RADIO CHANNEL MODELS IN MANUFACTURING ENVIRONMENTS Prof. Theodore S. Rappaport …faculty.poly.edu/~tsr/wp-content/uploads/CV/RCP/1989-06... · 2014. 1. 22. · Prof. Theodore S

RADIO CHANNEL MODELS IN MANUFACTURING ENVIRONMENTS

Prof. Theodore S. Rappaport and ScottY. Seidel Virginia Polytechnic Institute and State University

This paper was presented at the Wireless Information Networks Workshop, Rutgers University, June 15,.1989.

Abstract

This work has deyeloped statistical indoor radio propagation models for the analysis of

factory communications systems. These models will permit research into the development of

wideband wireless networks for AGVs, vision systems, and portable personal conununications

within factories. Models have been developed which characterize the discrete impulse response

of indoor radio channels for both line-of-sight (LOS) and obstructed (OBS) topographies. In

addition, the effects of transmitter-receiver (T- R) distance and receiver sensitivity are

incorporated in the models.

Introduction

Models which characterize the impulse responses of factory radio channels are useful in the

analysis of the maximum data rate which may be transmitted without requiring equalization,

and are needed for the development of sophisticated high data rate digital cormnunications

systems. Factory radio channels may be divided into two basic categories. '\Vhen there is a

direct path between the transmitter and receiver, LOS topography exists. Absence of such a

@ 1989 Rappaport and Seidel

path indicates an OBS topography [1]. Models have been developed for both LOS and OBS

topographies which describe the distribution of the number of multipath components, the

probability of receiving a multipath component at a particular excess delay, the distribution of

the amplitude of multi path components at a particular excess delay, and the correlation between

multipath component amplitudes over both space and time .

. Results

The impulse response h(t) of a linear system is a useful characterization since the output

of the system can be computed through convolution of the applied input with the impulse

response. In a multipath radio channel, the impulse response can be modeled statistically.

Instead of measuring the impulse" response, which requires. an accurate measurement of the

phase of multipath components, the multipath power delay profile I h\t) I has been measured

to provide data for amplitude and excess delay statistics for indoor factory multipath channels.

An example of the measured data is given in Figure 1. Multipath components are resolved to

7.8 ns resolution [1].

Path Number Distribution

Knowledge of the. number of multipath components is important for the simulation of

modulation and equalization techniques. The distribution of the number of multipath

components which exist above a certain threshold in LOS topographies is shown in Fig. 2 for

received power thresholds of 30, 39, and 48 dB below a ten wavelength free space reference.

These statistics have been computed from all profiles which have at least one multipath

@ 1989 Rappaport and Seidel 2

component existing above the particular threshold used. Note that a 48 dB threshold below a

lOA. reference implies a path attenuation of about 86 dB, close to the 90 dB maximum dynamic

range of our system. Also shown is the P~isson distribution of the number of multipath

components with the same mean value as the measured data. One can see that for increased

receiver sensitivity, the Poisson distribution is ·a poor model for the number of discrete

multipath components. With a less sensitive setting, the Poisson distribution provides a better

fit to the data. The ayerage number of multipath compone1,1ts per power delay profile was

computed over each local measurement area (in each loc~l measurement area, 19 profiles were

measured over a 1-m track). The distribution of the average number of multipath components

over 25 LOS factory channels from 5 different factories is shown in Figure 3 along with the

normal distribution with the same mean and standard deviation as the measured data. It can

be seen from Figure 3 that a uniform distribution which ranges from 9 to 35 paths, or a normal

distribution with a mean of 22.4 paths and a standard deviation of 8.6 paths are good models

for the average number of multipath components in LOS topographies. In obstructed

topographies, the uniform distribution extends from 1 to 35 paths, or for the normal

distribution, the mean is 17.7 paths with a standard deviation of 11 .. 0 paths. Intuitively, we

would expect fewer multipath components in OBS topographies due to shadowing. Given the

average number of multipath components for a particular receiver location, one needs to know

how that number changes as the receiver or transmitter is moved. The standard deviation of

the number of paths about the average is a linear function of the average of multipath

components. Figure 4 shows this model for LOS, and allows us to simulate how the discrete

number of multipath components changes as the receiver is moved over a local area.


Probability of Path Arrival

Once the number of multipath components is determined for a particular profile, it is

desirable to know the probability that a component will exist within a particular excess delay

interval. Figure 5, which has been computed from all of the 475 measured LOS profiles, shows

the probability that a multipath component is received above a certain path loss threshold.

