Subcarrier Combining for An Analog Single-Carrier Transmission

Transcription

1 Subaie Combiig fo A Aaog Sige-Caie Tasmissio Thah ai VO Shiya KUAGAI ad Fumiyui ADACI Depatmet of Commuiatios Egieeig Gaduate Shoo of Egieeig Tohou Uivesity Aza-Aoba Aamai Aoba-u Sedai iyagi Japa {vothahhai umagai}@mobieeeitohouajp adahi@eeitohouajp Abstat Aaog sige-aie tasmissio with fequeydomai equaizatio (aed aaog SC-FDE) was eety poposed i ode to impove pefomae of aaog siga tasmissio Aaog SC-FDE siga spetum has a ompex ojugate eatio betwee owe sidebad (LSB) ad uppe sidebad (USB) sie aaog siga is ea-vaued Expoitig this popety the eeived LSB ad USB subaies a be ombied to obtai a additioa fequey divesity gai I this pape a subaie ombiig method is poposed to impove the pefomae of aaog SC-FDE A theoetia aaysis of omaized mea squae eo (SE) pefomae is peseted to evauate the effet of subaie ombiig ad is ofimed by ompute simuatio It is show that subaie ombiig impoves effetivey the SE pefomae i mutipath fadig hae Keywods aaog SC-FDE; subaie ombiig; atea divesity I ITRODUCTIO Digita wieess siga tasmissio tehoogy has bee otiuousy evovig ad is widey adopted i most of wieess ommuiatio systems []-[] oweve aaog siga tasmissio is sti attative fom the viewpoit of spetum effiiey The siga badwidth of aaog siga tasmissio is muh aowe tha that of digita siga tasmissio beause eithe soue odig o hae odig is used Due to the aowbad atue the popagatio hae i the aaog siga tasmissio is osideed to be fequeyoseetive [3] Cosequety the eeived siga suffes fom fequet fades ad its quaity degades seveey whe eithe a tasmitte o a eeive moves duig ommuiatio I ode to oveome this pobem we eety poposed a aaog sige-aie tasmissio with fequey-domai equaizatio (aed aaog SC-FDE) [4] Aaog SC-FDE appies disete Fouie tasfom (DFT) fequey-domai spetum shapig ad mappig ivese DFT (IDFT) ad yi pefix (CP) isetio befoe tasmissio At the eeive oe-tap FDE [5]-[6] is appied to tae advatage of fequey-seetive fadig hae utiaess usig aaog SC-FDE is possibe based o the piipe of fequey-divisio mutipe aess (FDA) Theefoe the spetum effiiey is the same as ovetioa aaog siga tasmissio (ie it is iheety aowbad) e showed i [4] that aaog SC-FDE ahieves bette omaized mea squae eo (SE) pefomae tha the ovetioa aaog siga tasmissio I patiua ombiatio of distibuted spetum mappig [7] ad miimum mea squae eo (SE)-based FDE gives the best pefomae I aaog SC-FDE sie the aaog siga is ea-vaued the uppe sidebad (USB) ad owe sidebad (LSB) fequey ompoets (subaies) ae i a ompex ojugate eatio This ompex ojugate eatio motivates us to popose a subaie ombiig method fo aaog SC-FDE i ode to obtai a additioa fequey divesity gai Theefoe it is expeted to futhe impove the SE pefomae I this pape a theoetia aaysis of the SE pefomae is peseted ad is ofimed by ompute simuatio The esuts show that subaie ombiig impoves effetivey the SE pefomae of aaog SC-FDE i a mutipath fadig hae The emaide of this pape is ogaized as foows I Setio II the subaie ombiig method is poposed fo aaog SC-FDE The theoetia aaysis of SE pefomae is give i Setio III Setio IV povides the ompute simuatio esuts Fiay ousio is peseted i Setio V II SUBCARRIER COBIIG FOR AALOG SC-FDE The tasmissio system mode of aaog SC-FDE with subaie ombiig is iustated i Fig I this pape we oside a system with sige tasmit atea ad eeive ateas s(t) -CP t LPF -poit DFT s() yquist-ate sampig De-mappig -poit DFT Spetum shapig fite (a) Tasmitte Joit FDE & Subaie Comb (b) Reeive -poit IDFT Fig System mode appig s ( ) Rea pat output AGC -poit IDFT CP LPF s ( t ) t /5/$3 5 IEEE

