Effect of Co-channel Interference. : instantaneous signal power of the desired base station

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1 Wreless Couo ehologes C559 dved ops Couos geerg Leure 7 Ferury 3 sruor: Dr. ry B. Mdy y Srdhr Muuswy srdhr@wl.rugers.edu Mulple Re or Rylegh erferers ffe of Co-hel erferee roellulr evroes e reeved sgl e ole ofe osss of desred dre le of sgh LOS opoe oped y dffuse opoe. s se e evelope of e reeved sgl experees Re fdg. e se evroe e o-hel sgls e ssued o e Rylegh fded euse dre le of sgh ewee e o-hel ells s o lely o exs d e propgo p legs re uh loger. he proly of o-hel erferee lso lled s ouge proly s derved for e se of oly fdg. s : seous sgl power of e desred se so s : seous erferg sgl power of e se so... : uer of o-hel se sos s λ s e sgl o erferee ro SR s λ : reever reshold Ω K Ω where K s e Re for Ω [ s ] s e expeed vlue of s λ λ Ω Λ λ s hs o-erl h-squre dsruo w wo degrees of freedo. K K x K K x P S x exp K Ω x Ω Ω s hs expoel dsruo

2 PS P x x exp x Ω Ω λ < λ s e proly of o-hel erferee ouge proly ou P depede o-hel erferers P ou P s < λ s P λ s s le y λ s Λ PY y exp λ y λ λ P y s PY y dy PS s y s ds y λ P y s exp K λ λ P ou exp λ λ λ K Whe P ou s gve y P ou λ λ K exp λ For λ. db e proly of o-hel erferee w sgle erferer whe e desred sgl s Re fded w dffere Re fors d e erferg sgl s Rylegh fded s show Fgure. depede delly dsrued o-hel erferers s se P Y y hs e G desy fuo. y PY y λ Ω y exp! λω y

3 he proly of o-hel erferee s derved s P ou λ λ K Kλ exp C λ λ! λ Fgure Moduled Sgls d er Power Sperl Desy PSD Modulo s e proess of rsg e essge e plude frequey phse or oo of ese of e rdo rrer eer dgl or log for. Dgl odulo offers y dvges over log odulo. Soe dvges lude greer ose uy use of error orol odes whh dee d/or orre rssso errors greer seury eser ulplexg of vrous fors of d e.g vdeo d d voe d sophsed sgl proessg ehques le equlo o prove e overll ouo l perfore. s desrle o use dwd d power resoures os effely. Severl fors fluee e hoe of dgl odulo shee. desrle odulo shee provdes Low error res BR low reeved sgl o ose ros SR sy d os effeve o plee

4 Oupes u dwd Perfors well ulp fdg evroes xsg odulo shees do o suleously ssfy ll of ese requrees. Soe odulo shees re eer ers of e -error re perfore whle oers re eer ers of dwd effey. Depedg o e pplo rde-off s de whe seleg dgl odulo. he perfore of odulo shee s ofe esured ers of s power effeyη p d dwd effeyη B. Power ffey s esure of rdeoff ewee -error re BR heved y odulo shee d e sgl power requred o heve. η p s forlly defed s e ro of sgl eergy per o ose power sperl desy o heve er proly of error P e. p η o heve sy 6 P e Bdwd ffey hs desres e ly of odulo shee o oode d w led dwd. geerl resg e d re ples resg e dwd of e sgl. Soe odulo fors hve eer rde-off oers. Bdwd effey refles how effely e lloed dwd s uled d s defed s e ro of e d re R o e dwd B ouped y e oduled RF sgl. η R ps B B / H odulo shee w greer vlue of η B wll rs ore d gve speru lloo. Bu ere s fudel upper oud o hevle dwd effey gve y Sho s hel py forul C S S η B x log B where C s e hel py ps d s e sgl o ose ro. e desg of dgl ouo syse ere s rde off ewee dwd effey d power effey. For exple rodug hel odg reses e power effey d dereses e dwd effey where s hgher level odulo shees M-ry eyg derese power effey d rese dwd effey.

