The Importance of Fractional Bandwidth in Ultra-Wideband Pulse Design

Transcription

1 he Imorance of Fracional Bandwidh in Ulra-Wideband Pule Deign Mahew Welborn and John McCorle XremeSecrum, Inc. 8 Leeburg Pie, Suie 7 Vienna, VA 8 Abrac - Ulra-wideband (UWB) communicaion yem rovide exremely high daa rae while uing low ranmi ower relaive o narrowband yem. Recen reearch conclude ha uch yem have characeriic ha mae hem aroriae for higheed wirele newor alicaion. One of he diinguihing aec of he UWB ignal i an exremely high fracional bandwidh when comared wih convenional narrowband yem. hi aer decribe how a large fracional bandwidh lead o lower wor-cae fading in he reence of muliah for UWB communicaion yem, hereby roviding a ignifican advanage for a low-ower wirele yem. Alo included are meauremen made uing an acual UWB communicaion yem howing he magniude of ignal rengh variaion due o muliah inerference. I. INRODUCION hi aer reen an analyi of he role of fracional bandwidh in roviding robu erformance in muliah environmen for ulra-wideband communicaion yem. he deign of high-eed wirele newor for indoor environmen reen he yem deigner wih a number of very challenging requiremen. hi yem mu rovide low ower conumion (o uor mobiliy baery oeraion for mobiliy), low imlemenaion comlexiy and co, while ill roviding high erformance and daa rae in an indoor environmen []. he ey characeriic of uch indoor wirele channel i muliah/fading due o mulile caer. In aricular, indoor channel ofen reul in value for muliah delay read i horer han in oudoor environmen, and herefore relaively wide channel coherence bandwidh [6]. For n UWB yem, one of he mo imoran deign conideraion i he choice of he fundamenal ule hae ued o generae he UWB ignal. In hi aer, we analyze he effec of one aec of hi ignal deign, he ignal fracional bandwidh, on he erformance of he yem in a muliah environmen. Secion II rovide a he definiion of fracional bandwidh i he raio of ignal bandwidh o cener frequency, or more ecifically, (f H - f L )/(f H +f L ). Here f H and f L are he are he uer and lower band edge, meaured a ome fixed level (e.g. - or - db) relaive o he ea level of he ignal. hor review of yical UWB ignal characeriic. Secion III and IV decribe he effec of wide fracional bandwidh on fading due o muliah and ecion V relae hee reul o he conce of channel coherence bandwidh. Secion VI reen meauremen of an acual yem demonraing he variaion of received ignal rengh due o muliah inerference. II. CHARACERISICS OF UWB SYSEMS In general, UWB yem ue ignal ha are baed on rain of hor duraion ule formed uing a ingle baic ule hae. For uch a ignal, he inerval beween individual ule can be uniform or variable, and here are a number of differen mehod ha can be ued for modulaing he ule rain wih daa for communicaion. One common characeriic, however, i ha he ule rain i ranmied wihou ranlaion o a higher carrier frequency, and o UWB i omeime alo ermed carrier-le radio. In oher word, a UWB yem drive i anenna direcly wih a baeband ignal. Anoher imoran oin common o UWB yem i ha he individual ule are very hor in duraion, yically much horer han he inerval correonding o a ingle bi. We can rereen a general UWB ule rain ignal a a um of ule hifed in ime: ) = a ( ) ( ( ) = Here () i he modulaed UWB ignal, () i he baic ule hae, and a and are he amliude weigh and ime offe for he ule. Becaue of he hor duraion of he ule, he ecrum of a yical UWB ignal can be everal gigaherz or more in bandwidh. A wih any ule-amliude modulaion (PAM) yem, we can eaily derive he PSD of he ranmied ignal under he aumion ha he daa ymbol are random (indeenden and idenically diribued) and ha he ule are uniformly aced in ime (i.e =, where i one ymbol inerval). In uch a cae, he PSD i [7]: S( f ) = F σ µ { ( ) } = P( f ) + P( f ) P δ f = () //$7. IEEE 7

