Statistical modelling and computer simulation of
indoor radio channel
R. Ganesh
K. Pahlavan
Indexing terms : Radiocommunication, Simulation, Propagation
Abstract: Multipath profiles obtained from radio
propagation measurements at 910 MHz are used
to analyse the statistical characteristics of the
indoor radio channel. The data base is divided
into two classes : manufacturing floors and college
offices. In the manufacturing floors, there is plenty
of open space without any presence of walls, as a
result of which most of the received power is concentrated in the initial paths. The college office
areas have a wider spread of power in delay,
because of less open space and the frequent
obstruction of the signal between the transmitter
and the receiver by one or more walls. The statistical parameters required for computer simulation of multipath profiles in each environment are
determined. The arrival of the paths is shown to
fit a modified Poisson process and the amplitude
of the paths follow a log-normal distribution. The
mean and the standard deviation of the lognormal distribution are shown to decay exponentially with delay. To evaluate the performance of
this simulation model, the distribution of the
RMS delay spreads from the simulated profiles is
compared with that obtained from the measured
profiles.
1
Introduction
Indoor radio communications is currently studied for
applications such as wireless PBX systems, wireless local
area networks, universal portable phones and wireless
security systems. These applications will be complemented by wireless communications between mobile
robots, automatic guided vehicles (AGV) and other services unknown at the present time [l]. The dependence
of a wireless system on effective radio propagation
demands some measurement and modelling of the indoor
channel characteristics. A model for the channel enables
the system designers to simulate the channel for the
purpose of performance predictions and enables comparative study of various alternative models.
Radio propagation in an office environment is very
complex. The received signal usually arrives by several
paths reflected by walls, ceilings, and other fixed and
moving objects, around the transmitter and the receiver.
The difference in the arrival time of the signal from
Paper 79551 (E8), first received 11th June and in revised form 23rd
November 1990
The authors are with the Electrical Engineering Department, Worcester
Polytechnic Institute, Worcester, MA 01609, USA
IEE PROCEEDINGS-I, Vol. 138, NO.3, J U N E 1991
various paths is proportional to the length of the path
travelled, which is affected by the size and architecture of
the office and the location of the objects around the
transmitter and the receiver. The strength of the signal
arriving by such paths depends on the attenuation caused
by passage or reflection of the signal from various objects
in the area. The deterministic analysis of propagation
mechanisms in such an environment is not practical, and
statistical analysis must be used. A mathematical model
is formed for the channel. The statistics of the model
parameters are determined using the channel impulse
responses measured for various locations of the transmitter and the receiver.
One of the earliest statistical measurements of the
amplitude fluctuations and distance-power law for indoor
channels was reported by British Telecom [2]. Results of
these measurements give the power law representing the
signal attenuation as a function of the distance inside a
building. The first wideband indoor radio delay spread
measurements were reported by BellCore [3]. All the
reported wideband measurements for indoor channels are
concerned with the statistics of the multipath or the
power in the received profiles [l-51. The only attempt at
modelling the indoor radio channel, was reported by the
AT&T Bell Laboratories [SI. This model was based on
Turin’s model [7] for urban radio propagation and considers the rays of the multipath profile to have Poisson
arrivals, independent Rayleigh amplitudes and independent uniform phases. Based on the observation of the
channel profiles collected from a research laboratory in
the AT&T Bell Laboratories, Saleh and Valenzuela [6]
conclude that the paths arrive in clusters. The arrival of
the clusters is also assumed to have a Poisson distribution. They suggest that the paths and the clusters both
decay exponentially with a certain decay rate. The arrival
rate of the paths and the clusters are determined from the
statistics of the collected data. The distance-power relation and the multipath spread of the collected profiles
was also reported.
In the present study a wider range of statistics for
Turin’s model [7] were collected and compared for two
classes of buildings : manufacturing floors and college
offices. Five different areas in manufacturing floors and
two office areas in a college campus were used as the
measurement sites. The discrepancies following the
Poisson arrival assumption are reported based on the
empirical data collected. It is shown that the modified
Poisson process fits the arrival of the paths accurately for
both environments. The Rayleigh, Weibull, Nakagami,
log-normal, and Suzuki distributions are considered as
potential models for the amplitudes of the arriving paths.
