OFDM Tutorial. version 0.1

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Laureen Kimberly Taylor
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1 3.3.8 OFDM oia vio. Co Sia dciio.... aao ia oci oc aao ai ca oi hyica cha # aao aao civ diia ia oci diia ai i dic cha diia civ....4 hy i h cyic i?... 3 i iao co iaio aa QM oc IFF boc obaii ad addi h cycic i i dic cha dicad cycic i....8 ao o daa vco....9 o oci obai o... Fh! a ich dii..9. o coaio diaa o bcai... /

2 3.3.8 Sco h doc vi o vy baic a o a OFDM aiio y. h d o ch a doc ay b qioab ic h i aady a ah o iodcoy o hi oic. Hov h ai oivaio o a ch a doc a o aiiai y ih h ici o OFDM aiio y ad o doc y "ai o". h baic ia oci od i OFDM y a ovidd boh i h aao doai ad a a i dic dciio hich i hoh o b o iab o iaio oc. Fo h i dic oaio o h ia oci a i iaio oo i divd. h i b o vio o a baic iao: Pyho va io od (qid o MB y aay oci ad oi caabiii coaab o MB) MB Chooi o di oai vio i aiy o hioica ao. I ad i MB aod 993 o ao ay ciiic oai a. Oh oai a hov ad o Pyho ad i io od a. Ovi i bca aa ha Pyho ca b a vy ood bi o MB i o oc o ciiic oai. Coidi h ic a aachd o MB ad i oobo h ic o oa ovidi qiva cioaiy hod i o i ih h oo ayay. hi bco v o ioa h yo a o do o oai o -dcaio a ho h acc o a MB ic i o o iy. h vio o hi doc vov h oc i b o o ho o i a y dd iaio oo covi o advacd oic ch a ychoiaio i o h OFDM civ ad h iac o vaio icio cooy od i ay acica iaio o h ai ad h civ. Poai o ch oo i aiy Pyho ic io od C/C oa i ho ca h coaioa d i o aao ioac. /

3 3.3.8 Sia dciio. aao ia oci () () () () oc ai cha civ i i. -) od o ia aiio. oc h oc ovid co daa ybo. i a id i h a - i h boc id ; d o b OFDM ybo... aao ai OFDM ai a o avo Φ () o daa aiio. Moov ach OFDM ybo coi bcai ih c qci. Id do h b-cai id. h a o i i : - / Fho di a daio c (daio o h cycic i) ad h daio o a OFDM ybo. c Wih h diiio avo Φ () a d a : ( ) c o ohi Soi i i o covi o hi diiio ( c ) o ha o c hav ( ) o ohi ( ) o c (d o hi oy h i iva c i cad h cycic i). 3/

4 / Each OFDM ybo i a ihd oiio o h avo. Sciicay h h OFDM ybo i h ih a co b i daa o aiio (.. a o M-QM ybo). Fo h diiio o avo h h OFDM ybo i did o h iva h b iva c bo o h cycic i a o h h OFDM ybo. h i ia () i h qc o OFDM ybo. ) (.. ca oi h o ca diy i did a h Foi aoaio o h aocoaio cio R(). { } E R * { } d E S * ) ( * * * * Wh ai cd h cd va { } E * o-zo coibio occ oy i hav iaoy ad. { } { } E E * * ih *

5 / { } E σ ad iay { } o E σ * Hc h o ca diy i d a ) ( d S σ co ) ( d S σ co co ) ( d d S σ σ i 4 co ) ( S σ σ I a OFDM aiio y h b-cai aci i a / h ai ca coibio o ach b-cai occ a qci h h ca coo o a oh b-cai i zo.

3.3.8 icha.bi@ooai.co a i. -) oaid OFDM c..3 hyica cha # aao h hyica cha i ih chaacid by i cha i o () o i h qcy doai by i Foi ao G(). Iiiay a a id cha i o.

