSD f he QPSK fr h recangular and raised csine rllff pulse shapes: null--null andwidh R ρ R B R R ps/hz +αr /.75R PB.58

41 M-ary PSK During each signaling inerval f durain, ne f he M pssile signals s i is sen. π csπf c + i i,,..., M lg lg M M PB.59

42 s i M-ary PSK π π cs φ cs πf φ sin πf i φ cs i φ c c PB.6

43 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 8-ary phase-shif keying is M sin π / π / M d he average prailiy f syml errr is P e π erfc sin M 4 M d erfc PB.6

44 ransmissin Bandwidh Pwer specral densiy PSD f he M-ary PSK fr h recangular and raised csine rllff pulse shapes: PB.6

45 ransmissin Bandwidh ull--null andwidh efficiency f a M-ary PSK signal: ρ R B R / lg R M lg M ps/hz M ρ / BR PB.63