Though the Suzuki distribution fits some of the data
quite closely, the log-normal is shown to be the best dis153
tribution for all areas. The mean and the standard deviation of the log-normal distribution are shown to decay
exponentially with the path delays. The statistics provided in either of the two environments, are used to reproduce the measured profiles using computer simulation.
The distribution function of the RMS delay spread
obtained from computer simulation closely fits that
obtained empirically.
The mathematical formulation for the channel and the
measuring system overview are presented. The statistical
parameters required to regenerate the channel impulse
responses are described. The results of the data analysis
on the path arrival times and amplitudes obtained from
the two sets of measurements is discussed and the simulation procedure presented. The empirical and simulated
results are then compared. The summary and conclusions
are finally presented.
The mathematical model used for the complex low-pass
impulse response of the indoor radio channel was originally suggested by Turin [7] for the mobile radio and is
given by
The transmitted impulse 6(r) is received as the sum of L
paths with amplitudes { P k } , arrival times { ? k ) and phases
{&I. Several statistics are required
to regenerate a set of
measured profiles with a computer simulation. The statistics of the arrival times are required to identify the
existence of a path at a given delay. The fluctuations in
the path amplitudes should be fitted to a known probability distribution, identified with a set of parameters
(usually the mean and the standard deviation). The functions relating the mean and the standard deviation of the
distribution to the path delay should be determined so as
to accurately regenerate the path amplitude.
The channel impulse response has to be determined at
all possible locations in various indoor environments to
determine the required statistical parameters. There are
three phenomena affecting the impulse response at any
location in an indoor channel. The first is the fluctuations
in the received power. The second is the effect of multipaths caused by fixed objects such as walls or ceiling. The
third is the effect caused by moving humans or moving
objects, close to the transmitter and/or the receiver. All
the measurement data used in this work, were collected
when there was no traffic near the transmitter and the
receiver. The effect of traffic and local antenna movements is reported in Reference 8. The phases 8, are
assumed to be statistically independent uniform random
variables over CO, 271) [6,7].
The indoor radio measurements were performed at frequencies around 1 GHz. Very narrow pulses, which
resemble an impulse, were transmitted. If the duration of
these transmitted pulses is several times smaller than the
largest multipath spread, the receiver will observe several
isolated pulses for each transmitted pulse. In this case
L
h(T) =
1
PI, 6 ( T
- tk)ejVk
k= 1
L
%
Pk
k= 1
p(T
-
?k)eJek
where p(z) represents the narrow transmitted pulse.
154
receive
antenna
i
transmit
antenna
Q
power amp1if ier
attenuator
pre-amplifier
pre-amplifier
circuit
mixer
envelope
detector
Mathematical model and measurement data
base
2
The measurement set-up used for the multipath propagation experiments is shown in Fig. 1. It involves modulation of a 910 MHz signal by a train of 3 ns pulses with
a 500 ns repetition period [4] provided by a pulse generator. The choice of the 910 MHz carrier frequency is in
compliance with the FCC band allocations in the United
(2)
digitising
osci Iloscope
Fig. 1
personal
computer
Channel impulse response experimental set-up
States for indoor radio transmission. The modulated
carrier was input to a 45 dB amplifier. The output was
transmitted using a quarter-wave dipole antenna placed
about 1.5 m above the floor level. The stationary receiver
used a similar antenna to capture the radio signal. This
was followed by a step attenuator and a low-noise high
gain ( ~ 6 dB)
0 amplifier chain. The signal was then
demodulated using an envelope detector whose output is
displayed on a digital storage oscilloscope coupled to a
PC with a GPIB instrument bus. The components used
in the measurement set-up have a flat frequency response
in the 0.9 GHz range. The dynamic range of the receiver
display is limited to 25 dB because of the linear scale on
the digital storage oscilloscope. The actual dynamic
range of the measurement set-up was more than 100 dB.
