EECS 380: Wireless Communications Weeks 5-6

Transcription

1 EECS 380: Wireless Communicaions Weeks 5-6 Michael L. Honig Norhwesern Universiy April

2 Why Digial Communicaions? 1G (analog) à 2G (digial) à 3G (digial) Digiized voice requires abou 64 kbps, herefore he required bandwidh is >> he bandwidh of he voice signal (3 4 khz)! 2

3 Why Digial Communicaions? 1G (analog) à 2G (digial) à 3G (digial) Digiized voice requires abou 64 kbps, herefore he required bandwidh is >> he bandwidh of he voice signal (3 4 khz)! Can combine wih sophisicaed signal processing (voice compression) and error proecion. Greaer immuniy o noise/channel impairmens. Can muliple differen raffic (voice, daa, video). Securiy hrough digial encrypion. Fleible design possible (sofware radio). VLSI + special purpose digial signal processing à digial is more cos-effecive han analog! 3

4 Binary Frequency-Shif Keying (FSK) Bis: Ampliude ime 4

5 Quadraure Phase Shif Keying (QPSK) Bis: Ampliude ime 5

6 Binary Phase Shif Keying (BPSK) Bis: Baseband signal Ampliude ime 6

7 Ampliude Shif Keying (4-Level ASK) Bis: Baseband signal Ampliude symbol duraion ime 7

8 Baseband à RF Conversion Baseband signal sin 2πf c Passband (RF) signal T ime X Modulae o he carrier frequency f c Power signal bandwidh is roughly 2/T Power 0 frequency ß 0 f c frequency 8

9 Selecion Crieria How do we decide on which modulaion echnique o use? 9

10 Selecion Crieria How do we decide on which modulaion echnique o use? Performance: probabiliy of error P e. Probabiliy ha a 0 (1) is ransmied and he receiver decodes as a 1 (0). Compleiy: how difficul is i for he receiver o recover he bis (demodulae)? FSK was used in early voiceband modems because i is simple o implemen. Bandwidh or specral efficiency: bandwidh (B) needed o accommodae daa rae R bps, i.e., R/B measured in bis per second per Hz. Power efficiency: energy needed per bi o achieve a saisfacory P e. Performance in he presence of fading, mulipah, and inerference. 10

11 Eample: Binary vs. 4-Level ASK 3A A A -A -A -3A Rae = 1/T symbols/sec Bandwidh is roughly 1/T Hz Bandwidh efficiency = 1 bps/hz Rae = 2/T symbols/sec Bandwidh is roughly 1/T Hz Bandwidh efficiency = 2 bps/hz Wha abou power efficiency? 11

12 Noisy Baseband Signals 3A A A -A -A -3A Rae = 1/T symbols/sec Bandwidh is roughly 1/T Hz Bandwidh efficiency = 1 bps/hz Power =A 2 (ampliude squared). Rae = 2/T symbols/sec Bandwidh is roughly 1/T Bandwidh efficiency = 2 bps/hz Power = (A 2 + 9A 2 )/2 = 5A 2 Wha abou probabiliy of error vs ransmied power? 12

13 Probabiliy of Error Log of Probabiliy of Error BPSK 4-ASK 7 db (facor of 5) Signal-o-Noise Raio (db) 13

14 How o Increase Bandwidh Efficiency? 14

15 How o Increase Bandwidh Efficiency? Increase number of signal levels. Use more bandwidh efficien modulaion scheme (e.g., PSK). Apply coding echniques: proec agains errors by adding redundan bis. Noe ha reducing T increases he symbol rae, bu also increases he signal bandwidh. There is a fundamenal radeoff beween power efficiency and bandwidh efficiency. 15

16 The Fundamenal Quesion Given: B Hz of bandwidh S Was of ransmied signal power N Was per Hz of background noise (or inerference) power Wha is he maimum achievable daa rae? (Noe: depends on P e.) 16

17 Claude Shannon ( ) Faher of Informaion Theory Shannon s 1948 paper A Mahemaical Theory of Communicaions laid he foundaions for modern communicaions and neworking: The fundamenal problem of communicaion is ha of reproducing a one poin eiher eacly or approimaely a message seleced a anoher poin ransmier receiver 17

18 Claude Shannon ( ) Faher of Informaion Theory Shannon s 1948 paper A Mahemaical Theory of Communicaions laid he foundaions for modern communicaions and neworking: The significan aspec is ha he acual message is one seleced from a se of possible messages. The sysem mus be designed o operae for each possible selecion, no jus he one which will acually be chosen since his is unknown a he ime of design. ransmier receiver 18

19 Claude Shannon ( ) Faher of Informaion Theory Shannon s 1948 paper A Mahemaical Theory of Communicaions laid he foundaions for modern communicaions and neworking: The choice of a logarihm base corresponds o he choice of a uni for measuring informaion. If he base 2 is used he resuling unis may be called binary digis, or more briefly bis, a word suggesed by J. W. Tukey. log 2 M bis Transmier (M possible messages) receiver 19

