DSP ALGORITHM AND SYSTEM DESIGN FOR UWB COMMUNICATION SYSTEMS

Transcription

1 DSP AGOTH AD SYST DSG FO UWB COUCATO SYSTS YAG U (B..(Hos.), TU) A THSS SUBTTD FO TH DG OF AST OF GG DPATT OF CTCA & COPUT GG ATOA UVSTY OF SGAPO 6

2 ACKOWDGT would lke to exress my utmost arecato to my suervsors, Dr. Zhe Yuaj ad Prof. Har Krsha Gar, for be so uderstad, helful ad ecoura at all tmes rouh my research ad study atoal Uversty of Saore ad sttute of croelectrocs. am esecally rateful for e valuable udace ad costructve suestos offered by Dr. Zhe rouhout e develomet of s dssertato. would also lke to ak my freds, r. Cao zhe, ss Ya Jaa, r. Cao u, r. To Ya, ss Zhou Qaoer, ss We Xaoqa ad ss u aomao, for er kdess ad suortve work. ay aks to my famly, for always be ere for me, wheever ad wherever. astly also wsh to exted my arecato to all e oers who have, oe way or aoer, heled mak s dssertato a very reward oe. t has bee a leasure work toeer.

3 TAB OF COTTS ACKOWDGT... TAB OF COTTS... SUAY... V ST OF FGUS... V ST OF ABBVATOS... V ST OF ABBVATOS... V ST OF SYBOS... X TODUCTO.... Backroud.... Scoe of e Thess Orazato of e Thess... TATU VW.... & B-OFD.... ake ecever... 3 SYST OD & CV DSG Pulse-sha & odulato ulta Chael odel... 7

4 3.3 Bake ecever Structure PFOAC AAYSS Correlato ecevers S Crtero & Weer Soluto S Aalyss B xresso sadjustmet SUATO SUTS Theoretcal versus Smulated B ffect of µ o B Aroxmato B Comarso w Oer ake Structures COCUSO Cocluso emarks Future Works FCS ST OF PUBCATOS... 7

5 SUAY Ultra-Wdebad (UWB) commucato s recozed as oe of e most roms techoloes for ext eerato Wreless Persoal Area etwork (WPA) sce t has e otetal to rovde a low comlexty, low cost, low ower cosumto, ad hh data rate coectvty commucato systems. t reles o trasmsso of ultra-short ( aosecod scale) ulses ad avods us susodal carrers or termedate frequecy (F) rocess. Oe of e most sfcat features of UWB commucato s ts fe multa resolvablty. To maxmally exlot e chael dversty, a ake recever s usually emloyed to effectvely cature e multa eery. Covetoal ake recevers requre chael formato, clud e multa delay ad atteuato, to be rovded before comb e multa eery. However e chael formato s ukow to e recever ad dffcult to estmate ractcal UWB trasmsso systems. s ess, a ovel bld ake (Bake) structure s roosed for hh data rate low ower cosumto UWB commucato systems. The word bld here does ot mly at tra sequece ca be totally elmated, but refers to e fact at e chael formato s ot eeded for e ake system to erform effectvely. oer words, t avods e estmato of multa chael whch must be rovded for covetoal ake recever systems. The trascever comlexty s furer reduced by us Aalo-to- Dtal Coverter (ADC) work at sub-yqust saml rate. The closed form bt error rate (B) erformace aalyss s rovded as well. xtesve smulatos have bee carred out whch verfed e eoretcal aalyss. V

6 ST OF FGUS Fure. Frequecy & eery comarso for commucato systems Fure. FCC reulated sectral mask for UWB door commucato systems... 4 Fure.3 Oerato dstace ad data rate of major wreless stadards... 5 Fure.4 Comarso of UWB ad covetoal B trascever archtectures... 6 Fure. The B-OFD frequecy bad la Fure. A tycal trascever archtecture for a B-OFD system... 4 Fure.3 Waveforms for dervatves of Gaussa moocycle Fure.4 -UWB modulatos... 9 Fure.5 A eeral ake recever structure... Fure 3. Tycal Cs for UWB door chaels Fure 3. Bake recever archtecture Fure 5. Ta weht Fure 5. Ta weht dfferece ad ts hstoram Fure 5.3 Theoretcal versus smulated B for C-C Fure 5.4 ffect of µ o B aroxmato... 6 Fure 5.5 B erformace for C Fure 5.6 B erformace for C Fure 5.7 B erformace for C Fure 5.8 B erformace for C V

7 ST OF ABBVATOS A-STA ADC Aake ASC AWG B BPSK Bake CFJ CFO C C CS DC DS P FAS FCC FPGA FTT Aecy of Scece, Techoloy ad esearch Aalo-to-Dtal Coverter All ake Alcato-Secfc terated Crcut Addtve Whte Gaussa ose Bt rror ate Bary Phase Shft Key Bld ake Carrer Frequecy Jtter Carrer Frequecy Offset Chael mulse esose Chael odel Chael State formato Drect Curret Drect Sequece ffectve sotroc adated Power lectromaetc Federal Avato System Federal Commucato Commsso Feld Prorammable Gate Array Fast Fourer Trasform V

8 GPS F FTT S S PD P A B-OFD B-UWB BOA F FP S C S B OFD PA PDP PP Pake Global Posto System termedate Frequecy verse Fast Fourer Trasform sttute of croelectrocs mulse ado ter Symbol terferece east ea Square ow Probablty of Detecto ow Probablty of terceto ult-user Access ult-bad Orooal Frequecy Dvso ultlex ult-bad Ultra-Wdebad ult-bad OFD Allace atched Flter atched Frot-d Processor mum ea Square rror axmum ato Comb ea Square rror arrowbad Orooal Frequecy Dvso ultlex Pulse Amltude odulato Power Delay Profle Pulse Posto odulato Partal ake V

9 PT PSD &O F S S-V S Sake TD TFC TFK U- UWB WA WPA Pulse eetto Tme Power Sectral Desty eort & Order ado Frequecy oot ea Square Saleh-Valezuela Sal to ose ato Selectve ake Taed Delay e Tme Frequecy Code Tme Frequecy Kerel Ulcesed atoal formato frastructure Ultra-Wdebad Wreless ocal Area etwork Wreless Persoal Area etwork V

10 ST OF SYBOS A C J K Μ X m W A factor to ormalze e ulse eery Chael Caacty S cost fucto Total ta umber a brach Total brach umber Total umber of multa a chael sadjustmet Chael lo-ormal shadow coeffcet The m multa comoet a chael Chael Badwd ( t) d order Gaussa dervatve waveform m Gaussa ulse vector based o real chael tm l, k Gaussa ulse vector based o recever saml tm h ( t) Chael mulse resose r ( t) eceved sal r ( t) eceved sal for symbol s ( t) Trasmtted sal s Vector of sal after correlato w ( t) ose sal X

11 w, ose for l k k ta of l brach after correlato oerato w Vector of ose mxed w sal after correlato w Vector of ure ose after correlato K ( t) P ( f ) order Gaussa dervatve waveform tme doma order Gaussa dervatve waveform frequecy doma b Costellato for PA/Trasmtted symbol bˆ stmated symbol b Vector of tra sequece TH c User-secfc TH code for mulse c, Weht for l k k ta of l brach l k c, c c o Weht for k ta of l brach for symbol dur tra hase Ta weht vector Otmum ta weht vector o c otmum ta weht S c S ta weht d Costellato for PP e rror sal for symbol durato tra hase S e S error v, ut of e l k k ta e l brach l k v, ut of e k ta e l brach for symbol X

