Dec.11-14, th Intl, Comference on Mobile and Personal Communications, Unive of Warwick,England pp II. IMPULSE RESPONSE CHANNEL MODEL

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1 5th ntl, Comference on Moble and Personal Communcatons, Unve of Warwck,England pp Dec.11-14, 1989!'" MULTPATH PROPAGATON MODELS FOR N-BULDNG COMMUNCATONS Theodore S. Rappaport and ScottY. Sedel Vrgna Polytechnc nsttute and State Unversty Blacksburg, Vrgna, USA ABSTRACT Ths work has developed statstcal ndoor rado channel mpulse response models (SRCM) for the analyss of factory and open plan offce communcaton systems. These models wll permt research nto the development of wdeband wreless networks for autonomous 'guded vehcles (AGVs), vson systems, and portable personal communcatons nsde buldngs. Models have been developed whch characterze the dscrete mpulse response of ndoor rado channels for both lne-of-sght (LOS) and obstructed (ODS) topographes. The effects of transmtter-recever (T-R) dstance and recever senstvty are ncorporated n the models. Computer smulatons whch use the models presented here have recreated multpath power delay pmftles that are hghly representatve of actual measurements.. NTRODUCTON Models whch characterze the mpulse responses of factory rado channels would be useful n the analyss of both equalzed and unequalzed dgtal communcatons systems and arc needed to explore dversty, modulaton, and codng technques. Due to prevous lack of nterest by the manufacturng ndustry, factory rado propagaton models have not been developed. Current rado systems arc used to control large machnery or provde pagng. These systems arc generally narrow band (bandwdth < 2S khz) (1), However, there has been recent nterest by the EEE 82.4L standards commttee to develop ndoor rado systems whch accommodate data rates n exccas of Megabt per second. t s envsoned that n the future, large fleets of autonomous guded vehcles (AGV's) whch transfer sgnfcant amounts of work-n-process throughout the factory wll become cqmmon, and fleltblc portable communcatons wll be needed for smple confguraton of the factory floor ( 11. Control of an AGV network s not possble wth copper wre snce the vehcles wll have to be able to move throughout the entre factory. Optcal/nfra-red control s possble, but becomes severely hampered when a lne-of-sght path to a stato,nary base staton becomes obstructed. An advantage of electromagnetc radowave propagaton s the ablty to communcate n the absence of a lne-of-sght path. n order to support the antcpated hgh data rates of the factory and offce buldng of the future, wde bandwdths and complex multple accesa systems such as tme-dvson mu.ltplcx 1 tme dvson multple ac:cesa (TDM{fDMA) and drect sequence spread spectrum (DSSS) must be used. Determnaton of what multple access technque to mplement and the 1111Umum bt rate tbc channel can support wthout equalzaton requres knowp of the propagaton envronment. Moble corununcaton wthn a factory envronment nvolves reflec:ton, dfl'racton, and scatterng of rado waves by walls, celngs, and other man-ude objects such as heavy machnery and nventory, Because of thcac effects, the transmtted sgnal s lkely to arrve by more than one path throuah the medum. Ths s known as multpath propapton. The n:cevcd sgnal s the pbuor sum of the multpath components whch arrve at the recever. n narrow band transmsson, ths cauaea fluctuatons n the receved sp.al strength (CW fadng) (2,3,4). n wde band transmsson, a aeres of delayed, attenuated, and pbue shfted replcas of the transmtted sgnal arc receved. Ths leads to ntersymbol nterference (ls) n dgtal communcatons systems. Wdeband ndoor rado channel measurements have been made by a handful of researchers (4-7). Work n (4-6) has detaled measurements awfc n offce buldngs. However, there arc gross physcal dfferences between offces and factores (71. Buldng