Statistical modelling and computer simulation of indoor radio channel

Transcription

1 Statistical modellig ad computer simulatio of idoor radio chael R. Gaesh K. Pahlava dexig terms : Radiocommuicatio, Simulatio, Propagatio Abstract: Multipath profiles obtaied from radio propagatio measuremets at 9 MHz are used to aalyse the statistical characteristics of the idoor radio chael. The data base is divided ito two classes : maufacturig floors ad college offices. the maufacturig floors, there is plety of ope space without ay presece of walls, as a result of which most of the received power is cocetrated i the iitial paths. The college office areas have a wider spread of power i delay, because of less ope space ad the frequet obstructio of the sigal betwee the trasmitter ad the receiver by oe or more walls. The statistical parameters required for computer simulatio of multipath profiles i each eviromet are determied. The arrival of the paths is show to fit a modified Poisso process ad the amplitude of the paths follow a log-ormal distributio. The mea ad the stadard deviatio of the logormal distributio are show to decay expoetially with delay. To evaluate the performace of this simulatio model, the distributio of the RMS delay spreads from the simulated profiles is compared with that obtaied from the measured profiles. troductio door radio commuicatios is curretly studied for applicatios such as wireless PBX systems, wireless local area etworks, uiversal portable phoes ad wireless security systems. These applicatios will be complemeted by wireless commuicatios betwee mobile robots, automatic guided vehicles (AGV) ad other services ukow at the preset time [l]. The depedece of a wireless system o effective radio propagatio demads some measuremet ad modellig of the idoor chael characteristics. A model for the chael eables the system desigers to simulate the chael for the purpose of performace predictios ad eables comparative study of various alterative models. Radio propagatio i a office eviromet is very complex. The received sigal usually arrives by several paths reflected by walls, ceiligs, ad other fixed ad movig objects, aroud the trasmitter ad the receiver. The differece i the arrival time of the sigal from Paper 7955 (E8), first received th Jue ad i revised form 23rd November 99 The authors are with the Electrical Egieerig Departmet, Worcester Polytechic stitute, Worcester, MA 69, USA EE PROCEEDNGS-, Vol. 38, NO. 3, JUNE 99 various paths is proportioal to the legth of the path travelled, which is affected by the size ad architecture of the office ad the locatio of the objects aroud the trasmitter ad the receiver. The stregth of the sigal arrivig by such paths depeds o the atteuatio caused by passage or reflectio of the sigal from various objects i the area. The determiistic aalysis of propagatio mechaisms i such a eviromet is ot practical, ad statistical aalysis must be used. A mathematical model is formed for the chael. The statistics of the model parameters are determied usig the chael impulse resposes measured for various locatios of the trasmitter ad the receiver. Oe of the earliest statistical measuremets of the amplitude fluctuatios ad distace-power law for idoor chaels was reported by British Telecom [2]. Results of these measuremets give the power law represetig the sigal atteuatio as a fuctio of the distace iside a buildig. The first widebad idoor radio delay spread measuremets were reported by BellCore [3]. All the reported widebad measuremets for idoor chaels are cocered with the statistics of the multipath or the power i the received profiles [l-5. The oly attempt at modellig the idoor radio chael, was reported by the AT&T Bell Laboratories [S. This model was based o Turi s model [7] for urba radio propagatio ad cosiders the rays of the multipath profile to have Poisso arrivals, idepedet Rayleigh amplitudes ad idepedet uiform phases. Based o the observatio of the chael profiles collected from a research laboratory i the AT&T Bell Laboratories, Saleh ad Valezuela [6] coclude that the paths arrive i clusters. The arrival of the clusters is also assumed to have a Poisso distributio. They suggest that the paths ad the clusters both decay expoetially with a certai decay rate. The arrival rate of the paths ad the clusters are determied from the statistics of the collected data. The