Passband Data Transmission II References Frequency-shift keying Chapter 6.5, S. Haykin, Communication Systems, Wiley. H.1

Transcription

1 Passand Daa ransmission II Reerences Frequency-shi keying Chaper 6.5, S. Haykin, Communicaion Sysems, Wiley. H.

2 Inroducion Inroducion PSK and QAM are linear modulaion FSK is a nonlinear modulaion Similar o oher passand daa ransmission sysem, he uncion model o FSK is m i Signal ransmission encoder s s i x x Signal i Modulaor Channel Deecor ransmission decoder mˆ Carrier signal H.

3 FSK Binary FSK Symols and are disinguished rom each oher y ransmiing one o wo sinusoidal wave ha dier in requency. E cos i si elsewhere where i n + i or some ixed ineger and i, Noe: he wo sinusoidal waves mus e orhogonal H.3

4 FSK Example: I µ s, n 9 hen MHz and MHz. For sending a symol, he sinusoidal wave wih complees en cycles. I is a coninuous-phase signal as phase coninuiy is always mainained, including he iner-i swiching imes. Called coninuous-phase requency-shi keying CPFSK H.4

5 FSK he ransmied signal can e wrien as s Eφ and s Eφ where φi cos i < H.5

6 FSK hereore, he consellaion o inary FSK is E φ Decision oundary E E φ Consellaion o inary PSK Decision oundary E E H.6 φ

7 Generaion he inary daa sequence is irs applied o an on-o level encoder, a he oupu o which symol is represened y a consan ampliude o E and symol is represened y zero vols. X φ On-o level encoder + Inverer X φ H.7

8 Deecion he deecor consiss o wo correlaors wih a common inpu, which are supplied wih locally generaed coheren signals. he correlaor oupus are hen suraced. x X x φ + - y Decision device i i y > y < X x φ H.8

9 Deecion As he decision oundary is φ φ, choose i y > choose i y < H.9

10 Error Proailiy he received signal is y x x x φ d x φ d he mean o y is y E E Symol was sen Symol was sen H.

11 he variance o y is σ var x + var x N o No + N o Error Proailiy H.

12 H. Error Proailiy hereore, i symol was sen, + o o N E y N y y y exp exp σ σ and he error proailiy is exp symol was sen dy N E y N y P p o o + >

13 Le p z y +, N erc E As p p, E o / N exp E / N Pe erc o Error Proailiy [ z ] o E / N o dz he error proailiy o inary PSK is E p e erc. N o i.e., we have o doule he i energy-o-noise densiy raio, E / N o, o mainain he same i error rae as in a inary PSK sysem. H.3

14 H.4 Power Specra he general orm o inary FSK is elsewhere cos i i E s / sin sin / cos cos / sin sin / cos cos or symol or symol;- / cos c c c c c E E E E E s ± ± ± + ± Consider / and heir arihmeic mean equals o c

15 Power Specra E E s cos ccos / ± sin csin / he in-phase componen is independen o he inpu inary wave. he power specral densiy o his componen consiss o wo dela uncions. one dela uncion i aseand specrum is considered he quadraure componen is relaed o he inpu inary wave. he power specral densiy is 8E cos 4 H.5

16 Power Specra E E s cos ccos / ± sin csin / he average powers o he dela uncion adding up o one-hal he oal power o he inary FSK signal. he presence o hese wo discree requency componens provides a means o synchronizing he receiver wih he ransmier. H.6

17 H.7

18 Minimum-shi keying In addiion o he requency inormaion used in inary FSK, MSK use he phase inormaion. I improves he proailiy o error a he expense o increased receiver complexiy s E E cos cos + θ + θ or symol or symol θ is he value o he phase a ime θ sum up he pas hisory o he modulaion process up o ime H.8

19 M-ary Quadraure Ampliude Modulaion QAM Inroducion PSK is usually limied o BPSK, QPSK and 8-PSK. For urher reducing he ransmission andwidh, QAM is used. Example: Consider a voice signal wih 3kHz andwidh, I analog ampliude modulaion AM is used, he ransmission andwidh is x3khz 6kHz I analog single sideand modulaion SSB is used, he ransmission andwidh is 3kHz. H.9

20 M-ary Quadraure Ampliude Modulaion QAM Inroducion I digial mehod is used, he minimum sampling rae is x3khz 6kHz. I here are 56 levels or encoding, he daa rae is 48kps ransmission andwidh or BPSK is 4kHz ransmission andwidh or 64-QAM is 4kHz H.

21 Generaion I Q 4-PAM 4-PAM 6-QAM Modulaor I Q 3-PAM 3-PAM 4-QAM Modulaor H.

22 H. M-ary Quadraure Ampliude Modulaion QAM he M-ary QAM signal is deined y [ ] ± ±,...., sin cos s s k E a E s c k c k k φ φ where c c sin cos φ φ [ ] [ ] o k o k k k E E a s s

23 M-ary Quadraure Ampliude Modulaion QAM I here are M symols and L M, he M-ary square consellaion can always e viewed as he Caresian produc a one-dimensional L-ary PAM consellaion wih isel. hereore, we have { a } i i L +, L L +, L 3 M L +, L + L + 3, L L L + 3, L 3 M + 3, L + L L L L L, L L, L 3 M L, L + H.3

24 H.4 M-ary Quadraure Ampliude Modulaion QAM { } , 3, 3, 3 3, 3,,, 3, 3,,, 3, 3,3,3,3 3,3, 3,, 3, 3 3, 3,, 3,, L L L L L L L L L L L L L L L L L L a i i L M L M M L L Example: Consider a 6-QAM, L4