Notice that as the threshold level is decreased (path attenuation is increased), the probability

of receiving multipath components with excess delays greater than 50 ns increases more than

the probability of receiving multipath components with excess delays less than 50 ns. The

probability of path arrival in LOS topographies may be modeled as an exponentially decreasing

function of excess delay. This assumes no correlation on the interarrival times of multipath

components (i.e. the paths arrive independently) .

. In obstructed topographies, the probability of receiving a multipath component increases

from· 0.5 at an excess delay of 0 ns to 0.6 at an excess delay of 75 ns and then decreases

exponentially with excess delay. The effect of received power threshold cannot be overlooked

when determining the probability of path arrival. As seen in Figure 5, the shape of the

probability of path arrival curve changes significantly as the received power threshold is

changed. This shows that low power systems (for example, distributed antenna systems [8]) will

experience less time dispersion than higher power indoor radio systems.

The time of arrival of each multipath component is determined from the probability that a

multipath component exists at particular excess delay. A simple recursive algorithm, which ~

generates a uniform random number and compares it with the probability of path occupancy

(e.g. Figure 5) for each excess delay interval, is used to determine the initial excess delays at

which components exist. The algorithm halts on the first pass when a sufficient number (as

determined by the path number distribution) of multipath components are found. On

subsequent passes, the probability of path occupancy model is normalized to account only for


the remaining possible excess delays. This technique for generating the excess delays has

provided excellent agreement with the measured profiles, and is easily implemented on

computer.

Path Loss

The total power contained in a received multipath profile at · a particular

transmitter-receiver (T-R) separation of d meters is well described by the log-normal distribution

(normal distribution with values in dB) about a mean path loss law of the form dn [2].

Free-space path loss is assumed for the first 2.3 meters (lOA.) and mean values of n range from

1.8 to 2.8 [1,2]. In [1], it is shown that if multipath components have random phases, then

ensemble averages of wide band and narrow band (CW) measurements will fit the same dn path

loss law and will have a log-normal distribution about the fit. It is shown here that not only is

the total received signal power log-normally distributed about the mean, but the path loss of

discrete multipath components is also log-normally distributed about some mean dn(1') path loss

law. Generally n( '!) increases with '! (i.e. path loss is greater for components that arrive later in

the profile). Figure 6 is a scatter plot of path attenuation with respect to distance for the excess

delay interval 0-7.8 ns (-r = Ons) and shows that a mean path loss law of the form dn may be

assumed for individual multi path components which arrive within· a particular excess delay

interval. For this case, n(O) = 2.6. The best mean square fit of the dn path loss model and one

standard deviation about the mean are shown. The distribution of the power received in a

particular excess delay interval is log-normal about dn(1')' as shown in Fig. 7. In [3], we showed

the log-normal distribution is a good model for multipath power arriving in any excess delay

interval.


Figure 8 shows how the power law exponent n changes with excess delay for LOS and OBS

topographies. In obstructed topographies, the power of multipath components with small

excess delay obeys a path loss power law in which the signal attenuates (n increases) more

rapidly than in line-of-sight topographies. This is ~xpected since shadowing due to obstructions

caus_es attenuation to be greater than in unobstructed topographies. We found the· standard

deviation about the mean path loss law is relatively insensitive to excess delay and is

approximately 4 dB for LOS and 5 dB for obstructed topographies. The standard deviation for

, obstructed topographies is slightly larger than in LOS topographies since the effects of

shadowing cause greater variation in path attenuation as the receiver is moved from one local

area to another.

Multipath components fade as the receiver is moved over a local area (i.e. 1 meter track).:

It is important to understand the amount of fading which can occur as a result of small changes ..

in receiver location. Since a characterization of all the individual scatterers in an indoor channel

is futile, a statistical channel model is sought. We have found that individual multipath

components have signal strengths that are log-normally distributed over small scale distances.

Figure 9 is the cumulative distribution function (CDF) of the measured signal level and the

CDF of the log-normal distribution fit to the mean and standard deviation of the measured

signal level. \Ve have found that over the ensemble of local measurements, although the mean

signal level is highly dependent upon excess delay, the amount of fading (standard deviation)

about the mean is not. Thus, where some LOS components at -r = 0 undergo very slight, if any,

fading over a 1 meter track, at other locations, the LOS signal fades as much as signals arriving

later in the profile. Similarly, at some locations, signals which arrive later in the profile do not

fade (they are specular reflections from walls, etc.) _whereas at other locations, signals with large

excess delay fade rapidly.