2 Here σ and µ are he variance and mean, reecively, of he ymbol equence a and δ() i a uni imule or Dirac dela funcion. he fir erm on he righ-hand ide of () rereen he coninuou orion of he PSD and he econd erm how he reence of ecral line in he ranmi ignal []. If we furher aume ha he daa ymbol value are equi-robable and have zero mean, hen he execaion E{a }=µ i zero and he ecral line vanih a () imlifie o: σ S( f ) = P( f ) () In eiher of he above equaion, wheher here are ecral line reen or no, i i clear ha he PSD of he UWB ignal i rimarily deermined by he ecrum of he ule, P(f). For hi reaon, we ee ha in uch a UWB yem, he fundamenal relaionhi beween he ime-domain ule hae, i Fourier ranform and he PSD of he modulaed ignal i much he ame a for a narrowband PAM ignal. A hi oin, we are ready o furher analyze how he hae and ecrum of he UWB ule will direcly influence no ju he PSD of he ranmied ignal, bu alo he erformance of he UWB yem ielf in a muliah environmen. In aricular, we will how ha i i he fracional bandwidh of he UWB ule ha rovide much of he uerior erformance for a UWB communicaion yem. III. WIDE FRACIONAL BANDWIDH In aniciaion of regulaing UWB yem for wideread commercial ue, he FCC ha rooed ha UWB yem be ermied o oerae on an unlicened bai a exremely low ranmi ower level under he guideline of Par of he Code of Federal Regulaion. A ar of hi rooal he FCC ha enaively defined UWB yem a hoe ha have bandwidh exceeding % of heir cener frequency, or. GHz, whichever i le. A he ime of hi wriing, formal roceeding o evaluae hi rooal are ongoing. o underand he effec of he fracional bandwidh on he erformance of he UWB yem, we now reen a cla of ule ha can be ued o roduce waveform wih a wide range of fracional bandwidh. Uing hi cla of ule, we hen analyze he effec of a wide fracional bandwidh on he wor-cae everiy of fade caued by muliah inerference. hi cla of ule i baed on he Gauian monoule hown in Figure. Vol Vol nanoecond 4 nanoecond db db Hz.4.6 Hz Figure : A Gauian monoule, (), and i Fourier ranform, P (f). he ime and frequency domain equaion for hi ule are given here: and A e ( ) = e (4) ( ) ω P ( ω) = A π e ω e () hi baic ule i ued o derive an enire cla of ule by aing ucceive derivaive of he imedomain waveform. We will refer o hee differen ule by uing ubcri: n d A e n+ ( ) = e (6) n d hee ule are hown in Figure for value of n u o n=. A hi oin i i helful o noe a few roerie of he differen ule in hi cla. Fir, from he ime domain lo i i clear ha a he order of he derivaive increae, he number of zero croing in he ule alo increae. A he ule order increae, he ule begin o reemble inuoid modulaed by a Gauian ule-haed enveloe. From hi we would uec ha he fracional bandwidh for each of he ucceive ule decreae, ince more zero croing in he ame ule widh would correond o a higher carrier frequency inuoid modulaed by an equivalen Gauian enveloe. hi uicion i correc. In Figure, we ee a lo ha how he fracional bandwidh of he differen ule a a funcion of he meauremen oin (i.e. how far down from he ea of he ecrum we chooe o meaure he ignal bandwidh). A dicuion of he UWB roceeding i beyond he coe of hi aer. Secific rooal and a dicuion of relevan iue can be found in he Noice for Prooed Rulemaing for hee roceeding, FCC documen number -6, and oher ublic commen are available under FCC doce number

3 Figure : ime domain lo for he derivaive of he db Down from Pea Gauian monoule Fracional Bandwidh A Lef-Axi Meauremen Poin Derivaive Order Figure : Plo of fracional bandwidh veru meauremen oin (in db) for he monoule derivaive. he wor-cae for hi fading henomenon wih wo comonen ule occur when he comonen have equal amliude. In uch a cae, he waveform (ule in hi cae) will be added ogeher wih a relaive ime offe equal o he ah delay difference beween he wo ah. Becaue a UWB yem i baeband, he wo received ule can have eiher he ame or ooie olariy. For he ame-olariy cae, he reul een a he ouu of he correlaor will deend on he ah delay