25 M-ary Quadraure Ampliude Modulaion QAM he signal consellaion is φ Eo 3 E φ o H.5

26 M-ary Quadraure Ampliude Modulaion QAM he encoding o he message is as ollows: wo o he our is, namely, he le-mos wo is, speciy he quadran in he consellaion plane in which a message poin lies. hus, saring rom he irs quadran and proceeding counerclockwise, he our quadran are represened y,,, and. he remaining wo is are used o represen one o he our possile lying wihin each quadran o he plane. H.6

27 M-ary Quadraure Ampliude Modulaion QAM φ Eo 3 E φ o H.7

28 Error Proailiy he proailiy o correc deecion or M-ary QAM is Pc Pe ' where P e ' is he proailiy o symol error or he corresponding L-ary PAM. he proailiy o symol error or M-ary QAM is P P e P ' P ' e c e M erc E N o o H.8

29 Error Proailiy As he ransmied energy in M-ary QAM depends on he paricular symol ransmied, he proailiy o symol error is expressed in erms o he average value o he ransmied energy. Assuming ha he L ampliude level levels o he in-phase or quadraure componen are equally likely, we have M Eo Eav 3 hereore, P e M erc M 3E av N o H.9

30 Noncoheren sysems Inroducion For coheren sysems, he receiver is perecly synchronized o he ransmier, and he only channel impairmen is noise. In cerain siuaions, he receiver canno ollow he change o he received signal phase. Noncoheren deecion is used. H.3

31 Noncoheren inary FSK he ransmied signal is E si cos i For he nonchoheren deecion o his requencymodulaed wave, he receiver consiss o a pair o mached ilers ollowed y envelope deecor. H.3

32 x Filer mached o cos Noncoheren inary FSK Envelope deecor Sample a l Comparison device i i l l < > l l Filer mached o cos Envelope deecor Sample a l H.3

33 H.33 Noncoheren inary FSK [ ] [ ] [ ] [ ] [ ] τ τ τ τ τ τ τ τ τ d x d x d x y + sin sin cos cos cos For example, i he received signal is cos θ + x he upper mached iler oupu is

34 H.34 Noncoheren inary FSK he envelope, evaluaed a o he mached iler is [ ] [ ] [ ] / cos cos cos + + τ τ τ τ τ τ τ τ τ d x d x d x y

35 Noncoheren inary FSK For example, H.35

36 Error proailiy he i error rae or noncoheren inary FSK is E Pe exp N o H.36

37 Dierenial Phase-shi keying Inroducion he noncoheren version o PSK dierenial encoding o he inpu inary wave o send symol, advance he phase o he curren signal waveorm y 8. o send symol, he phase o he curren signal waveorm is unchanged. Provided ha he unknown phase θ conained in he received wave varies slowly, he phase dieren eween waveorms received in wo successive i inervals will e independen o θ H.37

38 H.38 Dierenial Phase-shi keying Suppose he ransmied DPSK signal equals o c E cos, he ransmied signal or is c c E E s cos cos i symol was sen

39 H.39 Dierenial Phase-shi keying + c c E E s cos cos i symol was sen

40 Generaion he dierenial encoding process sars wih an arirary irs i, serving as reerence. { } k Logic nework Delay { } d k { } d k Ampliude level shier Produc modulaor cos c DPSK signal I he incoming inary symol k is, leave he symol d k unchanged wih respec o he previous i. H.4

41 Generaion I he incoming inary symol k is, change he symol d k wih respec o he previous i. Example, { k } { k } d { d k } k k dk d Oupu phase H.4

42 Deecion x X cos c sin c X Delay Delay X X + y Decision device i i y > y < Suppose he carrier phase is unknown and he iniial phase is, he received signal is x Acos + θ c H.4

43 Deecion he oupu o he In-phase correlaor is A Acos c + θ cos c d cosθ A' cosθ and he oupu o he Quadraure-phase correlaor is A Acos c + θ sin c d sinθ A' sinθ. I he iniial phase is 8, he oupus are A'sinθ. A'cosθ and H.43

44 Deecion hereore, he wo received signal poins are A 'cosθ, A'sinθ and A'cosθ, A'sinθ φ φ H.44

45 Deecion he receiver measures he coordinaes x, x a ime and x, x a ime. I Q I Q hereore, x x + x I I Q x Q > i symol was sen x I x I + x Q x Q < i symol was sen H.45

46 Deecion Error proailiy he i error rae or DPSK is E Pe exp N H.46

47 Comparison o Digial Modulaion Schemes Proailiy o Error Signaling Scheme Bi Error Rae Coheren BPSK Coheren QPSK erc E / Coheren MSK N o Coheren FSK DPSK Noncoheren inary FSK erc exp exp E / N o E / N o E / N o H.47

48 Comparison o Digial Modulaion Schemes he i error rae or all he sysems decrease monoonically wih increasing value o E / N o H.48

49 Comparison o Digial Modulaion Schemes Bandwidh Eiciency Example: M-ary PSK or proailiy o symol error. M Bandwidh M ary Bandwidh Binary Average Power M ary Average Power Binary db db db db H.49

50 Example: Modems voiceand modem~3.3khz andwidh modem modulaor-demodulaor is a conversion device ha aciliaes he ransmission and recepion o daa over pulic swiched elephone nework PSN V. modem sandard modulaion scheme: QPSK i rae: 3ps symol rae: 3 auds H.5

51 Example: Modems V.3 modem sandard modulaion scheme: 6-QAM i rae: 96 ps symol rae: 4 auds V.34 modem sandard modulaion scheme: 4-QAM i rae: 88 ps symol rae: 349 auds H.5

52 Example: Modems V.3 modem sandard modulaion scheme: 6-QAM i rae: 96 ps symol rae: 4 auds V.34 modem sandard modulaion scheme: 4-QAM i rae: 88 ps symol rae: 349 auds H.5