20 Claude Shannon ( ) Faher of Informaion Theory Shannon s 1948 paper A Mahemaical Theory of Communicaions laid he foundaions for modern communicaions and neworking. Oher conribuions and ineress: digial circuis, geneics, crypography, invesing, chess-playing compuer, roulee predicion, maze-solving, unicycle designs, juggling Videos: Faher of he Informaion Age Juggling video 20

21 Shannon s Channel Coding Theorem (1948) noise Informaion Source bis Encoder inpu () Channel oupu y() Decoder Esimaed bis Informaion rae: Channel capaciy: R bis/second C bis/second R < C è There eiss an encoder/decoder combinaion ha achieves arbirarily low error probabiliy. R > C è The error probabiliy canno be made small. 21

22 Shannon Capaciy noise Informaion Source bis Encoder inpu () Channel oupu y() Decoder Esimaed bis Channel capaciy: C = B log(1+s/n) bis/second B= Bandwidh, S= Signal Power, N= Noise Power No fading 22

23 Caveas There eiss does no address compleiy issues. As he rae approaches Shannon capaciy, o achieve small error raes, he ransmier and (especially) he receiver are required o do more and more compuaions. The heorem does no say anyhing abou delay. To achieve Shannon capaciy he lengh of he ransmied code words mus end o infiniy! The previous formula does no apply wih fading, mulipah, frequency-selecive aenuaion. I has aken communicaions engineers more han 50 years o find pracical coding and decoding echniques, which can achieve informaion raes close o he Shannon capaciy. 23

24 Eample: GSM/EDGE Bandwidh = 200 khz, S/I = 9 db = è C = 200,000 log(8.943) 632 kbps This is wha would be achievable in he absence of fading, mulipah, ec. Currenly, EDGE provides hroughpus of abou 230 kbps. Up o 470 kbps possible using addiional ricks, such as adaping he modulaion and coding forma o mach he channel Ø Preceding Shannon formula is no direcly applicable. 24

25 Daa Raes for Deep Space Applicaions Mariner: 1969 (Mars) Pioneer 10/11: 1972/3 (Jupier/Saurn fly-by) Voyager: 1977 (Jupier and Saurn) Planeary Sandard: 1980 s (miliary saellie) BVD: Big Vierbi Decoder Galileo: 1992 (Jupier) (uses BVD) Turbo Code: 1993 Signal o Noise Raio 25

26 Binary Phase Shif Keying (BPSK) Bis: Baseband signal 26

27 Minimum Bandwidh (Nyquis) Pulse Shape This pulse has he minimum bandwidh for a given symbol rae. Given bandwidh B, he maimum symbol rae wihou inersymbol inerference (ISI) is B, he Nyquis rae.

28 Pulse Widh vs. Bandwidh signal pulse Narrowband Power bandwidh B = 1/T 2T ime frequency signal pulse Wideband Power bandwidh B = 1/T ime frequency 2T The bandwidh B = 1/T (symbol rae) is ofen called he Nyquis bandwidh. 28

29 Shifed Nyquis Pulses Bis:

30 Baseband Waveform (Nyquis Signaling) Bis:

31 Baseband à RF Conversion Baseband signal sin 2πf c Passband (RF) signal T ime X Modulae o he carrier frequency f c Power signal bandwidh is roughly 1/T Power frequency 0 ß 0 frequency f c

32 Passband Signal wih Differen Carrier Frequencies 32

33 Imporance of Synchronizaion T T Perfec synchronizaion ime T Offse causes severe ISI! ime Need perfec synchronizaion o avoid severe inerference! 33

34 Ecess Bandwidh signal pulse Power Minimum (Nyquis) bandwidh B = 1/T 2T ime frequency Adding ecess bandwidh eases filering and synchronizaion. 34

35 Ecess Bandwidh (Raised Cosine Pulses) Add ecess bandwidh o reduce self-inerference: Minimum BW ime frequency 35

36 Ecess Bandwidh: Definiion 50% ecess BW Minimum BW 100% ecess BW ime frequency Ecess bandwidh= (Toal bandwidh Nyquis bandwidh)/nyquis bandwidh 36

37 QPSK Signal Consellaion ampliude = 1 cos2πf c sin 2πf c 1 sin 2πf c cos 2πf c

38 Roaed QPSK Signal Consellaion

39 Roaed QPSK Signal Consellaion ampliude = 1 cos2πf c sin 2πf c 1 sin 2πf c cos 2πf c

40 In-Phase/Quadraure Componens sin 2πf c ( 1,0) cos2πf c ( 0, 1) (0,1) 1 (1,0) cos 2πf c (a,b) à a sin 2πf c + b cos 2πf c sin 2πf c b is he in-phase signal componen a is he quadraure signal componen