beween he wo ule, and will vary from double he ouu (for zero ah delay difference) o wo comleely reolved ule (for ah delay greaer han he ule widh). For inermediae value of ule delay (beween zero and he ule widh), he reuling correlaor ouu for he combined ule will deend on he hae of he ule and he ah difference. Figure 4 how he correlaor ouu relaive o a ingle ule for wo differen ule hae: one wih high fracional bandwidh ( H ) and one wih low fracional bandwidh ( L ). he boom axi how he ah difference beween he ule and he verical axi how ha he reuling normalized correlaion value range from o omehing le han one. For H, we ee ha he minimum ouu value i around.49 (-6. db), while for L he minimum normalized ouu value i abou.4 (- db). he imlicaion here i ha for ame-olariy ule, he wor oible fade due o wo equal-amliude muliah comonen i much wore for he ule wih he lower fracional bandwidh. In hi lo we ee ha he fracional bandwidh, meaured a he db down oin, range from abou 7% for () o le han % for (). IV. PERFORMANCE IN A MULIPAH ENVIRONMEN In a muliah environmen, he receion of mulile received comonen caering off differen objec can reul in eiher conrucive or derucive inerference. he differen ah lengh of he mulile comonen will caue hem o arrive wih differen ah delay, hu oenially ou of hae. o underand he role of fracional bandwidh in he yem erformance in a high muliah environmen, we will ue a imlified analyi ha deermine he wor-cae derucive inerference occurring when wo ignal comonen arrive a he receiver wih differen ime delay. For hi analyi, we aume ha he wo received comonen are added in he receiver and we comare he reuling ouu of a correlaor ha i maching he received ignal again he ranmied ule hae. Correlaor Amliude. Fracional BW =. Fracional BW = Pah Delay Differenial (n) Figure 4: Plo of correlaion value veru ule differenial ah delay for ule wih he ame olariy. hi effec i more comleely hown in Figure, where we lo he wor-cae fade for wo equalamliude comonen a a funcion of fracional bandwidh. hi lo how ha he wor-cae fade can be ignificanly wore for he ule wih lower fracional bandwidh. For he cae of wo ule wih unequal amliude (i.e. one larger ha he oher), he curve 7

4 equivalen o hoe in Figure 4 would ill be cenered around he value of one, bu would have maller amliude variaion, o we would ee ha he equal amliude cae i indeed he wor-cae. he concluion here i ha a high fracional bandwidh ule will allow he yem o exerience le evere fading in a muliah environmen. From a yem deign oin of view, hi mean ha he yem will require a lower margin for muliah fading in he lin budge and can herefore rovide more robu erformance wih le ranmi ower. Wor Cae Null Due o Muliah (db) Correlaor Amliude - Equal -Phae Relaive Bandwidh a db Figure : Plo of wor-cae fade veru fracional bandwidh for ame olariy ule.. Fracional BW =. Fracional BW = Pah Delay Differenial (n) Figure 6: Plo of correlaion value veru ule differenial ah delay for ule wih ooie olariy. For wo ule wih ooie olariy and imulaneou arrival, here would clearly be comlee cancellaion, regardle of he ule hae. here would be no remaining ignal for he correlaor o deec and he MF ouu would be zero (negaive infiniy db relaive o he ingle-ule ouu). For non-zero ah delay difference, however, we can again ee in Figure 6 ha he ule wih wider fracional bandwidh will rovide le exreme variaion from he nominal ingle-ule correlaor ouu, and hu more robu erformance. V. RELAIONSHIPS OF HESE RESULS O COHERENCE BANDWIDH hee reul howing he advanage of wide fracional bandwidh can alo be underood in he conex of he well-nown relaionhi beween ignal bandwidh and channel coherence bandwidh. hi relaionhi i baed on he aumion ha he channel can be characerized a having a characeriic coherence bandwidh over which ignal are liely o exerience imilar fading. hi coherence bandwidh, B c, i a aiical meaure of he range of frequencie