RMS Delay Spread

Figure 10 shows how the rms delay spread of LOS factory channels changes with respect

to received power threshold. The average rms delay spread and one standard deviation about

the average are shown. Notice that rms delay spread increases as the received power threshold

is decreased. The interpretation of multipath parameters such as rms delay spread are very

much conditioned upon the type of noise thresholding used.

Autocorrelation Coefficient Function

Inspection of the empirical data leads us to believe that some of the amplitudes of

multipath components which exist at various locations and time delays are correlated. This has

beeri found to be the case for urban mobile radio channels [4,5}. We assume that over distance

separations greater than several wavelengths, channels become uncorrelated over space. Over

excess delay differences greater than 100 ns, we have found multipath signal strengths on the

average become uncorrelated. Assuming independence between time and space, autocorrelation

coefficients (ACC) for received signal levels are estimated individually over time and space.

The conditional distribution of A(~2) given the value of A(~ 1) can be calculated by assuming

both random variables are from a jointly log-normal distribution with a conditional mean

(Ia)

and a conditional variance

(1 b)


where A is a multipath amplitude for a particular location ~ . ~ is a function of spatial location

x and excess delay 't'. raa is the space or time correlation [3]. In (1), means and standard

deviations have dB values. The previous general equations have been specialized for application

to spatial and temporal correlations over local areas [6}. The local distances and excess delay

values at which multipath signal amplitudes become uncorrelated are important in the analysis

of antenna diversity, burst errors, and fading.

We have shown that individual multipath components obey a log-normal fading

distribution [see Fig. 9] as a mobile is moved over a local area. We assume that multipath

amplitudes are also jointly log-normally distributed over local areas. If the amplitude of a

multipath signal which occurs at a particular excess delay at one location is known, then the

conditional amplitude of the multipath signal amplitude at a distance ~x away with the same

excess delay is log-normally distributed with mean and variance as derived from (Ia) and (I b).

When (1) is used for spatial correlations, e1 and e2 represent two different physical locations

which are within 1 meter of each other, and the means and variances on the righthand side are

determined from the statistics of the empirical database. In the spatial correlation case, the

excess delay is identical for all multi path components of interest; thus, a A(~2) will be equal to

(J A(~ I) and A( e 1) is equal to A( e2) as determined from a log-normal distribution about the mean

dn(-r) path loss. The computed spatial correlations of multi path amplitudes at a particular excess

delay are based only upon multipath components existing in at least 5 of the 19 profiles

measured along a 1 meter track. In addition, only those amplitudes of components which exist

are used in the computation of correlation coefficients.

Because the autocorrelation coefficient function (ACCF) varies widely from local area to

local area, and factory to factory, we have calculated an average ACCF based upon the

individual ACCF's found at each local area. Curves have been fit to the data based on a

combination of inspection and least-squares fit criteria. Figure 11 shows the average spatial

ACCF in LOS topographies as a function of spatial separation and excess delay. The function


is piecewise exponential with respect to separation and is exponential with respect to excess

delay. This function accurately approximates the average spatial ACCF for the measured data.

A similar method is used to compute aver~ge LOS temporal ACCF, except that now, ~ 1

and ~2 represent different excess delay times within the same multipath delay profile (i.e. same

location). In (1), A(~ 1 ) and A(~ 2) have different values because multipath components at

different excess delays have different distributions of the means [e.g. Fig. 8]. The standard

deviations on the right hand side are independently determined from an empirical distribution

of a values. The result is shown in Figure 12. Note that the first few components which arrive

early in a profile have strengths which are anti-correlated from the LOS signal. Components

which arrive later in the profile decorrelate rapidly without regard to excess delay value. We

have found that there is virtually no correlation between multipath component amplitudes ~

obstructed topographies.

Conclusion

We have presented statistical models for wideband power delay profiles inside factory

buildings. These models are based on the only known propagation measurements from factory

buildings. Although indoor radio channels cannot be completely characterized by first and

second-order statistics, they provide a more complete model of multipath propagation inside

buildings than the first order models that have recently appeared [7,9]. Models have been

presented here which quantify the number of multipath components which exist within a local

area, the probability of receiving multi path components within a particular excess delay interval,

the distribution of multipath component amplitudes, and the correlation between multipath

component amplitudes which exist at various spatial locations and excess delays over a local

one meter area. We have made good progress towards the development of channel models


which can be incorporated in computers to analyze the performance and design tradeoffs of

indoor radio networks of the future. An example of a computer generated power delay profile

is shown in Fig. 13 and may be compared to the actual data shown in Fig. 1. Excellent

agreement between computer generated proftles and actual measurements has been achieved,

although measurements in additional factories are needed to fully validate and r~fine our

models.·

Acknowledgements

~oichiro Takamizawa, a graduate student at Virginia Tech, assisted with the data

processing and wrote many of the plotter routines used in this research. This work has been

sponsored by a grant from the Purdue University Computer Integrated Design, Manufacturing,

and Automation Center (CIDMAC).