constructon technques, contents, and wall placements dffer for offce buldngs and manufacturng envronments. Asles n factores are often orthogonal and ntcncct one another. Metal machnery or nventory as well as metal celng trusswork arc present n factores. These surroundng objects can lead to sgnfcantly dfferent mpulse responses than tho measured n offce buldngs. n (9j,_a wde band system provded rms delay spread (eqn. 5) statstcs for factory channels at 13 MHz. Medan valuea of delay spread arc reported as 95 ns for lne-of-sght toposraphea and 15 ns for obstructed topographes. The rnallmum oblerwd delay spread wu 3 ll (7). Ths compares wth 5 na n a conventonal offce buudna (SJ. As noted n (71, there arc compellng reaaons why a atadstleal channel model needs to be developed for the factory envronment. Frst, the number of potental reflecton s too great to ncorporate nto a determnstc ray-tracng propagaton model. n addton, the locatons of potental scatterers vary consderably as transmtten and recevers are moved wthn a buldng, and from buldng to buldng. Whle t should be pos.,ble to. ncorporate a lmted number of specular reflectors by ray tracng, measurements whch yeld scatterng parameters for walls, celngs, and other common factory obstacles have not yet been reported n the lterature. Factory rado channels may be d\'ded nto two basc categores. When there s a drect path between the transmtter and recever lne-of-sght (LOS) topography exsts: absence of such a path ndcat an obstructed (ODS) topography!7). n ths paper, we present statstcal models that have been developed for both LOS and ODS topographes based upon the emprcal propagaton reported. n (7), These models descrbe the dstrbuton of the nunbcr of multpath components, the probablty of recevng a multpath component at a partcular excess delay, the dstrbuton of the ampltudes of multpath components at a partcular excess delay, and the correlaton between multpath component ampltudes over both space and tme. n addton to the development of the models, we have ncorporated the models nto a computer smulaton program. The smulator creates mujtpath channel power delay prordes wth the same ensemble statstcs as the measured data. t s antcpated that wth ths smulaton tool, we wll be able to predct the response at a recever of any transmtted sgnal by convoluton wth the smulated channel. Ths smulaton model wll then be able to detcnnne vable technques for multple access, channel codng, and equalzaton requred to provde the hgh data rate communcatons necessary for the factores of the future.. MPULSE RESPONSE CHANNEL MODEL The mpulse response h(t) of a lnear system s a useful characterzaton of the system snce the output of the system can be computed through convoluton of the appled nput wth the mpulse response. n a multpath rado channel, the mpulse response can be modeled statstcally. We assume that the multpath channel acta as a lnear falter wth a complex baseband mpulse respon11e. Ths has been shown to be a good model for varous propagaton channels such as propagaton by the onosphere or troposphere 181, urban multpath propapton (2,9-111, and ndoor multpath propagaton (.5,7). t sufru:cs to characterze the multpath channel by the low pau channel mpulse response ht,(t) whch s gven by hb(t) L«ke-l fc, 6(t- Tt)' k n (1), «t represents a real attenuaton factor, e'wc'' represents a lnoar phase shft due to propagaton delay, and Tt s the tme delay of the k-th path n the channel wth respect to the lne-of-sght path. Addtonal phase shfts may be nduced by reflecton coeffcents of scattcrers. By modulatng an RF carrer wth a 7.8 ns soundng probe, the output of the low pass channel closely approxmates the mpulse response h,(t). nstead of measurng the true mpulse response, whch requres an accurate measurement of the phase of multpath components, the mujtpath power delay profle h,(t) 2 wu measured n (7) to provde data for ampltude and eltccss delay statstcs -for ndoor factory multpath channels. When processng the data couected n (11, we fonn dscrete multpath power delay profdes () hb(t) 1 2 ::z L: Gl6(t - Tt) (2) k where the power proftle s quantzed nto bns havng 7.8 ns duratona. Wthn each bn, the arfs arc averqed to obtan an equvalent A at a djcrete ejwcss tme delay T 1 Dccauac power mpulse responaca wen: recorded at J./4 ntervals on a 1-m track at each mcuurement locaton, local (amall ecale) fadng of the ndvdual multpath compd\lcdts wu