This dynamic range is achieved by manually adjusting
the step attenuators at the receiver. A coaxial cable was
required to trigger the oscilloscope from the pulse generator of the transmitter to guarantee a stable timing reference. This measurement system is non-coherent and does
not include the phase associated with the arriving paths
[6, 71. These phases are reasonably assumed a priori to
be statistically independent uniform random variables
over CO, 271) [6,7].
The transmitter was moved to various locations in
each site. The received multipath profiles were stored in
the oscilloscope and then in the computer. Each stored
profile is an average over time of 64 impulse responses
collected during 15-20 s at one location. Care was taken
to prohibit any movement close to the transmitter and
the receiver during the measurement time. The distance
between the transmitter and the receiver varied between 1
and 100 feet. A total of 472 profiles are collected from
measurements made at different locations in five areas on
three different manufacturing floors [4] and two office
areas in the college campus.
The manufacturing floor environment is typically
characterised by large open areas, containing various
machinery and equipment of different sizes. There are
usually no walls between the transmitter and receiver,
and a 'direct' path is available for most of the locations.
To adequately represent statistical behaviour of such an
environment we selected five different manufacturing
IEE PROCEEDINGS-I, Vol. 138, No. 3, J U N E 1991
areas for measurement. The first area was a typical electronics shop floor containing circuit board design
equipment, soldering and chip mounting stations. The
second area consisted of test stations and storage for
common electronic equipment, partitioned by metallic
screens. The third area contained grinding machines,
huge ovens, transformers and other heavy machinery.
The fourth measurement site was a car assembly line
‘jungle’ floor having dense welding and body shop
equipment of all kinds. The last area was a vast open
space with very little equipment, used for final inspection
of the new cars coming out of the assembly line. The
number of profiles collected from the five areas were 54,
48, 75, 45 and 66, respectively, resulting in a total of 288
profiles representing the manufacturing environment.
Individual characteristics of these five areas as regards
radio wave propagations were reported in Reference 4.
The office environment has less open space and for
most of the locations, the ‘direct’ path is obstructed by
the presence of one or more walls. The environment as
presented to the radio waves, has considerable reflections
from the walls and ceilings. The office areas discussed
include several offices and a corridor, located on the third
floor of the Atwater Kent Laboratories at the Worcester
Polytechnic Institute. The offices are separated from the
receiver located in a central electronics laboratory by two
walls of sheet rock and some windowed glass on each
wall. The superstructure and the size of all the rooms in
this area are very similar. The corridor is around the electronics laboratory, separated by a sheet rock wall with
metal studs and some windowed glass. The office rooms
are located on the other side of this corridor. A total of
184 profiles were collected from these areas comprising
88 in the offices and 96 in the corridor.
Fig. 2a shows a profile of the received signal for a
transmitted pulse of 3 ns (3 dB width) at 910 MHz, with
minimum multipath spread and direct line of sight
between the transmitter and the receiver, depicting the
accuracy of the measurement set-up. Fig. 2b shows a
sample profile, with considerable multipath spread.
220
240
260
280
300
320
340
3
Statistics of the channel model parameters
The statistical parameters mentioned are derived from
the measured profiles described. The statistics of the path
arrival times ?k are first discussed. The path amplitude PI,
associated with each 7k is then fitted to a known probability distribution whose moments are functions of z ~ .
Results obtained from simulation of the model are then
compared with those obtained empirically. As mentioned
earlier, the data base is divided into two classes: manufacturing floors and college offices. For data analysis, the
arrival times in a measured profile is divided into 5 ns
bins and a threshold level is employed to detect a genuine
path in any bin.
3. I Arrival of the paths
A simple statistical model for the arrival of the paths
would be a Poisson process [SI, since the multipath propagation is caused by randomly located ‘objects’. The
path arrival distribution governed by a Poisson hypothesis was compared with the empirical data to find the
degree of closeness. The number of paths 1 in the first N
bins of each measured profile was determined. To determine the empirical path index distribution, the probability of receiving 1 paths in the first N bins P,(L = l) is
plotted as a function of 1. This procedure was repeated
for N = 5 , 10, 15 and 20 bins.