distace-power relatio ad the multipath spread of the collected profiles was also reported. the preset study a wider rage of statistics for Turi s model [7] were collected ad compared for two classes of buildigs : maufacturig floors ad college offices. Five differet areas i maufacturig floors ad two office areas i a college campus were used as the measuremet sites. The discrepacies followig the Poisso arrival assumptio are reported based o the empirical data collected. t is show that the modified Poisso process fits the arrival of the paths accurately for both eviromets. The Rayleigh, Weibull, Nakagami, log-ormal, ad Suzuki distributios are cosidered as potetial models for the amplitudes of the arrivig paths. Though the Suzuki distributio fits some of the data quite closely, the log-ormal is show to be the best dis- 53

2 tributio for all areas. The mea ad the stadard deviatio of the log-ormal distributio are show to decay expoetially with the path delays. The statistics provided i either of the two eviromets, are used to reproduce the measured profiles usig computer simulatio. The distributio fuctio of the RMS delay spread obtaied from computer simulatio closely fits that obtaied empirically. The mathematical formulatio for the chael ad the measurig system overview are preseted. The statistical parameters required to regeerate the chael impulse resposes are described. The results of the data aalysis o the path arrival times ad amplitudes obtaied from the two sets of measuremets is discussed ad the simulatio procedure preseted. The empirical ad simulated results are the compared. The summary ad coclusios are fially preseted. 2 Mathematical model ad measuremet data base The mathematical model used for the complex low-pass impulse respose of the idoor radio chael was origially suggested by Turi [7] for the mobile radio ad is give by The trasmitted impulse 6(r) is received as the sum of L paths with amplitudes {Pk}, arrival times {?k) ad phases {&. Several statistics are required to regeerate a set of measured profiles with a computer simulatio. The statistics of the arrival times are required to idetify the existece of a path at a give delay. The fluctuatios i the path amplitudes should be fitted to a kow probability distributio, idetified with a set of parameters (usually the mea ad the stadard deviatio). The fuctios relatig the mea ad the stadard deviatio of the distributio to the path delay should be determied so as to accurately regeerate the path amplitude. The chael impulse respose has to be determied at all possible locatios i various idoor eviromets to determie the required statistical parameters. There are three pheomea affectig the impulse respose at ay locatio i a idoor chael. The first is the fluctuatios i the received power. The secod is the effect of multipaths caused by fixed objects such as walls or ceilig. The third is the effect caused by movig humas or movig objects, close to the trasmitter ad/or the receiver. All the measuremet data used i this work, were collected whe there was o traffic ear the trasmitter ad the receiver. The effect of traffic ad local atea movemets is reported i Referece 8. The phases 8, are assumed to be statistically idepedet uiform radom variables over CO, 27) [6,7]. The idoor radio measuremets were performed at frequecies aroud GHz. Very arrow pulses, which resemble a impulse, were trasmitted. f the duratio of these trasmitted pulses is several times smaller tha the largest multipath spread, the receiver will observe several isolated pulses for each trasmitted pulse. this case L h(t) = P, 6(T - tk)ejvk k= L % Pk p(t -?k)ejek k= where p(z) represets the arrow trasmitted pulse. (2) The measuremet set-up used for the multipath propagatio experimets is show i Fig.. t ivolves modulatio of a 9 MHz sigal by a trai of 3 s pulses with a 5 s repetitio period [4] provided by a pulse geerator. The choice of the 9 MHz carrier frequecy is i compliace i with the FCC bad allocatios i the Uited receive trasmit atea atea Q atteuator power amp if ier pre-amplifier pre-amplifier mixer circuit evelope detector digitisig persoal Fig. osci loscope computer Chael impulse respose experimetal set-up States for idoor radio trasmissio. The modulated carrier was iput to a 45 db amplifier. The output was trasmitted usig a quarter-wave dipole atea placed about.5 m above