2 A Tasmit Siga Repesetatio At the tasmitte afte imitig badwidth by ow-pass fite (LPF) the aaog siga s(t) is samped at the yquist ate of /T The sampe sequee is the gouped ito a sequee of siga bos of sampes eah Eah siga bo {s(); } is tasfomed by -poit DFT ito fequey-domai siga bo {S(; } without eithe quatizatio o soue eodig The -th fequey ompoet S( / of LSB a be expessed as S( s( ) exp jπ s( )exp jπ( S ( () Fom Eq () it is obvious that thee is a ompex ojugate eatio betwee the fequey ompoets of LSB {S(; / } ad USB {S(; / } exept S() ad S(/) as show i Fig The spetum shapig fite is assumed as a idea bi wa LPF to tasmit the whoe spetum of aaog siga Afte the fiteig the mappig opeatio assigs the esutat fequey ompoets ove a boade badwidth havig (>>) othogoa subaies to tae advatage of hae fequey-seetivity (ie fequey divesity) The mappig is pefomed i aodae with distibuted mode [7] whee the fequey ompoets {S(; } ae mapped uifomy ove the badwidth havig subaies { X ( ); } as S( X ( ) () othewise The uused subaies whih ae oupied by zeos ae assiged to othe uses A exampe of distibuted mappig with 8 3 is iustated i Fig 3 The esutat fequey-domai siga havig subaies is tasfomed by -poit IDFT ba ito timedomai A siga bo {x(); } at a ate of / Ts ( / ) / T is obtaied as x( ) X exp jπ (3) The disete-time siga bos { x ( ); g } afte isetig CP a be expessed usig the equivaet ow-pass epesetatio as x( ) P x( mod ) (4) whee P is the aveage tasmit powe B Reeived Siga Repesetatio A quasi-stati fequey-seetive hae osistig of L distit popagatio paths is assumed whee the hae stays ostat duig the siga tasmissio peiod of oe bo The maximum time deay of hae is osideed to be shote tha the CP egth The hae impuse espose h (τ ) betwee the tasmitte ad the ( )-th eeive atea a be expessed as Fig Fequey ompoets of the aaog siga Use # Use # Use # Use # h S( Compexojugate / - S( X ( ) Fig 3 Distibuted mappig L ( τ ) h δ ( τ τ ) (5) whee h τ ad δ () ae the path gai with L E [ h ] (E[] deotes the esembe aveage opeatio) T s -spaed time deay of the -th path with τ ad deta futio espetivey The tasmitted sigas ae eeived by eeive ateas The disete-time eeived siga { ( ); g } at the -th eeive atea is desibed as L ( ) h x( ) z ( ) τ (6) whee z () is the ompex Gaussia oise sampe with zeomea ad vaiae /T s with beig the sige-sided powe spetum desity of the additive white Gaussia oise Afte emovig CP eah eeived siga bo is deomposed by -poit DFT ito othogoa subaies { R ; } R ( is expessed as R P X( Z (7) whee ( ad Z ( ae espetivey the hae gai ad the oise ompoet give by L τ h exp j π (8) v Z z ( ) exp j π The de-mappig whih is the evese opeatio of mappig doe at the tasmitte pis out the desied subaies R ad oespodig hae gai fo as R R ( ) (9) ( ) ' ' '

3 C Joit Subaie Combiig ad FDE By expoitig the ompex ojugate eatio i desied siga betwee LSB ad USB subaies joit subaie ombiig ad FDE is pefomed to demoduate the fequey ompoets { S ; } of eoveed aaog siga I additio the oespodig subaies fom othe ateas ae aso ombied as show i Fig 4 The -th demoduated fequey ompoet S ( ) is expessed as R ( ) / S { } R ( ) ( ) ( ) othewise R () whee ( ( ad ( ae SE-FDE weights desiged to miimize mea squae eo (SE) betwee the demoduated siga S ( ) ad tasmitted siga P S ( ) They ae deived as fo / () Γ ( ) Γ Γ ( ) fo ad / () I Eqs () ad () Γ PT s ad [] * deotes the ompex ojugate opeatio The demoduated fequey-domai siga { S ; } is the tasfomed ba ito the time-domai by -poit IDFT Afte appyig automati gai oto (AGC) [8] ad piig out the ea pat the demoduated timedomai siga { s ( ); } is give by s ( ) Re S exp jπ ε (3) s( ) Re{ μ( ) μoise( ) } whee ε μ ( ) ad μ oise ( ) ae espetivey omaizatio fato of AGC esidua ite-sampe itefeee () ad equivaet oise Fiay the aaog siga s ( t ) is eostuted by LPF fom disete-time sequee s ( ) III SE AALYSIS The SE fo evauatig tasmissio pefomae is defied by E[ s ( ) s( ) ] SE (4) E[ s( ) ] ithout oss of geeaity the tasmit siga is assumed to have uit aveage powe Fom Eq (3) the SE beomes SE E Re{ μ ( ) μ ( )} (5) [ ] oise (a) ithout subaie ombiig (b) ith subaie ombiig Fig 4 