a statistical model for indoor multipath propagation

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128 IEEEOURNAL ON SELECTEDREASN.COMMUNICATIONS,OL. SA G S, NO. 2. FEBRUARY 1987

A Statistical.Model for Indoor Multipath PropagationAbstract-The result s of indo ormultipathpropagationmeasure-

ments using 10 ns, 1.5 GHz, radarlike pulses are presented for a me-dium-size office building. The observed chan nel was very slowly timevarying, with the delay spread extending over a range up to about00ns and rms values of up o about 50 ns. The attenuation varied over a60 dB dynam ic range. A simple statistical multipath model of the in-door radio channel is also presented, whichits our measurements well,and more mportantly, appears to be extendable to other buildings.With this model, the received signal rays arrive in clusters. The rayshave ndependent uniform phases, and ndependent Rayleigh ampli-tudes with varianc es that decay expon entially with cluster and ay de-lays. The clusters, and the rays within the cluster, form Poisson arrivalprocesses with different, but fixed, rates. The clusters are formed bythe building superstructure, while the individual rays are formed byobjects in the vicinities of the transmitter and the receiver.

I. INTRODUCTIONT E use of radio for indoor data or voice communi-cations, e.g., within an office building, a warehouse,a factory, a hospital, a onvention center, or an partmentbuilding, is an attractive proposition. It would free heusers from the cords ying them to particular locationswithin these buildings, thus offering true mobility, whichis convenient and sometimes even necessary. It would alsodrastically reduce wiring in a new building, and. wouldprovide the flexibility of changing or creating variouscommunications services in existing buildings without theneed for expensive, time-consuming rewiring. The chal-lenge is to offer such services to themajority of the peoplein a building, not just a selected few. This would mostcertainly involve a sophisticated local radio communica-tions system whose engineering would require the knowl-edge of the spatial and temporal statistics of the signalattenuation, the multipath delay spread, and even the im-pulse response of the indoor radio channel involved.

Various measurements have been reported in the liter-ature for the attenuation of microwave CW signals prop-agating within buildings [l], [2] or into buildings [3]-[6].The work of Alexander given in [2], which was done at900 MHz, is particularly useful since it gives the powerlaw representing the signal attenuation as a function ofdistance for various types of building.

The first multipath delay spread measurements within abuilding were reported recently by Devasirvatham [7]. Heused a carrier at 850 MHz, biphase-modulated with a 40Mbit / s maximal-length pseudonoise code, resulting in a

Manuscript received January 23, 1986; revised September 24, 1986.The authors are with AT T Bell Laboratories, Crawford Hill Labora-IEEE Log Number 8612162.tory, Holmdel, NJ 07733.

25 ns time resolution. The measurements were made in alarge office building (AT&T Bell Laboratories main lo-cation in Holmdel, NJ), which occupies an area of 3 15 X110m and is 6 stories high.

In the present paper, we present the results of multi-path delay spread and attenuation measurements within amedium-size two-story office building (AT&T Bell Lab-oratories, Crawford Hill location in Holmdel, NJ), whosefirst floor plan is sketched in Fig. 1. The external wallsof this building are made of steel beams and glass, whilethe internal walls are almost entirely made of wood studscovered with plasterboard. The rooms contained typicalmetal office furniture and/or laboratory equipment. Themeasurements were made by using low-power 1.5 GHzradarlike pulses to obtain a large ensemble of the chan-nels impulse responses with a time resolution of about 5ns. Based on these measurements, as well as some of theothers cited above, we propose a statistical model of theindoor radio channel, which 1) has enough flexibility topermit reasonably accurate fitting of the measured chan-nel responses, 2) is simple enough to use in simulationand analysis of various indoor communications schemes,and 3) appears to be extendable (by adjusting its param-eters) to represent the channel within other buildings.

11. MEASUREMENTSETUPA schematic diagram of the measurement setup is shown

in Fig. 2.An RF sweep oscillator was used to generate a1.5 GHz CW signal, which was then modulated by a trainof 10 ns pulses with 600 ns repetition period, which islonger than any delay observed in the .test building. Thisradarlike signal was amplified and transmitted via a ver-tically polarized discone antenna [8] whose radiation pat-tern is omnidirectional in the horizontal plane. The dis-cone was chosen overa vertical dipole, which has analmost identical radiation pattern, because of its superiorbandwidth, which provided the flexibility of changing orsweeping the signaling frequency when desired.Theaverage transmitted power could be adjusted with a stepattenuator over a range from a fraction of a nanowatt toseveral milliwatts.

At the receiver, a second vertically polarized disconeantenna was used followed by a low-noise (3 dB noisefigure) FET amplifier chain with a 60-dB.gain over a fre-quency range of 1 to 2 GHz. (Actually, the state of po-larization of the receiving antenna did not matter from astatistical viewpoint.) The signal was then detected witha sensitive square-law envelope detector whose output wasdisplayed on a computer-controlled digital storage oscil-

0733-8716/87/0200-0128 01 .OO 987 IEEE


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SALEH AND VALENZUELA: INDOOR MULTIPATH PROPAGATION 129

TRANSMITTERR - i 3 4

L - l i iMETAL DOOR

Fig. 1 . Plan of the first floor of AT&T Bell Laboratories Crawford Hillbuilding in Holm del, NJ.

TRANSMITTER RECEIVERFig. 2 A schematic representation of the measurements setup.

loscope (Tektronix model 7854). The dynamic range ofour setup was more than 90 dB, which was achieved bymanually adjusting the step attenuator at the transmitteras well as the oscilloscopes vertical gain.

