Retraction Retracted: Modeling, Real-Time Estimation, and Identification of UWB Indoor Wireless Channels

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1 Hidawi Iteratioal Joural of Ateas ad Propagatio Volume 17, Article ID 13549, 1 page Retractio Retracted: Modelig, Real-Time Estimatio, ad Idetificatio of UWB Idoor Wireless Chaels Iteratioal Joural of Ateas ad Propagatio Received 7 March 17; Accepted 7 March 17; Published 13 July 17 Copyright 17 Iteratioal Joural of Ateas ad Propagatio. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Iteratioal Joural of Ateas ad Propagatio has retracted the article titled Modelig, Real-Time Estimatio, ad Idetificatio of UWB Idoor Wireless Chaels [1]. The article was foud to cotai a substatial amout of material from the followig published article: Yaya Li, Mohammed Olama, Seddik Djouadi, Aly Fathy, Teja Kurugati: Stochastic UWB wireless chael modelig ad estimatio from received sigal measuremets. Radio ad Wireless Symposium, pp IEEE, 9. The reuse icludes most of the itroductio, some of the methods ad results, ad all the coclusio. The authors do ot agree with this retractio as Li et al. were cited as Some prelimiary results usig SDEs to model UWB chaels were preseted iitially i [19]. The authors believe that the approximatio of the timevaryig wireless chael impulse respose is more geeral ad harder to prove ad solve (providig the arbitrary order approximatio while Li et al. provided the fixed order approximatio). The proof of Theorem is differet ad required additioal steps. New stochastic models for idoor wireless chaels ad their statistics are provided (eq. (6) (8)), as well as ew stochastic models for UWB idoor wireless chaels ad their statistics (eq. (3) (3)) ad geeralized forms of the models i Li et al. s study. The received sigal y(t) has triple summatios ad a phase term, while the received sigal i Li et al. s study (eq. (14)) has oly double summatios without a phase term. Refereces [1] M. M. Olama, S. M. Djouadi, Y. Li, ad A. Fathy, Modelig, real-time estimatio, ad idetificatio of UWB idoor wireless chaels, Iteratioal Joural of Ateas ad Propagatio, vol. 13, Article ID 46767, 8 pages, 13.

2 Hidawi Publishig Corporatio Iteratioal Joural of Ateas ad Propagatio Volume 13, Article ID 46767, 8 pages Research Article Modelig, Real-Time Estimatio, ad Idetificatio of UWB Idoor Wireless Chaels Mohammed M. Olama, 1 Seddik M. Djouadi, Yaya Li, ad Aly Fathy 1 Computatioal Scieces & Egieerig Divisio, Oak Ridge Natioal Laboratory, P.O. Box 8, MS 685, Oak Ridge, TN 37831, USA Electrical Egieerig & Computer Sciece Departmet, Uiversity of Teessee, 15 Middle Drive, Koxville, TN 37996, USA Correspodece should be addressed to Mohammed M. Olama; olamahussemm@orl.gov Received 1 July 13; Accepted 1 November 13 Academic Editor: Ai Bo Copyright 13 Mohammed M. Olama et al. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Stochastic differetial equatios (SDEs) are used to model ultrawidebad (UWB) idoor wireless chaels. We show that the impulse resposes for time-varyig idoor wireless chaels ca be approximated i a mea-square sese as close as desired by impulse resposes that ca be realized by SDEs. The state variables represet the iphase ad quadrature compoets of the UWB chael. The expected maximizatio ad exteded Kalma filter are employed to recursively idetify ad estimate the chael parameters ad states, respectively, from olie received sigal stregth measured data. Both resolvable ad oresolvable multipath received sigals are cosidered ad represeted as small-scaled Nakagami fadig. The proposed models together with the estimatio algorithm are tested usig UWB idoor measuremet data demostratig the method s viability ad the results are preseted. 