Passband Data Transmission I References Phase-shift keying Chapter , S. Haykin, Communication Systems, Wiley. G.1

Transcription

1 Passand Daa ransmission I References Phase-shif keying Chaper , S. Haykin, Communicaion Sysems, Wiley. G.

2 Inroducion Inroducion In aseand pulse ransmission, a daa sream represened in he form of a discree pulse-ampliude modulaed PAM signal is ransmied over a lowpass channel. In digial passand ransmission, he incoming daa sream is modulaed ono a carrier wih fixed frequency and hen ransmied over a and-pass channel. G.

3 Inroducion Inroducion he modulaion process making he ransmission possile involves swiching keying he ampliude, frequency, or phase of a sinusoidal carrier in accordance wih he incoming daa. here are hree asic signaling schemes: Ampliude-shif keying ASK Frequency-shif keying FSK Phase-shif keying PSK G.3

4 Inroducion ASK PSK FSK G.4

5 Inroducion Unlike ASK signals, oh PSK and FSK signals have a consan envelope. PSK and FSK are preferred o ASK signals for passand daa ransmission over nonlinear channel ampliude nonlineariies such as micorwave link and saellie channels. G.5

6 Classificaion of digial modulaion echniques Coheren and Noncoheren Digial modulaion echniques are classified ino coheren and noncoheren echniques, depending on wheher he receiver is equipped wih a phaserecovery circui or no. he phase-recovery circui ensures ha he local oscillaor in he receiver is synchronized o he incoming carrier wave in oh frequency and phase. G.6

7 Classificaion of digial modulaion echniques M-ary signaling In an M-ary signaling scheme, here are M possile signals during each signaling inerval of duraion. Usually, n M and n where is he i duraion. In passand ransmission, we have M-ary ASK, M-ary PSK, and M-ary FSK digial modulaion schemes. We can also comine differen mehods: M-ary ampliude-phase keying APK M-ary quadraure-ampliude modulaion QAM In aseand ransmission, we have M-ary PAM G.7

8 Classificaion of digial modulaion echniques M-ary signaling M-ary signaling schemes are preferred over inary signaling schemes for ransmiing digial informaion over and-pass channels when he requiremen is o conserve andwidh a he expense of increased power. he use of M-ary signaling enales a reducion in ransmission andwidh y he facor n log M over inary signaling. G.8

9 Coheren PSK he funcional model of passand daa ransmission sysem is m i Signal ransmission encoder si s i x x Signal Modulaor Channel Deecor ransmission decoder mˆ Carrier signal m i is a sequence of symol emied from a message source. he channel is linear, wih a andwidh ha is wide enough o ransmi he modulaed signal and he channel noise is Gaussian disriued wih zero mean and power specral densiy N /. o G.9

10 Coheren PSK he following parameers are considered for a signaling scheme: Proailiy of error A major goal of passand daa ransmission sysems is he opimum design of he receiver so as o minimize he average proailiy of symol error in he presence of addiive whie Gaussian noise AWGN G.

11 Power specra Coheren PSK Use o deermine he signal andwidh and co-channel inerference in muliplexed sysems. In pracice, he signalings are linear operaion, herefore, i is sufficien o evaluae he aseand power specral densiy. Bandwidh fficiency R Bandwidh efficiency ρ is/s/hz B where R is he daa rae and B is he used channel andwidh. G.

12 Coheren Binary Phase-shif Keying BPSK In a coheren inary PSK sysem, he pair of signals s and s used o represen inary symols and, respecively, is defined y s cosπf c s cosπf c + π cosπf c where, and is he ransmied signal energy per i. G.

13 Coheren Binary Phase-shif Keying BPSK For example, [ ] s d cos πf c d o ensure ha each ransmied i conains an inegral numer of cycles of he carrier wave, he carrier frequency f is chosen equal o n / for some fixed ineger n. c G.3

14 Coheren Binary Phase-shif Keying BPSK he ransmied signal can e wrien as s φ and s φ where φ π cos fc < G.4

15 Generaion of coheren inary PSK signals o generae a inary PSK signal, we have o represen he inpu inary sequence in polar form wih symols and represened y consan ampliude levels of + and, respecively. Signal ransmission si encoder Produc Modulaor s i φ cosπf c G.5

16 G.6 Generaion of coheren inary PSK signals his signal ransmission encoder is performed y a polar nonreurn-o-zero NRZ encoder. + inpu symolis inpu symol is i s he carrier frequency c n f / where n is a fixed ineger. i c i c i s f s s f s s if cos if cos π π

17 Deecion of coheren inary PSK signals o deec he original inary sequence of s and s, we apply he noisy PSK signal o a correlaor. he correlaor oupu is compared wih a hreshold of zero vols. x X x Decision device if if x x > < φ Correlaor G.7

18 G.8 Deecion of coheren inary PSK signals xample: If he ransmied symol is, cos f x c π and he correlaor oupu is c c c d f d f f d x x cos cos cos π π π φ

19 Deecion of coheren inary PSK signals Similarly, If he ransmied symol is, x. G.9

20 rror proailiy of inary PSK We can represen a coheren inary sysem wih a signal consellaion consising of wo message poins. he coordinaes of he message poins are all he possile correlaor oupu under a noiseless condiion. he coordinaes for BPSK are Decision oundary and. φ G.

21 rror proailiy of inary PSK here are wo possile kinds of erroneous decision: Signal s is ransmied, u he noise is such ha he received signal poin inside region wih x > and so he receiver decides in favor of signal s. Signal s is ransmied, u he noise is such ha he received signal poin inside region wih x < and so he receiver decides in favor of signal s. G.