the floor level. The statioary receiver used a similar atea to capture the radio sigal. This was followed by a step atteuator ad a low-oise high gai (~6 db) amplifier chai. The sigal was the demodulated usig a evelope detector whose output is displayed o a digital storage oscilloscope coupled to a PC with a GPB istrumet bus. The compoets used i the measuremet set-up have a flat frequecy respose i the.9 GHz rage. The dyamic rage of the receiver display is limited to 25 db because of the liear scale o the digital storage oscilloscope. The actual dyamic rage of the measuremet set-up was more tha db. This dyamic rage is achieved by maually adjustig the step atteuators at the receiver. A coaxial cable was required to trigger the oscilloscope from the pulse geerator of the trasmitter to guaratee a stable timig referece. This measuremet system is o-coheret ad does ot iclude the phase associated with the arrivig paths [6, 7. These phases are reasoably assumed a priori to be statistically idepedet uiform radom variables over CO, 27) [6,7]. The trasmitter was moved to various locatios i each site. The received multipath profiles were stored i the oscilloscope ad the i the computer. Each stored profile is a average over time of 64 impulse resposes collected durig 5-2 s at oe locatio. Care was take to prohibit ay movemet close to the trasmitter ad the receiver durig the measuremet time. The distace betwee the trasmitter ad the receiver varied betwee ad feet. A total of 472 profiles are collected from measuremets made at differet locatios i five areas o three differet maufacturig floors [4] ad two office areas i the college campus. The maufacturig floor eviromet is typically characterised by large ope areas, cotaiig various machiery ad equipmet of differet sizes. There are usually o walls betwee the trasmitter ad receiver, ad a 'direct' path is available for most of the locatios. To adequately represet statistical behaviour of such a eviromet we selected five differet maufacturig 54 EE PROCEEDNGS-, Vol. 38, No. 3, JUNE 99

3 ~~~~ ~ empirical areas for measuremet. The first area was a typical electroics shop floor cotaiig circuit board desig equipmet, solderig ad chip moutig statios. The secod area cosisted of test statios ad storage for commo electroic equipmet, partitioed by metallic screes. The third area cotaied gridig machies, huge oves, trasformers ad other heavy machiery. The fourth measuremet site was a car assembly lie jugle floor havig dese weldig ad body shop equipmet of all kids. The last area was a vast ope space with very little equipmet, used for fial ispectio of the ew cars comig out of the assembly lie. The umber of profiles collected from the five areas were 54, 48, 75, 45 ad 66, respectively, resultig i a total of 288 profiles represetig the maufacturig eviromet. dividual characteristics of these five areas as regards radio wave propagatios were reported i Referece 4. The office eviromet has less ope space ad for most of the locatios, the direct path is obstructed by the presece of oe or more walls. The eviromet as preseted to the radio waves, has cosiderable reflectios from the walls ad ceiligs. The office areas discussed iclude several offices ad a corridor, located o the third floor of the Atwater Ket Laboratories at the Worcester Polytechic stitute. The offices are separated from the receiver located i a cetral electroics laboratory by two walls of sheet rock ad some widowed glass o each wall. The superstructure ad the size of all the rooms i this area are very similar. The corridor is aroud the electroics laboratory, separated by a sheet rock wall with metal studs ad some widowed glass. The office rooms are located o the other side of this corridor. A total of 84 profiles were collected from these areas comprisig 88 i the offices ad 96 i the corridor. Fig. 2a shows a profile of the received sigal for a trasmitted pulse of 3 s (3 db width) at 9 MHz, with miimum multipath spread ad direct lie of sight betwee the trasmitter ad the receiver, depictig the accuracy of the measuremet set-up. Fig. 2b shows a sample profile, with cosiderable multipath spread. 