over which he channel aear fla, ha i, over which ecral comonen exerience equal amliude fading. A ignal i aid o exerience fla fading when i ignal bandwidh, B, i le han he coherence bandwidh of he channel, B <B c. In uch a cae, he reence of dee fade due o muliah can reul in dee fade o he ignal over i enire bandwidh, and correonding dee fade in received ignal energy []. When he ignal bandwidh i greaer han he channel coherence bandwidh, B >B c, he ignal i aid o exerience frequency elecive fading. In hi cae, he reence of dee muliah fade i unliely o affec he ignal over i enire bandwidh and he overall yem i herefore liely o exerience much le evere fade in received ignal energy han for fla fading []. When we comared he differen ule hrough in Figure, we howed hem for equal cener frequencie (roughly correonding o equal carrier frequencie when we conidered hem a inuoid modulaed by Gauian enveloe). For hee ule, he increaing order of he derivaive reuled in wider overall ule widh for each ucceive ule, and correonding narrower bandwidh abou he ame cener frequency. In ligh of he coherence bandwidh conce decribed above, hen, we ee ha for a given coherence bandwidh, he hif beween fla fading (narrow bandwidh ule) and frequency elecive fading (wider bandwidh ule) i a gradual hif. hi i quaniaively hown in Figure where we loed worcae fade deh veru fracional bandwidh. he reul of hi effec i hu een o mach our exiing underanding of he coherence bandwidh conce. he ule wih wide fracional bandwidh are een o have much le evere wor-cae fading han hoe wih lower fracional bandwidh. he imlicaion of hi fac on yem level deign for wirele newor i ha he yem need no have a large a margin o comenae for ignal fading due o muliah for a given environmen ince he everiy of he execed fading i much le. 76

5 VI. MEASURED RESULS IN A REAL-WORLD CHANNEL he analyical reul above are uored by meauremen made uing an acual UWB yem. hi yem wa oeraed a million ule er econd uing a ule hae ha roughly correonded o (). he yem wa ued o meaure roagaion lo in an indoor office environmen wih office, hallway and ariion, uch a migh be exerience by an indoor wirele newor. he ranmier-receiver diance wa lowly increaed and received ower (a indicaed by correlaor ouu) wa meaured a wo-foo inerval. Figure 7 how an examle of a lo of he received ignal rengh veru earaion diance. In hi cae, meauremen were made in a hallway wih rucural column and a meal boocae. he aricular meauremen hown in Figure 7 clearly indicae ha he meaured receive ower wa influenced by muliah roagaion, becaue he meaured ah lo value deviaed from he execed curve for free-ace ah lo. A variou oin he received ower i eiher greaer or le han execed, indicaing conrucive or derucive muliah inerference. he variaion of he meauremen relaive o he free-ace curve cloely mach hoe rediced by he curve in Figure, where he correlaor ouu ower i loed a a funcion of he differenial ah delay for wo muliah comonen. Alo hown i a curve for /R. roagaion lo, indicaing ha he ah lo a no ime wa a indicaed y ha curve. hee reul are alo conien wih meauremen made in reviou wor on wideband channel reored in [4], where relaively low level of muliah fading were meaured. UWB R. R!"!" Figure 7: Received ignal energy veru ranmierreceiver earaion diance in an office environmen. VII. REFERENCES [] heodore S. Raaor, Wirele Communicaion: Princile & Pracice, Prenice Hall, 996. [] John G. Proai, Digial Communicaion, McGraw Hill, Inc., 99. [] J. Foerer, E. Green, S. Somayazulu and D. Leeer, ``Ulra-Wideband echnology for Shor- or Medium- Range Wirele Communicaion," Inel echnology Journal, Q,. [4] M.Z. Win and R.A. Scholz, ``Ulra-Wide Bandwidh Signal in Muliah Environmen," IEEE Communicaion Leer, Vol., No., February 998. [] R.A. Scholz and M.Z. Win, ``Imule Radio," IEEE PIMRC 97. [6] Lawrence Milein, Wideband Code Diviion Mulile Acce, Proceding of RAWCON. 77