Joit subaie ombiig ad FDE with eeive atea divesity Sie μ ( ) ad μ oise ( ) ae ea-vaued ad statistiay idepedet the vaiae σ of μ ) μ ( ) μ ( ) is ( oise expessed by [ ] [ ] σ E μ ( ) E Re{ μ( )} σ σ (6) oise whee σ ad σ oise ae the vaiae of μ ( ) ad μ oise( ) espetivey They ae deived as (the deivatio is omitted fo the bevity) ( σ Γ σ oise ( whee ad ( ) is give by (7) / ( ) ( ) ( ) ( othewise (8) / (9) ( ) ( ) othewise The oditioa SE fo give set of hae gais { ; } a be auated fom Eqs (5) (7) as SE ( Γ { }) σ σ Γ oise () The deomiato of fist tem i Eq () expesses the powe oeffiiet of desied siga Fom Eqs () (8) ad () it shoud be oted that the powe oeffiiet of desied siga is omposed of the sum of ad ( fo exept / I ( S ( ) - fom othe ateas ( S ( ) ) - fom othe ateas ( )

4 othe wods subaie ombiig ahieves a atea divesity ode of appoximatey oweve the ahievabe divesity ode depeds o oeatio betwee ad ( (ie hae fequeyseetivity stegth) ideed This is disussed i simuatio esuts The aveage SE is umeiay auated by aveagig Eq () ove a possibe eaizatios of hae gai { ; } IV COPUTER SIULATIO A Compute Simuatio Coditio The oditios fo the umeia evauatio of theoetia aveage SE ad ompute simuatio ae summaized i Tabe I e assume the badwidth-imited (4 z) voie tasmissio (a ews aoue voie) A sampig ate of /T 8 z (sampe duatio of T 5 mse) a time-domai siga bo of 64 sampes a adjaet subaie iteva of 5 z ad a distibuted mappig ove 89 subaies ae aso assumed As a popagatio hae Rayeigh fadig hae havig a T s -spaed (T s T / μse) L6-path with expoetia powe deay pofie whee β is deay fato is osideed A vey sow (o bo fadig mode is assumed whee fadig stays uhaged ove eah bo of 89 sampes fo aaog SC-FDE The time deay of -th path is set to τ ad the maximum deay diffeee is ess tha CP egth Idea hae estimatio ad idea fast AGC ae aso assumed The evauatio of theoetia aveage SE is doe by ote-cao umeia omputatio method as foows The set of path gais { h ; L } is geeated fo obtaiig hae gai ad SE-FDE weight usig Eqs (8) () ad () This is epeated suffiiety to obtai the aveage SE TABLE I COPUTER SIULATIO CODITIO Siga tasmissio Aaog siga Sampig ate Aaog SC-FDE with Subaie Combiig Voie (shot ews) /T 8 z DFT size 64 Spetum shapig fite appig Idea bi wa LPF Distibuted mode Tota o of subaies 89 CP egth g 6 o of Tx ateas t o of Rx ateas 4 Chae FDE weight Chae estimatio & Fast AGC Fequey-seetive bo Rayeigh fadig L6-path expoetia powe deay pofie with deay fato β 3 6dB SE Idea Aveage SE Aveage SE 4 Simuatio g 6 βdb w/ subaie omb w/o subaie omb Theoetia Aveage omaized tasmit powe P/ (db) Fig 5 SE pefomae g 6 βdb Simuatio w/ Subaie omb ( t ) w/ STTD ( t ) Aveage omaized tasmit powe P/ (db) Fig 6 Compaiso betwee subaie ombiig ad STTD Aveage SE 3 4 Aaog SC-FDE w/ subaie omb L6 Simuatio β db β 3 db β 6 db Aveage omaized tasmit powe P/ (db) Fig 7 Impat of deay fato β o SE pefomae

5 Aveage SE P/ 49dB P/ 59dB Aaog SC-FDE w/ subaie omb theeby degadig the SE pefomae due to a smae divesity gai O the othe had Fig 8 pots the SE pefomae as a futio of omaized oot mea squae (ms) deay spead τ ms /T s whe β db It is see that as τ ms /T s > 5 (ie L > ) the additioa fequey divesity gai obtaied by subaie ombiig is suffiiet I othe wods the esut shows that the poposed subaie ombiig is effetive i the mutipath fadig hae 3 Simuatio βdb omaized ms deay spead τ ms /T s Fig 8 Impat of hae fequey-seetivity o SE pefomae B SE pefomae The SE pefomae of aaog SC-FDE with subaie ombiig is show i Fig 5 Fo pupose of ompaiso the pefomae of aaog SC-FDE without subaie ombiig is aso potted A faiy good ageemet betwee the umeia ad simuatio esuts is foud It is obvious that the SE pefomae of aaog SC-FDE is effetivey impoved by subaie ombiig owig to the additioa fequey divesity gai By expoitig the ompex ojugate eatio betwee the LSB ad USB spetum subaie ombiig with