Introduction to Orthogonal Frequency Division Multiplexing (OFDM) Technique

Transcription

1 Wireless Iformaio Trasmissio Sysem Lab. Iroducio o Orhogoal Frequecy Divisio Muliplexig (OFDM Techique Isiue of Commuicaios Egieerig Naioal Su Ya-se Uiversiy

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

3 OFDM Overview (1/3 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 3

4 OFDM Overview (2/3 OFDM Orhogoal Frequecy Divisio Muliplexig The basic priciple of OFDM is o spli a high-rae daa sream io a umber of lower rae sreams ha are rasmied simulaeously over a umber of sub-carriers. I elimiaes or alleviaes he problem of muli-pah chael fadig effec, low specrum efficiecy, ad frequecy selecive fadig. 4

5 OFDM modulaio OFDM Overview (3/3 Feaures No iercarrier guard bads Overlappig of bads Specral efficiecy Easy implemeaio by IFFTs Very sesiive o sychroizaio 5

6 OFDM Trasmier a( 0 cos ( 2πf 0 b( 0 Ipu f s Δ Daa d( Ecoder 1 { a ( + jb( } f f 0 + Δf, Δf 1 NΔ S/P si cos a( N 1 b( N 1 ( 2πf 0 ( 2πf N 1 MUX D( Chael si ( 2πf N 1 Figure 1 6

7 Muli-carrier Trasmissio Muli-carrier Sysems 8T 7

8 OFDM Sysem Model (1/3 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 NΔ Usig a wo-dimesioal digial modulaio forma, he daa symbols d( ca be represeed as a( + jb( a( : i-phase compoe b( : quadraure compoe 8

9 OFDM Sysem Model (2/3 +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 ( 2πf 0 ( 2πf N 1 MUX D( Chael +1 1 a( 0 Δ NΔ T a ( 1 a( N 1 b( N 1 si ( 2πf N 1 9

10 OFDM Sysem Model (3/3 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 NΔ, which makes he sysem less suscepible o chael delay spread impairmes. Small-scale fadig (Based o mulipah ime delay spread Fla Fadig 1. BW of sigal < BW of chael 2. Delay spread < Symbol preiod Frequecy Selecive Fadig 1. BW of sigal > BW of chael 2. Delay spread > Symbol preiod 10

11 11 Orhogoaliy (1/3 Cosider a se of rasmied carriers as follows: We ow show ha every wo carriers are orhogoal o each oher. <proof is i ex page> I summary: (2 1..., 0,1, for ( 2 0 Δ + N e N f j π ψ Δ N a b q p q p a b d b a q p ( ad for 0 for ( ( ( * ψ ψ

12 12 Orhogoaliy (2/3 --- Proof N a b q p N q p j e e N q p j e e d e d b a N q p j N b q p j N a q p j N b q p j b a N q p j b a q p Δ Δ Δ Δ Δ Δ Δ Δ ( ad for 0, ( 2 1 ( 2 ( ( ( 1 ( 2 ( 2 ( 2 ( 2 ( 2 * π π ψ ψ π π π π π

13 Orhogoaliy (3/3 NΔ 13

14 Frequecy Error Resuls i Ier-Carrier Ierferece (ICI Ier-Carrier Ierferece

15 Timig Sychroizaio Error Resuls i Ier-Symbol Ierferece (ISI No Orhogoal Ay More. 15

16 Mahemaical Expressio of OFDM Sigal (1/2 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 f d k, x( ψ ( f 0 a e + k, Re j 2πf T +, k, N 1 k 0 jb for T { (} d k, NΔ ψ ( kt 0,1, 2,..., N 1 0 (3 T 16

17 Mahemaical Expressio of OFDM Sigal (2/2 T : OFDM symbol duraio d k,, : rasmied daa o he -h carrier of he k-h symbol x( Re N 1 N 1 k, ψ ( kt ( 2πf ( kt b si( 2πf ( kt { a cos } k, k, (4 k 0 k 0 C If here is oly oe OFDM symbol ( i.e. k 0, i ca be simplified as: x( N 1 0 { a cos(2πf b si(2πf } (5 17

18 Muli-carrier Equivale Implemeaio by usig IDFT (1/6 Accordig o he srucure of Tx, i mus use N oscillaors. Tha icreases he hardware complexiy. The equivale mehod is usig IDFT (IFFT. 18

19 Muli-carrier Equivale Implemeaio by usig IDFT (2/6 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 by: where ad of - A f (, φ (, h carrier, N 1 Ss ( N f + Δf 0 f 1 0 A are ampliude, respecively. 19 ( e j ( 2πf + φ ( phase, (7 carrier frequecy

20 Muli-carrier Equivale Implemeaio by usig IDFT (3/6 The we sample he sigal a a samplig frequecy 1 Δ, ad A ( ad φ ( becomes: S s ( kδ φ ( A 1 N ( N 1 0 φ A A e The he sampled sigal ca be expressed as: j ( π ( f + Δf kδ+ φ 2 0 N 1 1 π Ss ( kδ N 0 (8 (9 (10 ( j( 2πf 0 kδ + φ j2 kδfδ A e e (11 20

21 Muli-carrier Equivale Implemeaio by usig IDFT (4/6 The iverse discree Fourier rasform (IDFT is defied as he followig: f ( kδ 1 N N 1 0 F ( Δf 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 e j 2πk N (12 (13 21

22 Muli-carrier Equivale Implemeaio by usig IDFT (5/6 If eq.(13 is saisfied, j( 2π f0kδ+φ A e 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. 22

23 Muli-carrier Equivale Implemeaio by usig IDFT (6/6 a( 0 cos ( 2πf 0 b( 0 Ipu f s Δ d( 1 { a ( + jb( } f f Δf, Δf NΔ si cos a( N 1 b( N 1 d( 0 d( 1 d( 2 si ( 2πf 0 ( 2πf N 1 ( 2πf N 1 D( Chael Ipu f s Δ d( 1 { a ( + jb( } f f Δf, Δf NΔf d( N 1 D( Chael 23

24 Cyclic Prefix (1/9 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. 24

25 Cyclic Prefix (2/9 Guard ierval leads o iercarrier ierferece (ICI i OFDM demodulaio 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 subcarrier 1. 25

26 Cyclic Prefix (3/9 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[ 1] d[ 2] d[ N 1] D D[] 0 D[] 1 D[] 2 [ N N g ] [ ] D N 1 D ~ [ k] 26

27 Cyclic Prefix (4/9 All delayed replicas of subcarriers always have a ieger umber of cycles wihi DFT ierval o ICI 27

28 Cyclic Prefix (5/9 Liear covoluio vs. circular covoluio N 28

29 Chael effec wih cyclic prefix Cyclic Prefix (6/9 Sigal afer removed CP 29

30 Cyclic Prefix (7/9 [ ] { [ ]} 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 Lh Received useful par [] [ ] [ ] 2 r[ ] [ ] [ ] [ ] r D N h where is N-poi circular covoluio (due o CP N Received symbol a k-h subcarrier Y k FFT{ r[ ] } FFT D[ ] N h[ ] Yk X k H k { } X k H k Useful propery for OFDM sysem o reduce complexiy of chael equalizaio 30

31 Cyclic Prefix (8/9 --- OFDM Receiver r~ ( r( Oupu daa Symbols 31

32 Cyclic Prefix (9/9 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 32

33 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: 33

34 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. 34