1. Itroductio Ultrawidebad (UWB) commuicatio systems have recetly attracted sigificat iterest from both the research commuity ad idustry sice the Federal Commuicatios Commissio (FCC) allowed limited ulicesed operatio of UWB devices i the USA [1]. They are commoly defied as systems that have either more tha % relative badwidth or more tha 5 MHz absolute badwidth. UWB techology has may beefits, icludig high data rate, low iterferece, less sesitivity to multipath fadig, low trasmit power, ad availability of low cost trasceivers []. Idustrial stadards such as IEEE a ad a have bee established i recogizig these developmets. The ultimate performace limits of a commuicatio system are determied by the chael it operates i [3]. Realistic chael models are thus of utmost importace for system desig ad testig. UWB propagatio chaels show fudametal differeces from covetioal (arrowbad) oes i may respects [4, 5], ad therefore the established (arrowbad) chael models caot be used. A umber of UWB chael models have bee proposed i the literature. A model for frequecy rage below 1 GHz is suggested i [6]. A statistical model that is valid for a frequecy rage from 3 to 1 GHz is proposed i [7] ad is accepted by the IEEE a task group as a stadard model for evaluatio of UWB system proposals. Sigificat experimetal work i office, residetial, ad idustrial eviromets has bee reported i this field such as i [8, 9]. Most of the proposed chael models are based o characterizig the discrete multipathcompoets.althoughthesemodelsareabletocapture the statistics of the chael, they caot be specified by a fiite umber of parameters sice their impulse resposes are geeral fuctios of time ad space ad therefore are ot easy to estimate directly from measuremets. A ecessary ad sufficiet coditio for represetig ay time-varyig (TV) impulse respose (IR) i stochastic state-space form is that it is factorizable ito the product of two separate fuctios of time ad space [1]. However, i geeralthisisotthecasefortheirofwirelesschaels. We show that the IR of idoor wireless chaels ca be approximated i the mea-square sese as close as desired by factorizable impulse resposes that ca be realized by stochastic differetial equatios (SDEs) i state-space form.

3 Iteratioal Joural of Ateas ad Propagatio I particular, the SDEs are used to model UWB idoor chaels ad are combied with system idetificatio algorithms to extract various parameters of the chael from received sigal measuremet data. The expected maximizatio (EM) ad the exteded Kalma filter (EKF) are employed i estimatig chael parameters as well as the iphase ad quadrature compoets, respectively. The EM ad EKF are chose sice they are recursive ad therefore ca be implemeted olie. These algorithms have bee recetly utilized i [11 13] to estimate the chael parameters ad states i arrowbad eviromets, ad therefore the formulatios of these algorithms are ot preseted i this paper. Experimets are coducted i our UWB laboratory to collect received sigal stregth measured data, which are used to determie theapplicabilityoftheproposedmodels.thesemodelsca be used i the developmet of a practical chael simulator that replicates wireless chael characteristics ad produces outputs that vary i a similar maer to the variatios ecoutered i a real-world UWB chael eviromet. Recetly, there have bee several papers o the applicatio of SDEs to modelig propagatio pheomea i radar scatterig ad wireless commuicatios. SDEs have bee successfully used to aalyze K-distributed oise i electromagetic scatterig i [14]. Autoregressive stochastic models for the computer simulatio of correlated Rayleigh fadig processes are ivestigated i [15]. A first-order stochastic autoregressive model for a flat statioary wireless chael is itroduced i [16]. Stochastic chael models based o SDEs for cellular ad ad hoc etworks have bee preseted i [1, 17, 18]. Some prelimiary results usig SDEs to model UWB chaels were preseted iitially i [19]. The advatage of usig SDE methods is based o the computatioal simplicity of the algorithm simply because estimatio is doe recursively. This meas that there is o eed to store ad process all measuremets; rather, at each time step, the estimator is updated usig the previous estimator values ad the ew iovatios. The paper is orgaized as follows. I Sectio,thegeeral TV arrowbad ad UWB idoor wireless chael impulse resposes are itroduced. I Sectio 3, we show that the impulse resposes for TV idoor wireless chaels ca be approximated i a mea-square sese as close as desired by impulse resposes that ca be realized by SDEs. The stochastic UWB chael models are developed i Sectio 4. I Sectio 5, experimetal setup ad umerical results are preseted. Fially, Sectio6 provides cocludig remarks.. The Geeral Time-Varyig Impulse Respose for Idoor Wireless Chaels The geeral TV impulse respose (i complex basebad) of a idoor wireless fadig chael is typically represeted by Saleh-Valezuela (SV) model give as [] L K l C (t; τ) = a kl (t, τ) exp (jφ kl (t, τ)) l=1 δ(t T l (t) τ kl (t)), (1) where C(t; τ) is the impulse respose of the chael at time t, due to a impulse applied at time t τ, a kl (t, τ) ad φ kl (t, τ) are, respectively, the radom TV tap weight ad phase of the kth compoet i the lth cluster, T l (t) is the delay of the lth cluster, τ kl (t) is the delay of the kth multipath compoet (MPC) relative to the lth cluster arrival T l (t), δ( ) is the Dirac delta fuctio, K l is the total umber of MPCs withi the lth cluster, ad L is the total umber of clusters that ca either be assumed fixed [1] or cosidered to be a radom variable [7]. Let s(t) be the trasmittedsigal;thereceivedsigalisthegiveby L K l y (t) = a kl (t, τ) exp (jφ kl (t, τ)) l=1 s(t T l (t) τ kl (t))+v (t), where V(t) is the measuremet oise process. For arrowbad systems, complex Gaussia fadig is covetioally used to describe the small-scale fadig. More precisely, the equivalet complex basebad represetatio cosists of Rayleigh-distributed amplitude ad uiformly distributed phase. This ca be related theoretically to the fact that a large umber of multipath compoets fall ito each resolvable delay bi, so that the cetral limit theorem is valid [3]. Therefore, a kl (t, τ) ad φ kl (t, τ) are statistically idepedet Rayleigh ad uiform (over [, π]) radom processes, respectively []. I UWB systems, the cetral limit theorem is ot valid, ad a umber of alterative amplitude distributios have bee proposed i the literature. The most commo empirically determied amplitude distributio i may UWB eviromets is Nakagami distributio, which is observed i [6, 8] ad cosidered i the IEEE a stadard [7]. Therefore, i UWB systems, a kl (t, τ) ad φ kl (t, τ) are statistically idepedet Nakagami ad uiform radom processes, respectively. I the ext sectio, the correspodig impulse respose with a kl (t, τ) ad φ kl (t, τ) for the timevaryig idoor wireless chaels i (1) isapproximatedia mea-square sese as close as desired by SDEs. 3. Approximatig the Time-Varyig Impulse Respose for Idoor Wireless Chaels by SDEs Now, we wat to represet the TV IR i (1) with a stochastic state-space form i order to allow well-developed tools of estimatio ad idetificatio to be applied to this class of problems. The followig theorem states a ecessary ad sufficiet coditio for the realizatio of the TV IR. Theorem 1 (see [1]). The impulse respose C(t; τ) of a TV system has a stochastic state-space realizatio if ad oly if it isfactorizable;thatis,thereexistfuctiosg( ) ad f( ) such that for all t ad τ,oehas () C (t; τ) =g(t) f (τ). (3) It is readily see from the expressio of the IR C(t; τ) of the idoor wireless chaels i (1) that i geeral it is ot