3 Statistics of the chael model parameters The statistical parameters metioed are derived from the measured profiles described. The statistics of the path arrival times?k are first discussed. The path amplitude P, associated with each 7k is the fitted to a kow probability distributio whose momets are fuctios of z~. Results obtaied from simulatio of the model are the compared with those obtaied empirically. As metioed earlier, the data base is divided ito two classes: maufacturig floors ad college offices. For data aalysis, the arrival times i a measured profile is divided ito 5 s bis ad a threshold level is employed to detect a geuie path i ay bi. 3. Arrival of the paths A simple statistical model for the arrival of the paths would be a Poisso process [S, sice the multipath propagatio is caused by radomly located objects. The path arrival distributio govered by a Poisso hypothesis was compared with the empirical data to fid the degree of closeess. The umber of paths i the first N bis of each measured profile was determied. To determie the empirical path idex distributio, the probability of receivig paths i the first N bis P,(L = l) is plotted as a fuctio of. This procedure was repeated for N = 5,, 5 ad 2 bis. The probability PN(L = l) for the theoretical Poisso path idex distributio is give by PN(L = l) =!! e- (3) l! where is the path idex, ad,u is the mea path arrival rate, give by N P= Cri i= this equatio ri is the path occurrece probability for bi i computed from the empirical data. Figs. 3 ad 4, show a compariso betwee the empirical path idex distributios ad the theoretical Poisso path idex distributios [9] for N = 5,, 5 ad 2. The Figures correspod to the maufacturig floor areas ad the college offices, respectively. These are plotted as cotiuous curves for clarity, though they have values for (4) time, s > - g3 3 p time, s b Fig. 2 Profile of received sigal a Miimum multipath spread; lie of sight operatio h Cosiderable multipath spread Fig. 3 Poisso path idex distributio for maufacturig floor areas theoretical, N=5 m, N = io V, V N = 5 A. A N = 2 EE PROCEEDNGS-, Vol. 38, NO. 3, JUNE 99 55

4 empirical ~~~~ empirical oly iteger path umbers. Cosiderable discrepacies are observed betwee the empirical ad the Poisso distributios for all values of N, irrespective of the eviromet. This discrepacy reflects a tedecy of the paths to arrive i groups, rather tha i a radom maer. To explai similar discrepacies, a modified Poisso model was proposed by Suzuki for urba radio chael modellig [lo]. Fig. 4 path idex Poisso path idex distributio for college oflces -~~~ theoretical ~. N=5 V,V N = 5.,U N = A,A N = 2 For the modified Poisso process, the probability of havig a path i bi i is give by Ai, if there was o path i the (i - )st bi, or by KN Ai, if there was a path i the (i - )st bi. The uderlyig probabilities of path occurreces i have the followig relatio with the empirical path occurrece probabilities ri : where, = rl. The modified Poisso path idex distributio is related to i s, by the followig recursive equatios [lo] : Pi(L = ) = Pl, i(l = l) + P2, i(l = ) (6) P2,i+(L = ) = P,,i(L = - l)kni+l + Pl, i(l = - l)ai+ (7) P,,i+,(L = ) = P2,i(L = U - KNi+i) + P, i(l = )( - Ai+ ) (8) where PAL = r) is the probability of havig paths i the first i bis, Pl, i(l = l) is the probability of havig paths i the first i bis coditioed o havig o path i the ith bi ad P2, i(l = l) is the probability of havig paths i the first i bis coditioed o havig a path i the ith bi. The process begis i bi where Pl, l(l = ) = -,, P2*,(L = ) = Al, P, l(l = r) = for 2 ad P2, l(l = l) = for 2 2 or <. Startig with a small value of KN ad miimisig the mea square error betwee the empirical ad theoretical modified Poisso path idex distributio foud usig eqs. 5 to 8, optimum values of KN are foud from the data for N = 5,, 5 ad 2. To aid simulatio, the optimal values of KN which are fuctios of the umber of bis are replaced by ew parameters Kis (i =, 2,..., 2), which are fuctios of the s i [. The Ki s are determied by liear iterpolatio. For the fial calculatio of the modified Poisso path idex distributio, 56 eqs. 5 to 8 are used agai with iterpolated Ki (i =, 2,..., 2) replacig KN (N = 5,, 5, 2). The optimum value of Ki ad Ai calculated, for the maufacturig floors ad the campus ofice areas, are show i Table. Figs. 5 ad 6, show a compariso betwee the empiri- Table : Measured parameters Bi Maufacturig College floors offices K. A. K. A > - (3.2 - P Q. - path idex Fig. 5 Modijied Poisso path idex distributio for maufacturig floor areas theoretical ~, N=5 V,V N = 5 D, N = A,A N = 2 r.3.5 r R. path idex Fig. 6 Modified Poisso path idex distributio for college offices modified Poisso empirical,o N = 5 V,V N = 5 D, N = A,A N = 2 EE PROCEEDNGS-, Vol. 38, No. 3, JUNE 99