12 v y Decso sal for Ta ut vector symbol b Bt eery Pulse eery P P detty matrx P P b umber of fers a ake umber of fers a Sake umber of fers a Pake c umber of chs each frame f umber of relcas each trasmtted symbol Oe sde ower sectrum desty of AWG P b Bt error rate (B) Q evector matrx Ta ut autocorrelato matrx ( ) Pulse correlato fucto ( ) S Delay sectrum h T c Ch durato T d axmum excess delay of e chael T mulse durato T r Pulse reetto tme T s Symbol durato X

13 T l Chael tme delay of e l cluster σ Stadard devato of a Gaussa radom varable σ e Varace of S error σ w l,k Varace of ose after correlato γ φ S rato Process a µ Adatato ste sze dur tra hase m Chael atteuato of e Pulse osto offset PP m multa comoet k,l Chael atteuato of e k multa e l cluster m Vector of chael atteuato m Chael delay of e k,l Chael delay of e m multa comoet k multa e l cluster l ecever saml terval of l brach l,k ecever saml tme of e k ta e l brach m Vector of Chael delay lk Vector of recever saml tme S Chael S delay sread Λ Λ S Delay betwee cosecutve Bake brach Cluster arrval rate of chael multa Daoal eevalue matrx X

14 ς evalue λ ay arrval rate of chael multa a cluster λ eevalue of autocorrelato matrx of ut data Successfully collected chael eery [ ] xectato oerato δ ( ) Drac delta fucto Q ( ) Comlemetary cumulatve dstrbuto fucto tr ( ) atrx trace oerato Covoluto oerato X

15 CHAPT : TODUCTO TODUCTO Ths chater ves a bref troducto of UWB commucato systems. UWB techoloy has bee used for more a a cetury. However t attracts real atteto bo dustry ad academy oly after e Federal Commucato Commsso (FCC) released a hue ew badwd of GHz for t. UWB alcatos clude, but ot lmt to, Wreless Persoal Area etworks (WPAs), sesor etworks, ma systems, vehcular radar systems, etc. The scoe ad orazato of e whole ess are also reseted s chater.

16 CHAPT : TODUCTO. Backroud Scetsts ad eeers have kow about UWB sals sce Gulelmo arco veted rado commucatos utlz eormous badwd as formato was coveyed by sark-a devces more a a cetury ao. However e sals were more dffcult to cotrol or detect a arrowbad (B, sle-frequecy) sals at at tme. oder UWB techoloy came to e cture sce 96s, whe e troducto of UWB mulse radar systems was motvated by e hh sestvty to scatters ad low ower cosumto alcatos []-[3]. Commercally, e early UWB vestato was larely uder e aes of e U. S. Deartmet of Defese at adoted wdebad sals rmarly for very accurate localzato ad ma e cotext of secure commucatos [4], [5]. Academcally, e UWB research ad develomet were larely oeered by Prof. Scholtz ad hs rou [6]-[9], [3], [8], [9], [3], focus maly o low-rate alcatos. UWB, as e ame suests, occues a very lare badwd for sal trasmsso whle e emsso ower s well below covetoal arrowbad or wdebad systems. Fure. below llustrates s cocet. UWB ulses sread eery over severalahertz rae of frequeces, as oosed to tradtoal arrowbad, whch covers a lmted bad of about 3 klohertz. Cellular hoes oerate e wdebad, whch covers about 5 meahertz.

17 CHAPT : TODUCTO arrowbad, 3 klohertz ery Wdebad, 5 meahertz Ultra-wdebad, several ahertz Frequecy Fure. Frequecy & eery comarso for commucato systems. The defto of UWB evolves w tme. The rule mak of UWB was oeed by FCC 998. The result Frst eort ad Order (&O) at ermtted deloymet of UWB devces was aouced o 4 February ad released Arl [], whch uleashed a very lare badwd of GHz to UWB trasmssos. Three tyes of UWB systems are defed s &O: ma systems, commucato ad measuremet systems, ad vehcular radar systems. Secfcally, UWB characterzes trasmsso systems w stataeous sectral occuato excess of 5 Hz or a fractoal badwd of more a %. The badwd ad sectral mask for door commucato systems assed by FCC s llustrated Fure.. t ca be see at e FCC reulated ower levels are very low (below -4.3 dbm), whch allows UWB techoloy to coexst w leacy servces such as 8.a wreless local area etwork (WA), radar systems, etc., as well as 3

18 CHAPT : TODUCTO overlay w sestve mltary ad cvla servces adjacet bads such as lobal osto system (GPS) ad federal avato system (FAS). Cellular hoes, for examle, trasmt u to 3 dbm, whch s equvalet to 7 hher ower sectral desty (PSD) a UWB trasmtters are ermtted []. Curretly e 8.5 Work Grou s utt efforts to stadardze UWB wreless rados for door multmeda trasmssos UWB P msso evel dbm GPS Bad.96.6 door mt Part 5 mt Frequecy GHz Fure. FCC reulated sectral mask for UWB door commucato systems. Based o e FCC reulato, UWB s mostly sutable for e short-rae hh-seed 4

19 CHAPT : TODUCTO alcatos amo oer wreless systems, as ca be see Fure.3. From Shao s eory [], ( S) C.44 W lo, (.) where C stadards for e chael caacty bts er secod, W reresets e chael badwd hertz ad S s e sal to ose rato, e chael trasmsso rate rows learly w chael badwd but oly loarmcally w S. oer words, e chael caacty creases much faster as a fucto of badwd a ower. Thus UWB has e otetal to offer hh data rate ( several hudred meabt er secod, bs) to emer hh-seed-demad alcatos. Dstace Coverae m m km km cellular G/.5G Cellular 3G Cellular Fure.3 Oerato dstace ad data rate of major wreless stadards. 5

20 CHAPT : TODUCTO A comarso betwee a basc UWB trascever ad a covetoal arrowbad trascever s show Fure.4. The ma dfferece betwee em s e sav of e comlex suerheterodye structure a UWB trascever. The trasmsso of UWB waveforms ca be free of se-wave carrers (called carrer-less short ulse techque [3]) ad do ot requre ay F rocess because ey ca oerate e basebad. Data ut odulator PA A F Flter BPF PF Demodulator Data Outut F F F (a) Tycal arrowbad trascever archtecture Data ut odulator F Flter A F Flter PF Demodulator Pulse Geerator PF Pulse Geerator PF (b) Tycal UWB trascever archtecture Fure.4 Comarso of UWB ad covetoal B trascever archtectures. To characterze e UWB roaato chael, may resoses have bee receved to e Call for Cotrbutos o UWB Chael odel [4]. Cosder varous roosals at otmally chose e resectve model arameters (such as mea excess delay, root mea square (S) delay, mea umber of sfcat as etc) to best ft e observed data, e 8.5.3a chael model task rou has adoted a modfed verso of e Saleh-Valezuela (S-V) model for door chaels [5]. The chael measuremets 6