References

[1]

[2]

[3]

[4]

[51

[6]

[7]

[8]

[9]

T.S. Rappaport, "Characterization of UHF multipath radio channels in factory buildings.'' IEEE Trans. on Ant. and Prop., to be published August 1989.

T. Rappaport, C. McGillem, "UHF Fading in Factories," IEEE J. Sel. Areas Comm., Special Issue on Portable and Mobile Corrununications; Vol. 7, No. 1, January 1989, pp. 40-48. '

S.Y. Seidel, K. Takamizawa, T.S. Rappaport, Radio Channel Modeling in Manufacturing Environments, An intermediate report (parts 2 and 3) prepared for Purdue University's CIDMAC, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, February 28, 1989.

A. Bajwa, J. Parsons, "Small Area Characterisation of UHF Urban and Suburban Movile Radio Propagation,"/£££ Trans. Veh. Tech., Vol. VT-21, No.1, February 1972.

G.L. Turin, F.D. Clapp, T.L. Johnson, S.B. Fine and D.Lavry, "A statistical Model of Urban Multipath Propagation," IEEE Trans. on Veh. Techno/,, vol. VT-21, pp. 1-9, Feb. 1972.

S.Y. Seidel, K. Takamizawa, T.S. Rappaport,'' Application of Second Order Statistics for an Indoor Radio Channel Model," IEEE Veh. Tech. Conf. May 1-3, 1989, San Francisco, CA.

A.A.M. Saleh and R.A. Valenzuela, "A statistical model for indoor multipath propagation," IEEE Journal on Sel. Areas in Comm., val. SAC-5, pp. 128-137, Feb. 1987.

A.A.M. Saleh, A. J. Rustako, Jr. and R.S. Roman, "Distributed Antennas for Indoor Radio Communications," IEEE Trans. Comm., val. COM-35, No. 12, pp. 1245-1251, December 1987.

P. Yegani, C. McGillem, "A Statistical Model for Line-of-Sight (LOS) Factory Radio Channels," IEEE Veh. Tech. Conf.May 1-3, 1989, San Francisco, CA.

@ 1989 Rappaport and Seidel 11 .

List of Figures

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Example of measured multi path power delay profile I h2(t) I Distribution of the number of multi path components

Distribution of average number of paths per profile within a local area

Scatter plot of average number of paths vs. standard deviation of number of paths

Probability a multipath component is received

Scatter plot of path attenuation vs. T-R separation

Distribut.ion of received signal about dn(-r) path loss law

Path loss law exponent (n) vs. excess delay (-t')

Distribution of multi path component amplitudes over a local area for a constant· excess delay

RM S delay spread vs. received power threshold

Average spatial ACCF model for LOS topographies

Average temporal ACCF model for LOS topographies

Computer generated multipath power delay profile I h\t) I


1 .. 0

!I '-

fJ.

Cll .~ :3 c

Q.

'tJ ~ .~ N .... ,... ~,

.: '-0 :

.00

,.. ~xcess Delay ens>

pc3ac

Figure 1. Example of measured multi path power delay profile I h2(t) I

/

~0.4 ..... ,..... ..... .c co .c 0

&:0.2

~0.2 .,.... ,..... .,.... .c co ..c 0

d: 0.1

~0.10 .,.... ,..... .,.... .c co .c 0

d: 0. 05

0.000

X

X X

Figure 2.

5 10 15 Number of

¢¢¢ ¢ ¢

¢ X X X X ¢ ¢ X ¢

X X X ¢X

Xx¢

Number of

Number of

LOS 30dB below 10l.

LOS 39dB below 10:\.

LOS 48d8 below 10:\.

Distribution of the number of multi path components

Figure 3.

