Introduction to OFDM

Transcription

1 E225C Lecure 16 OFDM Inroducion EE225C Inroducion o OFDM asic idea» Using a large number o parallel narrow-band subcarriers insead o a single wide-band carrier o ranspor inormaion Advanages» Very easy and eicien in dealing wih muli-pah» Robus again narrow-band inererence Disadvanages» Sensiive o requency ose and phase noise» Peak-o-average problem reduces he power eiciency o RF ampliier a he ransmier Adoped or various sandards DSL, 8211a, DA, DV 1

2 Mulipah can be described in wo domains: ime and requency ime domain: Impulse response ime ime Impulse response ime Frequency domain: Frequency response ime ime ime ime Sinusoidal signal as inpu Frequency response Sinusoidal signal as oupu Channel Modulaion echniques: monocarrier vs mulicarrier Channelizaion N carriers Guard bands Similar o FDM echnique Pulse lengh ~1/ Daa are ransmied over only one carrier Pulse lengh ~ N/ Daa are shared among several carriers and simulaneously ransmied Drawbacks Selecive Fading Very shor pulses ISI is comparively long EQs are hen very long Poor specral eiciency because o band guards Advanages Fla Fading per carrier N long pulses ISI is comparaively shor N shor EQs needed Poor specral eiciency because o band guards Furhermore I is easy o exploi Frequency diversiy I allows o deploy 2D coding echniques Dynamic signalling o improve he specral eiciency: Eliminae band guards beween carriers o use orhogonal carriers (allowing overlapping) 2

3 Orhogonal Frequency Division Modulaion N carriers Symbol: 2 periods o Daa coded in requency domain Symbol: 4 periods o Symbol: 8 periods o + ransormaion o ime domain: each requency is a sine wave in ime, all added up ransmi Channel requency response Receive ime Decode each requency bin separaely ime-domain signal Frequency-domain signal OFDM uses muliple carriers o modulae he daa ime-requency grid Daa N carriers Frequency Carrier Feaures No inercarrier guard bands Conrolled overlapping o bands Maximum specral eiciency (Nyquis rae) Easy implemenaion using IFFs Very sensiive o req synchronizaion =1/ One OFDM symbol ime Inercarrier Separaion = 1/(symbol duraion) Modulaion echnique A user uilizes all carriers o ransmi is daa as coded quaniy a each requency carrier, which can be quadraure-ampliude modulaed (QAM) 3

4 OFDM Modulaion and Demodulaion using FFs b b1 b2 bn-1 Daa coded in requency domain: one symbol a a ime IFF Inverse as Fourier ransorm ime d d1 d2 d3 dn-1 Daa in ime domain: one symbol a a ime P/S Parallel o serial converer d, d1, d2,, dn-1 ransmi ime-domain samples o one symbol d, d1,, dn-1 Receive ime-domain samples o one symbol S/P Serial o parallel converer ime d d1 d2 dn-1 FF Fas Fourier ransorm Decode each b requency bin b1 independenly b2 bn-1 Loss o orhogonaliy (by requency ose) ransmission pulses Recepion pulse wih ose d ψ k () = exp( jk2π/ ) y ψ k +m () = exp ( j2π (k + m )/ ) δ ψ k+ m () = exp( j2π (k + m + δ) / ) con δ 1/ 2 Inererence beween channelsk and k+m I m (δ ) = exp( jk2π / )exp( j(k + m + δ )2π / )d = ( 1 exp( j2πδ ) ) j2π(m + δ) I m (δ) = sinπδ π m + δ Summing up m m I 2 m (δ) ( δ) 2 N 1 1 m =1 m 2 ( δ) or N >> 1 (N > 5 Is enough ) Inererence: Im(? )/ en d Loss or 8 carriers m=1 m=3 m=5 m=7 Asymeric Frequency ose: oal ICI due o loss o orhogonaliy δ = δ =2-3 δ =1-35 δ = δ Pracical limi =2 d assumed -5 rv δ =1 Gaussian -55 σ=δ Carrier posiion wihin he band (N=16) ICI in d 4

5 Loss o orhogonaliy (ime) Le us assume a misadjusmen /2+ τ X i = c ψ k ()ψ * / 2 l ( τ )d + c 1 ψ k ()ψ * l ( τ )d /2 / 2+τ 2 consecuive symbols τ senmπ hen X i = 2, c c 1 mπ im=k-l, c = c 1 Or approximaely, when τ<< τ X 2mπ i = 2 τ mπ independen on m In average, he inerering power in any carrier is E X 2 i 2 = 4 τ = 2 τ 2 ICI 2log 2 τ, τ << Per carrier Loss or 16 carriers -5-1 m= m=5-3 m= Relaive misadjusmen τ Zone o ineres Inererence end ICI in d ICI due o loss o orhogonaliy N=64 Doubling N means 3 d more ICI N=8 τ assumed an Uniorm rv Max pracical limi ypical deviaion or he relaive misadjusmen Including a cyclic preix o comba he ime dispersion: including special ime guards in he symbol ransiions CP τ copy c Furhemore i convers Linear conv = Cyclic conv (Mehod: overlap-save) Wihou he Cyclic Preix Including he Cyclic Preix Symbol: 8 periods o i CP Symbol: 8 periods o i Passing he channel h(n) Channel: h(n)=(1) n / n n=,,23 Yi() Yi() Passing he channel h(n) Yi() Iniial ransien Loss o orhogonaliy Decaying ransien Iniial ransien remains wihin he CP he inclusion o a CP mainains he orhogonaliy Final ransien remains wihin he CP Yj() Yj() Symbol: 4 periods o i Symbol: 4 periods o i CP uncions: I acomodaes he decaying ransien o he previous symbol I avoids he iniial ransien reachs he curren symbol 5