21 CHAPT : TODUCTO showed a cluster of e multa arrvals whch s best catured by e S-V model. ore detals o e chael model wll be dscussed chater 3. Bascally, e very wde badwd of e trasmtted ulse allows fe resoluto of e multa comoets. Ths has bo ros ad cos. Fe delay resoluto mles e otetal for sfcat dversty as due to e lare umber of avalable as. However, e total receved eery s dstrbuted over a lare umber of as, whch meas e recever must be caable of ck u ad comb e multa eery a roer way. ormally a ake recever s emloyed for s job. summary, occuy hue badwd by trasmtt ultra short ( aosecod scale) formato-bar ulses, UWB rado has uque advataes at have lo bee arecated by e radar ad commucatos commutes: The wde badwd ad hh tme resoluto ablty of UWB sals eerally make em more robust to multa terferece ad chael fad; A drect alcato of e Shao's caacty eorem to a addtve whte Gaussa ose (AWG) chael shows at UWB systems offer a otetally hh data rate trasmsso caablty w caacty creas learly w badwd; The low trasmsso ower of e UWB sals traslates to a F sature w a low robablty of terceto ad detecto (P/PD), ad also roduces mmal terferece to roxmty systems ad mmal F heal hazards; The fe tme resoluto of UWB systems makes em ood caddates for 7

22 CHAPT : TODUCTO locato ad ra alcatos (w recso at e cetmeter level); ad ore mortatly, UWB systems have low system comlexty ad low cost, sce ey are essetally basebad systems ad ca be made early "all-dtal", w mmal F or mcrowave electrocs. 8

23 CHAPT : TODUCTO. Scoe of e Thess The whole roject s fuded ad suorted by e Aecy of Scece, Techoloy ad esearch (A-STA) UWB esearch roram, jotly collaborated betwee sttute of croelectrocs () of Saore ad atoal Uversty of Saore (US). The taret of s ess s to develo a ractcal ad effectve alorm for low comlexty recevers of mulse ado () UWB commucato systems. The eoretcal erformace aalyss s carred out detals w a closed form bt error rate (B) exresso derved. xtesve smulatos have bee doe to verfy e correctess of e dervato. The B erformace of e roosed archtecture s also comared w covetoal ake recevers to demostrate ts feasblty of mlemetatos. 9

24 CHAPT : TODUCTO.3 Orazato of e Thess chater, e backroud of UWB commucato systems s brefly troduced. Chater resets some relevat works whch have bee doe so far s area. Two ormal UWB trasmsso schemes, ad ult-bad Orooal Frequecy Dvso ultlex (B-OFD), are descrbed. Commo ake recever structure s also ve s chater. The ovel bld ake (Bake) alorm s roosed chater 3 w detaled exlaatos o e sal model, chael model ad recever structure, followed by -de erformace aalyss chater 4. Chater 5 shows e smulato results whch have verfed e eoretcal dervato, as well as comared e erformace of e roosed alorm ad covetoal meods. Cocluso remarks are ve chater 6 w suested future work.

25 CHAPT : TATU VW TATU VW Ths chater revews some of e related lterature works. Drect Sequece (DS) ad ult-bad Orooal Frequecy Dvso ultlex (B-OFD) are e two mostly emloyed UWB trasmsso techques. mulse ado () s e smlest ad most frequetly adoted form of DS-UWB, erefore t s e focus of s vestato. B-OFD has a major advatae flexble sectrum selecto, but e trascever structure s comlcated due to e resece of multle frequeces., o e oer had, oerates e basebad ad does ot requre ay F rocess, whch results much smlfed recever structure. Therefore scheme s adoted s ess. The mulse shae ad sal modulatos of -UWB are e revewed. The secod order dervatve Gaussa moocycle ad BPSK are chose our system. Commo ake recever structure s also revewed s chater. ake recevers are used to cature multa dsersed chael eery wreless commucato systems. All ake (Aake), Selectve ake (Sake) ad Partal ake (Pake) are commoly kow ake tyes. Performace ad comlexty are trade-offs cosder us dfferet tyes of ake structures. Chael state formato (CS) has to be rovded for ake recevers to work effectvely, but UWB chaels are very dffcult ad costly to be estmated real tme. Ths s why our Bake structure s roosed ad develoed.

26 CHAPT : TATU VW. & B-OFD There are dfferet ways of utlz e 7.5 GHz badwd assed by FCC UWB systems. O oe had, e sal ca be shaed so at ts eveloe exads e full frequecy sectrum. Ths s called -UWB [6]-[8], [5], also kow as ulsed UWB, ad t s oe of e smlest forms of DS-UWB. O e oer had, e hue bad ca be dvded to multle subbads, ad e sal ca be shaed so at t occues a subbad of 5-8 Hz. Ths s called multbad UWB (B-UWB) [6]-[8]. W e formato of e ult-bad OFD Allace (BOA) Jue 3, e OFD techque for each subbad was added to e tal multbad aroach to mrove e erformace due to OFD s heret robustess to multa [9], []. The B-OFD aroach allows for adatato to dfferet reulatory evromets by dyamcally tur off subbads ad dvdual OFD toes to comly w local rules of oerato o allocated sectrum. t also facltates future scalablty of e sectrum use. The bad la for e BOA roosal s show Fure.. The avalable sectrum of 7.5 GHz s dvded to 4 subbads each of 58 Hz. Subbads are roued to fve local chaels. Chael, whch cotas e frst ree bads, s madatory for all UWB devces ad rados whle e oer rema chaels are otoal. There are u to four tme-frequecy codes (TFC) er chael, us allow for a total of coets w e curret BOA roosal. addto, e roosal also allows flexblty to avod chael whe ad f Ulcesed atoal formato frastructure (U-) terferece, such as from 8.a, s reset [].

27 CHAPT : TATU VW Power Fure. The B-OFD frequecy bad la. The formato trasmtted o each subbad s modulated us OFD. OFD techque dstrbutes e data over a lare umber of carrers at are saced aart at recse frequeces. Ths sac rovdes e orooalty roerty whch revets e demodulators from see frequeces oer a er ow. The beefts of OFD are hh-sectral effcecy, reslecy to F terferece, ad lower multa dstorto. Fure. shows a tycal trascever archtecture for a B-OFD system. ex ( jπf c t) (a) Trasmtter structure. 3

28 CHAPT : TATU VW cos( πf c t) s( πf c t) (b) ecever structure. Fure. A tycal trascever archtecture for a B-OFD system. The trasmtter ad recever archtecture for a B-OFD system are very smlar to ose covetoal wreless OFD systems. The ma dfferece s at e B-OFD system uses a tme-frequecy kerel (TFK) to secfy e ceter frequecy for e trasmsso of each OFD symbol []. Deste e above metoed advataes rovded by B-OFD scheme, ere are also roblems assocated w s aroach. Comlcated trascever archtecture s a major cocer. Frstly, to eerate all e subcarrer frequeces, frequecy syeszer must be bult whch esures at system ca swtch betwee e ceter frequeces extremely fast (w a few aosecods). Secodly, local oscllators at e UWB trasmtter ad recever ed are roe to msmatch ad ve rse to multle carrer frequecy offset/jtter (CFO/CFJ) []. Uless comesated for, CFO/CFJ s kow to derade e system erformace severely. Thus B-OFD eeds for CFO sestvty aalyss, low comlexty CFO estmators, ad er-subcarrer based chael estmato modules. astly, e addtoal FFT/FFT modules e trascever systems add about 5% of e dtal 4