6 3.3.8 a i. -) oaid OFDM c..3 hyica cha # aao h hyica cha i ih chaacid by i cha i o () o i h qcy doai by i Foi ao G(). Iiiay a a id cha i o. a hi iiicaio ay b dod. Fho a ii daio o () i ad. () did o c..4 aao civ h i ia o h civ i dod (). c * ( ) ( ) d () i h oi coibio o h civ. c ( ) ( ) d Dii h h id OFDM ybo by () 6/

7 / c d obv ha () i did o h ii i iva ohi o did c Gay ia () ova h cociv ia () by a i a o c. hi ova i d o h cha i o (). I ad o ic ih h i a o h cociv ia. So h a o () i icd o i iva c I i ho h a o h civ ia oci o ac h ia iva o h OFDM ia. c d Ii h diiio qaio o h avo cio c c d ad c c d h ia i h Foi ao G() vaad a qci. c d G Hc c G Ui h ia i h iva c a o coc daa ybo. c c c c c d G d

8 c ( c ) d ( ) G d ( ) G ( ) G( ) c d c Hc by G( ) c ( c ) d c icha.bi@ooai.co ( c ) d o.3 diia ia oci.3. diia ai Each OFDM ybo i cocd o a o co daa ybo dod by. I hi oaio hav idic o idica h b-cai id - id o h OFDM ybo Fo ach id (OFDM ybo) h daa ybo a aod io a qc y i qaio y o ( ) ohi Sqc y y y ( ) y ( ) y ( -) y ( -) cao b d dicy o aiio. Iad y i dd o a o qc z by addi a ii h i. Fo ao aid a i hi doc h i i cocd o h a a o qc y. o : i ay cho a ha h ai b o iiica a o h cha i o. h qc (ao o a OFDM ybo) i h h cocaaio o o qc z y ( -) y ( -) y ( -) y ( -) y ( ) y ( ) y ( -) y ( -) Sic a iio o a o y o h i h a o qc z h - 8/

9 / qa z hi oy i iia o iodiciy ad h i i cooy dod a "cycic i" o hi ao. h oa h o qc z i o h aid qc i h h aoiio o b-qc z. ohi o z ) ( Fo idic i h a - a z a h cycic i. Dii h cio ohi o ay i b-qc z by z Ui h a qaio h aid qc z i d a z z May bicaio o OFDM ia oci di a i dic avo by ohi hich iv z z.3. i dic cha h dic cha i o i dod by. W i aay a a ii b o a. I i cd hov ha oy a o o id M < a iiica. h dic cha o a covoio o h i qc z.

10 3.3.8 b h cha o ia. z ( ) h a io dai. Hov o iiicaio a oib by ai io acco ha avo cio. ad i o. boh a did ov a ii a o idic. Fo a iv i id id hav - hich ic o h a - So ca iodc ii aio ii o. ( ) Fo a o covi oaio id by ( ) ad a i. i did o h iva -. Hc ay va o i iqy did by h id ( ). Wavcio ( ) a did o () - -() () Ii h ii oib va o i - a : -() () ad -() () () () ( ) () () () ( ) ( )/() /() /

11 3.3.8 / ( ) ( )/() /() ad iay (-) ( ) I hi ca o OFDM ybo coib o h o. I i ay o ha o a o OFDM ybo ih id a cod by iybo ic ISI o h cdi OFDM ybo ih id ( ). (-) H oy OFDM ybo ih id coib o h o qc..3.3 diia civ ida civ od dc qc ad aiio i io ch o boc (id ) o () a. W hav ha h i a o ach boc ay b d o ISI. So h i o dicad h adi a ad ai h a o (-) Ii ohi h va o i aay o -. So hav

12 3.3.8 / ooi a - o id i o (-) o obv ha - o o ad o h ciic choic o id. o o (-). Hc di. h civ a i o cov aid daa ybo o h h OFDM ybo. o hi d vaa o Ui obai o R-odi hi qaio yid o o a o o-zo va oy i. o B i h DF o h cha i vaad a qcy ia.

