Introduction to OFDM Systems

Transcription

1 Wireless Iformaio Trasmissio Sysem Lab. Iroducio o OFDM Sysems Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

2 Oulie OFDM Overview OFDM Sysem Model Orhogoaliy Muli-carrier Equivale Implemeaio by Usig IDFT (IFFT Cyclic Prefix (CP 2

3 Wireless Iformaio Trasmissio Sysem Lab. OFDM Overview Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

4 OFDM OFDM Overview Orhogoal Frequecy Divisio Muliplexig Frequecy Divisio Muliplexig (FDM or muli-oe sysems have bee employed i miliary applicaios sice he 196Os. OFDM employs muliple carriers overlappig i he frequecy domai. 4

5 OFDM Overview Sigle carrier (SC vs. muli-carrier (MC Sigle carrier : daa are rasmied over oly oe carrier Selecive fadig Muli-carrier : daa are shared amog several carriers ad simulaeously rasmied Fla fadig per subcarrier 5

6 OFDM Overview The basic priciple of OFDM is o spli a high-rae daa sream io a umber of flower rae sreams ha are rasmied simulaeously over a umber of sub-carriers. I elimiaes or alleviaes he problem of muli-pah chael lfadig effec, low specrum efficiecy, i ad frequecy selecive fadig. 6

7 OFDM Overview OFDM modulaio Feaures No iercarrier guard bads Overlappig of bads Specral efficiecy i Easy implemeaio by IFFTs Very sesiive o sychroizaio 7

8 Applicaios of OFDM Techology Broadbad Wired Access: Asymmeric Digial Subscriber Loop (ADSL, Digial Muli-oe (DMT. Wireless LANs (IEEE a/g, IEEE , HIPERLAN-2 Digial Broadcasig (DAB, DVB-T, DVB-H WiMAX (IEEE Series, 3GPP Log Term Evoluio (3GPP LTE, 4G. Wireless Persoal Area Nework (WPAN: IEEE a/MBOA Power Lie 8

9 Wireless Iformaio Trasmissio Sysem Lab. OFDM Sysem Model Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

10 OFDM Sysem Model Muli-carrier Block Trasmissio frequecy ime 8T 10

11 OFDM Sysem Model OFDM: A block modulaio scheme ha rasmis a block N source symbols i parallel by usig subcarriers Sub-carriers are orhogoal i ime, bu overlapped i frequecy. 1 Frequecy spacig: Δ f T FFT T FFT cos(2 π f cos(2 π ( f +Δ f d

12 OFDM Sysem Model +1 NΔ a( 0 T a ( 0 cos ( 2πf 0 b( 0 Ipu Daa d( Ecoder 1 { a ( + jb( } f s Δ S/P si cos a( N 1 ( 2π f 0 ( 2πf N 1 MUX D( Chael +1 1 a( 0 Δ T a ( 1 a ( N 1 NΔ b ( N 11 a Figure 1 si ( 2πf N 1 12

13 OFDM Sysem Model A OFDM sysem rasmier show i Figure 1. The rasmied waveform D( ca be expressed as D( where f N 1 0 { a( cos(2πf + b( si(2πf } (1 f Δf ad Δf NΔΔ Usig a wo-dimesioal digial modulaio forma, he daa symbols d( ca be represeed as a( + jb( a( : i-phase compoe b( : quadraure compoe 13

14 OFDM Sysem Model The serial daa elemes spaced by Δ are grouped ad used o modulae N carriers. Thus hey are frequecy divisio muliplexed. The sigalig ierval is he icreased o, which NΔ makes he sysem less suscepible o chael delay spread impairmes. Small-scale fadig (Based o mulipah ime delay spread Fla Fadig Frequecy Selecive Fadig 1. BW of sigal < BW of chael 1. BW of sigal > BW of chael 2. Delay spread < Symbol preiod 2. Delay spread > Symbol preiod 14

15 Wireless Iformaio Trasmissio Sysem Lab. Orhogoaliy Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

16 Orhogoaliy Orhogoaliy Cosider a se of rasmied carriers as follows: (2 1..., 0,1, for ( 2 0 Δ + N e N f j π ψ q p a b d b for ( ( ( * ψ ψ Δ N a b q p d a q p ( ad for 0 ( ( ψ ψ 16

17 Orhogoaliy Orhogoaliy b q p j b 2π ( d e d a j b j b a N q p j b a q p Δ ( ( ( 2 ( 2 ( 2 * ψ ψ π N q p j e e N q p j N q p j Δ Δ Δ ( 2 ( 2 ( 2 π π π e e N q p j b a N q p j N b q p j Δ Δ Δ 1 ( 2 ( 1 ( 2 ( 2 π π π N q p j Δ 2π ( N a b q p Δ ( ad for 0, 17

18 Orhogoaliy NΔ 18

19 Mahemaical Expressio of OFDM Sigal { ( } From above, we kow ha ψ is he orhogoal sigal se. A OFDM sigal based o his orhogoal sigal se ca be wrie as: where x ψ ( N 1 ( Re dk ψ ( kt, k 0 f f0 d e j 2πf + T a k, k, + for, T NΔ jb k,, (3 0,1, 2,..., N 1 0 T 19

20 Mahemaical Expressio of OFDM Sigal T : OFDM symbol duraio d k,, : rasmied daa o he -h carrier of he k-h symbol x( Re N 1 Ck, ψ ( kt 0 N 1 k ( 2πf ( kt b si( 2πf ( kt { a cos } k, k, (4 k 0 If here is oly oe OFDM symbol ( i.e. k 0, i ca be simplified as: x( N 1 00 { a cos(2πf b si(2πf } (5 20

21 Wireless Iformaio Trasmissio Sysem Lab. Muli-carrier Equivale Implemeaio by Usig IDFT (IFFT Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

