A Novel Approach based on UWB Beamforming for Indoor Positioning in None-Line-of-Sight Environments

Transcription

1 A Novel Approach based on UWB Beamforming for Indoor Posiioning in None-Line-of-Sigh Environmens Amr Elaher and Thomas Kaiser Faculy of Engineering, Duisburg-Essen Universiy, Deparmen of Communicaion Sysems, Bismarcksr. 8, 4757 Duisburg, Germany. amr.elaher, Absrac Accurae wireless indoor posiioning in non line-of-sigh (NLoS environmens is an open research opic due o inerfering dense mulipah propagaion. The key challenge is o reliably deec he direc pah (DP from he ransmier o he receiver so as o enable accurae posiioning calculaions. In our conribuion a novel approach called BeamLoc has been inroduced o perform his ask. Spaial informaion is assigned o he ransmied radio signal such ha he DP can be easier deeced hrough a unique spaial signaure. In his way, no only inerfering reflecions can be miigaed, bu also he DP can be principally capured even if i is aenuaed by an objec o some exen. BeamLoc relies on combining Ulra-Wideband (UWB echnology wih muliple anennas enabling UWB beamforming, which shows several beneficial properies for posiioning. Among all oher wireless echniques based on EM waves only UWB allows sufficien resoluion in cenimeer range due o is enormous bandwidh, Besides, UWB beamforming does no suffer from ambiguiies (so-called graing lobes and herefore enables narrowing he main lobe only by widening he anenna separaion [2]. Moreover, UWB beamforming doubles he array gain compared o narrowband soluions and herefore halves he required number of anennas [2]. The aim of his conribuion is o inroduce he BeamLoc approach and o give preliminary resuls. Afer a brief inroducion and some basic definiions (secions and 2, mulipah and NLoS are discussed in he succeeding wo secions. Secion 5 demonsraes he principles of BeamLoc and secion 6 presens preliminary simulaion resuls. Finally, conclusions and fuure work are conduced in secion 7. I. INTRODUCTION In his conribuion we presen a novel approach based on UWB beamforming for accurae indoor posiioning. The major idea relies on equipping a ransmier, which is o be locaed, wih he knowledge of a coordinae sysem. Carrying spaial informaion in he ransmied signal allows a localizaion even under NLoS siuaions as long as he aenuaion caused by an obsacle does no exceed a cerain hreshold. Noe ha here he ransmier ( is o be locaed, because high sampling raes and demanding synchronizaion a he receiver ( likely cause a higher power consumpion, which is relevan for baery driven devices like robos. Moreover, in order o keep he insallaion effors for a posiioning sysem as low as possible, a minimum number of receivers - here also called access poins (APs - is desirable. Fig. shows muliple rooms separaed by concree walls. In analogy o a cellular nework known from mobile communicaions we call his seup an indoor posiioning nework (IPN. Each room is equipped by a single AP being insalled in he cener of each rooms ceiling. Noe ha for simpliciy we consider only he wo-dimensional case. The hree-dimensional case (3D will be par of fuure research and succeeding publicaions. For reference purposes we se he AP- (firs room a (x, y = (, in he origin of he coordinae sysem. One addiional room wih AP-2 is sufficien o sudy he argeed NLoS scenario, Wihou resricion of generaliy, he ransmier is always locaed in room a an unknown posiion (x T, y T. We assume ha he size of each room is small enough o be covered by one access poin, bu large enough o assume planar wave propagaion. Furhermore, boh he ransmier and he APs are able o perform beamforming. This can be achieved eiher by a single roaing mechanical anenna wih is specific direciviy paern or by a circular anenna array consising of N T (number of anennas a he ransmier and N R (number of anennas a he receiver co-locaed anennas. II. BASIC DEFINITIONS For reasons of clariy we inroduce firs he relevan erms: Line of Sigh (LoS: The and he can see each ohers wihou any obsacles beween hem. So, he aenuaion beween hem is only caused by he air and free-space propagaion. Non-Line of Sigh (NLoS: The and he can no see each ohers due o an obsacle causing significan aenuaion beween