41 In-Phase/Quadraure Componens ( 2 / 2, sin 2πf c 2 / 2) cos 2πf c ( 1 2 / 2, 2 / 2) sin 2πf c 2 2 sin(2πf c) + cos(2πf 2 2 = sin(2πf + π / 4) c c ) ( 2 / 2, 2 / 2) ( 2 / 2, 2 / 2) cos 2πf c

42 Eample Consellaions QPSK sin 2πf c cos 2πf c sin 2πf c BPSK 8-PSK cos 2πf c 16-QAM quadraure in-phase

43 Eample Consellaions QPSK sin 2πf c cos 2πf c sin 2πf c BPSK quadraure in-phase 8-PSK sin 2πf c cos 2πf c cos 2πf c cos 2πf c sin 2πf c 16-QAM quadraure in-phase

44 Quadraure Modulaion cos2πf c in-phase signal even bis Baseband Signal X source bis Spli: Even/Odd + ransmied (RF) signal odd bis Baseband Signal X sin 2πf c quadraure signal

45 Modulaion for Fading Channels Problems: 1. Ampliude variaions (shadowing, disance, mulipah) 2. Phase variaions 3. Frequency variaions (Doppler) Soluion o 1: 1. Avoid ampliude modulaion 2. Power conrol Soluion o 2 & 3: 1. Avoid phase modulaion (use FSK) 2. Noncoheren demodulaion: does no use phase reference Differenial coding/decoding 3. Coheren demodulaion: Esimae phase shifs caused by channel. 4. Increase daa rae/doppler shif raio

46 Binary Frequency-Shif Keying (FSK) Bis:

47 Minimum Shif Keying (MSK) Bis: Frequencies differ by ½ cycle Used in GSM 47

48 Binary Differenial Modulaion (i+1)s bi = 0: 0 o phase shif waveform for ih symbol (i+1)s bi = 1: 180 o phase shif 48

49 Binary Differenial Modulaion (i+1)s bi = 0: 0 o phase shif waveform for ih symbol (i+1)s bi = 1: 180 o phase shif 49 Drawback: a deecion error for he ih bi propagaes o he (i+1)s bi.

50 Eample: DQPSK sin 2πf c cos 2πf c sin 2πf c bis: sin 2πf c 10 cos 2πf c sin 2πf c cos 2πf c 11 cos 2πf c consellaion for ih symbol consellaion for (i+1)s symbol Used in IS

51 Coheren Phase Deecion Receiver mus deermine where symbol begins (need phase reference)

52 Coheren Phase Deecion Receiver mus deermine where symbol begins More complicaed han FSK. Transmier mus send pilo symbols. Known o receiver, used o measure phase. Pilo symbols are overhead (no informaion bis).

53 Probabiliy of Error (no fading) Probabiliy of error BPSK DPSK FSK DPSK requires abou 1 db more power han BPSK FSK requires abou 3 db more power 1 db 3 db Signal-o-Noise Raio (db)

54 Probabiliy of Error wih Fading more han 20 db!

55 Orhogonal Frequency Division Mulipleing (OFDM) subsream 1 Modulae Carrier f 1 source bis Spli ino M subsreams subsream 2 subsream M Modulae Carrier f 2 + OFDM Signal Modulae Carrier f M

56 OFDM Specrum Toal available bandwidh Power Daa specrum for a single carrier f 1 ß 0 f 2 f 5 f 6 f 3 f 4 subchannels frequency M subcarriers, or subchannels, or ones

57 OFDM Specrum Toal available bandwidh Power Daa specrum for a single carrier f 1 ß 0 f 2 f 5 f 6 f 3 f 4 subchannels frequency M subcarriers, or subchannels, or ones Orhogonal subcarriers è no cross-channel inerference

58 Measured OFDM Specrum 2 MHz

59 OFDM Eample: a 20 MHz bandwidh, M=64 (48 for daa payload) Subchannel bandwidh = 20 MHz / 64 = khz Symbol rae / subchannel = 250 kilosymbols/sec Toal symbol rae = = 16 Msymbols/sec Bi rae? 16 QAM/subchannel è 4 bis/symbol = 1 Mbps/subchannel, or 64 Mbps oal 64 QAM/subchannel è 6 bis/symbol = 1.5 Mbps/subchannel, or 96 Mbps oal Includes overhead (synchronizaion, error correcion, conrol) Acual daa rae: 36 / 54 Mbps

60 Why OFDM?

61 Eplois frequency diversiy Why OFDM? channel gain signal power (wideband) f 1 f 2 bis are coded across subcarriers subcarrier bandwidh < coherence bandwidh B c Frequencies far ouside he coherence bandwidh are affeced differenly by mulipah. frequency Fla fading on each subchannel simplifies receiver (no mulipah/isi) Slower symbol rae on each subchannel simplifies signal processing. Drawback: signal ampliude varies a lo; high peak-o-average power.