2 observed. Thus. each measurement s not onjy a functon of tme delay but also of space. For a poston x, on a gven track. the baseband power mpulse respone can be approxmated by hb(txo) = L: L A(X)!S(t - T K(X)). (J) X xo K where the excess delay tmes (T Kl are quantzed to 7.8 ns ntervals. Thus. fluctuatons of dscrete multpath strengths and delays may be statstcally modeled over local areas, and thee models are presented n ths paper. ll. MULTPATU CHANNEL PARAMETERS Wde band multpath channels arc grossly quantfed by ther mean. excess delay (T) and nns delay spread (a) (4-7, tc former s the frst moment of the power delay profde and s defned to be L«Tr where o, =- L«'.,, k The latter s the square root of the second central moment of the profdo and s defned to be L«T fl J? - () 2 where _1r (S) a, n (4) and (5), the delays of each profle are measured relatve to a rust detectable sgnal (lne-of skbt) arrvng at ". The term, n (4) and (S) s a relatve meaawe of receved power for a gven profle. Statltc:l on mean excess delay and nns delay spread for factory tadn channels are gven n 171 AJthOUJh the range of rms delay spread s the same for lne-of slgbt and obataucted topo8faphes (35-15 ns except for one tneast1mllent locaton), the medan value of rms delay spread s slghtly greater n obstructed topographes (los ns) than n Une-of sght topographes (95 ns). V,!XPERMBNTAL PROCEDURE EU:? &-c: ::) c::: : ::1 (,::.,o. c :::.-::::::J t:::j"j.l.lkcj O:y U l-:ocw\ whch measured the attenuated, dstorted, and delayed versons of a repettvely transmtted 1 ns (7.8 ns rms uraton) pulse. The measured data were couected from 5 dutcrent measuent locatons wthn fve djtcrnt factory buudlnss n ndana. At each mcaaurement locaton, the recever was moved along a l m track n order to examne the characterstcs of mult path sgnal fadng over l m local areas. Data were measured at nneteen dacrcto locatons along the l m track. Upon processng, the amputudo of each.mujtpath component s scaled to a loa free space reference whch nduced a 38 db propasaton loa. Tho excess delay tme axs WQ dvded nto 7.8 ns bns for detennnaton of the models presented n tw. paper. 1\ threshold for each prordc n a l m local area s determned based on the average of the 19 profles measured n that l m local area. A mnmum receved power threshold of 48 db below a loa free space referenc:o was used for computaton of the models based on the maxmum dynamc range of tbe recever. An example of a meuuted muldpath mpulae rcsponac for a 1-m kx:al n WS topography s &ven n Fsure. (4) V. DlSTRBUTJON OF THE NUMBER OF MULTPATH COMPONENTS Knowledge of the number of multpath components s mportant for the smulaton of modulaton and equalzaton technques and for the determnaton of the fonn of the channel model. f there ate lkely to be a small number of paths ( < S whch arc caused by obvous reflectng objects), then a ray-tracng model would seem plausble. However, f components from many paths arrve at the recever a statstcal model s useful for analyss. ' The model for the number of multpath components receved n an ndvdual profle wthn a l m OC.l area s found to be Gaussan dtrbuted, as shown n Fgure 2 for LOS. The mean of the Gaussan dstrbuton s a random varable whch s dfferent for each l m local area, and s unformly dstrbuted from 9 () to JS (36) multpath components for LOS (ODS) topo8f1phcs. The standanl devaton of the Gaussan dstrbuton s lnearly related to the mean. For LOS, fl..492 x (avg. num. ofmultlpath components. 