13 3.3.8 G o G h daa ybo i h o G G Coai o h qcy diiv dioio o h cha ao o a co ai cocio o h bcai ih h iv o h cha dic qcy o a h bcai qcy. ay h civ ha o o h ia oci :. dc qc ad aiio i io ch o boc (id ) o () a. I a aca iaio hi aiioi od qi o ychoiaio bohad. a h civ d o o h o ay h i ad h ychoiaio aoih ovid hi ioaio.. h cycic i o h i ovd o h daa boc. I h cha i o i aoaby ho coad o h i b o ISI o adac OFDM ybo. 3. h aii daa boc ha h. yi h FF o hi boc ad coci ach a o h FF o by iyi ih h iv o h co cha ai a hi bcai qcy ovid a oiby cad vio o h aid co ybo. 4. Coc daa ybo by ayi a cai aco. acica civ od hav o ay hod hich ovid h qid cai aco GC cio..4 hy i h cyic i? o b i 3/

14 Iac o a OFDM ia o Icio h vioy d aao/diia od o OFDM aiio cdd ay icio iodcd by hada o h ai ad civ. I ay acica aiio caio vaio icio b coidd. by a ico i o h icio i aid h : X cio. I-/Q ibaac qada ha o o -covio ch. ida O i ca o a dic -covio ai 3. i dioio 4. Pha oi o -covio 5. oiaii o h X hih o aii RX cio. Pha oi o do-covio. i dioio 3. I-/Q ibaac qada ha o o do-covio ch 4. ida qcy o 5. ychoiaio o o OFDM ybo ii Mo o h icio a byod h co o hi doc. Oy h iac o ida qcy o i did i o dai i hi doc. 3. iac o ida qcy o Fo ao o iiciy h c o ida qcy o i did o diia OFDM aiio. ai a ih h civd qc b icd h do h qcy o. i h ai qcy o h civd qc. h qc i aiiod i io ch o boc (id ) o () a. ai h i a o ach boc a dicadd. h aii a o boc ih id i h : (-) Ii ( ) ( ) 4/

15 / ohi h va o i aay o -. So hav ooi a - o id i o (-) o obv ha - o o ad o h ciic choic o id. o o (-). Hc di. h civ a i o cov aid daa ybo o h h OFDM ybo. o hi d vaa o Ui obai o R-odi hi qaio yid

16 / o cod o oio do o oib. B o a a qcy o a aoab ood aoiaio o i { o h a o a d a o Ui oy ohi ad dii M M o d havi ha i h DF o h cha i vaad a qcy ia. G

17 / G M G o yi cai aco (/) (/) ad coci o qcy dd ai (/G) yid G G M o G Ioi h coo ha obv ha oy o h daa ybo i covd acy. Wih qcy o h i b aay o co a ad a daa ybo coib o hi. Moov co a ica ih h b o b-cai.

18 i iao 4. co Doa baic ici o a i dic OFDM aiio y. a i a iaio oa i b i i Pyho o io od. Oc hi aoach o iia oa i b i i MB ad SCIB. 4. iaio aa... b o bcai ; o ic icicy hod b a o o... h o cycic i _OFDM... b o OFDM ybo d i iaio cha_i... vco o co a o h cha i o _o_... oaid qcy o 4.3 QM oc Pyho od QMSoc.y ovid va QM daa ao. Cy od odaio hod a :. 4-QM Soc4QM(boc_). 6-QM Soc6QM(boc_) 3. 3-QM Soc3QM(boc_) QM Soc64QM(boc_) 5. 8-QM Soc8QM(boc_) QM Soc56QM(boc_) a: qa_vc Soc4QM(boc_) boc_... b o 4-QM ybo qa_vc... co y aay o adoy ad 4-QM ybo ; (qa_vc) boc_ 4.4 OFDM odao 4.4. IFF boc h h QM daa vco b d by a co vco ih -. h IFF boc o h OFDM odao oc h o vco io a co vco y i qaio. 8/