4 Iteratioal Joural of Ateas ad Propagatio 3 factorizable i the form (3) sicea kl (t, τ) ad φ kl (t, τ) are arbitrary fuctios of t ad τ. However,oewillshowthat i geeral C(t; τ) ca be approximated as close as desired by afactorizableirfuctio. Theorem. I geeral, the IR C(t; τ) of the idoor wireless chael i (1) ca be approximated as close as desired by a factorizable fuctio. Proof. The IR C(t; τ) of the idoor wireless chael has fiite eergy; that is, C (t; τ) L ([, ) [, )), (4) where L ([, ) [, )) is the Hilbert space of square itegrable complex valued fuctios defied o [, ) [, ) with the orm f := [,)[,) f (t; τ) dτ dt <, f (t; τ) L ([, ) [, )). Likewise defie L ([, )) as the stadard Hilbert space of square itegrable complex valued fuctios defied o [, ) uder the orm x := x (t) dt, x L ([, )). (6) The space L ([, )) cotais all fiite eergy sigals defied o [, ). TheIRC(t; τ) of the chael has a fiite eergy ad belogs to L ([, ) [, ));thatis, (5) C := [,)[,) C (t; τ) dτ dt <. (7) Sice the trasmitted ad received sigals are fiite eergy sigals, the IR ca be viewed as a itegral operator mappig trasmitted sigals i L ([, )) ito L ([, )); that is, if s L ([, )),the y (t) = The tesor space C (t; τ) s (t τ) dτ L ([, )). (8) L ([, )) L ([, )) := {F (t, τ) L ([, ) [, )) : F (t, τ) = α k (t) φ k (τ), α k (t) L ([, )), φ k (τ) L ([, )), iteger} is dese i L ([, ) [, )); thatis,forayε>,there exist {α k } 1,{φ k} 1 L ([, )) such that [] μ := C (t; τ) (9) α k (t)φ k (τ) ε (1) ad μ. This implies that i the -orm, C(t; τ) ca be approximated to ay desired accuracy by a IR of the form α k(t)φ k (τ), which is factorizable by puttig g(t) := [α 1 (t) α (t) α (t)] ad f(τ) := [φ 1 (τ) φ (τ) φ (τ)] T,whereTdeotes vector or matrix traspose. The optimal approximatio of C(t; τ) by fuctios i L ([, )) L ([, )) correspodig to (1)cabewritte as μ := if α k (t) L ([,)), φ k (τ) L ([,)) C (t; τ) α k (t) φ k. (τ) (11) For arbitrary, expressio (11) isothigbuttheshortest distace betwee the impulse fuctio C(t; τ) ad the space L ([, )) L ([, ));thatis,μ = dist(c(t; τ), L ([, )) L ([, ))). The problem is to fid the miimizig fuctios {α k } 1, {φ k} 1.Thisproblemhasbeesolvedi[] for arbitrary positive. However, for fixed positive, the problem becomes the shortest distace, deoted by μ o := dist(c(t; τ), S),fromC(t; τ) to the set S:= {F(t, τ) = α k (t) φ k (τ),α k (t) L ([, )), φ k (τ) L ([, )),> fixed}. (1) Note that S isotasubspaceadisotacovexsetsiceitis ot closed uder additio. Therefore, the argumet preseted i [] does ot hold aymore sice the orthogoal projectio oto the set S is ot liear. Followig [], the impulse respose is viewed as a itegral operator T mappig trasmitted sigals from L ([, )) ito L ([, ));thatis,if s l L ([, )),they l (t) L ([, )),where y l (t) =(Ts l ) (t) := C (t; τ) s l (t τ) dτ. (13) Sice the impulse respose is fiite eergy, the operator T is a Hilbert-Schmidt or a trace class operator [, 3]. Let us deote the class of Hilbert-Schmidt operators actig from L ([, )) ito L ([, )) by C ad the Hilbert- Schmidt orm HS is defied by T HS = [,)[,) C(t; τ) dτ dt, T C. (14) The operator T admits a spectral factorizatio of the form [, 3] T= i=1 λ i ] i ψ i, (15) where is the tesor product, λ i > with λ i λ i+1, i = 1,,..., ad both {] i } 1 ad {ψ i } i=1 are orthoormal sequeces i L ([, )) adaregiveby ] i (t) = C (t; τ) ψ i (τ) dτ, ψ i (τ) = C (t; τ) ] i (t) dt. (16)