4.77). (6) n obst"jctcd topographes, the lnw regresson s Fgure 2. a x (avs. num. of multpath components.89). (7)...,. ll.l S1;N 3.5!, Dstrbuton of the number of muttpath components receved n an ndvdual profle wthn a l.. m local area. Gaussan: average 31.9, standard dev1aton l3.5. Fgure J shows the model supermpoled on the emprcal data for LOS. Bach data pont represents measurements n a l m local area. The lmted data ndcate that the average number of receved mujtpath components s comp.mbte n LOS and ODS topographes; the extents of the unfonn dstrbuton arc smlar. Ths result s not surprsng when one cottsders that BS topography only refers to whether or not a LOS path s present between the transmtter and recever. Snce most multpath components are due to reflectons from surroundng objects. there s approxmately equal lkelhood of recevng mult1path components n LOS and ODS topographes n unparttoned buldmgs.. 1 Ffgure 1. Example of measured LOS profle for a l.. m local area. V. PRODABLTY OP MUL'tlPATF COMPONENT ARRVAL One= the number of multpath components s detcnnned for a partcular rrofalc, t s desrable to know the probablty that a component wll arrve wthn a partcular excess delay nterval. Fgure 4 ndcates the probablty a multpath component wll be detected wth \ ampltude pater than the mnmum threshold le\'el, for LOS topopbes. ths assumes no correlaton on the nterarrval tmes of mulllpath components (.e. tho paths arrve ndependently but wth dfferent probabltes). Tbt s dfferent from models for urban moble rado channels f2,9,1j and an oftacc envmnment (Sf, wheremultpath components wens modeled to arrve n cluatera rather than ndependently.. However, open plan oftkea and factory buldngs contan reflectng objects that are located unformly throughout the workspace.. n obstfucted topographes, the probablty of recevng a mujtpath component nc:reues from.55 at an excess delay of ns to.7 at an exccsa delay of 75 ns and then decreases exponentally as excess delay ncteues. Ths can be seen n Pgwc S whlch shows the probablty of multpath component ann for ODS topognq,hes at a 48 db tluabold belo':v a loa frect 1J*18 ce.

3 5 "'...! 2 Fgure 3. / X X X/ / Average Number of Paths / 3.>x S1gla (Average Number of Paths ,. LOS l -j l J Scatter plot of the average and standard devaton of the number of multpath components receved n an ndvdual profle wthn a 1-m local area for 25 dfferent local areas (LOS). 4 V. PATH LOSS The total power contaned n a receved multpath delay profle at a partcular transmtter-recever (T-R) separaton of d meters s well descrbed by the log-normal dstrbuton (normal dstrbuton wth values n db) about a mea path loss law of the form dn {1,3,7J. Free-space path loss s assumed for the ftrst 2.3 meters (OJ.) and mean values of n range from 1.8 to , 7J. t s shown here that not only 8 the total receved gnal path loss log-normally dstrbuted about the mean, but the average path loss of dscrete multpath components over a 1-m local area s also log-normally dstrbuted about some mean dn(r) path loss law where n(r) s a functon of excess delay, but not of T-R separaton. The data from (7J suggest that n general, n(t) ncreases wth r (.e. path lo8 s greater for components that arrve later n the proftle). The average power contaned n a multpath component at a partcular T -R separaton (n meters) and excess delay (T) was assumed to be of the form: T-R separaton ) Attn. (db below OJ.) = lox n(r) x log ( 2. 