The transmitter was fixed in the hallway near the centerof the first floor of the building (see Fig. 1 with its an-tenna located at a height of about 2 m. The receiver, withthe antenna at the same height, was moved to collect mea-surements in the hallway and in several rooms throughoutthe same floor. (No floor-to-floor penetration measure-ments are presented since the signal level in that case wasgenerally too small to detect with our setup.) A total of 8rooms were measured with about 25 pulse responses atvarious locations within each room. Both the transmitterand the receiver were stationary during the acquisition ofeach pulse response. For reasons to be explained in thenext section, the transmitted signal frequency was sweptat a rate of about 100Hzover 100 MHz around the1.5-GHz center frequency. The waveform processing ca-pability of the oscilloscope was used to average the re-ceived frequency-swept pulse responses, and to transferthat average to a computer for storage. Theveraging pro-cess took about 15 s to complete. To freeze the channelduring that time, we made sure that people in the vicinityof the transmitting and receiving antennas, or those n thehallway between the antennas, stopped moving. (Peoplemoving within their offices, or in other locations in andaround the building, had a negligible effect on the mea-surements.) A coaxial cable was used to trigger the oscil-loscope from the transmitters pulse generator to guaran-tee a stable timing reference under our swept conditions.111. MATHEMATICAL FORMULATIONF THE METHOD F

MEASUREMENTSEach transmitted RF radarlike pulse has the complex

time domain representation

where p ( t ) is the baseband pulse shape (which in ourcasehas a width of about 10ns), w is the RF angular frequency(which is nominally 27r x 1.5 GHz in our experiment),and is an arbitrary phase.

The channel is represented by multiple paths or rayshaving real positive gains { P k } ,propagation delays { T k } ,and associated phase shifts { 8 k } ,where k is the path in-dex; in principle, k extends from 0 to 00. Thus, the com-plex, low-pass channel impulse response is given by [9]

where 6 ( ) is the Dirac delta function;Because of the motion of people and equipment in and

around the building, the parameters P k , T k , and 8 k are ran-domly time-varying functions. However, the rate of theirvariations is very slow compared to any useful signalingrates that are likely to be considered, e.g., higher thantens of kbit / s . Thus, these parameters can be treated asvirtually time-invariant random variables.It follows from (1) and 2) that the received signal,which is the time convolution of x ( t )and h ( t ) , s givenby

Upon passing through the square-law envelope detector,as indicated in Fig. 2, the power profile displayed on theoscilloscope becomes

I y l ) l2 = e e { P k P I P ( t - T k ) P ( t - T lk le j [ O k - O ~ + 4 n - 7 4 1 1 (4)

If there were no overlap of pulses, i.e., in our experi-ments, if T k - T[ 0 ns when k I then (4) wouldhave reduced to

which is much simpler to use than 4) n estimating the0 s and the T S from the measured I y t ) 2waveform.To obtain the simplification of ( 5 )even with pulse over-lap, we make the reasonable assumption that the 8s arestatistically independent uniform random variables over[0, 27r). In this case, the mathematical expectation of (4)with respect to the 8s yields

which is identical to ( 5 ) but allows for pulse overlap.The mathematical expectation with respect to the 8s

was, in effect, accomplished in our experiment by aver-aging the oscilloscopes power waveform while sweepingthe transmitted RF frequency. Indeed, if the total sweptbandwidth Af is sufficiently large, it can be shown using


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130 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. SAC-5, NO. 2 , FEBRUARY 1987

In our case, Af = 200 MHz, which is sufficient to sat-isfy (7) for pulses that are separated by more than about4 ns. Thus, overlapping pulses of closer separation couldnot be resolved and were considered to belong to onepath.

Given a frequency-averaged power profile s ( , andknowing the shape of the transmitted pulse p ( t ) ,we needto find pairs { (Q, p i ) , k = 1, 2, 3, * } that fit 7)under some minimum error criterion. A reasonable wayof doing this is by picking { rk ] to represent discrete pointson the time axis, say, every 1-5 ns, then proceeding tofind the corresponding { p: } to minimize the mean-squareerror involved in fitting (7) under the constraint hat 0: 20, all k . This is a classic problem in quadratic program-ming, whose rigorous automated solution is somewhat in-volved. Because of the limited number of waveforms thatwe had to process (8 rooms times 25 profiles per room),we actually performed an interactive heuristic computeroptimization.The resulting errors were still within themeasurement uncertainty.

Iv. REVIEW F MEASURED ESPONSESA typical sequence of pulse responses involved in mea-

suring a room is shown in Fig. 3.Actually, the responsesshown are frequency-averaged power profiles, s ( t ) , asdefined in (7). In all cases, the orizontal time axis covers10 ns per division, thevertical axis is linear in power (notdecibels), and the vertical sensitivity of the oscilloscopeis left unchanged. The dB numbers shown in the variousfigures corresponds to the setting of the transmitters stepattenuator.

Fig. 3(a) shows the squared envelope of the transmittedpulse obtained by adirect coaxial connection betweentransmitter and receiver. In Fig. 3(b), the receiving andtransmitting antennas are both located in the hallway at al-m separation. Some pulse broadening is observed, andthe peak signal level has dropped by about 34 dB. This isonly 2 dB more than the theoretical free-space powertransmission ratio [101

p,,/pt,,, = G,G, [w 4 d ( 8 )where Gt and G, ( . 6 ) are, respectively, the gains ofthe transmitting and receiving disconentennas, X( = 0.2m) is the RF wavelength, and r ( = lm ) is the an-tenna separation. Note that, within a building, this rela-tion is expected to hold only for small r, where the directline-of-sight ray dominates all other rays.