5 4 Iteratioal Joural of Ateas ad Propagatio The sum (15) has either a fiite or coutably ifiite umber of terms. The above represetatio is uique. The Hilbert- Schmidt orm of T is also give by T HS = λ i <. (17) The spectral factorizatio (15) yields the followig represetatio for the impulse respose C(t; τ) [3]: i C (t; τ) = λ i ] i (t) ψ i (τ). (18) i=1 It follows that the miimum i (11)isgivebytakig. α k (t) =λ k ] k (t), φ k (τ) =ψ k (τ),,,...,. (19) To further illustrate this result, ote that {] i } i=1 ad {ψ i} i=1 are orthoormal systems, ad simple computatios yield C (t; τ) λ k ] k (t)ψ k (τ) = C (t; τ) λ k. () Schmidt i [4] showed that for ay other fuctios f i (t), g i (τ) L ([, )), i = 1,,...,,thefollowig iequality holds: C (t; τ) f k (t)g k (τ) C (t; τ) λ k, (1) ad therefore the miimum i (11) isgiveby(19). The optimal approximatio follows as μ o = (t; τ) λ k ] k (t)ψ k = λ C (τ) () k k=+1 ad μ o.thatis,byicreasig,therhsof()ca be made arbitrarily small. I other words, for large eough, the followig approximatio is optimal i a mea-square sese: ad is factorizable. C (t; τ) λ i ] i (t) ψ i (τ) (3) i=1 The correspodig SDE is the give by [1] dx (t) =f(t) dw (t), y(t) =g(t) X (t), (4) where X(t) is the state of the chael ad W(t) is the stadard Browia motio. Sice state-space realizatios of impulse resposes are ot uique [1], a realizatio of the followig form i terms of the iphase ad quadrature compoets for the kth path withi the lth cluster ca be used as [1, 17] dx I kl (t) =AI kl (t) XI kl (t) dt + BI kl (t) dwi kl (t), I kl (t) =H I kl (t) XI kl (t), dx Q kl (t) =AQ kl (t) XQ kl (t) dt + BQ kl (t) dwq kl (t), Q kl (t) =H Q kl (t) XQ kl (t), (5) Trasmitted sigal (Volt) Time (s) Figure 1: Trasmitted sigal of a 3-picosecod Gaussia pulse shape. Door Wood table Wood table Metal wall Metal table Receivers Trasmitter Figure : The idoor eviromet cosidered i our experimet. where I kl (t) ad Q kl (t) are, respectively, the iphase ad quadrature compoet processes, X I kl (t) ad XQ kl (t) are, respectively, the state vectors of the iphase ad quadrature compoets, {W I kl (t)} t ad {WQ kl (t)} are two idepedet t stadard Browia motios which correspod to the iphase adquadraturecompoets,respectively,ada I kl (t), AQ kl (t), B I kl (t), BQ kl (t), HI kl (t), adhq kl (t) are matrices of appropriate dimesios. Note that I kl (t) ad Q kl (t) are two idepedet Gaussia processes with zero-mea ad equal variaces; that is, Var(I kl (t)) = Var(Q kl (t)) = Var(N kl (t)), wheren kl (t) is either I kl (t) or Q kl (t) [13]. They are related to the tap weight a kl (t, τ) ad phase φ kl (t, τ) by the expressios a kl (t, τ) = Ikl (t, τ) + Q kl (t, τ) ad φ kl(t, τ) = arcta(q kl (t, τ)/i kl (t, τ)), respectively. I the ext sectio, the stochastic arrowbad ad UWB idoor chael models are developed. 4. Stochastic State-Space Models for UWB Idoor Wireless Chaels I arrowbad systems, the equivalet idoor complex basebad represetatio cosists of Rayleigh-distributed amplitude ad uiformly distributed phase []. Thus, the Metal table Widow

6 Iteratioal Joural of Ateas ad Propagatio 5 Received sigal (Volt) st cluster d cluster Time (s) Figure 3: The measured UWB received sigal. 3rd cluster stochastic arrowbad idoor state-space chael model ca be represeted as where dx kl (t) =A kl (t) X kl (t) dt + B kl (t) dw kl (t), L K l y (t) = (Ckl I (t) X kl (t)) +(C Q kl (t) X kl (t)) l=1 e j arcta(cq kl (t)x kl(t)/c I kl (t)x kl(t)) s(t T l (t) τ kl (t))+d(t) V (t), X kl (t) =[X I kl (t)t X Q kl (t)t ] T, W kl (t) =[W I kl (t)t W Q kl (t)t ] T, (6) A kl (t) =[ AI kl (t) A Q kl (t)], B kl (t) =[ BI kl (t) B Q kl (t)], C I kl (t) =[HI kl (t) ], CQ kl (t) =[HQ kl (t)], I kl (t, τ) =C I kl (t) X kl (t), Q kl (t, τ) =C Q kl (t) X kl (t), (7) where V(t) is the measuremet oise which is assumed to be Gaussia with zero-mea ad uit variace ad the tap weight process a kl (t, τ) = (C I kl (t)x kl(t)) +(C Q kl (t)x kl(t)) ad the phase process φ kl (t, τ) = arcta(c Q kl (t)x kl(t)/c