UWB Indoor Delay Profile Model For Residential and Commercial Environments

Transcription

1 UWB Indoor Delay Profle Model For Resdental and Commercal Envronments S.S. Ghassemzadeh 1, L. J. Greensten, A. Kavčć 3, T. Svensson 3, V. Tarokh 3 Abstract We present a statstcal model for the delay profle of ultra-wdeband channels n ndoor envronments. Two knds of profles are defned, namely the multpath ntensty profle (MIP) and the power delay profle (PDP). The MIP s he delay profle at a pont n space, whle the PDP s a local spatal average. The model s based on 6, complex frequency response measurements from commercal buldngs and resdental homes, wth the transmtter and recever both n lne-of-sght (LOS) and non-lne-of-sght (NLS) of each other. Smulatons usng the PDP model show excellent statstcal agreement wth the measured data. Index Te Multpath Intensty Profle, multpath fadng, Power Delay Profle, root mean square delay spread, UWB. I. INTRODUCTION ne proposed applcaton of Ultra-Wdeband (UWB) O technology s to wreless personal area networks (WPAN), where the workng envronment would be nsde resdental and commercal buldngs [1]. To characterze the rado channel of such envronments over ultra-wde bandwdths, we conducted measurements n sngle-famly dwellngs and commercal locatons, spannng a frequency range from to 8 GHz. Large-scale propagaton results from these measurements, specfcally the path loss, are reported n a companon paper []. In ths paper, we report on the features of small-scale propagaton, specfcally the delay profle. Several statstcal models for UWB channel behavor have been proposed, both n standards contrbutons (e.g., [3]) and n publshed papers [4]-[7]. Here, we buld on the delay profle modelng approaches taken n [6] and [7], whch were based on extensve measurements taken n homes and centered on 5 GHz. The dfferences n our new database are three-fold: (1) The measurement bandwdth s 6 GHz, rather than 1.5 GHz; () commercal buldngs are measured n addton to homes; and (3) measurements are made at Ths materal s based upon research supported n part by the Natonal Scence Foundaton under the grant No. CCR and Alan T. Waterman award, grant No. CCR Any opnons, fndngs and conclusons or recommendaton expressed n ths publcaton are those of the authors and do not necessary reflect the vews of the Natonal Scence Foundaton. S.S. Ghassemzadeh (saeedg@research.att.com, correspondng author) s wth AT&T Labs-Research, Florham Park, NJ, USA. L.J. Greensten s wth WINLAB-Rutgers Unversty, Pscataway, NJ, USA. A. Kavčć, T. Svensson and V. Tarokh are wth the Dvson of Engneerng and Appled Scences, Harvard Unversty, Cambrdge MA, USA spatal postons about each nomnal locaton. The mpact of the latter change s that t permts us to estmate the power delay profle (PDP), whch s the local spatal average of the squared magntude of the mpulse response (normalzed to have an area, over delay, of 1). The quantty modeled n [6] and [7] was the PDP at a sngle pont, whch we called the multpath ntensty profle (MIP). Here, we model both the PDP and MIP, for both lne-of-sght (LOS) and non-lne-ofsght (NLS) paths. Our prmary nterest, however, s the PDP. The paper s organzed as follows: Secton II descrbes our MIP modelng and ts extenson to PDP modelng. Secton III descrbes the data collecton and reducton. Secton IV derves the models and quantfes ther parameter values. In Secton V, PDP models are presented, for both LOS and NLS paths, and are used to smulate a new database of complex frequency responses that well-matches the measured data. A. Defntons II. MODELING BACKGROUND Multpath channels are assumed to be lnear and thus completely defned by ther mpulse responses. The tme- and locaton-dependent mpulse response for a gven transmtreceve path can be wrtten as = j (,, t d) ht (,, d) = a( t,, de ) φ δ( - ) where a (t,,d) and φ (t,,d) are the ampltude and phase of the th multpath, arrvng wth excess tme delay ; d s the path length; and L s the number of resolvable multpaths. The mpulse responses of ndoor UWB channels have been shown to be essentally tme-nvarant [5], whch allows us to defne the tme-nvarant multpath ntensty profle for a gven recever poston as X( ) = P δ ( - ) () where = P = and P = 1 (3) a = a = Two key parameters used to characterze multpath are the (1)