The probability PN(L= l) for the theoretical Poisson
path index distribution is given by
PN(L= l ) =
!
!e-”
l!
(3)
where I is the path index, and ,u is the mean path arrival
rate, given by
N
(4)
P = Cri
i= 1
In this equation ri is the path occurrence probability for
bin i computed from the empirical data.
Figs. 3 and 4, show a comparison between the empirical path index distributions and the theoretical Poisson
path index distributions [9] for N = 5, 10, 15 and 20. The
Figures correspond to the manufacturing floor areas and
the college offices, respectively. These are plotted as continuous curves for clarity, though they have values for
360
time, ns
>
g3
3
.-
p
1
0
2
4
6
8
1 0 1 2 1 4
bin number
0
320 340
360 380 400 420
440
Fig. 3
460
time, ns
b
Fig. 2 Profile of received signal
a Minimum multipath spread; line of sight operation
h Considerable multipath spread
I E E PROCEEDINGS-I, Vol. 138, N O .3, J U N E 1991
~~~~
~
Poisson path index distribution for manufacturing floor areas
theoretical
empirical
0,0 N = 5
m,
N
io
15
V, V N
=
=
A. A N
= 20
155
only integer path numbers. Considerable discrepancies
are observed between the empirical and the Poisson distributions for all values of N , irrespective of the environment. This discrepancy reflects a tendency of the paths to
arrive in groups, rather than in a random manner. To
explain similar discrepancies, a modified Poisson model
was proposed by Suzuki for urban radio channel modelling [lo].
-~~~
Poisson path index distribution for college oflces
theoretical
~
0.0 N = 5
.,U
N = 10
V,V N
A,A
N
Table 1 : Measured parameters
Bin
Manufacturing
floors
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
path index
Fig. 4
eqns. 5 to 8 are used again with interpolated K i (i = 1, 2,
. . ., 20) replacing KN ( N = 5, 10, 15, 20). The optimum
value of Ki and Ai calculated, for the manufacturing
floors and the campus ofice areas, are shown in Table 1.
Figs. 5 and 6, show a comparison between the empiri-
empirical
= 15
= 20
College
offices
K.
A.
K.
A.
0.964
0.932
0.900
0.868
0.836
0.804
0.772
0.740
0.708
0.676
1.340
1.440
1.540
1.636
1.732
5.796
6.388
6.980
7.572
8.164
0.4513889
0.5418182
0.5217417
0.4942650
0.5146308
0.5442811
0.5484897
0.5127087
0.5711924
0.36491 1 5
0.3444129
0.2928466
0.3592564
0.2782416
0.1 192904
0.1300228
0.1044048
0.101 9357
0.0901229
0.0810876
0.697
0.666
0.634
0.602
0.570
0.539
0.507
0.475
0.443
0.41 1
0.589
0.595
0.602
0.608
0.614
1.056
1.1 17
1.1 77
1.238
1.299
0.3636364
0.6408464
0.6288999
0.7164743
0.7313251
0.7230882
0.7350161
0.8171411
0.7717720
0.6645216
0.6733878
0.6594670
0.6470692
0.6743552
0.4608082
0.4402552
0.4432566
0.3898038
0.3576177
0.3297661
0.4 -
For the modified Poisson process, the probability of
having a path in bin i is given by A i , if there was no path
in the (i - 1)st bin, or by KN Ai, if there was a path in the
(i - 1)st bin. The ‘underlying’ probabilities of path
occurrences I i have the following relation with the
empirical path occurrence probabilities ri :
0.3
-
>
.--
-
I
n
(3 0.2 n
PQ
0.1
where 1, = rl.