I kl (t)x kl(t)) are idepedet Rayleigh- ad uiform-distributed radom processes, respectively. I this case, the tap weight process a kl (t, τ) has the followig statistics [5]: E{a kl (t, τ)} = π Var (N kl (t)), E{(a kl (t, τ)) p }=(Var (N kl (t))) p/ Γ(1+ 1 p), Var {a kl (t, τ)} = ( π ) Var (N kl (t)), (8) where Γ(p) is the gamma fuctio. I UWB systems, as metioed earlier, the most commo amplitude distributio of the received sigal is Nakagami distributio [6 8]. Its probability desity fuctio is give by [6] f (x) = Γ (m) (m Ω )m x m 1 exp ( m Ω x ), (9) where m.5is the shape parameter, Γ(m) is the Gamma fuctio, ad Ω cotrols the spread of distributio. The mparameter is ofte modeled as a radom variable [6]. For iteger value of m, the distributio describes m orthogoal idepedet Rayleigh-distributed radom variables. That is, for M Rayleigh-distributed radom variables Z i,theprobability desity fuctio of radom variable Y, defied as Y= M i=1 Z i,isgivebyanakagamidistributiowith parameter m=m[7]. Sice multiple orthogoal idepedet Rayleigh-distributed radom variables ca geerate Nakagami distributio, the stochastic UWB idoor state-space chael model ca be represeted by dx ikl (t) =A ikl (t) X ikl (t) dt + B ikl (t) dw ikl (t), L K l y (t) = (Cikl I (t) X ikl (t)) +(C Q ikl (t) X ikl (t)) where l=1 M kl i=1 e j arcta(cq ikl (t)x ikl(t)/c I ikl (t)x ikl(t)) s(t T l (t) τ kl (t))+d(t) V (t), X ikl (t) =[X I ikl (t)t X Q ikl (t)t ] T, W ikl (t) =[W I ikl (t)t W Q ikl (t)t ] T, C I ikl (t) =[HI ikl (t) ], CQ A ikl (t) =[ AI ikl (t) A Q ikl (t)], B ikl (t) =[ BI ikl (t) B Q ikl (t)], ikl (t) =[HQ ikl (t)], (3) I ikl (t, τ) =C I ikl (t) X ikl (t), Q ikl (t, τ) =C Q ikl (t) X ikl (t), (31)

7 6 Iteratioal Joural of Ateas ad Propagatio Normalized frequecy 3 1 Nakagami (m = 3; Ω =.8) 1st cluster Received sigal amplitude (mv) (a) Normalized frequecy 4 Normalized frequecy Nakagami (m = 3; Ω =.18) Received sigal amplitude (mv) Measuremets Nakagami distributio 3 1 Nakagami (m = 5; Ω =.4) d cluster Received sigal amplitude (mv) 3rd cluster (c) Figure 4: Histogram of measuremet data for the domiat paths withi the three clusters that are best fit to Nakagami distributios. Received sigal (Volt) st cluster Time (s) (a) Received sigal (Volt) 1 3 3rd cluster 1 Received sigal (Volt) d cluster Time (s) Estimated Measured (b) Time (s) (c) Figure 5: Measured ad estimated received sigals usig the EM algorithm combied with the EKF for the 1st, d, ad 3rd clusters. where L is the total umber of clusters, K l is the total umber of resolvable delay bis (paths), ad M kl is the umber of oresolvable delay bis withi the resolvable delay bi k i cluster l.ithiscase,thetapweightprocessa kl (t, τ) has the followig statistics [5]: E{a kl (t, τ)} = Var (N kl (t)) Γ((1/) (M kl +1)), Γ(M kl ) E{(a kl (t, τ)) p }=(Var (N kl (t))) p/ Γ((1/) (M kl +p)), Γ(M kl ) Ω kl =Var (N kl (t)) Γ(M kl +1). Γ(M kl ) p, (3) (b) It ca be oticed i (3) that the received sigal measuremet, y(t), is a oliear fuctio of the state variables of the model. The UWB chael parameters are estimatedusigtheemalgorithm,adtheiphasead quadrature compoets are estimated directly from received sigal measuremets usig the EKF. A filter-based EM algorithm together with the EKF is employed to estimate the chael model parameters ad states i (3). These filters use oly the first- ad secod-order statistics ad are also recursive ad therefore ca be implemeted olie. These algorithms have bee recetly utilized i [11 13] to estimate the chael parameters ad states i arrowbad eviromets, ad therefore the formulatios of these algorithms are ot preseted i this paper. Experimetal results demostratig the applicability of these algorithms i UWB idoor eviromets are discussed i the ext sectio.

