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.
@ 1989 Rappaport and Seidel 3
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
@ 1989 Rappaport and Seidel 4
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.
@ 1989 Rappaport and Seidel 5
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.
@ 1989 Rappaport and Seidel 6
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)
@ 1989 Rappaport and Seidel 7
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
@ 1989 Rappaport and Seidel 8
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
@ 1989 Rappaport and Seidel 9
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).
@ 1989 Rappaport and Seidel 10
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
@ 1989 Rappaport and Seidel 12
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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