Fig. 3(c) is obtained by moving the receiver about 60m, still in the hallway directly in front of the room inquestion (R-139 in Fig. 1). A strong 60 ns echo now ex-ists, .which was found to occur as a result of a reflected

50a a

5000000Fig. 3 . sample sequence of frequency-averaged power-profile measure-ments. The dB figures represent settings of the transmitters attenuator.

Fig. 4. Four interesting examples of frequency-averaged power profiles.

wave from the metal door in the right-hand side of Fig.1. The signal level dropped from the previous 1-m loca-tion by about 30 dB.

Fig. 3(d)-(g) corresponds to four measurements insidethe room on the vertices of a 0.23-m square (9-in tile).The received echos now extend over about 100 ns, andthe signal level has dropped by an additional 25 dB rela-tive to the previous location in the hallway. Notice somespatial correlation among the four profiles. Notice alsothat the groups of rays starting at about 60 ns in Fig. 3(d)-(g) coincide with the small echo n Fig. 3(c), which istaken in the hallway just outside the room.

Fig. 4 shows four other measured pulse responses indifferent locations within the building. Fig. 4(a) (RoomL-159 in Fig. 1) shows two clearly separated clusters ofarriving rays covering a 200ns time span. Fig. 4(b) (RoomR-134 in Fig. 1)shows a 100ns delayed echo that is muchstronger than the first arriving rays. Fig. 4(c) (hallway infront of Room R-134 ,i n Fig. 1) shows a strong echo thatis delayed about 325 ns, which is the largest delay of arelevant echo that we observed. Fig. 4(d) corresponds tomeasurements done where both transmitter and receiver


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SALEH AND VALENZUELA: INDOOR MULTIPATH PROPAGATION 131

were on the second floor of the building, with the receiverlocated in a large ( = 13 X 17 m) open machine shop withcinder-block surrounding walls. Notice the high densityof the received rays over the entire 200 ns time axis.

V . THE MULTIPATHOWERGAINAND RMS DELAYSPREAD

A . DefinitionsGetting the set of pairs { Tk, k }, as defined in (2),

and deducing their joint statistics is, of course, the ulti-mate desired result of modeling. However, there are twosimple parameters that are useful in describing the overallcharacteristics of the multipath profile. These are he totalmultipath pow er gain

G = c P ikwhich is actually less than unity, and the m s delay spreadr111

UT E 4 T - , (10)where

The power gain is useful in estimating such things asthe signal-to-noise ratio of a communications system. Therms delay spread is a measure of the temporal extent ofthe multipath delay profile, which relates to performancedegradation caused by intersymbol interference. In fact,in some communications systems with data rates smallcompared to 1 /aT, Tis found t0 be the most importantsingle parameter determining the performance [121. This,however, is not true in general [121.

The above parameters can actually be obtained directlyfrom the received frequency-averaged power profile, s ( t )defined in (7), without the need to know the individual0's and 7's . Define the received power profile moments

mM = t " s ( t ) t , n = 0 , 1 , 2,

--m

the transmitted pulse moments,mm , = t " p 2 ( t ) t , n = 0 , 2,--a,

the corresponding averages-t : = M , / M o , n = 1,2,t i = m , / m o , n = 1,2,-

and the variances -= t 2 - t s ) , .u; = t ; - ( t p- 2

D I S T R N C E F R O MOURCE,ETERSFig. 5. Measured signal attenuation versus distance relative to 1-m sepa-ration. The dashed lines are for different values of the distance-powerlaw exponent.

It can be shown thatG '= M o / m o , ( 1 8 )-7 = t, - fp, (19)

u : = us - up (20)2Note that G and uT but not 7, are independent of thechoice of the time origin.B. Distance-Power Law

The spatial average value E of the multipath power gainin the neighborhood of a point at a distance r from thetransmitter is, in general, a decreasing function of r . Usu-ally, this function is represented by a distance-power lawof the form. G(r) - r - a . (21)In free space, a = 2, and the power gain Qbeys an in-verse-square law as given by (8).

-

A logarithmic plot of our measured attenuationL ( r ) = -1OlOgm [G(r) /G(1 m)], (22)

in decibels, versus r , in meters, is given in Fig. 5.Notethat G (1 m) can be computed reasonably accurately from

Each rounded square in Fig. 5represents one measure-ment with the receiver located in the same hallway as thetransmitter. These measurements obey a power-law rela-tion with a < 2, which is the result of a waveguidingeffect. Each asterisk in Fig. 5represents the average ofabout 20 points within a room at the indicated distancefrom the transmitter. Recall, from Fig. 1 , that all therooms are located off the same hallway containing thetransmitter. The value a = 3 fits our room measurementsreasonably well.

The single point indicated by the sharp sign in Fig. 5represents the average of about 20 measurements whereboth the transmitter and the receiver were in the secondfloor of the building, with the receiver located in a large

(8).