22 rror proailiy of inary PSK For he firs case, he oservale elemen x is relaed o he received signal x y x [ s + w ] i x φ d + φ d w φ d x is a Gaussian process wih mean x : x i [ x i [ ] + w φ d] G.

23 G.3 and variance σ : ] [ ] [ o o o i i N d N ddu u u N ddu u w u w ddu u w u w d w x x φ φ φ δ φ φ φ φ φ σ

24 G.4 rror proailiy of inary PSK herefore, he condiional proailiy densiy funcion of x, given ha symol was ransmied is + o o N x N x x x f exp exp π σ πσ

25 rror proailiy of inary PSK and he proailiy of error is p f x dx x + exp πn o No Puing z x +, we have N p o π erfc / N o N o exp [ z ] dz dx u erfc u exp z dz π G.5

26 G.6 rror proailiy of inary PSK Similarly, he error of he second kind o N p p erfc and hence o e N p erfc

27 Quadriphase-shif keying QPSK QPSK has wice he andwih efficiency of BPSK, since is are ransmied in a single modulaion symol. he daa inpu d k is devided ino an inphase sream d I, and a quadraure sream d Q. G.7

28 d k Quadriphase-shif keying QPSK d I d Q G.8

29 Quadriphase-shif keying QPSK he phase of he carrier akes on one of four equally spaced values, such as π/4, 3π/4, 5π/4, and 7π/4. s i where i,,3,4. cos[πf c + i π / 4] elsewhere is he ransmied signal energy per symol; is he symol duraion; f c n / ; G.9

30 Quadriphase-shif keying QPSK ach possile value of he phase corresponds o a unique dii. For example, for i, for i, for i3 and for i4. only a single i is change from one dii o he nex G.3

31 Quadriphase-shif keying QPSK he ransmied signal can e wrien as s i where cos[πf cos[πf + i ]cos[i sin[πf si φ + si φ c c c π / 4] π / 4] ]sin[i π / 4] φ cos[πf c]; φ sin[πf c] G.3

32 Quadriphase-shif keying QPSK Inpu dii Phase of QPSK si s i π/4 / / 3π/4 / / 5π/4 / / 7π/4 / / G.3

33 G.33

34 Generaion of coheren QPSK signals he incoming inary daa sequence is firs ransformed ino polar form y a nonreurn-o-zero level encoder. he inary wave is nex divided y means of a demuliplexer ino wo separae inary sequences. he resul can e regarded as a pair of inary PSK signals, which may e deeced independenly due o he orhogonaliy of φ and φ. G.34

35 φ cosπf c s i X si Polar NRZ Demuliplexer + s s i X φ sinπf c G.35

36 Deecion of coheren QPSK signals x X x Decision device if if x x > < φ In-phase channel muliplexer Quadraure channel X x Decision device if if x x > < φ G.36

37 rror proailiy of QPSK he consellaion of QPSK is φ φ G.37

38 G.38 rror proailiy of QPSK he received signal is w s x i + and he oservaion elemens are + ± d w d x x φ φ + ± d w d x x φ φ

39 rror proailiy of QPSK As a coheren QPSK is equivalen o wo coheren inary PSK sysems working in parallel and using wo carriers ha are in phase quadraure. Hence, he average proailiy of i error in each channel of he coheren QPSK sysem is p erfc / N erfc o N o G.39

40 G.4 rror proailiy of QPSK As he i error in he in-phase and quadraure channels of he coheren QPSK sysem are saisically independen, he average proailiy of a correc decision resuling from he comined acion of he wo channels is + o o o c N N N p p erfc 4 erfc erfc

41 G.4 rror proailiy of QPSK he average proailiy of symol error for coheren QPSK is herefore / if erfc erfc 4 erfc >> o o o o c e N N N N p p

42 rror proailiy of QPSK In a QPSK sysem, since here are wo is per symol, he ransmied signal energy per symol is wice he signal energy per i, and p e erfc N o G.4

43 rror proailiy of QPSK he i error rae of QPSK is BR erfc N o herefore, a coheren QPSK sysem achieves he same average proailiy of i error as a coheren inary PSK sysem for he same i rae and he same / No u uses only half he channel andwidh. G.43

44 M-ary PSK During each signaling inerval of duraion, one of he M possile signals s i is sen. π cos πf c + i i,,..., M G.44

45 M-ary PSK he signal consellaion of M-ary PSK consiss of M message poins which are equally spaced on a circle of radius. For example, he consellaion of ocaphas-shif keying is P e π erfc sin M 4 No M G.45

46 Power specra of M-ary PSK signals he symol funcion is g oherwise where log M and is he i duraion. S f As he energy specral densiy is he magniude of he signal s Fourier ransform, he aseand power specral densiy is sin πf πf log M sinc f log M G.46

47 Power specra of M-ary PSK signals Normalized o f G.47

48 B Bandwidh efficiency he andwidh required o pass M-ary signal main loe is given y Qsinc log M R log M herefore, he andwidh efficiency is ρ R B log M G.48

49 Passand Digial ransmission Passand digial ransmission allows more efficien use of he allocaed RF andwidh, and flexiiliy in accommodaing differen aseand signal formas. xample Moile elephone Sysems GSM: GMSK modulaion is used a variaion of FSK IS-54: π/4-dqpsk modulaion is used a variaion of PSK G.49

50 Phase Recovery Carrier Synchronizaion wo ways in which a local oscillaor can e synchronized wih an incoming carrier wave ransmi a pilo carrier use a carrier-recovery circui such as a phase-locked loop PPL G.5