The modified Poisson path index distribution is
related to I i s, by the following recursive equations [lo] :
Pi(L = 1) = P l , i(L = l)
P2,i+1(L= I )
=
0
+ P 2 ,i(L = I )
(6)
P,,i(L = 1 - l)KNIi+l
+ P l ,i(L = I - l)Ai+
1
path index
Fig. 5
Modijied Poisson path index distribution for manufacturing
floor areas
(7)
P,,i+,(L
= 1) = P2,i(L = U1 - K N I i + i )
theoretical
~~~~
0.5 r
empirical
~
0,0 N = 5
D, 0 N = 10
+
P I , i(L = I)(1 - Ai+ 1 )
(8)
where PAL = r) is the probability of having 1 paths in the
first i bins, P l ,i(L = l) is the probability of having 1 paths
in the first i bins conditioned on having no path in the ith
bin and P 2 ,i(L = l) is the probability of having 1 paths in
the first i bins conditioned on having a path in the ith
bin. The process begins in bin 1 where Pl, l(L = 0) = 1
- I,, P 2 *,(L = 1) = Al, PI,l(L = r) = 0 for 12 1 and
P 2 , l(L = l) = 0 for I2 2 or 1 < 0. Starting with a small
value of K N and minimising the mean square error
between the empirical and theoretical modified Poisson
path index distribution found using eqns. 5 to 8,
optimum values of KN are found from the data for
N = 5, 10, 15 and 20. To aid simulation, the optimal
values of KN which are functions of the ‘number of bins’
are replaced by new parameters K i s (i = 1, 2, . . . , 20),
which are functions of the bin numbers i [111. The K i s
are determined by linear interpolation. For the final calculation of the modified Poisson path index distribution,
156
-
V,V N
A,A
N
= 15
= 20
R
r” 0.3
n
0.1
0
path index
Fig. 6
Modified Poisson path index distribution for college offices
_ _ _ _ modified Poisson
______
empirical
V , V N = 15
0,O N = 5
A , A N = 20
D, 0 N = 10
IEE PROCEEDINGS-I, Vol. 138, N o . 3, J U N E 1991
cal path index distributions and the modified Poisson
distributions, for the manufacturing floors and the college
ofice areas, respectively. The curve fittings show considerable improvement over those of the Poisson model
shown in Figs. 3 and 4. This suggests that the paths do
not arrive randomly but in groups, and the presence of a
path at a given delay is greatly influenced by the presence
or absence of a path in the earlier bins. The modified
Poisson model utilises the empirical probability of
occurrence for each bin. The Poisson model just uses the
sum of the probabilities of occurrence for all bins.
3.2 Path amplitudes
Rayleigh, Weibull, Nakagami-m, log-normal and Suzuki
distributions were considered as potential models for the
path amplitudes. In the indoor environments fluctuations
in the signal amplitude are quite high because of fading,
so the signal amplitude level was converted to decibels,
and treated as a random variable. Using the method outlined in Reference 12, the parameters of the theoretical
distribution functions were determined from the measured amplitudes of the signal in the bins. Figs. 7 and 8
show the comparisons between the theoretical and the
.o
1
0.8
0.6
-n
e
1
.D
h 0.4
0.2
I
0
I
-2 0
-30
Fig. 7
-1 0
0
10
signal with respect to median, dB
CDF ofpath amplitude in bin 1 in manufacturingfloor areas
....... LOG
_ _ _ _ _ _ _ NAK
RAY
actual
~
~~~~
I
20
I
30
suz
WE1
1.0
0.8
0.6
1
.c
.-
D
n
9
a 0.4
-1 5
-20
Fig. 8
~
-1
0
-5
0
5
10
signal with respect to median, dB
CDF ofpath amplitudes in bin j f o r college oflces
. . . . . . . LOG
_ _ _ _ _ _ _ NAK
-~~~ RAY
actual
IEE PROCEEDINGS-I, Vol. 138, NO.3, J U N E 1991
15
suz
20
WE1
157
experimental distributions for bin 1 in the manufacturing
floor areas and bin 5 in the college office areas, respectively. The horizontal axis is normalised to the median
value of the data in decibels.
The error criterion of the Cramer-Von Mises test [ l o ]
was used to compare the goodness of fit among the five
distribution functions. This criterion is defined as
CO2 =
jfmi.lP(x) - P*(x)]2 d P ( x )
turing floor and the college ofice areas, respectively. The
decay rate was 5.0 for the mean and 4.0 for the standard deviation for the manufacturing floors. In these
(9)
where P ( x ) is a theoretical CDF and P*(x) is an experimental CDF. Table 2 shows w 2 for various distributions
for bins 1, 2, 3, 5, 7, 15 and 20, in the manufacturing
floors and the college offices. Both log-normal and
Suzuki distributions cause close fits, but the log-normal
provides a better overall fit to the empirical distributions.