5 ~ actual ~ actual RAY cal path idex distributios ad the modified Poisso distributios, for the maufacturig floors ad the college ofice areas, respectively. The curve fittigs show cosiderable improvemet over those of the Poisso model show i Figs. 3 ad 4. This suggests that the paths do ot arrive radomly but i groups, ad the presece of a path at a give delay is greatly iflueced by the presece or absece of a path i the earlier bis. The modified Poisso model utilises the empirical probability of occurrece for each bi. The Poisso model just uses the sum of the probabilities of occurrece for all bis. 3.2 Path amplitudes Rayleigh, Weibull, Nakagami-m, log-ormal ad Suzuki distributios were cosidered as potetial models for the path amplitudes. the idoor eviromets fluctuatios i the sigal amplitude are quite high because of fadig, so the sigal amplitude level was coverted to decibels, ad treated as a radom variable. Usig the method outlied i Referece 2, the parameters of the theoretical distributio fuctios were determied from the measured amplitudes of the sigal i the bis. Figs. 7 ad 8 show the comparisos betwee the theoretical ad the.o.8 - e.6 D h.4.2 Fig sigal with respect to media, db CDF ofpath amplitude i bi i maufacturigfloor areas suz WE... LOG NAK ~~~~..8 c D.6 9 a.4 Fig sigal with respect to media, db CDF ofpath amplitudes i bi jfor college oflces... LOG NAK -~~~ RAY suz WE EE PROCEEDNGS-, Vol. 38, NO. 3, JUNE 99 57

6 experimetal distributios for bi i the maufacturig floor areas ad bi 5 i the college office areas, respectively. The horizotal axis is ormalised to the media value of the data i decibels. The error criterio of the Cramer-Vo Mises test [lo] was used to compare the goodess of fit amog the five distributio fuctios. This criterio is defied as CO2 = jfmi.lp(x) - P*(x)]2 dp(x) (9) where P(x) is a theoretical CDF ad P*(x) is a experimetal CDF. Table 2 shows w2 for various distributios for bis, 2, 3, 5, 7, 5 ad 2, i the maufacturig floors ad the college offices. Both log-ormal ad Suzuki distributios cause close fits, but the log-ormal provides a better overall fit to the empirical distributios. t is also easier to simulate log-ormal tha Suzuki radom variables to represet path amplitudes. The ihomogeeities of the idoor chael result i variatios i the mea ad variace of the amplitudes for differet delays. To simulate these chagig parameters, the distributio for their variatios should be kow. The scatter plots of mea ad stadard deviatio of the log-ormal distributio as a fuctio of the delays were fitted to decayig expoetials of the form Ae- lr + B where is the decay rate, z is the delay ad A ad B are costats. Figs. 9 ad show the mea ad the stadard deviatio ad their expoetial fits for the maufac-.7r.6.5 E.4 > - 5.3? r a turig floor ad the college ofice areas, respectively. The decay rate was 5. for the mea ad 4. for the stadard deviatio for the maufacturig floors. these O. t a b Fig. Characteristics of log-ormal distributio i college ofices Dashed lie is a expoetial fit a Mea b Stadard deviatio areas most of the received power is cocetrated i the iitial paths resultig i a faster decay of the received power with delay. The college office areas exhibited a wider spread of power i delay ad thus a slower decay for the received power with delay. The decay rate was 35.5 for the mea ad 28.3 for the stadard deviatio i the college offices. The scatter plots give the values of the mea ad stadard deviatio for the path amplitude, give the existece of a path at that delay. The modified Poisso process decides whether or ot a path exists at a give delay b Fig. 9 Characteristics of log-ormal distributio i maufacturig poor areas Dashed lie is a expoetial fit a Mea b Stadard deviatio Table 2: Mea square error o2 4 Results of simulatios Usig the statistics give for the path arrivals ad amplitudes, the chael multipath profiles ca be regeerated with a computer simulatio. This simulatio capability ca be used i the desig ad testig of commuicatio systems as a substitute for costly hardware experimets. The results of the simulatio are compared with those obtaied empirically. The criteria for compariso is the distributio fuctio of the RMS delay spreads. For radio commuicatio i the idoor eviromet, the RMS delay spread of the chael [4] gives a measure of performace degradatio caused by itersymbol iter- Bi Maufacturig floors College offices LOG NAK WE RAY SUZ LOG NAK WE RAY suz. ~-4.32~-36.58~-43.99~-3.3~-48.9~-59.62~-45.5~-~ 2.58~-3.~-~ x x -3.4 x x -3.2 x x -~ 4.52 x -~ 3.37 x x x x x x x x.~.82 x 2.6 x 5.8 ~-4.2~-35.7~-4 3.7~-3.57~-4.85~-4.45~-39.3 ~ ~-32.64~-~ x x x x x x x x.27 x lo- 7.5 x 5.7 x 6.38 x lo-.3 x 4. x 4.7 x 4.8 x 4.5 x x -~ 8.4 x 3.86 x io-.94 x -3. x -~ 2.6 x -~ 2.4 x 3. x -~.83 x 58 EE PROCEEDNGS-, Vol. 38, No. 3, JUNE 99