3 Ths smple power law model has been used n (1,3,14J. Fgure 6 shows how the power law exponent n changes wth excess delay for LOS and ODS topographes. One would expect for LOS topographes, n(o) = 2 (free space). Howl vcr, emprcal data reveal that the LOS sgnal s slghtly more lossy than n free space. Ths s probably due to fadng caused by unresolved components (.e. components caused by floor and celng rcnectons) whch arrve wthn the frst 7.8 ns of the measured profles, and also may be due to smearng mposed by the data processng. n obstructed topographes, the power of multpath components wth small excess delay obeys a path lm1s power law n whch the sgnal attenuates (n ncreases) more rapdly than n lne-of-sght topographes. Ths s expected snce shadowng due to obstructons causes attenuaton to be greater than n unobstructed topographes (3J. The standard devaton about the mean path loss law has been found to be relatvely nsenstve to ecess delay and s modeled as 4 do for LOS and 5 db for obstructed topographc:. The standard devaton of the average multpath component ampltude for obstructed topographes s slghtly larger than n LOS topographes snce the effects of shadowng cause greater varaton n path attenuaton as the recever s moved from one local area to another. (8) J f 1.. 1!. : J ::! Fgure 4. l.t Probablty of multpath component arrval (LOS). c c cu c a Q. an LOS- OBS r \\.: El<cesa 1l1y T1111t1, [ns)! \.j : 4 5 J!l!.. J.... J f... Fgure 5. lm.... b-.,ta, (1111 Probablty of multpath component arrval (OBS). Fgure 6. Varaton of power law exponent n( T)' wth excess delay (LOS and OBS). We have shown that the mean power contaned n a partcular excess delay nterval averaged over a 1-rrt local area can be reasonably modeled by a power law of the form dn(t), The log normal dstrbuton was found to be rea.'!dnable for the dstrbuton of path loss about the mean d <r) model. Ths agrees wth prevous results for urban and ndoor rado channels (3,9,1 OJ. The precedng model s useful for predctng global (large-scale) power. levels for ndvdual multpath components. However, multpath components fade as a recever s moved over a local area (.e. meter track). t s mportant to understand the amount of fadng whch can occur as a result of small changes n recever locaton.

4 Fgure 7 shows the cumulatve dstrbuton functon of multpath component ampltudel at a partcular lne-of-sght memurement locaton (PBBC) for tho LOS component (T = ns) over a meter local area. Also plotted s the log-normal (normal n db) dstrbuton wth a mean and standard devaton equal to that of the measured data. Fgure 7 ndcates that a log-normal dstrl?uton s a good model for sgnal strengths over meter local areas. The result that local fadng s log-notmal and not Raylegh agrees wth [ OJ for urban moble rado channels. Ths may be caused by the fnte resoluton of the measurement apparatus,.e., paths wth deep fadng wll not be detected. The ampltude of such deep fades wll be lost n the nose. n addton, we have only a lmted number of data pont ( 19) wth whch to determne the dstrbuton, so t s dffcult at present, to project wth confdence the valdty of ths model. A t.o. -.5 ;;,...t. 25 Exc111 Dele' 39.1 na Nllft e 5 S1gntl LYl Dtlow lol The condtonal dstrbuton of A( 3) gven the value of A( 1 ) can be calculated by assumng both random varables form a jontly log-normal dstrbuton wth a condtonal mean - - ( _)aa<e,> A(2)1A( 1 ) = A(2) + raa(a(tl A(2)) A(t)- A(J) a A< > (9a) and a condtonal varance (9b) where A s a mult path ampltude for a partcular locaton. s a functon of spatal locaton x and excess delay T r.. s the space or tme correlaton ( 151. n (Eq. 9), means and standard devatons have values n decbels. The prevous general equatons have been specalzed for applcaton to spatal and temporal correlatons over local areas [15,161. The spatal CCF of the memured data averaged over dfferent measurement arem for LOS and OHS topographes vares over space and excess delay. The model for the average spatal correlaton coeffcent functon, based on mnmum mean squared error fts to the data, s shown n Fgure 8 for LOS topographes. The average temporal correlaton coeffcent functon for LOS topographes can be found n [ 16, Fgure Rj. \...,. '""., h,,.,,.,...,..l.