It is also easier to simulate log-normal than Suzuki
random variables to represent path amplitudes.
The inhomogeneities of the indoor channel result in
variations in the mean and variance of the amplitudes for
different delays. To simulate these changing parameters,
the distribution for their variations should be known.
The scatter plots of mean and standard deviation of the
log-normal distribution as a function of the delays were
fitted to decaying exponentials of the form Ae-’lr + B
where is the decay rate, z is the delay and A and B are
constants. Figs. 9 and 10 show the mean and the standard deviation and their exponential fits for the manufac0.7r
0.3
5 0.2
O.’
t
0’
0
I
I
I
30
40
1
10
20
bin number
a
01
I
0
10
I
I
I
20
30
40
bin number
b
Fig. 10 Characteristics of log-normal distribution in college ofices
Dashed line is an exponential fit
a Mean
b Standard deviation
0.6
0.5
E 0.4
0
areas most of the received power is concentrated in the
initial paths resulting in a faster decay of the received
power with delay. The college office areas exhibited a
wider spread of power in delay and thus a slower decay
for the received power with delay. The decay rate was
35.5 for the mean and 28.3 for the standard deviation in
the college offices. The scatter plots give the values of the
mean and standard deviation for the path amplitude,
given the existence of a path at that delay. The modified
Poisson process decides whether or not a path exists at a
given delay.
>
.-
5 0.3
?
0.2
0.1
01
0
I
10
1
I
I
20
30
40
bin number
a
1.0r
4
0‘
1
0
10
I
I
I
20
40
30
bin number
b
Fig. 9 Characteristics of log-normal distribution in manufacturing
p o o r areas
Dashed line is an exponential fit
a Mean
b Standard deviation
Results of simulations
Using the statistics given for the path arrivals and amplitudes, the channel multipath profiles can be regenerated
with a computer simulation. This simulation capability
can be used in the design and testing of communication
systems as a substitute for costly hardware experiments.
The results of the simulation are compared with those
obtained empirically. The criteria for comparison is the
distribution function of the RMS delay spreads. For
radio communication in the indoor environment, the
RMS delay spread of the channel [4] gives a measure of
performance degradation caused by intersymbol inter-
Table 2: Mean square error o2
Manufacturing floors
Bin
LOG
1
2
3
5
7
15
20
158
NAK
WE1
College offices
RAY
SUZ
LOG
NAK
WE1
RAY
suz
1.10~10-~
~
1.11 ~ 1 0 - 41.32~10-36.58~10-43.99~10-3 1.30~10-48.09~10-59.62~10-45 . 5 0 ~ 1 0 -2.58~10-3
8.57 10-5 1.04 10-3 6.62x 10-4 2.53x 10-3 1.40x 10-4 4.97 10-4 1.87x 10-3 1.02x 10-3 7.06 x 1 0 - ~ 4.52x 1 0 - ~
2.06 x
1.37x 10-4 5.58 x 10-4 3.06 x 10-4 1.67x 10-3 9.71x 10-5 2.34x 10-4 7.10x 10-4 4.91x 1 0 . ~ 1.82x
1.81~ 1 0 - 41.02~10-35.07~10-4 3.70~10-3 1.57~10-41.85~10-41.45~10-39.31 ~ 1 0 - 43.56~10-32 . 6 4 ~ 1 0 - ~
4.61
x
x
10-4
2.81
x
10-3
2.60
5.02
x
10-4
2.22 10-4 4.60x 10-4 1.62 10-4 2.71 x 10-3 1.39 x 10-4 6.91 10-4
7.22x
1.27 x lo-” 7.50 x
5.71 x
6.38x lo-“ 1.03x
4.11 x
4.07x
4.18x
4.15x
2.34 10-3 6.50x 1 0 - ~ 8.40x
3.86x io-” 1.94x 10-3 1.10 x 1 0 - ~ 2.60 x 1 0 - ~ 2.40x
3.00x 1 0 - ~ 1.83x
IEE PROCEEDINGS-I, Vol. 138, N o . 3, J U N E 1991
ference, in the system. It is an important parameter for
determining data rate limitations of standard and equalised modems [13]. It is also used for performance prediction of spread spectrum modems [141.