7 ~ ~ Poisso/Rayleigh ferece, i the system. t is a importat parameter for determiig data rate limitatios of stadard ad equalised modems [3]. t is also used for performace predictio of spread spectrum modems [ 4. The arrival arrival of Fig. first step i simulatio to geerate the path times. The basic model for simulatio of the times is the modified Poisso brachig process. The delay axis is divided ito bis of legth ad the stadard deviatios of the log-ormal distributio were determied from the associated expoetial fits i Figs. 9 ad. The phase agles could be chose from a uiform distributio ad added to each path to complete the picture..6 r --+x %. - a Fig. 2 Path occurrece probabilities for maufacturigfloor areas empirical ~ simulated _ Fig. Modified Poisso process path exists o path exists 5 s. The simulatio for each profile starts with bi. The presece or absece of a path i each bi is determied usig Table ad Fig.. Figs. 2 ad 3 compare the path occurrece probabilities as obtaied from these simulated profiles with those obtaied from the measured profiles i the maufacturig floors ad the college office areas, respectively. These probabilities are plotted as cotiuous curves for the purpose of clarity, although they oly have values at iteger s. The experimetal ad the simulated path occurrece probabilities are show to be very close. The path occurrece probability would be a horizotal lie at the mea path arrival rate if the path arrival times were to follow a Poisso process. The path amplitudes were geerated from the logormal distributio for each bi with a path. The meas Fig. 3 Path occurrece probabilities for college offices empirical ~-~~ simulated To evaluate the performace of the simulatio model, the cumulative distributio of RMS delay spreads as computed from the simulated profiles was compared with that obtaied from the measured profiles. Figs. 4 ad 5 show these comparisos for the maufacturig floors ad. a.6 - Z._ - D L Q > _._ RMS delay spread, s Fig. 4 Distributios of RMS delay spreads for maufacturiyjoor areas..... modified Poisso/log-ormal empirical EE PROCEEDNGS-, Vol. 38, No. 3, JUNE 99 59

8 ~ empirical college offices, respectively. The dashed lies i these figures are the cumulative distributios of the RMS delay spreads computed from simulatio. The path amplitudes t was show that the arrival of the paths from a modified Poisso process ad the amplitude of the paths fit a log-ormal distributio. The mea ad the stadard.c.8 x. c -.6 L a RMS delay spread, s Fig. 5 Distributios of RMS delay spreads for college offices Poisso/Rayleigh... modified Poisso/log-ormal are simulated based o the expoetial fits to the scatter plots of the meas ad stadard deviatios. The solid lies i Figs. 4 ad 5 represet the actual cumulative distributio of the RMS delay spreads measured from the maufacturig floors ad college offices, respectively. The match betwee the empirical ad the simulated distributios ca be see to be very good. The statistical model give i Referece 6 cosiders Poisso path arrivals ad Rayleigh amplitudes. Simulatio was also carried out for the Poisso/Rayleigh combiatio for purposes of comparisio. The mea path arrival rate was used to determie the presece or absece of a path i ay bi for the Poisso arrivals. The measured powers i each bi were used to determie the Rayleigh amplitude of a existig path. The RMS delay spread was computed for each of these simulated profiles ad their distributio fuctio is show i Figs. 4 ad 5. The match betwee the modified Poisso/log-ormal simulatio ad the empirical results is sigificatly better tha that provided by the Poisso/Rayleigh simulatio. The weakess of the Poisso/Rayleigh simulatio is more obvious i the maufacturig floor eviromet. 