29 CHAPT : TATU VW basebad rocess comlexty, whch also results more ower cosumto. scheme, o e oer had, avods us susodal carrers or ay F rocess so at t reatly reduces e trascever comlexty ad overall ower cosumto. Therefore t s adoted our system w ts smler trascever archtecture. works by trasmtt basebad ulses of very short durato, tycally o e order of aosecod or sub-aosecod, ereby sread e eery of e rado sal very ly from ear DC to a few ahertzes [8]. The shae of e ulse secfes e frequecy sectrum of e trasmtted sal ad well desed ulse shae allows maxmum emtted ower uder FCC frequecy mask. A varety of ulse shaes ad er corresod frequecy sectrums have bee roosed ad dscussed [3]-[8]. Amo em, e most frequetly emloyed ulse shaes are e dervatves of Gaussa fucto. The tme doma ad frequecy doma reresetatos of e order Gaussa dervatve ( t) ad ( f ) P are ve (.) ad (.) [8], resectvely, ( 3 t ) /! / / 4k k / 4k k ( ) t / / t 4 σ σ π e, (.) k ( k )! k! ( )!! where ( )!! ( ) ( 3) K 3 fucto whch s assocated w e ulse durato., σ s e stadard devato of e Gaussa P ( f ) 4 ( ) ( π ) / ( σ ) / / 4 π f σ f e. (.)!! ( ) where reresets e maary art of a comlex umber. 5

30 CHAPT : TATU VW Fure.3 shows e waveforms of st order to 4 order dervatve Gaussa moocycles ad er corresod ower sectrums. t ca be see at creas e dervatve order of e Gaussa moocycle has e effect of shft e frequecy sectrum to occuy a hher frequecy rae so at t ca better ft FCC frequecy mask. However hher order dervatve moocycle s ot feasble from crcut ersectve as well as maematcal tractablty. s ess, a commoly used d order Gaussa moocycle s emloyed w ulse durato of T. 5 s. The mulse ca be wrtte as, a smlfed verso from (.): t σ t ( t) A 3.5 e, (.3) σ where σ s related to e ulse wd by T 7σ w T be e durato of a sle ulse whch covers 99.99% of e total ulse eery, ad A s a factor to ormalze e ulse eery to oe. 6

31 CHAPT : TATU VW st order d order 3rd order 4 order Am ltude Tme (s) (a) Tme doma dervatves of Gaussa waveform. Power Sectrum (db) st order d order 3rd order 4 order Frequecy (GHz) (b) PSD of dervatves of Gaussa waveform. Fure.3 Waveforms for dervatves of Gaussa moocycle. 7

32 CHAPT : TATU VW Three tyes of modulatos are usually emloyed -UWB systems. They are ulse osto modulato (PP), ulse amltude modulato (PA), ad bary hase shft key (BPSK) or bhase modulato [6]. PP s based o e rcle of ecod formato w two or more ostos tme, referred to e omal ulse osto, as show Fure.4 (a). The rah shows - PP, where oe bt s ecoded oe mulse. Addtoal ostos ca be used to rovde more bts er symbol. The tme delay betwee ostos s tycally a fracto of a aosecod, whle e tme delay betwee omal ostos s called ulse reetto tme (PT), T r e rah, ad t s much loer to avod terferece betwee mulses. PP was mostly adoted e early develomet of UWB rados whe eat ultra short ulses were dffcult to mlemet []. PA s based o e rcle of ecod formato w e amltude of e mulses, as show Fure.4 (b). The rah shows -PA, ad more bts ca be rovded er symbol by us more levels of dfferet amltudes. BPSK or bhase modulato, formato s ecoded w e olarty of e mulses, as ca be see Fure.4 (c). a more eeral sese, BPSK ca also be rearded as a secal case of a -PA. Oer modulato techques have also bee exlored [9], [3] ad ey are bascally derved or combed from e above metoed ree basc tyes. 8

33 CHAPT : TATU VW.5 "" "".5 "" "".5 "" "" T PP Tr -.5 PA T - BPSK T (a) PP (b) PA (c) BPSK Fure.4 -UWB modulatos. -UWB trasmts formato by sed extremely short ulses w low duty cycle, so e trasmtted ower ca be small. t requres o carrer modulato ad F ower amlfer whch results smle archtecture. ts fe tme resoluto roerty makes t robust to multa fad. To effectvely exlore e chael dversty, a ake recever s usually emloyed at e recever ed. 9

34 CHAPT : TATU VW. ake ecever a tycal wreless evromet, a electromaetc () wave traverses a multtude of as from e trasmtter to e recever, whose les are uequal eeral due to deflectos, reflectos ad scatters. The comoste sal at recever sde s e suerosto of tme shfted, amltude scaled, olarzato rotated ad hase altered coes of e trasmtted sal, ad t s called multa dstorted. The exact umber of multas deeds o e eometry of e evromet, e locato of e trascevers, e lacemet of e obstructve ad o-obstructve objects, ad e roertes of materals used costructo. eeral e chael mulse resose (C) of a multa fad chael ca be modeled as: h ( t) mδ ( t m ) m, (.4) where m ad m rereset e chael atteuato ad e roaato delay of e multa comoet ad ey are referred to as chael state formato (CS). δ ( ) s e Drac delta fucto. reresets e total umber of multa comoets ad m usually. The chael amltude resose s ormalzed such at: m m. (.5) et s ( t) rereset e trasmtted sal, e e receved sal after ass rouh e multa chael s: ( t) s( t) h( t) w( t) r

35 CHAPT : TATU VW m ( t ) w( t) s, (.6) m m where w ( t) s AWG w two sde ower desty sal eery s dsersed multa comoets.. Ths exresso dcates at e ( k ) Tf kt f dt T f y k s ˆ ) ( t ktf ( k ) Tf kt f dt T f y k γˆ r( t) s ˆ ) ( t ktf γˆ â k ( k ) Tf kt f dt T f ( ) y k s( t kt f ˆ ) γˆ Fure.5 A eeral ake recever structure. A eeral ake structure s show Fure.5. t cossts of multle fers (correlators) where each fer ca extract oe of e multa comoets rovded by e chael. The oututs of all e fers are arorately wehted ad combed to rovde e multa dversty. The equvalet matched flter (F) verso of e recever volves a matched frot-ed rocessor (FP) (matched oly to e trasmtted waveform) followed by a taed delay le (TD) ad a comber [3]. The FP resolves multa comoets whose delays dffer by at least oe ch durato, T c,

36 CHAPT : TATU VW aroxmately equal to e verse of e sread badwd. The outut of FP s assed rouh a TD fler w tas, whch are combed w maxmum rato comb (C) for e best ossble erformace. The deal S at e outut of ake recever s ve by [3]: γ m, (.7) b / m where s e bt eery of e trasmtted sal. W, (.7) recovers e b m m larest ossble S of e receved sal. The B erformace s show to be [3]: ( S ) Q( γ ) P b Q, (.8) where Q ( ) s e comlemetary cumulatve dstrbuto fucto. A deal ake s referred to as all ake (Aake), whch dcates e recever w ulmted resources ad stat adatablty so at t ca resolve all e multa comoets. To acheve s, t requres T d Tc correlators/tas, where d / T s e maxmum excess delay. There are hudreds of multa comoets a tycal UWB chael. Therefore Aake s urealstc due to e ower cosumto, des comlexty ad chael estmato [3]. t ca oly serve as a bechmark at rovdes a uer lmt to e achevable erformace. Selectve ake (Sake) ad artal ake (Pake) are two commoly emloyed comlexty-reduced ake structures whch rocess oly a subset of avalable multa