19 3.3.8 y hi i h iv dic Foi ao cad by a aco. I Pyho (od y) a i MB h iv FF cio i() ovid h oaio o coc o h cai aco (/) iodcd by h i() cio iy by. a y_vc *y..i(qa_vc) # Pyho y od 4.4. obaii ad addi h cycic i y_vc i a co vco ih y_vc y_vc y_vc- y_vc- h a o y_vc a h a o h cycic i. cycic_i y_vc- y_vc- y_vc- I Pyho cycic_i i obaid hoh a ici oaio o h vco y_vc ad SCIB hav iia idi oaio). (MB cycic_i y_vc-: h cycic i i dd o vco y_vc. h dd vco i dod od_vc. I Pyho hi i achivd i od_vc y.cocaa( (cycic_i y_vc) ) o dicy iho iciy cai vco cycic_i od_vc y.cocaa( (y_vc-: y_vc) ) 4.5 i dic cha Co a o h cha i o a od i a vco _cha_i. W a a h o M a. o a h oaiaio o oa o i h icio M < i iod. B hi i ay o ch o a icio ic o cc oaio (o iybo ic o adac OFDM ybo o ISI ) qi M < < Sad i a di ay: h h M o h cha i o ha b ha h h o h cycic i. 9/

20 h i dic cha o aiodic covoio a did by qaio P i h i...a o h i qc h...a o h cha i o...a o h o qc cha o icha.bi@ooai.co I h ciic ca o hi iaio oa qc i a h a o od_vc. Hc id i i -. I o h a h a o _cha_i. h i qc ha a h o (M-) - M- h a (M-) a o ova ih i (M-) a o h cociv id OFDM ybo. Fii a OFDM ybo ho qi va ia oci : # h cha... _vc.covov(od_vc _cha_i) # i io vco _vc _vc _vc _vc: _vc _vc: # coc o cha o o a OFDM-ybo _vc:m- _vc:m- ova_od # av ova a o c OFDM ybo o ybo ova_od _vc 4.6 qcy o o ay a qcy o o aay _vc i ca a vco o_vc o () a ( ) # qcy o o civ o_vc.(. *.i * _o_ *.aa()) iyi aay _vc by o_vc yid h OFDM ybo _vc_o ih qcy o. # ay qcy o _vc_o _vc * o_vc /

21 dicad cycic i h i a a h cycic ic oiby abd by ISI. So h civ dicad hi a o h aay _vc_o. h aii a i od i a aay od_c o h. # dicad cycic i a od_c _vc_o: od_c i qiva o qc i cio ivi h daa vco Gi bac o h aid daa ybo i a o ocd.. aicaio o FF (I ca o a aa cha a do. h FF yid h qc o a.). qcy dd ai cocio d o h cha i o W aady divd a qaio o h covd daa : o G h a G i accoihd ayi h () cio avaiab i Pyo/y o MB. ddiioay a cocio aco (/) b aid. d i ca h a a cai aco o h b a ai cocio (/) o hi. Sa o qcy dd cha ai G a obaid o h FF o h dic cha i o. h va o h i o a od i aay h. Ui G..(h ) ovid h a G a aay G. I o iiic iao h i o i id. Hc oy d o co i oc. h a cha ai o a aid OFDM ybo. daa_c (/)*..(od_c) / G I a daa_c i h qc o aid daa ybo. h daa boc ca b h ocd o obai ioaio ch a bi o a ia coaio diaa o idivida b-cai c. So a a ovidd i h b-cha. /

22 o oci Cy h iaio oo oy o diay o h coaio diaa (I-/Q o) o coaio diaa o bcai /

The CFD Drag Prediction Workshop Series: Summary and Retrospective. David W. Levy Cessna Aircraft Company and the DPW Organizing Committee

The CFD Drag Prediction Workshop Series: Summary and Retrospective. David W. Levy Cessna Aircraft Company and the DPW Organizing Committee CD D icio oo i: u oci Di. C Aic Co D izi Coi o, o, oiu Dio, CA - u 1 CD D icio oo i: u oci, D izi Coi Di.. i C Aic Co w. ioco, o C., oi i, i oi Co:, Huio c,. oui Cio. u, ic A., o H. oio AA c C. o io Ci