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132 IEEE JOURNAL ON SELECTEDREAS IN COMMUNICATIONS, VOL. SAC-5, NO. 2, FEBRUARY 1987a 1llVmH

at . 5>+JH

ImmL

RMS D E L R Y SPREAD, sFig. 6 . Measuredcumulativeprobabilitydistribution of the rms delayspread for all rooms (solid line), and the result of a si,mulation using ourmodel (dashed line).

open machine shop with cinder-block surrounding walls[same room as that for Fig. 4(d)]. Unlike theone-dimen-sional hallway geometry of Fig. 1, the shop in this casewas located off a second hallway that is perpendicular tothe transmitters hallway. This resulted in a value of aslightly larger than 4. This is in more general agreementwith Alexanders resuits [2] for this type of building; Ac-cording to him, a can even be as large as 6 for officebuildings with metalized partitions. (In a recent confer-ence, Murray, Arnold, and Cox [19] reported on valuesof a between 3 and 4 measured in our building at 815MHz.)C. Statistics of the rms Dela y Spread

Our measured rms delay spread, (T,, ithin the individ-ual rooms was,not generally correlated with the distanceto the ransmitteras had been previously predicted bySchmid [131. Rather, it was somewhat related to the localsuriounilings of the transmitter and the receiver, e.g., totheir proximity to such large reflectors as the end metaldoors in Fig. 1; This is more consistent with the result ofTurin et al. [141 of the urban mobile-radio channel.

The combined cumulative distribution of T,esultingfrom a total of about 150 measurements within 7 roomson the first floor of the buildi,ng (see Fig. 1) is plotted bythe solid line in Fig. 6.The results indicate that the rmsdelay spread has a median value of about 25 ns and amaximum value of about 50 ns. These numbers are a fac-tor of five less than those measured by Devasirvatham ina much larger office building [7]. (In a recent coriference,Devasirvatham [20] repofled on rms delay spread of up to200 ns measured in our building at 85.0 MHz. This largevalue, however, occurred only when the received signallevels were extremely low, e. g. , 100-140 dB of path loss.When he truncated the data to a subset having path lossless than 100 dB, as is the s ituationin our case, he ob,-tained results comparable to ours.)

We did not include in Fig. 6 the handful of measure-ment taken in thehallway, which occasionally yieldedvalues of a, much larger than 50 ns. For example, themeasurement of Fig. 4(c) corresponds to T,150 ns. In

fact, hallway measurements were excluded from ourmodel development process altogether because, unlikeroom measurements, they include a direct line-of-sight rayfrom transmitter o receiver as well as strong rays withlong delays, which is not the typical situation in mostof-fice buildings.

VI. PROPOSED ODELA . BasicConjectures

We employ the discrete representation of the channelsimpulse response given by 2). As mentioned earlier, thephase angles {& } will be assumed a priori to be statis-tically independent random variables with a uniform dis-tribution over [0, 27r j . We believe hat this s self-evidentand needs no experimental justification. Our goai now isto find the joint statistics of the paths gains { P k } and ar-rival times { T k }

We start with theattractiveconjecture, which waspioneered by Turin et al. [14] in modeling urban mobile-radio channels, that { Tk } forms a Poisson arrival-time se-quence with some mean arrha1 rate X. The.path gain f l kassociated with every TL s then picked from some prob-ability distribution whose moments (e.g., mean and meansquare) are functions of Tk that eventually vanishes forlarge values of 7 k .

For simplicity, it would be desirable to have a modelwith X being a constant and the 0s statistically indepen-dent from one another. A straightforward implementationof these features, however, can ead to inconsistency withour experimental observations, as will be discussed next.B . Clustering o Rays

Observations of measured pulse responses, such assome of those given in Figs. 3 and 4, indicate that raysgenerally anjve in clusters.Similar observations werefound in the experimental data of Turin et al . [14]. Thisis clearly not consistent with a simple Poisson arrival-timemodel with constant X. Indeed, Turin et alt as well assubsequent researchers [15], [16] who further refined theirwork, abandoned this model in favor of a Markov-typemodel in which the time axis is, in effect, divided intobins, with the probability of a ray arriving within agiven bin related to whether or not a ray actually arrivedin the previous bin. Furthermore, in their model, the pathgains in successive. bins were also correlated. Althoughthese features of their model fit the experimental data well,including the ray clustering effect, the Markovian natureof their model makes its use in analysis quite complex.

We now present an altemative multipath model, whichis flexible enough to fit the experimental data reasonablywell, while retaining the basic features of a constant-ratePoisson arrival-time process and mutually independentpath gains, thus making its use in analysis relatively sim-ple. In addition, and perhaps more importantly, the modelcan be explained from a physical viewpoint, thus makingit more readily extendable to other types of buildings.


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SALEH A N D VALENZUELA: INDOOR MULTIPATH PROPAGATION 133

C. General Description of the ModelOur model starts with the physical realization that rays

arrive in clusters. The cluster arrival times, i.e:, the.,ar-rival times of the first rays of the clusters, are modeled.asa Poisson arrival process with some fixed rate A.Withineach cluster, subsequent rays also arrive according to aPoisson process with another fixed rate X. Typically, eachcluster consists of many rays, i.e:, X >> A.Let the arrival time'of the lth cluster be denoted by T1,z = o , 1 , 2 , * * * Moreover, let the arrival time of thekth ray measured from the beginning of the lth cluster bedenoted by r k l , ' k= 0 , 1, 2 , . By definition, for thefirst cluster, TO = 0, and for the first ray within the lthcluster, rO1 0. Thus, according to our model, Tl and Tklare described by the independent interarrival exponentialprobability density functions

P(T11Tl-1) = A exp [-A( - T,-,)] , 1 > 0 ,(23)