37 CHAPT : TATU VW comoets. Sake selects e b best (w larest stataeous S) out of total multa comoets ad combes em us C [33]-[35], whle Pake has fers at tract e frst as arrved at e recever [36], [44]. Sake requres fast adatablty, kowlede of stataeous values of all multas ad effcet chael estmato, ad s erefore more comlex a Pake. Systems emloy varous tyes of ake structures ad er erformaces have bee reorted [], [33]-[46]. However ake mlemetato ca be effectve oly whe e CS s avalable or ca be roerly estmated at e recever. Ths oses a major roblem UWB commucatos, sce eve f we ot to utlze oly a few (e.. fve stroest out of hudreds of) as, accurate estmato of e fve stroest chael as ad er corresod delays s requred. Chael estmato has lo bee a challee UWB systems. mulse resose estmator for UWB chaels has bee reseted [3], [47]-[5]. Comutatoal comlexty of e chael estmator [3] ad [47] creases w creas umber of multa comoets, ad s uaffordable for realstc UWB chaels. oreover, chael estmators requre e ADC to work at over-saml rate to et e correct estmato of e tme delays. W e UWB sub-aosecod-wd mulse, e ADC saml rate s e formdable rae of over GHz [] whch s very costly. s ess, a low comlexty bld ake (Bake) structure s roosed, whch does ot requre ay CS yet rovdes accetable B erformace. The saml rate requred for e recever ADC s also reatly reduced. 3

38 CHAPT 3: SYST OD & CV DSG 3 SYST OD & CV DSG The roosed system model ad recever archtecture are reset s chater. Pulse sha ad modulato of our system s dscussed. BPSK s adoted for e sake of maematcal smlfcato a multa door chael models are emloyed ad e lare umber of multas s observed. The Bake recever structure s e roosed. t cossts of mult braches of ake fers ad each brach s samled at dfferet rates. The recever model arameters are chose based o chael delay rofles. 4

39 CHAPT 3: SYST OD & CV DSG 3. Pulse-sha & odulato As dscussed chater, e d order dervatve of a Gaussa ulse, ( t) ve (.3), s adoted our system des sce t s oe of e mostly used mulses -UWB ad t ca be easly eerated for smulato. However e alorm reseted s ess s also alcable to oer ulse shaes. eeral, e trasmtted waveform of a -UWB system s ve by []: TH s( t) b / t T c T d f f c, (3.) / f where s e ulse eery at e trasmtter ed. To crease S at e recever ed, each symbol s rereseted by f relcas, each relca trasmtted er frame of durato T f >> T. T f s also kows as PT. For mult-user access (A), TH c reresets e usersecfc tme ho (TH) code. very frame s dvded to c chs w each of durato T c, ad TH c T corresods to a tme shft dur e c frame. W [, ] m k deot e -ary formato symbol trasmtted dur k symbol durato, (3.) subsumes PP ad PA. Whe d m ad b, (3.) models -ary k k k PP for UWB trasmssos, ad d k s e ulse osto offset. Whe bk mk ad d k, (3.) descrbes -ary PA. TH To smlfy e aalyss s ess, sle user evromet s cosdered ( c ) ad BPSK ( d ) modulato s emloyed our system. oreover, each symbol s / f 5

40 CHAPT 3: SYST OD & CV DSG trasmtted by oe ulse to crease e trasmsso rate ( ). The e trasmtted sequece s much smlfed from (3.) ad ca be wrtte as: f where { ±} ( t T ) s ( t) b, (3.) b s e bary data trasmtted ad s s T reresets e bt durato. The quatty Ts φ s called e rocess a ad should be much reater a to T mmze e ter symbol terferece (S). At e same tme, trasmsso rate decreases w creas φ. Thus comromse must be made betwee erformace ad caacty. Alouh e erformace aalyss s ess s carred out us BPSK modulato, e results ca be easly exteded to PP or oer modulato schemes. 6

41 CHAPT 3: SYST OD & CV DSG 3. ulta Chael odel Sce most of e evsoed UWB commercal alcatos wll be door commucatos, UWB door chaels are cosdered s ess. The 8.5.3a Task Grou roosed a door chael model whch s a modfed verso of e well kow Saleh-Valezuela (S-V) model ovember [4]. S-V door chael model was establshed 987 based o measuremets utlz low ower ultra-short ulses of wd s ad ceter frequecy.5 GHz a medum sze, two-story offce buld [5]. ulta comoets arrve at e recever rous (clusters) s model. ultle rays are observed w each cluster. The cluster ad ray arrvals are bo Posso dstrbuted. ayleh dstrbuto s assumed for e multa a matude w a exoetally decay ower rofle. The cluster heomeo has bee exermetally cofrmed characterz UWB door chaels. Thus UWB door chael models are derved from S-V model w a coule of slht modfcatos. A loormal dstrbuto raer a a ayleh dstrbuto for e multa a s adoted sce t fts e measuremet data better [4]. addto, deedet fad s assumed for each cluster as well as each ray w e cluster. The multa chael model s erefore exressed as [4]: h K ( t) X δ ( t T ) l k, (3.3) k, l l k, l where X s e lo-ormal shadow, k, l s e multa a coeffcet of e k multa of e l cluster, T l s e delay of e l cluster ad k, l s e delay of k 7

42 CHAPT 3: SYST OD & CV DSG multa comoet relatve to e l cluster arrval tme. Cluster ad ray arrvals are deedet Posso dstrbuted w rate Λ ad λ, resectvely, ad λ > Λ. The total umber of as s defed as e umber of multa arrvals w exected ower w db from at of e stroest arrval a. The detaled UWB multa chael characterstcs ad arameters for chael model to chael model 4 (C-C4) are rovded [4]. Tycal realzatos of e chael mulse resose eerated for C-C4 are show Fure 3.. t ca be see at e multa comoets for each tye of e chael are eormous. For C3 ad C4, ere are eve more multas reset ad e dsersed chael le s also loer a at for C ad C. Whe do erformace aalyss chater 4, e smlfed C model ve (.4) s adoted stead of (3.3), ad e chael s vewed as cosst of dscrete tme mulse resoses. 8

43 CHAPT 3: SYST OD & CV DSG Amltude Tme (s) Amltude Tme (s) (a) C (b) C.5.. Amltude Amltude Tme (s) Tme (s) (c) C3 (4) C4 Fure 3. Tycal Cs for UWB door chaels. 9

44 CHAPT 3: SYST OD & CV DSG 3.3 Bake ecever Structure ( t) v,k v, K v, z z c,k c, K z c, s( t) h( t) w( t) r( t) ( t) v,k v, K v, z z z c,k c, K c, d ( t) v, v K, K v, z z z c, K c, K c, y e bˆ Fure 3. Bake recever archtecture. The roosed Bake recever structure s show Fure 3.. t cossts of braches w K tas each brach. The receved sal r ( t) s delayed by a small tme each cosecutve brach to esure at e recever does ot samle at e same tme stace. After at e sal s correlated w a locally eerated ulse ( t) ad e samled at dfferet rates every brach. ach brach reresets a Bake brach w a uque saml terval {,,, } saml rate, < < K <, where e fastest l K s well below e yqust rate. The samled data are roerly wehted by e ta coeffcets {, c,, c, c, c, K, c, K c } c,,, K,,, K,, K K ad summed u to form e decso sal y. The decso rule s: 3