8 Iteratioal Joural of Ateas ad Propagatio 7 5. Experimetal Setup ad Numerical Results AsimpleGaussiapulsewithcleapulseshapeadarrow pulse width is chose as UWB source sigal. The experimetalsetupissimilartotheoei[8]. It comprises a 3- picosecod Gaussia pulse (see Figure 1) thatmodulatesa carrier sigal cetered at 8 GHz ad is trasmitted through a omidirectioal UWB atea. Multiple directioal Vivaldi subarray receivig ateas are located at distict locatios i a idoor eviromet to receive the modulated pulse sigal. Each received modulated Gaussia pulse is amplified through a low oise amplifier (LNA) ad the stored i a multichael Tektroix TDS8 samplig oscilloscope. The trasmitter is located ext to a metal wall. The receivig atea is placed 1 cm away from the trasmitter ad the moved alog the same directio away from the trasmitter for cm, 5 cm, 1 m, ad m. This sceario is demostrated i Figure. Ithiseviromet,thetras- mitted sigal suffers from reflectio from the metal wall, ceilig, or floor or is scattered by the corer of the metal table, ad the it reaches the receiver. Figure 3 shows the measured received sigal which cosists of three clusters. The measuremet data are amplified by 3 db ad it ca be see i Figure 4 that the domiat path i each cluster is best fit to Nakagami distributio with differet parameters. For example, the domiat path i the first cluster is best fit to Nakagami distributio with parameters m = 3ad Ω =.8. This idicates that there are three oresolvable delay bis withi this path (i.e., M 11 =3).Figure 5 shows the measured ad estimated received sigals usig the EM algorithm together with the EKF for the three clusters usig a 4th-order model. It ca be oticed that the UWB received sigal has bee estimated with very high accuracy ad it takes little iteratio for the estimatio algorithm to coverge. At a certai time istat, the system parameters for the domiat path i the 1st cluster, which cosists of three oresolvable delay bis, are estimated as follows: A 111 = [ [ 1 ], [ ] A 11 = [ [ 1 ], [ ] A 311 = [ [ 1 ], [ ] B 111 = [ [ ], [ ] B 11 = [ [ ], [ ] B 311 = [ [ ], [ ] C I 111 = C I 11 = C I 311 =[1 ], C Q 111 = C Q 11 = C Q 311 =[ 1 ], D = [.8765]. (33) Notice that the EM algorithm estimates B ad D istead of B ad D. Also ote that the parameters L, K l, M kl, T l, ad τ kl areassumedkowthroughtheestimatioprocess. I fact, the parameters L, K l,adm kl ca be estimated by various estimatio algorithms such as miimum descriptio legth [9], multiple hypothesis testig [3], expoetial fittig test [31], ad liear piecewise variatio [3]. Ad a soudig device is usually dedicated to estimate the time delay of each discrete path (i.e., T l ad τ kl )suchastherake receiver [33]. 6. Coclusio This paper describes a geeral scheme for extractig mathematical UWB idoor chael models from oisy received sigal measuremets. The UWB chael models are represeted i stochastic state-space form, i which its system output produces Nakagami-distributed received sigal stregth ad it is show to approximate the geeral TV IR of the chael as close as desired. Experimetal results idicate that the measured data ca be regeerated with high accuracy. Ackowledgmets This paper has bee authored by employees of UT-Battelle, LLC, uder Cotract o. DE-AC5-OR75 with the US Departmet of Eergy. Also, this work was supported i part by NSF Grat o. CMMI Refereces [1] Federal Commuicatios Commissio, First report -48,. []M.Z.WiadR.A.Scholtz, Impulseradio:howitworks, IEEE Commuicatios Letters,vol.,o.,pp.36 38,1998. [3] A. F. Molisch, Wireless Commuicatios, IEEE Press/Wiley, New York, NY, USA, 5. [4] R. C. Qiu, A geeralized time domai multipath chael ad its applicatio i ultra-widebad (UWB) wireless optimal receiver part III: system performace aalysis, IEEE Trasactios o Wireless Commuicatios,vol.5,o.1,pp , 6.

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