P(Tkl 1 T ( k - 1 ) 1 ) = exp [ - X ( T k l - T(k-l)l)], > 0.(24)

Let the gain of the kth ray of the Zth cluster be denotedby P k l and its phase by 6k[. Thus,, nstead o f (2), our com-plex, law-pass impulse response of the channel is givenby

m mh(t) = pkleieu6(t - 7 - Tkl). (25)1=0 k = O

Recall that { e k l } are statistically independent uniformrandom variables over [0 , 27). Furthermore, the { Pk [ }are statistically independent positive random variableswhose probability distributions are to be discussed in Sec-tion VI1 and whose mean square values { P i l } are mono-tonically decreasing functions of { T1 and { Tkl}. In ourmodel,

Pi1 E P2 T, k l )= ~ ( 0 ,) e-n/'e-7k//~, (26)

where P2(0,0) = P , is the average power gain of thefirst ray of the first cluster, and r and y are power-delaytime constants for the clusters and the rays, respectively.A sketch that clarifies our model' up to this point is givenin Fig. 7.

Note that clusters generally overlap. For example, iffor some k, rkl Tl+ - T1, hen the Zth and the I +1)th clusters overlap for all subsequent values of k. Typ-ically, however, r > y and the expected power of therays in a cluster decay faster than the expected power ofthe first ray of the next cluster. Thus, if A T T1 - T1is sufficiently large such that exp [ - A T / y ] 1) = 0.26 to 0.15. With only eight roomsmeasured, we cannot at this point be more precise in pick-


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ing A . In Section VIII-A we will see, from another pointof view, that 1 A : 300 ns.B. The Ray Arrival Rate , X

By resolving the individual rays in about 200 powerprofile measurements similar to those in Figs.3and 4 weestimate 1/ X to be in the range of 5-10 ns. The rangeuncertainty comes from the fact that our ray-resolving al-gorithm, coupled with our measurements sensitivity, sunable to detect many weak rays, in particular, those fall-ing near strong rays. The higher the sensitivity, the more(weak) rays we would find, and hence, the larger the valueof X. At the same time, theprobability distribution of thepath gains { Pk } would be increased for small values of6s: Thus, the appropriate choiceof X is strongly coupledto the probability distribution of the P s . We find that.aconsistent choice is 1/ X = 5 nscoupled with Rayleigh-distributed P s having the appropriate mean-square value(see Section VII-D). Actually, as will be discussed later(see Section VIII-B), smaller values of 1/ X could havebeen employed, even down to the limiting value of zero(i.e., continuous ray arrival process). This, however, isbeyond our measurement time resolution.C . The Ray and the Clu ster Powe r-De cay TimeConstants, y and

As mentioned in Section VII-A, the number of arrivaltimes of clusters, say, T o, T I , * ,TL,are he same forall locations within a given room. I t follows from (26)that, within that room, the expected value of the ray poweras a function of time, measured from the arrival point ofthe first ray of the first cluster, is given by

Lp2 = ~ ~ 0 ,) C e - f i / r e - ( r - f i ) / y ( t - T ~ ,1=0(271

where U ( t ) s the unit step function, which equals onefor t 0 , and zero for t C 0. A sketch of (27) is shownin Fig.(a).

n estimate of P 2 t ) , and hence of y and r, was ob-tained for a given room by aligning the time origin andtaking the average of many measured power profiles, s ( ) ,within that room. Actually, what one obtains from thisprocess is an estimate of the time convolution of P 2 t )and p 2 t ) , he square of the transmitted pulse. However,since this pulse is narrow, the-effect of the convolution isnegligible. Four different examples of such space-aver-aged s ( t ) are shown in Fig. 8.. More than 20 power pro-files were averaged in each case. Fig. 8(a) indicates thatonly one cluster reached the receiver in that case. Eachofthe remaining cases shows two arriving clusters. The timespread evident in the leading edges of a few clusters inFig. 8 is mainly due to fundamental uncertainty in align-ing the time origins of the various measured power pro-files.

By fitting decaying exponentials to each cluster in Fig.8, as well as to similar measurements taken in other

Fig. 8. Four spatially averaged power profiles within various rooms. Thedashed lines correspond to exponential power decay profile of the raysand the clusters.

rooms, we find that, on the average, rays within a clusterdecay with an approximate time constant of y = 20 ns(see dashed lines in Fig. 8). Similarly, by fitting decayingexponentials through the leading peaks of successive clus-ters, we find that the clusters themselves decay, on theaverage, with an approximate time constant of J = 60 ns(see dashed lines in Fig. 8).

The use of exponentials in (26) and (27) to representthe decays of the powers of the rays and clusters as func-tions of time has an intuitively appealing interpretation.Consider, for example, our physical picture of the raysbouncing back and, forth in the vicinity of the receiverand/or the .transmitter to form a cluster. On the average,with each bounce, the wave suffers some average delay(say, equivalent to the width of a room), and some aver-age decibels of attenuation (which depends on the sur-rounding materials of the walls, furnitures, etc.). In thiscase, the power level in decibels of each successive raywould be proportional to the time delay of that ray, whichresults in our exponential power decay characteiistics.Note that from this picture, y and would be increasedif the building walls were more reflective and/or if thesizes of the rooms and the building itself were increased.D . The Probab ility Distribution of the Path Gains, { Pk l }

So far, ouy_model gives the expected value of the pathpower gain Pil as a function of the associated cluster andray delays Tland T ~ ~ .e now make the assumption, whichis reasonably supported by ourobservations, hat heprob&ility distribution of the normalized power gainP L / P i l is independent of the associated delays, or for thatmatter, of the location within the building. Under this as-sumption, we can ut the measured power gains of all ourresolved paths into one, supposedly homogeneous, datapool by simply normalizing by the appropriate (i.e., mea-sured within the same room and having the same delay)spatially averaged power profiles, such as those shown inFig. 8.