2 Fg. 1. Scatter plot of α vs. d for NLS paths: a) Resdental, b) Commercal. mean excess delay,, and the delay spread,, defned as L 1 L 1 P and P ( ) (4) = = = = Snce the MIP, (), s non-negatve and ntegrates to 1, t has the propertes of a probablty dstrbuton over the delay parameter,. Then, and can be vewed as the frst moment and second central moment, respectvely, of the MIP. All of the above concernng the MIP apples equally to the PDP, wth one dfference: Each a n (3) s replaced by ts local spatal average value. In our measurements [] and data reductons, 5 values of a are obtaned for each delay (ndexed by ), correspondng to 5 spatal postons on a cm cm grd for each nomnal locaton. Ther numercal average s our estmate of the local spatal average of a. In what follows, the MIP and PDP are statstcally modeled usng the same process. For the MIP, only one pont on the 5-pont grd s used; n the PDP case, all are used. B. Mathematcal Form Followng [6] and [7], we treat the delay profle (MIP or PDP) as a decayng exponental over delay, multpled by a lognormal process over delay. In db form, the MIP s P C = K-α + S > K-α + S } = for LOS fornls where P represents the db values of P n (3), C, K and α are constants defnng the medan profle, and s a (5) Fg.. Scatter plot of g vs. for NLS paths: a) Resdental, b) Commercal. normalzng parameter, so that α s dmensonless. (Our choce for s dscussed later.) The devatons from ths medan are characterzed by a zero-mean, normally dstrbuted random process, S, wth standard devaton σ s. It can therefore be wrtten as S = y σ s, where y s a zero-mean, unt-varance normal random process on. The man dfference between LOS and NLS profles s the strong term C at the lowest delay ( = ) for LOS paths, correspondng to the drect ray from transmtter to recever. The model n [6] fts (5) to the data for each locaton; produces a common set of parameters for all locatons n a gven home; and then derves the dstrbutons, over all homes, of the extracted parameters. The model n [7] provdes a more n-depth characterzaton (as explaned below) and acheves ths by frst poolng the data over all homes. In the present study, we apply the more detaled model of [7] to each resdental (or commercal) buldng separately, and then characterze the varaton over buldngs of the extracted parameters. III. DATA COLLECTION AND REDUCTION We used a network analyzer to measure complex frequency responses centered at 5 GHz, over a measurement bandwdth of 6 GHz. Data were collected n homes and commercal buldng stes, both on LOS and NLS paths. For each buldng type and path type, we chose about 3 receve locatons, wth transmtter-to-recever separatons rangng from.8 m to 1.5 m. For each locaton, we made 5 spatal measurements on a cm x cm horzontal grd. The total database thus conssted of about 6, complex frequency responses. For each measurement, we dd the followng:

3 We removed the effects of hardware by usng the stored calbraton data. Ths ncluded the antenna patterns. We performed a 161-pont nverse-fourer transform, resultng n a complex mpulse response wth tme delay rangng from ns to 66 ns, wth a bn sze of ps. We computed the magntude-square of the complex mpulse responses. We estmated the frst multpath arrval and shfted the responses n tme so that the frst arrval tme corresponds to ns. For each locaton, we ether used the data from the center of the grd only, to get the local MIP; or averaged the squared magntudes over all 5 grd postons, to get the local PDP. Fnally, we normalzed the profle to acheve unt area wth a nose floor of about 1 db above the measurement