eeive ateas a ahieve simia divesity ode to ( )-bah eeive atea divesity oweve a pefomae degadatio of appoximatey 3 db is see i ompaiso betwee subaie ombiig havig eeive ateas ad the ase havig eeive ateas without subaie ombiig The easo is disussed as foows At the eeive two subaies havig ompex ojugate eatio i desied siga ae used fo subaie ombiig to epodue two fequey ompoets Theefoe the demoduated fequey ompoets aso have the ompex ojugate eatio theeby poduig the ompex ojugate eatio betwee LSB ad USB of the eoveed aaog siga I othe wods the impat of ite-sampe itefeee ad oise beomes doube those i aaog SC-FDE without subaie ombiig afte the opeatio of IDFT ad ea-pat output This eads to the pefomae degadatio As ieases the spae divesity gai beomes the domiat fato of pefomae impovemet Theefoe the effet of subaie ombiig whih eads to the pefomae impovemet visiby beomes smae as show i Fig 5 Fig 6 shows ompaiso betwee the effet of subaie ombiig ad spae-time tasmit divesity (STTD) [9] o aaog SC-FDE I ase of usig STTD the umbe t of tasmit ateas was set to t Fig 6 ofims that athough the sige tasmit atea is used subaie ombiig ahieves simia divesity ode to -bah STTD A mio diffeee is see beause the subaie R ( ) at / aot obtai additioa fequey divesity gai by subaie ombiig as the othes The additioa divesity gai obtaied by subaie ombiig depeds o the stegth of hae fequey-seetivity Ivestigatio esuts of this impat o SE pefomae ae show i Figs 7 ad 8 Fig 7 shows the SE pefomae i ase of deay fato β 3 6 db whe L 6 It is ofimed that β (a uifom powe deay pofie) gives the best pefomae As β ieases the hae fequey-seetivity beomes weae V COCLUSIO I this pape by expoitig the ompex ojugate eatio betwee the LSB ad USB subaies of a ea-vaued siga a subaie ombiig method fo aaog SC-FDE is poposed i ode to obtai a additioa fequey divesity gai ad theefoe futhe impove the SE pefomae A theoetia aaysis of the SE pefomae was peseted ad ofimed by ompute simuatio It was show that subaie ombiig a effetivey impove the SE pefomae i a mutipath fadig hae The simia divesity ode to -bah STTD is obtaiabe athough the sige tasmit atea is used The impat of hae fequey-seetivity o SE pefomae was aso ivestigated to show the effetiveess of subaie ombiig I this pape the tasmissio of sige aaog siga steam was peseted oweve it shoud be oted that mutipe aaog siga steams usig the poposed aaog SC- FDE a be tasmitted based o the FDA piipe whih ahieves the same spetum effiiey as the ovetioa aaog siga tasmissio system Aso i this pape the pefet hae estimatio was assumed The hae estimatio fo aaog SC-FDE is eft as ou impotat futue study Aso eft fo ou futue study is the pefomae ompaiso betwee the poposed aaog siga tasmissio ad digita siga tasmissio REFERECES [] Y Kim BJ Jeog J Chug C-S wag JS Ryu K- Kim ad YJ Kim Beyod 3G; visio equiemets ad eabig tehoogies IEEE Commu ag vo 4 o 3 pp -4 ah 3 [] Y Pa ad F Adahi Ehaed adio aess tehoogies fo ext geeatio mobie ommuiatio Spige 7 [3] A Godsmith ieess ommuiatios Cambidge Uivesity Pess 5 [4] T Vo S Kumagai T Obaa ad F Adahi Aaog sige-aie tasmissio with fequey-domai equaizatio IEICE Tas Commu voe97-b o9 pp Sept 4 [5] D Faoe SL Aiyavistau A Beyami-Seeya ad B Eidso Fequey domai equaizatio fo sige-aie boadbad wieess systems IEEE Commu ag vo 4 o 4 pp Api [6] F Adahi Tomeba ad K Taeda Fequey-domai equaizatio fo boadbad sige-aie mutipe aess IEICE Tas Commu vo E9-B o 5 pp ay 9 [7] G yug J Lim ad DJ Goodma Sige aie FDA fo upi wieess tasmissio IEEE Vehiua Teho ag vo o 3 pp 3-38 Sept 6 [8] Y a Z ag L Li ad Y Zhao A fast automati gai oto sheme fo IEEE 854 eeive Po IET d Iteatioa Cofeee o ieess obie ad utimedia etwos (IC) pp 67-7 Ot 8 [9] T Vo S Kumagai ad F Adahi A ove aaog siga tasmissio usig joit spae-time tasmit divesity ad eeive atea divesity Po IEEE 8th Vehiua Tehoogy Cofeee (VTC4-Fa) Sept 4