The cumulative distribution of Pil/z,btained as de-scribed above, is shown by the solid line in Fig. 9. Thedashed line in that figure is the unity-mean exponential.


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SALEH A N D VAL E NZ UE L A: INDOOR MULTIPATH PROPAGATION 135tually the sum of many independent rays arriving withinour time resolution. Invoking the central limit theoremthen leads to the aforementioned complex Gaussian pro-cess. This is basically the same logic leading to the con-tinuous Rayleigh model, or more precisely, the Gaussianwide-sense stationary uncorrelated scattering (GWSSUS)model of the urban mobile radio channel advocated byBello, Cox, and others [17], [18], [12]. On the other hand,Turin and others [14]-[16] model the same channel ashaving discrete correlated rays with log-normal ampli-tudes. By comparison,our model of the indoor radio

R A Y POWER N O R M R L I Z E D TO AVERRGE channel consists of discrete uncorrelated rays with Ray-Fig. 9. Measuredcumulativeprobabilitydistribution of thenormalizedray lei& amplitudes- As will be Seen shortly, our model canpower for all rooms (solid line), and the best fitting exponential distri- easily be extended to a continuous model of the GWSSUSbution (dashed line). tY Peacumulative distribution, P [ /3:1//3i1 X ] = exp -X),which appears as a straight line on the semilog plot. Thisresults in the exponential probability density function,

for the path power gain, or, equivalently, the Rayleighprobability density function,

P ( P k 1 ) = ( 2 P k I / Z ) exp ( -P;l/Z , (30)for the path voltage gain.As mentioned earlier, our ray-resolving algorithm, cou-pled with our measurement sensitivity, is unable to detectmany weak rays, in particular, those falling near strongrays. Thus, in fitting the unity-mean exponential cumu-lative distribution to the data in Fig. 9, we let the totalnumber of resolved rays be a loating optimization param-eter, instead of fixing it to the actual number observed. Ineffect, we let the optimization procedure estimate thenumber of weak rays that we could have missed. As in-dicated from Fig. 9, with the solid line intercepting theordinate axis at a value of about 0.8 instead of 1 , a 25percent increase in the total number of rays is needed toachieve the best fit. This increase s reflected in the choiceof X given in Section VII-B. As can be observed from theshaded area in Fig. 9, the power of the needed rays is lessthan about 25 percent of the local average. Such weak

VIII. USING THE MODELA . Simulation Procedure

Suppose that we wish to simulate the indoor channelbetween a centrally located transmitter/receiver and someroom at a distancer . The first step is to generate the clus-ter arrival times, Tl , T 2 , , through the use of theexponential distribution of (23) with To = 0. Before pro-ceeding with the generation of the rays within the clus-ters, we need to estimate P2 ( 0 ,0), the average power ofthe first ray of the first cluster. This quantity is directlyrelated to the average multipath power gain E ( r ) for theroom in question. It follows from (21), (23), and Fig. 5that c r) G 1m) r - a , where G 1 m) can be approx-imated by (8), and a = 3 to 4 in our building, but can beup to 6 in other builds [2].

The relation between E ( r ) and P2 0,0) can be ffrom the definition of G n Section V-A, and from P 2 t ) ,the expected value of the ray power as a function of time,given in (27). With X being the average number of raysper unit time, it follows that

G ( r ) = X p t> dt0

rays could indeed have been missed by our ray-resolving The summation term in (31) is usually dominated by thealgorithm. first term, i.e., the first cluster. For example, with T1sta-other distributions could have fit our path gain dataas age value of this summation is rR. The accounts(30). For example, a log-normal distribution, with a stan- ters. In our case, with r = 60 ns and n between 200without inflating the number of weak rays as was doneabove. However, we believe that those undetected weak Considering the +7 dB deviation in fitting E ( r ) to thepower law r --OL shown in Fig. 5 , the small increase (= 1

It is appropriate t mention at this point that various tistically described in (23), it can be &own that the aver-as, Or even better than, he Rayleigh distribution Of for the first cluster and accounts for subsequent clus-

d a d deviation of about 4 dB, fits our data well, even and 300 ns, this average value is between 1.3 and 1.2.

exist, and that the Rayleigh distribution, dB) due to subsequent ,-lusters can safely be neglected.which is much simp1er to with in than the (Note, however, that these delayed clusters have a majorlog-normal distribution, is quite adequate for our model.-Having rays with Rayleigh amplitudes and uniformphases, which corresponds to a Gaussian Pro- olaced v ( 1 + yA). Thedded 1 accounts for theirst ray of each cluster.Actually, morecompletecomputationwould yield 31) with yX re-cess, can physically occur if what we call a ray is ac- However, usually yX >> 1 , and (31) s avalidapproximation.< , .


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136 IEEEOURNAL ON SELECTEDREASNOMMUNICATIONS, VOL. SAC-5, NO. 2, FEBRUARY 1987effect on the value of the rms delay spread.) We can fi-nally compute b * ~ , ) from

p 2 ( 0 , o >= ~x)-~G I) r-a (32)where G ( 1 m) is given approximately by (8) , with r= 1.