equpment s average nose-floor. The populaton of derved delay profles s a set, correspondng to two buldng types (resdental and commercal) and two path types (LOS and NLS), wth about 6 locatons measured for each combnaton. In each of the four categores, we developed a statstcal model for both the MIP and the PDP. The remander of the paper descrbes these models and the comparsons among them. A. Delay Spread Statstcs IV. MODEL FITTING Usng (4), we computed the delay spread statstcs for ndvdual profles. Table I shows the statstcs of for resdental and commercal buldngs. For ndvdual locatons, we notced that the delay spread found from ether the MIP or ts correspondng PDP was smlar. In fttng data to (5), we use the same value for over all profles wthn a common category of path type (LOS or NLS) and buldng type (resdental or commercal). The value we use for each category s the average of the values n Table I for MIPs and PDPs. B. Intra-Buldng Model Fttng As a startng pont, we ft (5) to all measured profles. The result s a parameter set χ 1 ={C n,m,α n,m,σ S,n,m,d n,m,y n,m }, where m s an ndex over locatons wthn buldng n, and d n,m s the correspondng T-R separatons. The vector y n,m ncludes all y taken from buldng n and locaton m. We confrmed that y n has a Gaussan dstrbuton as reported earler n [6] and [7]. We do not nclude the analyss of the constant K, snce t s unquely specfed by the unt summaton constrant. Slope dependence on dstance: The dependence between the slope {α m } n and T-R separaton {d m } n (over all locatons m wthn the buldng n) s modeled as α ( d ) = α -γ log ( d ) + ε (6) m m 1 m where α and γ are constants and ε s a zero-mean Gaussan random varaton wth standard devaton σ ε. The parameter α s the average slope at the reference dstance of 1 meter and γ captures the average slope decay wth dstance. Fg. 1 shows the scatter plot of α m vs. d m for NLS paths n typcal resdental and commercal settngs. The result of fttng (6) to a sngle buldng ndexed by n s the parameter set χ ={α,n,γ n,σ ε,n }. Power dependence of the frst return on dstance: On LOS paths, the dependency between the power of the frst multpath {C m } n and the T-R separaton {d m } n, s modeled as C ( d ) = C -γ log ( d ) + ε, (7) m m C 1 m C where C and γ C are constants characterzng the average power of the frst multpath at 1 meter, and ts decay wth dstance, respectvely. The random varaton ε C s zero-mean Gaussan, wth standard devaton σ C. Fttng (7) results n another set of parameters χ 3 ={C,n,γ C,n,σ C,n }. Multpath correlaton: We fnd the multpath correlaton from the vector y n usng the same method as n [7]. We confrm that the correlaton between multpaths arrvng wth a separaton of k bns can be modeled by an exponentally decayng functon, 1 ρy ( k ) a e = -bk > k =, (8) k where a and b are constants. The result s a set of correlaton varables χ 4 ={a n,b n } over buldngs ndexed by n. Small-scale shadowng: Smlar to [7], we decompose the random process y as y g x = (9) where x s a statonary zero-mean, unt-varance Gaussan varaton and g s a determnstc functon of ndex. From the vector y n, we analyzed g separately for each buldng and found t to be an exponental functon of tme delay, Table I: DELAY CHARACTERISTICS FOR RESIDENTIAL AND COMMERCIAL BUILDINGS Resdental Commercal σ σ M LOS I P NLS P LOS D P NLS

4 Table II. STATISTICS OF MODEL PARAMETERS ACROSS RESIDENTIAL BUILDINGS LOS MIP NLS MIP LOS PDP NLS PDP Set Parameter Mean Std Mean Std Mean Std Mean Std α χ γ σ ε C NA NA NA NA χ 3 γ C NA NA NA NA σ C NA NA.84. NA NA χ 4 a b σ χ 5 β σ S exp,. (1) g = σ β Fg. llustrates the scatter plot of g vs. for NLS paths n typcal resdental and commercal buldngs. We estmated the parameters σ and β for each buldng, and found σ S,n as the sample average of σ S,n,m (set χ 1 ) over dfferent locatons m for buldng n. The result s the parameter set χ 5 ={σ,n,β n,σ S,n }. C. Model Parameter Statstcs The sets χ, χ 3, χ 4 and χ 5 