hem. However, he signal ransmied by he device can sill be deeced by he because his aenuaion and he propagaion loss is lower han he recepion signal power hreshold. A wall build of concree wih a widh of 2cm and an approximae aenuaion of 2dB (ypical db per cm, indicaed in fig., is an example for such an obsacle. Blocked-Line of Sigh (BLoS: Same siuaion as NLoS bu in BLoS he received power is below he recepion signal power hreshold. A meal shee is an example. Direc pah (DP: The DP is he sraigh line connecing he and he. In he LoS scenario i is known as he LoS pah. In NLoS i does no equal o he connecion line (see below in general because of Snell s law. Noe ha he DP is he only pah which carries he relevan informaion for accurae posiioning purposes because he ravel ime along he DP is proporional o he disance beween ransmier and AP. Connecion line (CL: The piecewise sraigh line which connecs he wih he in NLoS siuaions. I is no coninuously sraigh because of validiy of Snell s law by propagaion hrough an obsacle. In case of normal incidence or in he LoS scenario, he CL equals o he DP. See Fig. for an illusraion. Because of he chosen seup, he is always in LoS wih AP- and NLoS wih AP-2. so ha he DP equals he CL only beween AP- and he ransmier. III. MULTIPATH EFFECT Wireless indoor elecromagneic ransmission is characerized by dense mulipah propagaion meaning L >> in he impulse response (IR L = α l δ( τ l l= from he ransmier o he receiver. α l is he aenuaion and τ l he delay associaed wih he l-h pah. Noe ha despie he enormous UWB bandwidh each single pah canno be generally resolved by he

2 Room Room 2 AP ϑ i ϑ i ϑ Concree wall AP 2 Fig.. Indoor posiioning nework (IPN. receiver. Taken his IR represenaion ino accoun we can disinguish four principal scenarios, which are illusraed in Figure 2. In he firs scenario, an unobsruced DP does exis; herefore, l = represens he DP so ha α > α l, l >, τ < τ l, l >. In his raher ideal scenario known from radar applicaions he DP can be easily separaed. In he second scenario he DP sill exiss, bu he anenna beam paern (BP does no seer is maximum ino he DP direcion. Hence, anoher pah, e.g. refleced by meal, migh be larger in magniude which complicaes reliable DP separaion and localisaion. In mahemaical erms we may wrie τ < τ l, l >, bu a similar condiion on α l does no hold rue for he second scenario. The hird scenario reveals he major challenge in NLoS environmens: he DP sill arrives firs, bu now wih a disinc smaller magniude due o objec peneraion loss. Hence, he same mahemaical relaions as in he second scenario are valid bu usually wih a raher small value of α. The las scenario may no occur ofen, bu i demonsraes a furher challenge in NLoS propagaion; while peneraing hrough a maerial an elecromagneic wave may change is speed of propagaion significanly. This propery is closely relaed o he maerial s dielecric consan as will be discussed laer. Hence, he DP, can neiher be he firs nor he sronges in general, so ha neiher an inequaion for α nor τ can be given. IV. NLOS EFFECT When an EM wave ravels hrough differen mediums, he inciden grazing angle (ϑ i and he ransmied (or refraced one (ϑ, see Fig., behave according o Snell s law µr ɛ r cos(ϑ i = µ r2 ɛ r2 cos(ϑ, ( where (µ r, ɛ r and (µ r2, ɛ r2 are he relaive permeabiliy and he dielecric consan of air and concree, respecively. Since he CL equals he DP only if he inciden ray is perpendicular o he wall surface he accuracy for posiioning will generally suffer in NLoS scenarios. Moreover, since peneraing maerial of an EM wave reduces is speed υ = c ɛr a loss in accuracy is expeced furher. An approximaion for a loss caused by a wall of concree is calculaed by [6] P b λ 2 H = P i (4π 2 d ( (R he jϑ h 2 ( (R 2.5 h2 e jϑ h2 2 e 2αd, (2 P b λ 2 V = P i (4π 2 d ( 2.5 (Rvejϑ v 2 ( (R v2e jϑ v2 2 e 2αd, (3 and illusraed in Fig. 3. P i and P b are he inciden and he by-passed power, respecively. λ is he signals wavelengh, d is he propagaion disance inside he wall, R h and R v are he reflecion coefficien (horizonal (H, verical (V from air o obsacle and R h2 and R v2 are he reflecion coefficien (H and V from obsacle o air. ϑ and ϑ 2 are he grazing angles from air o obsacle and from obsacle o air, respecively. α