22 Muli-carrier Equivale Implemeaio by usig IDFT Accordig o he srucure of Tx, i mus use N oscillaors. Tha icreases he hardware complexiy. The equivale mehod is usig IDFT (IFFT. 22

23 Muli-carrier Equivale Implemeaio by usig IDFT I geeral, each carrier ca be expressed as: S c ( A c ( e j ( 2π f +φ ( c c (6 We assume ha here are N carriers i he OFDM sigal. The he oal complex sigal S s ( ca be represeed dby: S s N 1 1 j + ( A ( e N 0 where f f 0 + Δ f ad A (, φ (, f are ampliude, of - h carrier, respecively. 23 ( 2πf φ ( phase, (7 carrier frequecy

24 Muli-carrier Equivale Implemeaio by usig IDFT The we sample he sigal a a samplig frequecy 1 Δ, ad A ( ad φ ( becomes: S s ( kδ φ ( φ A 1 N ( N A e A j ( π ( f + Δf kδ+ φ 2 0 The he sampled sigal ca be expressed as: N 1 1 π Ss ( kδ N 0 (8 (9 (10 ( j( 2πf 0 kδ + φ j2 kδfδ A e e (11 24

25 Muli-carrier Equivale Implemeaio by usig IDFT The iverse discree Fourier rasform (IDFT is defied as he followig: f ( kδ N 1 1 j 2 π k N F ( Δf e (12 N 0 Comparig eq.(11 ad eq.(12, he codiio mus be saisfied i order o make eq.(11 a iverse Fourier rasform relaioship: Δf 1 NΔ (13 25

26 Muli-carrier Equivale Implemeaio by usig IDFT If eq.(13 q( is saisfied, A e j( 2π f0kδ+ φ is he frequecy domai sigal S s ( kδ is he ime domai sigal Δf is he sub-chael spacig NΔ is he symbol duraio i each sub-chael This oucome is he same as he resul obaied i he sysem of Figure 1. Therefore IDFT ca be used o geerae a OFDM rasmissio sigal. 26

27 Muli-carrier Equivale Implemeaio by usig IDFT a ( 0 cos ( 2πf 0 Ipu f s Δ b( 0 si( 2πf 0 d( D ( 1 { a ( + jb( } cos( 2πf N 1 f Ipu f s Δ f Δf, Δf NΔΔ a( N 1 b( N 1 d( 0 d( 1 d( 2 si ( 2πf N 1 d ( D( 1 { a ( + jb( } f f Δf, Δf NΔf d( N 1 Chael Chael 27

28 Frequecy Error Resuls i ICI 28

29 Sychroizaio Error Resuls i ICI No Orhogoal Ay More. 29

30 Wireless Iformaio Trasmissio Sysem Lab. Cyclic Prefix (CP Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

31 Cyclic Prefix I mulipah chael, delayed replicas of previous OFDM sigal lead o ISI bewee successive OFDM sigals. Soluio : Iser a guard ierval bewee successive OFDM sigals. 31

32 Cyclic Prefix Guard ierval leads o iercarrier ierferece (ICI i OFDM demodulaiod I DFT ierval, differece bewee wo subcarriers does o maiai ieger umber of cycles loss of orhogoaliy. Delayed versio of subcarrier 2 causes ICI i he process of demodulaig d subcarrier 1. 32

33 Cyclic Prefix Cyclic prefix (CP : A copy of he las par of OFDM sigal is aached o he fro of iself. Ipu daa symbols d[ ] d [ 0] D[] 0 d[ 1] d[ 2] D D[ 1] D[] 2 [ N N g ] d [ N 11 ] D[ N 1] D ~ [ k] 33

34 Cyclic Prefix All delayed replicas of subcarriers always have a ieger umber of cycles wihi DFT ierval o ICI 34

35 Cyclic Prefix Liear covoluio vs. circular covoluio N 35

36 Chael effec wih cyclic prefix Cyclic Prefix Sigal afer removed CP 36

37 Time-Domai Explaaio Cyclic Prefix 37

38 Cyclic Prefix 38

39 Cyclic Prefix Specrum of chael respose h wih legh L (smaller h ha N g H k FFT h [ ] { [ ]} Received ~ complee OFDM sigal ~ r D h, 0 N + N + g L [] [ ] [ ] 2 h Received useful par r[ ] [ ] D[ ] h[ ] r N where is N-poi circular covoluio (due o CP N Received symbol a k-h subcarrier k { r[ ] } FFT{ D[ ] N h[ ] } X k H k Y FFT X k Y k H k Useful propery for OFDM sysem o reduce complexiy of chael equalizaio 39

40 Cyclic Prefix (OFDM Receiver r~ ( r( Oupu daa Symbols 40

41 Cyclic Prefix Oe of he mos impora reasos o do OFDM is he efficie way i deals wih mulipah delay spread. To elimiae ier-symbol ierferece (ISI almos compleely, a guard ime is iroduced for each OFDM symbol. (The guard ime is chose larger ha he delay spread 41

42 Badwidh Efficiecy I a classical parallel sysem, he chael is divided io N o-overlappig sub-chaels o avoid ier-carrier ierferece (ICI. The diagram for badwidh efficiecy of OFDM sysem is show below: 42

43 Summary The advaage of he FFT-based OFDM sysem : The use of IFFT/FFT ca reduce he compuaio complexiy. The orhogoaliy bewee he adjace sub-carriers will make he use of rasmissio badwidh more efficie. The guard ierval is used o resis he ier-symbol ierferece (ISI. The mai advaage of he OFDM rasmissio echique is is high performace eve i frequecy selecive chaels. The drawbacks of he OFDM sysem : I is highly vulerable o sychroizaio errors. Peak o Average Power Raio (PAPR problems. 43