have model parameters for the full model, ftted to ndvdual buldngs. The statstcs for the model parameters, over all buldngs, are summarzed n Tables II and III for resdental and commercal buldngs, respectvely. We summarze our fndngs as follows. Slope dependency on dstance: From the set χ, we see that α s hgher for PDPs (faster decay) than for the MIPs; also that γ changes sgnfcantly between buldngs and s nversely correlated wth α. The cross-correlaton coeffcent between α and γ s hgh (>.54) for both MIPs and PDPs. We fnd α to approxmately follow a Gamma dstrbuton over buldngs, as does ˆ γ = γ + 1. Fg. 3 shows the dstrbuton of ˆ γ over buldngs for NLS resdental and commercal envronments. The result s the same for LOS paths. We fnd σ ε to have less varaton between buldngs than α and γ, and to be uncorrelated wth both of them. Power dependency of frst return on dstance: We fnd C and σ C from χ 3, to be constant over buldngs. The slope γ C shows varaton between buldngs that can be modeled usng a Gaussan dstrbuton. Multpath correlaton: We found that the correlaton between adjacent multpaths s generally small for MIPs. The mean of a (average correlaton between two adjacent multpaths) s below.35 n all envronments. Comparng the correlaton for commercal and resdental buldngs, we fnd resdental buldngs to show sgnfcantly more correlaton than commercal buldngs. Also, the correlatons are 1 We add to γ to ncorporate negatve values of γ nto the one-sded gamma dstrbuton. substantally hgher for PDPs wth the mean of a rangng from.54 to.86 over all envronments. Tme delay dependence on model varatons: We fnd the parameters σ, β and σ S, to vary nsgnfcantly between buldngs. Also, σ S s smaller for PDPs than for MIPs. The key dfferences between the MIP and PDP models resde n the decay constant α, the lognormal standard devaton σ S, and the correlatons between paths. All these dfferences are explanable n te of the averagng used to estmate the PDPs, whch smooths both spatal varatons and the effects of nose. Hereafter, we focus on the PDPs. D. Key Parameters n a Smplfed Model A new PDP model can be constructed usng the complete statstcal characterstcs of the channel. Ths approach s not chosen snce t would result n hgh model complexty wthout suffcent ncrease n accuracy. Instead, we have chosen to lmt the number of model parameters, focusng on capturng the key features of the PDPs. From the results of the prevous secton and from model smulaton experments, we conclude that a smplfed model Fg 3. Dstrbuton of ˆ γ for NLS paths: Resdental (b) Commercal.

5 TABLE III. STATISTICS OF MODEL PARAMETERS ACROSS COMMERCIAL BUILDINGS LOS MIP NLS MIP LOS PDP NLS PDP Set Parameter Mean Std Mean Std Mean Std Mean Std α χ γ σ ε C NA NA NA NA χ 3 γ C.45.6 NA NA NA NA σ C NA NA.88. NA NA χ 4 a b σ χ 5 β σ S can be constructed usng the parameters gven n Tables II and III. The model components are as follows. Parameters at the reference dstance: We characterze the parameter α n (6) as a constant wth value fxed to ts mean from Tables II and III. For LOS paths, we smlarly defne C to be fxed. Buldng dependency: We fnd γ and γ C to vary between buldngs. We characterze γ by the random varable γ = γˆ, where ˆ γ has a gamma probablty dstrbuton wth densty ˆ γ A 1 B 1 p( ˆ γ AB, ) = ˆ γ e (11) A B Γ( A) and Γ(A) s the gamma functon Γ ( A) = ( A 1)! (1) The constants A and B are gven n Table IV. For model smplcty, we fx γ C to ts mean value for each buldng type. Dstance dependency: We can capture the random effects of locaton (T-R separaton) wthn a buldng on the slope α and frst LOS path gan C. We do so va zero-mean Gaussan random varatons ε and ε C, wth standard devatons σ ε and σ C, respectvely. The parameters σ ε and σ C are fxed to ther mean values for each buldng type. Small-scale shadowng: For model smplcty, we set g at 1 over all (.e., y has the same varance over all ), elmnatng parameters σ and β. Also, we fx the correlaton