6 Cyclic Preix g Muli-pah componens τ max x Sampling sar 8211a Sysem Speciicaion Shor raining sequence: AGC and requency ose GI2 1 2 GI OFDM Symbol GI OFDM Symbol Long raining sequence: Channel esimaion Sampling (chip) rae: 2MHz Chip duraion: 5ns Number o FF poins: 64 FF symbol period: 32µs Cyclic preix period: 16 chips or 8µs» ypical maximum indoor delay spread < 4ns» OFDM rame lengh: 8 chips or 4µs» FF symbol lengh / OFDM rame lengh = 4/5 Modulaion scheme» QPSK: 2bis/sample» 16QAM: 4bis/sample» 64QAM: 6bis/sample Coding: rae ½ convoluional code wih consrain lengh 7 6

7 Frequency diversiy using coding Random errors: primarily inroduced by hermal and circui noise Channel-seleced errors: inroduced by magniude disorion in channel requency response ime-requency grid Daa bis Frequency ad carriers Frequency response =1/ ime Errors are no longer random Inerleaving is oen used o scramble he daa bis so ha sandard error correcing codes can be applied Specrum Mask Power Specral Densiy -2 d -28 d -4 d carrier Frequency (MHz) Requires exremely linear power ampliier design 7

8 Adjacen Channel and Alernae Channel Rejecion Dae Minimum Adjacen Channel Alernae rae Sensibiliy Rejecion Channel rejecion 6 Mbps -82 dm 16 d 32 d 12Mbps -79 dm 13 d 29 d 24Mbps -74 dm 8 d 24 d 36Mbps -7 dm 4 d 2 d 54Mbps -65 dm d 15 d 32 d blocker 16 d blocker Signal Frequency Requires join design o he ani-aliasing iler and ADC OFDM Receiver Design Yun Chiu, Dejan Markovic, Haiyun ang, Ning Zhang EE225C Final Projec Repor, 12 December 2 8

9 OFDM Sysem lock Diagram Synchronizaion Frame deecion Frame sar g Frequency ose compensaion Sampling error» Usually less 1ppm and can be ignored 1ppm = o 1% o a sample every 1 samples 9

10 Sysem Pilo Srucure IEEE 8211a OFDM xer Shor Preamble Gen Long Preamble Gen OFDM Daa Pah 1 x 8 = 8 us 2 x x 32 = 8 us = 8 us = 8 us = 8 us GI2 1 2 GI Signal GI Daa GI Daa Signal Deecion, AGC, Channel & Fine Freq Diversiy Selecion Ose Esimaion Coarse Freq Ose Es,iming Sync Rae, Lengh Daa Daa 1

11 Shor & Long Preambles 1+j j Shor Preamble +1 Period = 16 Chips Long Preamble Period = 64 Chips Correlaion o Shor Preamble Correlaion Fine iming Auo- Correlaion Coarse iming 11

12 Synchronizaion 16 d d d d d * * * * Σ d d d d From AGC Moving Auo- Corr Uni Moving SP Corr Uni d d d d * * * * Σ Shor Preamble (LU) From AGC Impairmens: Muli-Pah Channel c c c Ch Impulse Response Auo-Correlaion w/ Muli-Pah Channel Response 12

13 Impairmens: Frequency Ose Fine Frequency Ose Es Accumulaor Complex Muliplier Sync Signal 13

14 Coarse-Fine Join Esimaion & Decision Alignmen Error Correcion Average over 16 chips π π π 1 8 π π π C π A D Average over 64 chips Coarse Fine ±1ppm D 58GHz Folding ADC Vin Folding Signal π π π Frequency Ose Compensaion Decision Alignmen Channel Join Coarse- Fine Es Ose Corr 14

15 Perormance Summary Parameers Number o sub-carriers OFDM symbol req Modulaion Scheme Sampling clock req Sync Frame Sar Accuracy Freq Ose Es Range Freq Ose Es Accuracy Criical pah delay Silicon area oal power consumpion Merics 48 daa +4 pilo 4 ms PSK up o 64-QAM 2 MHz 8 chips (CP = 16 chips) ± 5p = ± 58 GHz 1% (@ 15d SNR) 127 ns 397,8 mm MHz 15