-..'. - ' l..td,,. UYbU V U l.ltjol.ll t..ufjuflt!'fll.. ampl-tudes ovef a 1-m local area at au excess delay of T=391ns. We have found that over the ensemble of local measurements, although the mean sgnal level s hghly dependent upon excess delay (log-normal about dn< >), the amount of fadng (standard devaton) about the mean s not. Thus, where some components at 'l' = undergo very slght, f any, fadng over a meter track, at other locatons, the frst arrvng sgnal fades as much as sgnals arrvng later n the profle due to multple sub-paths wthn the resoluton of the measurement system. Smlarly, at some locatons, sgnals whch arrve later n the profle do not fade (they are specular reflectons from walls, etc.) whereas at other locatons, sgnals wth large excess delay fade sgnfcantly. The standard devaton of the multpath component ampltudes over a l m local area for a constant excess delay nterval ranges from.25 db to 4.d8. 1 ;. J... :.l Fgure 8. ;::! Average spatal correlaton coeffcent functon model (LOS). V. CORRELATON COEFFCENT FUNCTON The dstances and excess delay values at whch multpath sgnal ampltudes become uncorrelated are mportant n the analyss of antenna dversty, burst errors, and fadng. nspecton of the emprcal data leads us to beleve that some of the ampltudes of multpath components whch exst at varous locatons and eltcess tme delays are correlated. We assume that over dstance separatons greater than several wavelengths, channels become uncorrelated over space. That s to say, the ampltude of a multpath component at a partcular excess delay wll be uncom:lated wth the ampltude of a component measured by a dstant recever at the same excess delay. Over excess delay dfferences greater than a few hundred nanoseconds, we assume multpath sgnal strengths become uncorrelated snce the reflectons are due to dfferent scatterers. We have shown that ndvdual multpath components obey a loa nonnal fadns dstrbuton (see Fgure 7) as a moble s moved over a local area. We assume that multpath component ampltudes are also jontly log nomally dstrbuted over local a.reas. Although ths s not neceuuly true, t provdes a tractable method n whch to compute correlaton coeffcents and apply them n a propagaton smulator. X. SMULATON RESULTS An mportant consderaton n the evaluaton of smulated results s ther lkeness to emprcal measurements. Smulated proflles must look lke actual mea. data, and over an ensemble of smulated measurements. they must posses smlar tme dsperson and path loss statstcs. Fgure 9 shows an example of the lnear channel mpulae response for a smulated LOS topography over a l m local area. From comparson wth Pgure, t can be seen that ths proftlc represents a vable multpath channel mpulse response for a factory rado channel and appears very smlar to those reported n [7). The number of multpath components changes from proftle to proftle, and multpath ampltudes fade as the smulated recever s moved. The dstrbuton of the number of multpath components, the probablty of recevng multpath components at partcular excess delays, and the ampltude of multpatb components over large-scale and small ecale areas arc accurately recreated. Fgure 9 s a typcal smulaton result.

5 X. CONCLUSON We have prented statstcal models for wdeband power delay proftles nsde open plan buldngs. These models are based on propagaton measurements from fve factory buldngs. Models have been presented whch quantfy the number of multpath components whch arrve wthn 5 ns of the ftrst detected pulse, the probablty of recevng multpath component wthn a partcular eltcess delay nterval, the dstrbuton of multpath component ampltudes, and the correlaton between multpath component ampltudes whch ex5t at spatal locatons and e;w.:cess delays over a one meter local area, t should be noted that all models