is an aenuaion facor for non-perfec dielecric. Observe ha due o he dependence of he by-passed power on λ an UWB signal will experience a frequency dependen disorion meaning ha i s shape will change. Hence, equipping he receiver wih a mached filer for superior noise suppression will be of limied success in pure NLoS environmens. V. BEAMLOC APPROACH The succeeding Fig. 4 shows a coarse flow char of our BeamLoc approach. BeamLoc is mainly based on he above menioned beneficial properies of UWB beamforming, like he double db-gain [2], and can be summarized in he following wo seps. Searching for he lock mode (SLM: c is he speed of ligh and ɛ r is he maerial s dielecric consan which ypically varies from o some ens, e.g. ɛ r,air =.6, ɛ r,concree = 9, ɛ r,waer = 8

3 Fig. 2. (P b /P i [db] a An unobsruced DP in almos ideal LoS scenario. τ b An unobsruced aenuaed DP caused by he BP in LoS scenario. Wall τ c An obsruced aenuaed DP equals he firs pah in NLoS scenario. Liquid d An obsruced aenuaed DP equals he second pah in NLoS scenario. A principal skech of four scenarios in LoS and NLoS-environmens Wall hickness (cm τ τ 2 3GHz(H 3GHz(V 5GHz(H 5GHz(V Fig. 3. EM waves Power loss due o propagaion in wall. ϑ = 25. emis a signal carrying he curren mainlobe direcion θ T. The mainlobe roaes wih an angular sepsize of θ sep. Noe ha is equipped wih a compass in order o achieve a common reference, while he AP s are only needed o be calibraed once during is insallaion procedure, afer receiving he value of θ T, AP- and AP-2 roae sends he value of is seering angle θ T AP- and AP-2 delay and sum he received signal a each anenna elemen according o θ R = θ T ± 8 seering angle AP- and AP-2 calculae afer MF wih p T ( he maximum insananeous power according o: P AP /AP 2 (θ R = max(r AP /AP 2 ( p T ( sends he new value of is seering angle θ T = θ T + θ sep P(θ R Fig. 4. No θ /2,Lock = Flowchar of he proposed algorihm. Posiion esimaion argmax θr P AP /AP 2 (θ R IS Yes θ T > 36? heir beams owards θ R = θ T ± 8 and calculae he received maximum insananeous power P AP /AP 2 (θ R afer mached filering (MF beween he received signal r AP /AP 2 ( and he pure ransmied pulse p T (. Noe ha he sign denoes a cross correlaion operaion. Noe also ha θ R is measured from he posiive x-axis as a common reference, increases is seering angles by θ sep and ransmis he updae θ T + θ sep. Again AP- and AP-2 calculae he received maximum insananeous power a θ R = (θ T + θ sep 8, afer one complee roaion he individual maximum of P AP /AP 2 (θ R w.r.. θ R deermines he wo lock mode (LM angles θ AP,LM, θ AP 2,LM. Observe ha wihin he LM boh AP s should seer heir mainlobes owards he ransmier, so ha mulipah propagaion is now miigaed and he posiion esimaion can sar now, The following wo figures show exemplary he insananeous power in a non- LM and he LM for a simplified 5-pah channel model and 4 ransmi and receive anennas. Noe ha in he non-lm he firs reflecion shows a larger insananeous power Non LM Time (ns Fig. 5. Algorihm oupu in a ypical non-lm siuaion

4 P(θ R LM Fig. 7 shows some ypical resuls as a funcion of he number of anennas. The laer significanly impacs he beampaern and wih more anennas a superior noise suppression as well as an increased direciviy is expeced resuling in an improved localizaion. Uniform circular arrays (UCA are assumed a he APs and he wih a UCA radius r of.3 meers and he ransmi pulse is given by he second derivaive of a Gaussian pulse as.2 p T ( = 4π( τ 2 e 2π( τ 2, ( Time (ns Fig. 6. Algorihm oupu in a ypical LM siuaion Exploiing lock mode (ELM: Once boh locked modes are deermined, AP- and AP-2 are equipped wih each direcion of arrival (DoA so ha he posiion can be calculaed by inersecion. Noe ha his approach is vulnerable o any model mismach since a small angular variaion may resul in a disinc posiioning error. However, in his inroducory paper our resuls are no furher improved by succeeding ime of arrival (ToA esimaion, which would benefi from he enormous UWB bandwidh due o is high emporal resoluion. This and several oher issues are par of fuure work. In a firs conclusion, by exploiing he beneficial properies of UWB beamforming, he above approach BeamLoc is principally able o locae