parameters a and b at ther mean values, gven n Tables II and III. A. NLS Paths V. PDP MODEL AND SIMULATIONS Combnng our fndngs, we construct the overall NLS PDP model from (5) to (1) as ( ) P(, d) = K α + γ log d + ε + σ x 1 S (13) The model parameters are summarzed n Tables IV. Agan, the constant K, s found from the unt summaton constrant on the PDP. B. LOS Paths From (5), we see that the LOS PDP model s based on the model for NLS envronment for all multpaths except the frst one. We characterze the frst multpath by usng (8). Then the complete model s gven as C γc log 1( d) + εc for = P(, d) = K α + Otherwse γ log 1( d ) + ε + σs x (14) where the model parameters are summarzed Table IV. As for the NLS model, K s found such that the unt sum constrant s satsfed. C. Smulatons We smulate the PDPs from (13) and (14) for the same number of buldngs and set of dstances as n our database. For smulaton purposes, we frst select ether commercal or resdental buldngs, and then ether NLS or LOS paths, and then choose the approprate parameter values from Table IV. We then generate realzatons of γ (for buldngs). For each realzaton of γ, we generate 75 realzatons of ε (3 T- R separatons and 5 grd postons) and 75 realzatons of ε C f LOS paths are beng smulated. For each realzaton of ε, we generate 1 values of x (for multpaths wth excess delay of to ns), and construct a sngle PDP. Our am s to calculate certan statstcs from the smulated database of delay profles and to compare them wth those obtaned from TABLE IV. MODEL PARAMETERS VALUES. Resdental Commercal LOS NLS LOS NLS α A B σ ε C 4.7 NA 4.68 NA γ C 1.35 NA.38 NA σ C.84 NA.88 NA a b σ S

6 Fgure 5. Commulatve dstrbutons of delay spread n resdental buldngs Fgure 4. Average profles for NLS paths: a) Resdental, b) Commercal. the measured database. The average PDP for NLS paths n resdental and commercal buldngs are shown n Fg. 4. Probablty dstrbutons of the delay spread n resdental buldngs, for both LOS and NLS paths, are gven n Fg. 5. In these comparsons of smulated and measured data, we fnd that the model perfo very well,.e., captures key statstcal propertes of the channel. Further comparsons are n progress. VI. CONCLUSION We have shown how deas from two separate UWB multpath channel models, can be combned to capture detaled characterstcs of the multpath channel and the statstcal varablty between buldngs. Model smulatons demonstrate good performance n capturng channel propertes. Further data collecton for both knds of buldngs would be helpful n confrmng model stablty. Meanwhle, testng of the model s contnung. Also, further data reductons, to characterze the spatal statstcs at a locaton, would help to enrch the model. REFERENCES [1] IEEE , IEEE standard for wreless personal networks (WPAN), URL: [] S.S. Ghassemzadeh, L.J. Greensten, A. Kavcc, T. Svensson, V. Tarokh, Statstcal path loss model for resdental and commercal buldngs, Proceedngs IEEE VTC Fall 3, October 3. [3] Channel-Modelng-Subcommttee-Report for IEEE-8.15.SG3a- URL: [4] D. Cassol, M.Z. Wn and A. Molsch, The ultra-wde bandwdth ndoor channel: from statstcal model to smulatons, IEEE J. Sel. Areas Commun., Aug.. [5] S.S. Ghassemzadeh, et.al., Measurement and modelng of an ultrawdeband ndoor channel, IEEE Trans. on Commun., to appear. [6] S.S. Ghassemzadeh, L.J. Greensten, T. Svensson, and V. Tarokh, A multpath ntensty profle model for resdental, Proceedngs IEEE WCNC-3, March 3. [7], An mpulse response model for resdental wreless channels, Proceedngs IEEE Globecom, December 3, to appear. ACKNOWLEDGEMENT The authors thank Dr. Alexander Hamovch and Dr. Ham Grebel for use of ther anechoc chamber at the New Jersey Insttute of Technology; Mr. Chrs Rce of AT&T Labs- Research, for valuable comments and suggestons on the hardware set-up; and lastly but not least, all the homeowners from AT&T Labs and Harvard Unversty who gracously allowed us to nvade ther premses wth our measurements.