Figure 4.

a o.1e ~ zca

en cucn ct-r4 cau t..cn ~:l ~ v 0.50 .... ocn

.c ~

<4-JCD -a.. ~ -.... .00 ca .0 0

~ 0.25 I

I

I I

I I

I I

I I

I I

Average • 22.4 Sigma • 8.6

0. 00 .._.... __ ......_ __ __,_ __ __._ ___ L....-__ ...~.....-__ -..L.--J

0 10 20 30 40 50 60

Averagt Number of Paths

Distribution of average number of paths per proftle within a local area

en ..c <1-J

20

cf 15

10

5

X

X

X

X

LOS

X

/' /X

X X X X X

X

0 0-~--_.----~--------~--------~------~ t10 20 . 30_ 40

Average Number of Paths

Sigma • 0.528 • (Average Number of Paths- 5.1)

Scatter plot of average number of paths vs. standard deviation of number of paths

I v

i

t.O

.... •..c &a ~ ... Cl) .... "CC. u > .... ~· u > u. c! ....

• .... a a,... u

>o.Q .... ~~~~ .... "CC ~

i~ .g" t

0.0 0

.... •..c c CliO ~ ... tn ..., "CC. u > .... ~u

i.O

u > u u ! .... 0.5 • .... a

a,.... cu

>-.a .... ~~~~ .... "CC ~

.a CD -~ .a a " t

Figure 5.

iOO 200 300' <400 500

Excee• Delay TiM. [nel

Excea• DeliY T1•. [nsl

Probability a multipath component is received

~

1111 ........ l X X

_,.

• _,.r _,.

_,. ------ X _,___...-

I - _,. _,. . 30 .-JC---- X_,-"1C -- ---- X

c - --- -a _,. .... _,. -..., -• 20 _ ....

::II .... c .... -• -..., --..., -~ -10

n • 2.8

ligM • 5.~ d8

0 • to 20 ..a T-A Sep .. at1on [Ill

Figure 6. Scatter plot of path attenuation vs. T-R separation

i.O ca ..,..,..--CQ CD .... u CD

~ 1\ roof

cu > ID _J

,... 0.5 ca

c at .... en 'to-0

>o. Excess Delay • 7.8 ns .... .... ,... n • 2.6 .... .a Sigaa • 5.4 dB ca .a 0

&:: 0.0

-iO -a -6 -4 .;..2 0 2 4 6 8 10 Signil Level dB about Best Fit

Figure 7. Distribution of received signal about dn('r) path loss law

c .4J c cu c 0 c. ~ ]1: 10 ....J

c.. cu ]1: 0 a..

2

3

···.·· ·· .. ·

4

5 0 100

LOS-

OBS .......

· ..... .... . . . .. ,.

00 o I t 0 I ····.

200 300 400 Excess Delay Time, (nsl

Figure 8. Path loss law exponent (n) vs. excess delay (T)

1.0 ca CD CD ~ u CD

~ 1\

..... Qa > Qa _J

..... ca 0.5 c: a -en .... a ~ ..... Excess Delay a 39.1 ns -..... Mean • 37.0 dB -.a

Sigma • 2.1 dB ta .a 0 c.. a.

0.0 25 30 35 40 45

Signal Level dB below 10>.

.·.

500

50

Figure 9. Distribution of multipath component amplitudes over a local area for a constant excess delay

~ 150~--~--~~r--.--.---.--.---.--.-~,--., .s 1:J ca u c.

LOS

c5r 100 >CD ,..... QJ 0

r.n X a: QJ C) n:J t.. QJ

> <

50

0 18 21 24 27 30 33 36 39 42 45 48 Received Power Threshold below 101 [dB]

Figure 10. RM S delay spread vs. received power threshold

Figure 11.

Figure 12.

1.0

.1 a. s ~

~ .I ~ ~

-o. J

a

sea

I" .. I

I 0

Average spatial ACCF model for LOS topographies

.J ~ .I i ~

l.a

a. s

a.cr

-0. J

25

50

75

100

.... 300 I ....

2aa 1 I

100 ~ ~

4' I

41

Average temporal ACCF model for LOS topographies

1.0

Normalized Power

(Linear Scale)

0.5

0.0

0

COMPUTER GENERATED PROFILE L1NI•af•SIGH1 10POGRAPHT

125

250

375 a sao

Exc~ss Delay (ns)

Figure 13. Computer generated multipath power delay profile I h2(t) I

1.0

Local lm A·rea

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RADIO CHANNEL MODELS IN MANUFACTURING ENVIRONMENTS Prof. Theodore S. Rappaport …faculty.poly.edu/~tsr/wp-content/uploads/CV/RCP/1989-06... · 2014. 1. 22. · Prof. Theodore S