45 CHAPT 3: SYST OD & CV DSG Dur e tra hase, e TD coeffcet set { } least mea square (S) meod [5]: ˆ f y > b. (3.4) f y < c, s udated adatvely us e l k e d y, (3.5) c c µ e v, (3.6) l, k l, k l, k where d reresets e desred sal, e reresets e error, l k c, reresets e adatato value of ta c,, l {,, K, }, l k k {,, K, K}, ad l k v, s ut of e k ta e After { } l k l brach for symbol. c, covere to er otmum values, e alorm wll exam e atter of e ta values. There are certa tas at do ot samle at ay correct tme stace of e multa, ad ese ta values covere to very small umbers ear zero. Thus ey ca be dscarded sce clud em oly adds e ose comoet ad cosumes more hardware. O e oer had, whe e ta haes to samle at e correct tme stace of ay multa, e ta value wll covere to e chael atteuato value corresod to at delay tme, ad e successfully samled eery wll be couted to e decso sal. ore detals o s wll be revealed e ext chaters. From e roosed structure ad alorm, t ca be calculated at e total saml terval for each receved data bt s {,,, } K. The choce of, K, K ad are closely related to e chael rofle. eferr to e ower 3

46 CHAPT 3: SYST OD & CV DSG delay rofle (PDP) of C-C4, t s foud at e chael multa comoets ad eery reduce exoetally w tme delay [4]. Thus t makes sese to samle at a reduced rate for cosecutve braches,.e., < < K <. At e same tme, e total saml terval should cover most of e dsersed chael eery. The S delay sread, defed as e secod cetered momet of e delay sectrum of a stochastc chael, s commoly used to descrbe a dsersed chael PSD: σ ( ) S, (3.7) where S S h h ( ) ( ) d d ad ( ) S s e delay sectrum. The S delay sread for h C-C4 s 5 s, 8 s, 4 s, ad 6 s [4], resectvely. As a suesto, t may be set:,,, K,.< ξ <. 5, (3.8) ξ ad ( ) ( K ) ξ S,.5 < ξ < 4. (3.9) Accord to our vestato ad smulato, e above suested rae of ξ ad ξ ca acheve ood B erformace by catur eouh multa eery. 3

47 CHAPT 4: PFOAC AAYSS 4 PFOAC AAYSS Thorouh erformace aalyss of e roosed recever s carred out s chater. Frstly correlato recevers are dscussed because ake structure cossts of a umber of correlators. To determe e otmum ta wehts, mum ea Square rror (S) crtero s adoted ad Weer soluto s derved based o s. However, e ta wehts obtaed ractcally are adated us S techque, where ere s a addtoal error term assocated w e adatato ste sze. The outut S s e derved cosder e S error, from whch e fal B exresso s obtaed. 33

48 CHAPT 4: PFOAC AAYSS 4. Correlato ecevers The ake structure s used to roduce a wehted sum of e oututs from a set of correlato recevers. So e erformace aalyss bes w e sal ass rouh e correlato recevers. eferr to Fure 3., some vectors are defed whch wll aear s chater: Tra sequece: T b [ b bk b ] ; (4.) Chael atteuatos: ; (4.) m [ ] T K Chael delays: ; (4.3) m [ ] T K ecever saml tmes: T [,, K, K ], (4.4) lk where, l,k, k,k, reresets e saml tme of e brach; l, k K k ta e l Gaussa ulse vector based o real chael tm: ( t T ) ( t T ) ( t T ) T K ] ; (4.5) m [ s s s 34

49 CHAPT 4: PFOAC AAYSS Gaussa ulse vector based o recever saml tm: ( t T ) ( t T ) ( t T ) T ] ; (4.6) l, k [ s, s, K s, K Ta weht: T c [ c, c, K c, K c, c, K c, K K c, K ]. (4.7) From (.4), (.6) ad (3.), e receved sal r ( t) ca be exressed as: ( t) s( t) h( t) w( t) r b s m m m ( t T ) δ ( t ) w( t) ( t T ) w( t) b m s m. (4.8) m Due to e low duty cycle roerty of -UWB trasmssos, t s reasoable to assume at ere s o S reset. For smlfcato of aalyss, e waveform for detecto of e symbol ca be wrtte as: r ( t) b ( t T ) w( t) b T m w( t) m s m m m. (4.9) After e ulse correlator ad ADC saml, e k ta ut of e l brach s: v l, k Ts T l, k Ts l, k Ts T l, k Ts l, k r ( t) ( t T ) b s T m m l, k dt ( t T ) s l, k dt 35

50 CHAPT 4: PFOAC AAYSS ( t T ) Ts T l, k w t Ts s dt l, k l, k ( l, k m ) wl k, (4.) b l, k, where Ts T l, k ( ) ( t T ) ( t T )dt l, k m, (4.) Ts l, k s m s l, k ad w, s e addtve ose after correlato oerato. ts ower ca be calculated as: l k σ w ' [ w ] wl, k l, k l, k Ts T l, k w t s l k l, k Ts T l, k ( t T ) dt w( t' ) ( t' T ) T s Ts s dt', l, k l, k [ ] ( t T ) Ts T l, k w t Ts s dt l, k l, k ( t T ) Ts T l, k Ts s dt l, k l, k. (4.) Thus.e., w, s Gaussa dstrbuted w zero mea ad two sde ower desty l k, l, k w. Sce e ulse eery s ormalzed,.e., ( ),,, w l, k. t s obvous at ( ) l, k m whe l k m > T,, as e ulse durato of ( t) s 36

51 CHAPT 4: PFOAC AAYSS T. Assume ere are fers at correctly samle e multa comoets out of e K total fers, e (4.) ca be wrtte as: v wl, k b ( ) w whe l, k l, k whe l, k l, k m m < T > T, (4.3) K, s a subset of vector m where { },, rereset e correctly samled chael mulse resose. et rereset e successfully collected chael eery rato:, (4.4) e e mssed chael eery rato s. Sort v l, k order of ad costellate to form e ut ta vector: where: [ w ( ) w b ( ) w K b ( ) v b w b s w w K w K w ] T K, (4.5) [ ( ) ( ) K ( ) ] T s, (4.6) [ w w ] T w, (4.7) K w [ w w w ] T w. (4.8) K K K The e detecto sal after weht comb s, exressed vector form: 37

52 CHAPT 4: PFOAC AAYSS y c T v. (4.9) 38

53 CHAPT 4: PFOAC AAYSS 4. S Crtero & Weer Soluto To determe e otmum weht vector c o, S crtero s emloyed ad c o ca be exressed as: co ar m J, (4.) c where J [ d y ], (4.) reresets e mea square error (S) cost fucto. The well kow Weer soluto ves [5]: c o T ( [ vv ]) [ d v]. (4.) T To solve (4.), we exam [ vv ] ad [ d v] searately e follow. From (4.5), ad ote at sal ad ose (w zero mea) are ucorrelated: b T s w T T T [ vv ] [ b s w ] w K K w S K, (4.3) where 39

54 CHAPT 4: PFOAC AAYSS 4 O S, (4.4), (4.5) K K K, (4.6) ad P P deotes e P P detty matrx. Therefore, [ ] K T S vv. (4.7) The desred sal for e data bt s ve by: T f b dt t b d. (4.8) From (4.5) ad (4.8), [ ] K K s w w s v b b d, (4.9) where K deotes e colum vector w K zero elemets. Substtute (4.7) ad (4.9) to (4.): K K o s S c s S. (4.3) From (4.4), t s observed at S s a rak- symmetrc matrx. Us eevalue decomosto [5], t ca be wrtte as:

55 CHAPT 4: PFOAC AAYSS T S QΛ SQ, (4.3) where ( ) ( ) s e matrx cota all e eevectors of Q, (4.3) O ( ) Λ S S ad, (4.33) s a daoal matrx w equvalet eevalues of S : ς,,, K, (4.34) as e daoal elemets. ecall e matrx verso lemma [5]: ad let ( A BCD) A A B[ C DA B] DA, (4.35) A, B Q, C Λ S, T D Q, e: T S ( QΛ Q ) S T T [ Q Q] Q QΛ S. (4.36) quatos (4.37)-(4.39) below derve e exresso for S ste by ste: Λ T S Q Q ( ) ( ) ( ) O 4