Now we can proceed to generate the rays within theclusters.First, he relative ray arrival times { 7 k l } aregenerated through the use of the exponential distributionof (24). Next, the ray amplitudes { I } axgenerated fromthe Rayleigh distribution of (30), with b i l given by (26).To complete the picture, the associated phase angles { e k l }are chosen from a uniform distribution. Depending on theapplication, he process of ray and cluster generationwould stop when the average power of the generated raysdrops below some threshold.As mentioned in Section VII-A, we estimate the meantime between clusters in our building to be in the range1 A = 200-300 ns. To resolve this uncertainty, we sim-ulated the channel as described above, computed the rmsdelay spread T,or each simulation point, and plotted itscumulative distribution. With our other parameters beingy = 20 ns, r = 60 ns, and 1 / X = 5 ns, the best fit tothe cumulative distribution obtained directly from mea-surements, the solid line in Fig. 6, was for l / A = 300ns. The corresponding distribution obtained from simu-lations is given by the dashed line in Fig. 6.B. Discrete versus Continuous Model

Thus far, our model is presented as a discrete ray ar-rival process. This would be more convenient for use instudies using computer simulations. We now examine thepossibility of having a continuous-model.We note that, by letting the ray arrival rate X approachinfinity, while having p 2 ( 0 ,0) approach zero such thattheir product is finite and satisfies (32), and by noting thatthe complex ray gains form a Gaussian process, our modelmathematically approacheshe continuous GWSSUSmodel mentioned in Section VII-D. Such a model wouldbe more suitable for analysis [121, [171. Some measuredpower delay profiles, such as the one shown in Fig. 4(d),suggest that such a continuous model might indeed rep-resent the physical reality. On the other hand, other mea-surements, such as hose of Fig. 3(d)-(g), which weretaken on the vertices of an 0.23-m square, suggest a dis-crete model. This follows from the orrelation evident be-tween the various profiles, which could be attributed tothree or four dominant waves traversing the observationpoints.

With our time resolution of about 5 ns, and with ourfinding of a mean time between rays of 1/ X 2: 5 ns, weare unable to determine whether the indoor radio channelis best described by a discrete or a continuous model. Inmany studies, the answer to this question may not be rel-evant, while in others, the answer may be important. Forexample, a truly discrete model would yield a strong spa-tial correlation of the amplitudes of the rays rewived in

some vicinity. This would yield some space diversity sys-tems useless. A continuous model, on the other hand, re-sults in the opposite conclusion. We believe from ourmeasurements that, in most situations within the indoorchannel, a continuous model or, equivalently, a high-den-sity discrete model, is closer to the physical reality. How-ever, as mentioned earlier, some exceptions do exist. Adefinitive settlement of this issue awaits future experi-ments involving either a better time resolution or simul-taneous measurements with two or more closely spacedreceiving antennas.

IX. SUMMARYND CONCLUSIONSWe presented the results of 1.5 GHz,pulsed, multipath

propagation measurements between two vertically polar-ized omnidirectional antennas located on the same floorwithin a medium-size building (AT&T Bell Laboratories,Crawford Hill location in Holmdel, NJ). A novel methodof measurement was used, which involves averaging thesquare-law-detected received pulse response whilesweeping the frequency of the transmitted pulse. This en-abled us to resolve the multipath channel impulse re-sponse within about 5 ns.

Our results show the following. 1) The indoor channelis quasi-static, r very slowly ime varying (related to peo-ples movements). 2) The nature and statistics of thechannels impulse response is virtually independent of thestates of polarization of the transmitting and receiving an-tennas, provided that there is no line-of-sight path be-tween them. 3) The maximum observed delay spread inthe building was 100-200 ns within rooms, with occa-sional delays of more than 300 ns within hallways. 4)Themeasured rms delay spread within rooms had a medianvalue of 25 ns, and a maximum value of 50 ns, both beinga factor of five less than those measured by Devasirva-tham in a much larger building [7]. 5 ) The signal atten-uation with no line-of-sight path varied over a 60 dB rangeand seems to obey an inverse distance-power aw with anexponent between 3 and 4, which is in general agreementwith Alexanders results [2] for this type of building.

We have also developed a simple statistical multipathmodel of the indoor radio channel, which fits our mea-surements well and, more importantly, appears to be ex-tendable (by adjusting the values of its parameters) toother buildings. In our model, the rays of the receivedsignal arrive in clusters. The received ray amplitudes areindependent Rayleigh random variables with variancesthat decay exponentially with cluster delay as well as withray delay within a cluster. The corresponding phase an-gles are independent uniform random variables over[0, 27r). The clusters, as well as the rays within a cluster,form Poisson arrival processes with different, but fixed,rates. Equivalently, the clusters and the rays have expo-nentially distributed interarrival times. The formation ofthe clusters is related to the building superstructure (e.g.,large metalized external or internal walls and doors). Therays within a cluster are formed by multiple reflections


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SALEH A N D VALENZUELA: INDOOR MULTIPATH PROPAGATION

from objects in the vicinities of the transmitter and thereceiver (e.g., room walls, furnishings, and people).A detailed summary of the method of using the modelwas given in Section VIII. Both a discrete and a contin-uous version of the model are possible. The former is moresuitable for computer simulations, while the latterwouldbe more desirable in analysis.