are smple models n that they can be programmed n a smulator wth a smple unform random number generator ( 1). The most mportant asset, however, s that the models can be used to smulate multpath channel condtons that are very realstc, and may thus be used for meanngful bt error rate and co-channel analyses. n addton, smulaton of other multpath channels s possble based on the framework of the smulator presented n ths paper by changng the models presently used. Thus, t wll not be dffcult to ncorporate models of multpath channel behavor measured n dfferent ndoor envronments. Fgure 9. P Example of smulated LOS profle.for a 1-m local area. X. ACKNOWLEDGEMENTS Kochro Takarnzawa asssted wth the data processng. The authors wsh to thank Dwayne llawbaker for hs assstance n preparng ths paper. Ths work has been sponsored hy a grant from the Purdue Unversty Computer ntegrated Desgn, Manufacturng, and Automaton Center (CDMAC). REFERENCES RMS Delay Spread s a common measure of the temporal e:uent of a multpath channel mpulse response. The cumulatve dstrbuton functons of the smulated data arc gven n Fgure l for LOS and ODS topographes. The medan value of rms delay spread are approxmately 8 ns for LOS and 95 ns for ODS topographes. These are sughtly smaller than the values presented n f71 llowever, the models used n the smulaton were detennned based on a subset of the data n [7J whch dd not nclude some of the most tme-dspersve measurement locatons. Path loss statstcs provde e:ttcellent agreement wth emprcal data shown n f7, Fgure 8J T.S Rappaport, "ndoor Rado Communcatons for Factores of the Future," EEE Communcatons Magazne, vol. 27, no,. 5, pp , May Hashem, "Smulaton of the urban rado propagaton," EEE Trans. on Veh. Techno!., vol. VT-28, pp , August T.S. Rappaport, C.D. McGllem, "UHF Padt;g n Factores," EEE Journal on Set. Areas n Comm., vol. SAC-7, pp.4-48, Feb D.M.J. Devasrvatham, "Multpath tme delay srread n the dgtal portable rado envronment," EEE Communcatons Magazne, Vol. 25, No.6, pp. J-21, June "' Ul. u. 75 v ' "'" c% A.A.M. Saleh and R.A. Valenzuela, "A statstcal model for ndoor multpath propagaton," EEE Journal on Set. Areu n Comm., vol. SAC-5, pp , Feb R. Bulttude, G. Bedal, "Propagaton Characterstcs on Mcrocellular urban moble rado channels," EEE J. Set. Areas Comm., Vol. SAC-7, No., Specal ssue on Portable and Moble Rado Communcatons...5 Smulated LOS Slnulated OBS 7. TS. Rappaport, "Characterzaton of UHF Multpath Rado Propagaton nsde Factory Buldngs," EEE Trans. Ant. Prop., Vol. 37, no. 8, pp , Aug ,_;_.:..: J 2 RMS Otley Spread, (nsl G.L. Turn, "Communcaton through nosy, random-multpath channels," RE Nat. Conv. Rec., pt. 4, pp , G.L. Turn, F.D. Clapp, T.L. Johnson, S.D. Pne and D.Lavry, "A statstcal model of urban multpath propagaton," EEE Trans. on Veh. Techno!., vol. VT-21, pp. 1-9, fleb. 19n H. Suzuk, "A statstcal model for urban rado propagaton," EEE Trans. Comm., vol. COM-25, pp , July W.C.Y. Lee, Moble Communcaton.r Engneerng, McGraw-Hll, c Fgure 1. Cumulatve Dstrbuton Functon of rms delay spread of smulated LOS/OBS factory rado channels. 12. A. Zogg, "Multpath Delay Spread n a Hlly Regon at 21 MHz," EEE Trans. Veh. Tech., Vol. VT-36, No. 4, November 1987, pp

6 13. J.P. de Week, P. Mcrk, R. Lorenz, "Power Delay Proflles Measured n Mountanous Terran," 38th EEE Vehcular Technology Conf. Proceedng.,, 15 June, 19R8, Phladelpha. PA, pp. los. 14. D.C. Cox, "91 MHz Urban Moble Rado Propagaton: multpath characterstcs n New York Cty," EEE Trans. Comm., Vol. COM 2l, Nov. 1973, pp S. S.Y. Sedel, "UHF ndoor Rado Channel Models for Manufacturng Envronments," Masters Thess, Vrgna Polytechnc nsttute and State Unversty, Blacksburg VA, Aug S.Y. Sedel, T.S. Rappaport, K. Takamzawa, "Applcaton of Second-Order Statstcs for an ndoor Rado Channel Model," 39th EEE Veh. Tech. Conf. Proceedngs, San Francsco, CA, May 1989.