5 Defo of Bdwd B Fgure shows e plo of power sperl desy S f of oduled sgl. here re dffere defos for e dwd of oduled sgl gve s: solue Bdwd: he rge of frequees for whh S f ull-ull Bdwd: Wd of e loe of S f Hlf Power 3-dB Bdwd: ervl ewee frequees whh e psd hs dropped o hlf power FCC Defed Bdwd: FCC defes dwd s d whh leves exly.5% ove e d d.5% elow e d. h s 99% of sgl power s oed w ouped dwd. Fgure Sdrd Represeo of Dglly oduled sgl For y dgl odulo shee v d s e wre e sdrd for s

6 v { v exp πf } s Re s e rrer plude x x... x L s e soure syol sequee L s e eory leg s e syol duro s equvle shpg fuo of duro he d-pss wvefor s e represeed e qudrure for s v osπf v sπf where v v v Q Q he wvefors v d v Q re ow s e -phse d qudrure opoes respevely of v. evelope phse for s osπ f φ where v vq d φ v v Q Power sperl desy evluo for d-pss sgls oduled dpss sgl e wre e for { v exp π f φ } s Re φ s rdo phse uforly dsrued over [ π π ] s { v exp π f φ v exp πf φ } he uo-orrelo fuo of s s gve y

7 ss [ s s ] [ v v exp 4πf πf φ ] [ v v exp πf ] ss 4 4 [ v v exp 4πf π φ ] [ exp ] f v v πf 4 4 he oplex se d sgl s v s depede of e rdo phse esele verge. herefore ss exp πf exp πf he power sperl desy S ss f s e Fourer rsfor of. ss φ. [] deoes e S ss f S f f S f f Se e ove equo redues o S ss f S f f S f f he ove expresso shows e psd of e d-pss wvefor s s opleely deered y e psd of s oplex evelope v. for e sdrd for represeo of v s gve y [ v v ] [ ] Uder e ssupo e soure sequee s sory rdo proess we wre e ove equo s [ ]

8 ' ' ' ' ] [ ' ' he uoorrelo fuo of v s perod w perod. h s v s ylosory rdo proess. he uoorrelo e oed y g e e verge of gve y d ] [ d ] [ d ] [ d ] [ d ] [ he power sperl desy of v s gve y π d f d f S exp ] [ π d f d exp f d f d f exp exp exp π π π exp exp exp f d f du fu u π π π

9 [ B f B f ] S f exp π f he ove equo shows S f depeds o e orrelo properes of e soure sequee d e for of e equvle shpg fuo. B f s e Fourer rsfor of. Referees [] Gordo L. Suer Prples of Mole Couo Kluwer de Pulshers 996 [] heodore S. Rpppor Wreless Couos: Prples d Pre Pree-Hll 996 [3] Joh G. Pros Dgl Couos MGrw-Hll Pulshers Four do [4] ry B. Mdy Leure oes

10 C559 Wreless Couo ehologes sruor: Prof. ry B Mdy Leure 8 Ferury 8 Sured y Prvee Goplrsh prvee@wl.rugers.edu. Represeo of Modulo Fors. plude Shf Keyg SK: SK s ler odulo shee w o os evelope. SK hs e dvge of eg ore sperlly effe oer odulo shees hvg os evelope. However plude o lery degrdes e perfore of SK. he oplex evelope e represeed s follows v x h where { x} oplex soure syol sequee { x x } h plude shpg pulse v 3 xpressed e sdrd for x x x h eory less odulo SK d-pss sgl hs e followg qudrure represeo πf Q s Re{ v e } v os πf v s πf where 4 v v vq v d v Q re e -phse d qudrure phse opoes of e oplex low-pss equvle sgl. Q lso s Re{. x x h.osπf s Πf}. x h osπf x h sπf 5 Q d e evelope phse represeo s x h osπf θ where Q Q x x x d x x Q θ. 6 hus oe o plude d phse of e SK sgl deped o e oplex syol. However e sples for of SK whh s e flr PMPulse plude Modulo oly e sgl plude s vred ordg o e soure syol. hs s oplshed y g x x rel.o-off KeygOOK s spel se of M-PM w M d x {} he ss fuos re : φ h os πf ; oerwse 7