ACKNOWLEDGMENTWe thank Prof. P. J . McLane for many stimulating dis-

cussions, especially about the discrete versus continuousmultipath models. We also thank L. J . Greenstein, D. J .Goodman, and M. M. Kavehrad for their useful sugges-tions and comments, and R. A. Semplak and G. J . Owensfor their design of the discone antennas used in the ex-periment. We also acknowledge the valuable contribu-tions of R. D . Nash in the early phase of the experiment,and the able help of M. F. Wazowicz in maintaining theequipment. Last, but not least, we thank T. A . Saleh and0 . Saleh for their help in the tedious task of gatheringthe valuable experimental data.

REFERENCES[l ] S. E. Alexander, Radio propagation within buildings at 900 MHz,Elec tronLet t . , vol. 18, no. 21, pp. 913-914, Oct. 14, 1982.[2] S . E. Alexander, Characterizing buildings for propagation at 900MHz, Electron Lett . , vol. 19, no. 20, p. 860, Sept. 29, 1983.[3] H. H. Hoffman and D. C. Cox, Attenuation of 900 MHz radio wavespropagating into a metal building, ZEEE Trans.AntennasPropa-g a t . , vol. AP.30, pp. 808-811, July 1982.[4] D. C. Cox, R. R. Murray, and A. W. Noms, Measurements of 800MHz radio transmission into buildings with metallic walls, Bell Syst.Tech. J . , vol. 62, no. 9, pp. 2695-2717, Nov. 1983.[5] -, 800 MHz attenuation measured in and around suburbanhouses, AT&TBell Lab. Tech. J . , vol. 63, no. 6, pp. 921-954,[6] D. M. J . Devasirvatham, Time delay speed measurements of 850MHz radio waves in building environments, in GLOBECOM 85Con$ R e c . , vol. 2, Dec. 1985, pp. 970-973.[7] -, The delay spread measurements of wideband radio signalswithin a building, Electron. Lett . , vol. 20, no. 23, pp. 950-951,Nov. 8, 1984.[8] A. G. andoian, Three new antenna types and their applications,Proc. IRE, vol. 34, no. 2, pp. 70W-75W, Feb. 1946.[9] J . G. Proakis, DigitalCommunications. New York: McGraw-Hill,1983, ch. 7.[lo] S . Ramo, J . R. Whinnery, and T. Van Duzer, Fields and Waves nCommunicationElectronics. New York: Wiley, 1965, p.717, eq.

[ l l ] D. C. Cox, Delay Doppler characteristics of multipath propagationat 910 MHz in a suburban mobile radio environment, ZEEE Trans.Antennas Propaga t. , vol. AP-20, pp. 625-635, Sept. 1972.[12] B. Glance and L. J.. Greenstein, Frequency selective fading effectsin digital mobile radio with diversity combining, ZEEE Trans. Com-mun. , vol. COM-31, pp. 1085-1094, Sept. 1983.[13] H. F. Schmid, A prediction model for multipath propagation of pulse

signals at VHF and UHF over irregular terrain, ZEEE Tra ns. An-tenna Propagat. , vol. AP-18, pp. 253-258, Mar. 1970.

July-Aug. 1984.

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[14] G. L. Turin, F. D. Clapp, T. L. Johnston, S.B. Fine, and D. Lavry,A statistical model of urban multipath.propagation, ZEEE Trans.

[15] H. Suzuki, A statistical model for urban radio propagation, ZEEETrans. Commun., vol. COM-25, pp. 673-680, July 1977.[16] H. Hashemi, Simulation of the urban radio propagation channel,ZEEE Trans. Veh. Technol., vol. VT-28, Aug. 1979.[17] A. P. Bello and B. D. Nelin, The effect of frequency selective fad-ing on the binary error probability of incoherent and differentially co-

herent matched filter receivers, ZEEE Trans. Commun. Sys t . , vol.CS-11, pp. 170-186, June 1963.[18] D. C. Cox and R. P. Leck, Correlation bandwidth and delay spreadmultipath propagation statistics for910 MHz urban mobile radiochannels, ZEEE Trans. Commun., vol. COM-23, pp. 1271-1280,

Nov. 1975.[19] R. R. Murray, H. W. Arnold, and D. C. C o x 815 MHz radio at-tenuation measured within a commercial building, in Dig. Z986ZEEEZnt. Symp. Antennas Propagat. , vol. 1, June 1986, pp. 209-212.[20] D. M. J . Devasirvatham, A comparison of time delay spread mea-

surements within two dissimilar office buildings, in ZCC86 Con$R e c . , vol. 2, June 1986, pp. 852-857.

Veh. Technol. , vol. VT-21, pp. 1-9, Feb. 1972.

Reinaldo A. Valenzuela (85) received theB.Sc.(Eng.) degree from the School of Engineer-ing, University of Chile, in 1977. He received thePh.D. degree in 1982 through the study of tech-niques for transmultiplexer design.From 1975 to 1977 he worked for Thomson-CSF (Chile) in the setting-up and commissioningof large telecommunication networks. In 1978 hejoined the Department of Electrical Engineering,Imperial College, London, England, where, in1981, he was appointed a Research Assistant,

sponsored by British Telecom for the study of digital filters for CODECapplications. He then joined DATABIT Ltd. (U.K.) where he participatedin the analysis and design of a full duplex, echo cancelling system for thetransmission of 88 kbits/s data and analog voice signals over the subscriberloop. Since 1984 he has been a member of the Communications MethodsResearch Department, AT&T Bell Laboratories, Holmdel, NJ, where hehas been studying local area networks issues such as indoor microwavepropagation and the integration of voice and data in multiple access packetnetworks.

a statistical model for indoor multipath propagation

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