56 CHAPT 4: PFOAC AAYSS 4 O O O. (4.37) T T S Q Q Q QΛ O O O O O

57 CHAPT 4: PFOAC AAYSS 43 O. (4.38) Substtute (4.5) ad (4.38) back to (4.36): Ι Ι Ι S O 4 O S 4. (4.39) To obta e otmum value of ta weht from (4.3), s S 4 S

58 CHAPT 4: PFOAC AAYSS 44 4 O 4 4 γ, (4.4)

59 CHAPT 4: PFOAC AAYSS where γ s e ut S defed as: γ, (4.4) Comar (4.3) ad (4.4), e otmum ta wehts ca be obtaed as: c o ( ) γ,, K,. (4.4),, K, K 45

60 CHAPT 4: PFOAC AAYSS 4.3 S Aalyss The otmum ta wehts obtaed Secto 4. are derved us Weer soluto. ractcal mlemetatos, e ta wehts are adated recursvely us S techque. Thus ere s a addtoal error term assocated w e adatato ste sze µ for each ta weht as follows: c c e, (4.43) S o S where e varace of e error s ve by [53]: σ σ µ J m e S e µλ, (4.44) whe e ta value coveres. The mea value of e error s zero whe e ta value coveres. Here Weer soluto s acheved [53]: J m s e mmum value of e cost fucto (4.) whe e otmum T o T [ vv ] c o J d m c, (4.45) ad λ s e eevalue assocated w e autocorrelato matrx of e ut data ve by (4.3). From (4.3), (4.5), (4.6), (4.3) ad (4.33), e eevalue of (4.3) ca be derved as:,, K, λ. (4.46),, K, K 46

61 CHAPT 4: PFOAC AAYSS 47 By substtut (4.3), (4.8), (4.3) ad (4.4) to (4.45), e mmum value of e cost fucto ca be calculated as: s S S s S K m T b J. [ ] s S s T [ ] [ ] T K K K K γ. (4.47) From (4.44), (4.46) ad (4.47), e varace of e S error term, for,,, K, ca be exressed as: m J e µ γ µ µλ µ σ. (4.48) Smlarly, for K,,, K, e S error term s:

62 CHAPT 4: PFOAC AAYSS 48 m J e µ γ µ µλ µ σ. (4.49) The decso sal, y, as show (4.9), ca be exressed as e sum of two terms: K S S K S v c v c v c y v c T. (4.5) From (4.5), (4.4), ad (4.43), S S w b e v c γ S S e b w w e b γ γ. (4.5) Smlarly, t ca be show: K S K S K S w e w e v c. (4.5) Substtut (4.5) ad (4.5) back to (4.5), e decso sal s show to be: K S S v c v c y K S S S w e e b w w e b γ γ

63 CHAPT 4: PFOAC AAYSS 49 K S S w e e b w b γ γ. (4.53) The frst term e above equato reresets e sal orto, whle e rest ree terms are e ose duced by e chael as well as S adatato rocess.

64 CHAPT 4: PFOAC AAYSS B xresso The erformace of e roosed recever s evaluated by e B t ca acheve. From (.8), e B s determed by e recever outut S. eferr to (4.53), e outut S ca be obtaed by tak e rato of e sal ower over e exected ose ower e decso sal: K S S o w e e b w b S γ γ. (4.54) Assume e S error s ucorrelated w e ose [5],.e., [ ] [ ] [ ] K j K w e w e j S j S K K,,,,,,. (4.55) The e deomator of (4.54) s smly e sum of e exectatos of e ree dvdual square terms, sce e ose ad S error bo have zero mea. The ree exected square terms are evaluated oe by oe e follow. γ γ w w

65 CHAPT 4: PFOAC AAYSS 5 [ ] γ σ γ w w γ. (4.56) e S e b σ. (4.57) Substtute (4.48) to (4.57): e b S µ γ µ. (4.58) [ ] [ ] K e e w K w e K S K S w e w e σ σ σ σ σ. (4.59) Substtut (4.48) ad (4.49) to (4.59), t ca be show: K w e K S µ γ µ µ γ µ. (4.6) The deomator of (4.54) s e sum of (4.56), (4.58) ad (4.6):

66 CHAPT 4: PFOAC AAYSS 5 K S S w e e b w γ K µ γ µ µ γ µ µ γ µ γ γ γ µγ γ γ µγ γ γ γ µ γ K. (4.6) Substtute (4.6) to (4.54), e outut S ca be exressed as: γ γ µγ γ γ µγ γ γ γ µ γ γ o K S γ µγ γ γ µγ γ γ γ µ K. (4.6)

67 CHAPT 4: PFOAC AAYSS f e ste sze µ s very small ad aroaches to, e frst term e deomator of (4.6) ca be ored ad e S term s much smlfed: S o γ. (4.63) γ Therefore e B ca be easly obtaed from e outut S as (.8): ( S ) Q( γ ) Pb Q o. (4.64) 53

68 CHAPT 4: PFOAC AAYSS 4.5 sadjustmet The msadjustmet of e cost fucto due to e S adatato s ve by [5]: ( ) µ T tr( [ vv ]) J Μ ex, (4.65) J where tr ( ) deotes e trace oerato o e matrx ad ( ) S. m J reresets e excess ex From (4.3), (4.4)-(4.6), tr T ( [ vv ]) tr( S ) tr( ) tr( ) K ( ) ( K ) K. (4.66) Substtut (4.66) to (4.65), e uer boud of e msadjustmet ca be show to be: µ K µ K Μ. (4.67) γ low ower alcatos (small ), e msadjustmet ca be cotrolled to be very small w small eouh adatato ste sze µ. 54

69 CHAPT 5: SUATO SUTS 5 SUATO SUTS s chater, extesve smulatos are carred out to verfy e eoretcal results derved chater 4 as well as to comare e erformace of e roosed Bake w oer reular ake structures. The smulato setu s as follows: e d order dervatve Gaussa moocycle as (.3) ad chael models C-C4 as 8.5.3a [4] are emloyed. BPSK modulato s adoted w e trasmsso rate at Hz. The ulse wd should be arrow eouh to mmze e S ad ft to e FCC sectrum, whle ulses w too arrow wd are dffcult to eerate mlemetato ad requre extremely hh saml rate. Cosder e tradeoff, e ulse wd s set to.5 s. Therefore e badwd of UWB sal s aroxmately 4 GHz. As s s a mulse rado scheme where o carrer s used, e oerat frequecy bad would be to 4 GHz. The emsso ower ca be adjusted to meet e FCC frequecy mask. ote Carlo realzatos w, ulses each tral are used for e B calculato. For C-C, 5 ake braches are used w 8 tas each brach as we have foud s sett ca acheve comettve erformace to oer ake structures ad e mrovemet s ot sfcat by add more braches or tas. eferr to secto 3.3 ad equatos (3.8) ad (3.9), e saml rates for every brach are set to.5 s,.65 s,.85 s,. s ad.4 s, resectvely; s set to be.65 s. For C3-C4, 6 ake braches are used w 8 tas each brach sce ese two chaels have more multa comoets a C-C. 55