a even in NLoS environmens as long as he received signal arrives wih a minimum hreshold ampliude. VI. SIMULATION RESULTS In his secion preliminary simulaion resuls will be given in order o underline he effecive operaion of BeamLoc. For reasons of simpliciy and clariy, single pah channel in addiive whie Gaussian noise (AWGN is considered as a launching poin owards mulipah- AWGN channels. For reasonable simulaion ime, he following resuls reflec average performance based on few posiions giving a primary indicaion for he sysem behavior. More sophisicaed scenarios and a horough invesigaion are pars of fuure research. ε (m r = N T = N R Fig. 7. sysem performance in single pah channel in erms of N = N T = N R a SNR = 2 db. where τ =.4ns. Each room has a size of x m 2. We consider his size as a es bench. Wall hickness is se o.3 m. AP- and AP- 2 are se a (, and (.3,, respecively. SNR = lg( P S P N, where P S and P N are he signal and he noise power, respecively, is se o 2 db a each anenna elemen before delay and sum beamforming. Observe a raher sauraion as a funcion of he number of anennas in Fig 7. The ineviable error floor origins from sysem-inheren error occurs like he non-pencil beam of he and and a sep size of one degree. ɛ(m is he error due o he difference beween he original locaion and he esimaed one. P(θ R θ R ( Fig. 8. Received maximum power level a AP-2 Fig. 8 shows he received power level afer MF a AP-2, where he is locaed in room. I can be observed ha P AP 2(82 = P AP 2 (83 which confirms he previous discussion. A furher improvemen could be achieved by increasing he radius r since his posiively affecs he beam paern in erms of a narrower main lobe. Fig. 9 shows he performance of he proposed algorihm in mulipah channel. Since here is no common channel model known for localisaion purposes, a simple ray racing algorihm has been designed based on reflecions by walls in he firs room and ransmissions hrough he concree wall separaing he wo rooms shown in Fig. o race he pure ransmied pulse a each anenna elemen hrough mulipah propagaion. Then, he received signal a each anenna elemen is again delayed and summed o produce he beamformer oupu. SNR is again assumed o be 2 db a each anenna elemen before beamforming. Noe ha as he number of anenna elemens increases, he main-o-side lobe raio increases so ha inerfering mulipah can be beer supressed and he general performance converges closer and closer o he single pah scenario a high SNR.

5 ε (m r = N T = N R Fig. 9. Sysem performance in a mulipah channel in erms of N = N T = N R a SNR = 2 db. VII. CONCLUSION AND FUTURE WORK The aim of his conribuion was o inroduce a novel approach for localisaion in NLoS environmens. We call his approach BeamLoc in order o reflec he inheren beamforming and he vial lock mode. The device o be locaed emis is curren mainlobe direcion wihin he ransmi signal, so ha despie mulipah propagaion DoA esimaion reduces o a receive power maximizaion. Preliminary simulaions show he principal feasibiliy of BeamLoc, bu much more work is needed for a ruly meaningful evaluaion. This is currenly undergoing in our research group and he resuls will be presened in furher publicaions. REFERENCES [] F. Anderson, W. Chrisensen, L. Fulleron and B. Koregaard, Ulrawideband beamforming in spare arrays. IEE Proceedings-H, Vol. 38, No. 4, Augus, 99. [2] S. Ries and T. Kaiser, Ulra Wideband Impulse Beamforming: I s a Differen World, Special Issue on Signal Processing in UWB Communicaions, invied paper, o appear 25, Elsevier Science. [3] J. Y. Lee and R. A. Scholz, Ranging in dense mulipah environmens using an UWB radio link, IEEE Journal on Seleced Area in Communicaions, 22, Submied. [4] hp:// [5] hp:// [6] S. Shibuya, A Basic Alas of Radio-Wave Propagaion, Yokohama-Japan, Corona Publishing Co., Ld., 983. [7] R. C. Qui, A Generalized Time Domain Mulipah Channel and Is Applicaion in Ulra-Wideband (UWB Wireless Opimal Receiver Deign- Par 2: Physics-Based Sysem Analysis, IEEE Transacions on Wireless Communicaions, Vol. 3, No. 6, November 24. [8] A. Molisch, Ulrawideband propagaion channels - heory, measuremen and modelling, IEEE Transacions on Vehicular Technology, special issue on UWB., To appear fall/winer 25.