11 φ h s πf ; oerwse 8 Usg ese ss fuos we represe s s follows: Q s xφ x φ 9 where. he syol eergy s x. Q populr for of SK s M-ry QM where e soure syols x x x re hose fro M-ry osello suh Q x x { ± ± 3... ± } M he sgl spe dgr for 6-QM would loo le Fg elow. φ φ PSD of SK x Fro 6 Se x h B f x x H f S Fg : Sgl osello for 6-QM. f B f x B f x [ ] [ ] x x H f H f [ x x ] 3 f e soure syols re ero e d uorreled we ge S f H f σ x 4 where σ x [ x ] se e ero s e vre of e soure syols. he plude shpg pulse s very ofe hose o e e squre roo rsed ose pulse h

12 β π β π 4β os s h 4β 6β π 5 where β s e roll-off for. he orrespodg Fourer rsfor H f s H f f β π s f β β β f 6 pre e pulse h s rued o leg yeldg e ew pulse ' h h re 7 he orrespodg Fourer rsfor eoes ' H f H f s f 8 Pulse ruo leds o sdeloe regeero. he PSD of SK s ploed elow. Fg: PSD of SK usg squre roo rsed ose pulse shpe w β. 5

13 . Orogol Frequey Dvso Mulplexg OFDM Mulp uses osderle ersyol erferee S sgle rrer syses espelly hgh res. OFDM ulrrer syse s lo odulo shee desged o o e effe of ulp frequey seleve fdg. OFDM syse lo of serl soure syols eh of duros s overed o lo of prllel oduled syolseh of duro s.yplly s hose suh s >> where s e rs dely spred. See e e do s fold rese e syol duro redues e effe of ul-p dely spred. Correspodgly e frequey do e wded frequey seleve hel s deoposed o rrowd hels suh eh prllel hel eouers los fl fdg. h of e soure syols s rsed prllel y eployg orogol surrers. Suh shee hs prl dvges euse y redue or eve ele e eed for equlo. OFDM s eg used Dgl udo Brodsg DB d Dgl Vdeo BrodsgDVB urope d e 8. WL sdrd. s eg osdered for use rodd ouos for 4 geero wreless syses. he oplex evelope of OFDM sgl s desred y x v where φ re e oroorl wvefors gve y φ 9 π φ h exp u H f s s fuo w ulls ulples of f h regulr pulse fro o. hus e surrers whh re pled ervls of overlp e e do u re orogol e frequey do s e pe of eh surrer odes w e ulls of ll e oer surrers. hus { φ } re orogol. e epoh soure syols re rsed usg ds surrers. Se OFDM s yplly used for hgh d res x re usully hose fro QM osello. s o e oed OFDM s us ulplexg ehque d does o spefy odulo shee d y odulo shee e used. f y owg esg e hel dffere odulo shees e eployed e dffere surrers dpve odulo o gve proved perfore. he OFDM sgl lso e expressed e sdrd for s v x

14 π x h x exp x x x... x s soure syol e epoh where h u regulr pulse fro o Fro e oo s ler soure syols re rsed prllel. Bss fuos: π φ h exp... ; Oe of e or dvges of OFDM s e odulo e perfored e dsree do usg verse Dsree Fourer rsfor DF or e ore opuolly effe verse Fs Fourer rsfor FF. o llusre s osder gore e frequey offse π er exp d le h u. he π v x exp s s 3 y leg s. f we sple v ss s ssfyg yqus rero we ge π o v s x exp... 4 s esly see { } o s e FF of e lo x hus e OFDM rser wll loo le Fg 3 elow. x x Serl Prllel rs o FF o Crrer Prllel Serl Modulor x Fg 3: OFDM rser

15 he reever would slrly volve DF of FF fer geg e sgl o sed. hough S s suslly redued e los opleely eled y usg gurd d e egg of e OFDM syol. he leg of e gurd d s ovously hose suh s greer e rs dely spred. s o e oed resg e syol duro o ouer ulp es OFDM syse ore proe o fs fdg. PSD of OFDM he PSD of OFDM e oed y reg OFDM s depede odulo o orogol surrers re sepred frequey y. For sgl osello w ero e d w plude shpg fuo h e PSD of e oplex evelope s S f σ x H f where 5 σ x [ x ] π Se x h x exp for e surrer 6 B f x H f x f δ x H f 7 f h u s used H f s f where s x s πx πx he PSD for s se s ploed for 3 dffere vlues of Fg 4 elow S f db orlsed f fs Fg 4: PSD of OFDM w dffere uer of surrers s oserved for lrge vlues of e PSD eoes ore fl e s dwd rego. herefore s e lo leg eoes lrge e sperl effey pprohes of