70 CHAPT 5: SUATO SUTS 5. Theoretcal versus Smulated B S alorm s used for ta estmato. Fure 5. catures e weht ( absolute value) for every ta after alorm coveres C whe S s 5 db. t s ot easy to fd out e reshold value to dscard e ms-samled tas s rah aloe. order to clearly obta e roer reshold, some techques are emloyed as follows. Frstly e st order dervatve of e tab weht s calculated ad lotted Fure 5. (a). The ese data are u-samled by a factor of 4 sce e oral data ool s too small (cotas oly 39 data) for ts dstrbuto atter to be foud. ext e hstoram of e u-samled data set s lotted Fure 5. (b). t ca be easly see from Fure 5. (b) at e cut-off ot should be set at.. Back to Fure 5. (a), e reshold value. corresods to ta. The dfferece of ta value after ta are very small, ad t ca be see from Fure 5. at e ta wehts after ta (ta to ta 4) are very small, whch meas e successfully catured eery rato was aroud /4.5. So for C e eoretcal B calculato was set to.5. Based o s estmato of, e eoretcal B erformace curve s lotted accord to (4.64), whch matched very well to e smulated B curve, as show Fure

71 CHAPT 5: SUATO SUTS.4. Dscard Ta Ta Weht Ta umber Fure 5. Ta weht. Weht Dfferece Ta umber (a) Ta weht dfferece. P robablty D esty Sfcat Ta Weht Dfferece Ta Weht Dfferece (b) Hstoram after usaml. Fure 5. Ta weht dfferece ad ts hstoram. 57

72 CHAPT 5: SUATO SUTS - B C Theoretcal C Smulated C Theoretcal C Smulated C3 Theoretcal C3 Smulated C4 Theoretcal C4 Smulated S (db) Fure 5.3 Theoretcal versus smulated B for C-C4. The curves for C-C4 Fure 5.3 are obtaed e same maer. ractce, ere s o eed to clude all e tas e Bake comb. After tal adatato ad estmato by tra data set, roer reshold s obtaed ad small-value-tas are dscarded. Therefore e recever comlexty ca be furer smlfed. s smulato, e tal set-u was 4 fers for C-C ad 48 fers for C3-C4. After ta coverece, e rema useful fers were less a, erefore reatly smlfed e recever comlexty. 58

73 CHAPT 5: SUATO SUTS 5. ffect of µ o B Aroxmato secto 4.4, e S exresso s much smlfed from (4.6) to (4.63) whe we assume e ste sze µ s very small,.e., t s assumed: F γ K µ, (5.) γ ( ) γ µγ γ γ µγ w small eouh µ. Ths secto exames e effect of µ o e valdty of e aroxmato. s smulato,, ad K were set to.5,, 5 ad 8, resectvely, whch are cosstet w e revous secto. To esure e stablty of e S alorm, e ste sze µ s bouded by < µ < [5] where s e autocorrelato matrx ve by (4.3). From (4.66), 3tr e trace of e matrx s also assocated w e ower of ut sal ad ut S. For a fxed ulse eery, e smaller e ut S, e ber e ose ower, ad e ber e trace. So µ should be uer bouded by e smallest ut S whch s db our smulato. t s also foud from (5.) at F s roortoally related w. However ber results ber tr ad smaller uer boud of µ, erefore smaller F. To rove s, two smulatos were carred out w set to 3 ad 3, resectvely. The B s obtaed us (.8) ad (4.6). Whe 3, t s calculated at µ. t ca be see from Fure 5.4 (a) at whe µ s less a 3 max.6.6 3, e B erformace s almost ot affected by e varato of µ. oer 59

74 CHAPT 5: SUATO SUTS words t s reasoable to dscard F, e frst term of e deomator (4.6), f 3 µ <.6. Whe 3, t ca be calculated at µ. The 5 max.6 smulato results s show Fure 5.4 (b) ad e same arumet ales. Therefore e aroxmato from (4.6) to (4.63) s very arorate. - - B Ste Sze mu (a) B aroxmato whe 3. So db So db So 4 db So 6 db So 8 db - So db So db So 4 db So 6 db So 8 db - B X Ste Sze mu (b) B aroxmato whe 3. Fure 5.4 ffect of µ o B aroxmato. 6

75 CHAPT 5: SUATO SUTS 5.3 B Comarso w Oer ake Structures The B erformace of Bake ad covetoal Aake, ad Sake w 5 ad fers of C-C4 are show Fure 5.5 to Fure 5.8. t s see at e Bake acheves satsfactory erformace (w less a 5dB deradato for C-C ad less a db deradato for C3-C4 from Aake, resectvely) wout emloy chael estmato. ote e saml rate for each brach of Bake s at sub-yqust sal rate. our setu, e ulse durato s.5 s ad e saml rate for e frst brach s.5 s, whch s at oe quarter of e yqust rate (.5 s). Saml rates for subsequet braches are eve less as ere are less eery we ca collect at lare delay tmes. Ths reatly relaxes e ADC requremets ad sfcatly reduces e ower cosumto of e recever ractcal mlemetatos. Aake Sake- Sake-5 Bake - B S (db) Fure 5.5 B erformace for C. 6

76 CHAPT 5: SUATO SUTS - Aake Sake - Sake-5 Bake B S (db) Fure 5.6 B erformace for C. - Aake Sake- Sake-5 Bake B S (db) Fure 5.7 B erformace for C3. 6

77 CHAPT 5: SUATO SUTS - Aake Sake- Sake-5 Bake B S (db) Fure 5.8 B erformace for C4. 63

78 CHAPT 6: COCUSO 6 COCUSO 6. Cocluso emarks s ess a ovel Bake recever structure s roosed for UWB trasmsso systems. The erformace aalyss of e roosed alorm has bee carred out w closed form B exresso followed by smulatos whch rove e valdty of e eoretcal aalyss ad e feasblty of e mlemetato. The frst two chaters ve a bref troducto of UWB hstory ad des cosderatos. Two ma UWB trasmsso schemes, ad OFD, are reseted ad er advataes ad drawbacks are comared. -UWB s emloyed s ess due to ts relatvely smle recever archtecture. The rcle of ake recevers for wreless alcatos s also dscussed s chater. Aake, Sake ad Pake are descrbed ad comared. The major drawback assocated w covetoal ake structure s at t requres chael formato clud multa delays ad atteuatos to be kow or correctly estmated at e recever ed, whch s ot ractcal real lfe UWB alcatos. The Bake recever archtecture s reseted chater 3. Frstly system model s dscussed. BPSK modulato s emloyed our system to smlfy e follow maematcal aalyss. ulta chael models C-C4 for UWB door chaels are adoted. Bake recever structure s e roosed w e brach ad ta umber determato crtero. Chater 4 focuses o erformace aalyss. t bes w correlato recever sce ake 64

79 CHAPT 6: COCUSO structures are bascally a combato of correlato recevers. S crtero s used to determe e otmum ta wehts ad Weer soluto s obtaed. S meod s emloyed dur adatato hase, ad ere s a error term assocated w e adatato ste sze. Ths s also dscussed s chater. Outut S s e calculated ad closed form B s obtaed based o t. xtesve smulatos are carred out ad e sfcat results are ve chater 5. Theoretcal aalyss s roved to be vald by comar w e smulated B. There s a comlcated term assocated w ste sze whch s ored revously to smlfy e S exresso. To verfy e arorateess of dro s term, e effect of e ste sze o e aroxmato s examed. Fally, e erformace of e roosed structure s also comared w Aake ad Sake. t s roved at e roosed structure requres o chael state formato ad acheves a much reduced saml rate w sfcat erformace loss comar w covetoally ake recevers. 65