5 Summary ad coclusios Multipath profiles obtaied from radio propagatio measuremets at 9 MHz were aalysed to determie a suitable method for computer simulatio of the idoor radio chaels. the maufacturig floors there is plety of ope space usually without ay presece of walls, most of the received power is therefore cocetrated i the iitial paths. The college office areas have a wider spread of power i delay, because of less ope space ad the frequet obstructio of the sigal betwee the trasmitter ad the receiver by oe or more walls. The statistical parameters required for computer simulatio of multipath profiles i each eviromet were also determied deviatio of the log-ormal distributio were show to fit decayig expoetials. The simulatio procedure was detailed ad the parameters determied from the modified Poisso process ad log-ormal distributio were used to regeerate the idoor radio chael multipath profiles. The distributio of the RMS delay spreads computed from simulatio was show to closely fit the empirically obtaied distributio. Chael profiles were also simulated with Poisso arrivals ad Rayleigh amplitudes ad the distributio fuctio of the RMS delay spreads computed from such simulated profiles had a weaker fit to the empirical data. The modified Poisso/ log-ormal combiatio was show to provide a better model for simulatio. Although additioal research is required for cofirmatio, it is aticipated that this simulatio techique ca be exteded to other kids of eviromet by adjustig the value of its parameters. As with ay other simulatio model, it ca be effectively used i the desig ad testig of commuicatio systems as a substitute for costly hardware experimets. System desigers ca use it for performace predictios ad comparative study of various alteratives. Alexader [l5] has show the effect of differet types of buildig costructio o the distace/ power law gradiet. The relatioship of the parameters i this simulatio model with the buildig costructio materials is a subject worth explorig. 6 Ackowledgmets We wish to thak T. Hotalig for help o the implemetatio of the measuremet set-up ad K. Zhag for assistace i coductig the experimets. This work was supported i-part by the Natioal Sciece Foudatio (USA) uder cotract NCR A short versio of this paper was preseted at EEE GLOBECOM 89. EE PROCEEDNGS-, Vol. 38, NO. 3, JUNE 99

9 7 Refereces PAHLAVAN, K.: Wireless itra-office etworks, ACM Tras. 8 lf Syst., 988, 6, (3), pp ALEXANDER, S.E.: Radio propagatio withi buildigs at 9 MHz. Proc. EEE t. Cof. Ateas ad propagatio, New York, 983, pp DEVASRVATHAM, D.M.J.: Time delay spread measuremets of 85 MHz radio waves i buildig eviromets. EEE GLOBECOM 985 Cof. Rec., December 985.2, pp PAHLAVAN, K., GANESH, R., ad HOTALNG, T.: Multipath propagatio measuremets o maufacturig floors at 9 MHz, Electro. Lett., 989, 25, (3), pp MOTLEY, A.J., ad PALMER, D.A.: Directed radio coverage withi buildigs. Proc. EE Cof. Radio spectrum coversio techiques, September 983, EE Cof Pub SALEH, A.A.M., ad VALENZUELA, R.A.: A statistical model for idoor multipath propagatio, EEE J. Sel. Areas. Commu., 987, SAC-5, (2), pp TURN, G.L., CLAPP, F.D., JOHNSTON, T.L., FNE, S.B., ad LAVRY, D.: A statistical model of urba multipath propagatio, EEE Tras., February 972, VT-2, pp GANESH, R., ad PAHLAVAN, K.: Effects of traffic ad local movemets o the multipath characteristics of the idoor radio chael, Electro. Lett., 99, 26, (7), pp. 8G82 9 GANESH, R., ad PAHLAVAN, K.: O the arrival of paths i fadig multipath idoor radio chaels, Electro. Lett., 989, 25, (2), pp SUZUK, H.: A statistical model for urba radio propagatio, EEE Tras., 977, COM-25, pp HASHEM, H.: Simulatio of the urba radio propagatio chael, EEE Tras., August 979, VT-28, pp LORENTZ, R.W.: Theoretical distributio of multipath fadig process i mobile radio ad determiatio of parameters by measuremets. Deutsche Budespost Forschugsistitut Techical Report 455 TBr 66, March 979 (i Germa) 3 SEXTON, T.A., ad PAHLAVAN, K.: Chael modelig ad adaptive equalisatio of idoor radio commuicatio, EEE J. Sel. Areas Commu., 989, SAC-7, pp PAHLAVAN, K., ad CHASE, M.: Spread spectrum multiple access performace of orthogoal codes for idoor radio commuicatio, EEE Tras., May 99, COM-38, pp ALEXANDER, S.E.: Characterisig buildigs for propagatio at 9 MHz. Electro. Lett., 983, 9, (2), p. 86 EE PROCEEDNGS-, Vol. 38, No. 3, JUNE 99 6