16 sgle rrer odulo w del yqus flerg. Furer provee PSD e oed y usg squre roo rsed ose pulse u desroys e surrer orogoly whh leds o degrded error re perfore..3 Phse Shf Keyg PSK We osder e geerl se of M-ry PSK. 8 v where x h x πxhp exp M ± ± 3... ± M x x o eory { } h s e plude shpg fuo h p s e phse shpg fuo M s e se of e osello he syol eergy s e se for every syol d so s e plude. Fro e oo s ler e foro s oed e phse hee e e. Ofe e phse shpg pulse h u squre roo rsed ose pulse gve s h 4 os p whle e plude shpg pulse β π β s π 4β h s usully e β 9 6β π d e orrespodg squre roo rsed ose speru s H f π s f β f β β β f 3 he sgl spe dgr of 8-ry PSK s show Fg 5 elow

17 φ o 45 φ Fg 5: Sgl spe dgr of 8-ry PSK PSD of PSK s ssued e soure syols re uorreled d eqully lely d defed y e se x { M ;... M } 3 ow πxhp x h exp fro 8 M g expeo we ge where Rellg equo 5 S [ x ] h πhp f s 3 M Mx x s s f x M s ' ' πf ' πf πf f x e d x e d e

18 dd uorreled syols33 πf [ x x ] e hp hp x πf h p h e dd M s π [ hp hp ] πf h h e π h h π p M s hp u we ge f e phse shpg fuo s o g e l 6. S M πf f h h e dd H f f e plude shpg fuo s h u s πf S f πf we ge p πf π f dd s where 37 o e fr oprso o BW effey w dffere M e frequey vrle us e orled y e ervl. For M-ry sglg log M 38 hus S f log M s πf πf log M log M

19 Fg 6: PSD of M-ry PSK for dffere M Coprg e dwd effey for dffere M we ge e resuls show le elow usg e relo R η β where R s e re d B s e ull-o-ull dwd B M η B le : Bdwd effey depedg o lphe se s oserved w rese e dwd effey s provg. Referees:. Gordo L. Suer Prples of Mole Couo So Hy Couo Syses Joh Pros Dgl Couos. 4..B Mdy Clss oes

20 ppedx: Sgl Spe Represeo of Sgls hs represeo s used for e do represeo or hrero of e ere lss of sed wvefors. y se of M fe eergy sgls { v } M e represeed ers of oroorl ss fuos φ where <M { } Bses re oroorl > φ φ d δ where δ s e Kroeer Del Fuo. h of e M sgls e represeed s v v φ ;... M where v v φ d s e proeo of e sgl v oo e ss fuo φ. hus o fxg e oroorl ss fuos sgl v e represeed veor oo s follows: v v v v... v lso e represeed ers of se of rel oroorl ss he dpss wvefors s fuos re defed e ervl [ ]. he orrespodg veor oo would e: where we requre s s s... s ' s 3 rel oroorl ss fuos. Sgl ergy Correlo d ulde Dse { } Cosder e dpss wvefor π f s Re v e of fe duro [ ] sgl s ' ' s d s d. he eergy of e φ s s 4 lso e represeed ers of e sgl eergy of e low-pss equvle s follows: πf πf v { } e v Re v e d πf v e v v d e πf e πf v 4 f { e } d d Re v π d d 5 6 7

21 f f >> syol duro os y yles of e rrer e seod er. hus v d v lso e ross-orrelo ewee s d s s ρ s s d s s 8 9 ers of e low-pss equvle πf πf πf πf v e v e v e v e d 4 ρ 4πf Re v v d Re{ v v e } d v v v v Re s e seod er s f >> v v he ulde dse d ewee wo sgls s d s s defed s d s s ρ ρ f 3 4