The first step in simulation
to generate the path
arrival times. The basic model for simulation of the
arrival times is the modified Poisson branching process
of Fig. 11. The delay axis is divided into bins of length
and the standard deviations of the log-normal distribution were determined from the associated exponential fits
in Figs. 9 and 10. The phase angles could be chosen from
a uniform distribution and added to each path to complete the picture.
0.6 r
% 0.1 -
--+x
a
0
0
I
I
I
I
10
20
30
40
bin number
Fig. 12
Path occurrence probabilities for manufacturingfloor areas
~ _ _ simulated
_
__ empirical
Fig. 11
Modified Poisson process
__
path exists
no path exists
5 ns. The simulation for each profile starts with bin 1.
The presence or absence of a path in each bin is determined using Table 1 and Fig. 11. Figs. 12 and 13
compare the path occurrence probabilities as obtained
from these simulated profiles with those obtained from
the measured profiles in the manufacturing floors and the
college office areas, respectively. These probabilities are
plotted as continuous curves for the purpose of clarity,
although they only have values at integer bin numbers.
The experimental and the simulated path occurrence
probabilities are shown to be very close. The path
occurrence probability would be a horizontal line at the
mean path arrival rate if the path arrival times were to
follow a Poisson process.
The path amplitudes were generated from the lognormal distribution for each bin with a path. The means
I
I
I
I
10
20
30
40
bin number
Fig. 13 Path occurrence probabilities for college offices
~-~~ simulated
_ _ empirical
To evaluate the performance of the simulation model,
the cumulative distribution of RMS delay spreads as
computed from the simulated profiles was compared with
that obtained from the measured profiles. Figs. 14 and 15
show these comparisons for the manufacturing floors and
1.0-
0.a.-
0.6 ZI
-
._
-
I
D
0
n
L
Q
0.4 -
0.2
0
-
I
0
Fig. 14
~
~
10
I
20
I
I
30
40
_._...
---->
50
60
R M S delay spread, ns
70
Distributions of RMS delay spreads for manufacturinyjoor areas
Poisson/Rayleigh
. . . . . . . modified Poisson/log-normal
IEE PROCEEDINGS-I, Vol. 138, N o . 3, J U N E 1991
80
I
90
100
___ empirical
159
college offices, respectively. The dashed lines in these
figures are the cumulative distributions of the RMS delay
spreads computed from simulation. The path amplitudes
It was shown that the arrival of the paths from a
modified Poisson process and the amplitude of the paths
fit a log-normal distribution. The mean and the standard
1.c
0.8
0.6
x
-n
c
.-
0
n
a
L
0.4
0.2
0
10
20
30
40
50
60
R M S delay spread, ns
70
80
90
100
Fig. 15 Distributions of R M S delay spreads for college offices
_ _ _ _ Poisson/Rayleigh
. . . . . . . modified Poisson/log-normal
empirical
~
are simulated based on the exponential fits to the scatter
plots of the means and standard deviations. The solid
lines in Figs. 14 and 15 represent the actual cumulative
distribution of the RMS delay spreads measured from the
manufacturing floors and college offices, respectively. The
match between the empirical and the simulated distributions can be seen to be very good.
The statistical model given in Reference 6 considers
Poisson path arrivals and Rayleigh amplitudes. Simulation was also carried out for the Poisson/Rayleigh combination for purposes of comparision. The mean path
arrival rate was used to determine the presence or
absence of a path in any bin for the Poisson arrivals. The
measured powers in each bin were used to determine the
Rayleigh amplitude of an existing path. The RMS delay
spread was computed for each of these simulated profiles
and their distribution function is shown in Figs. 14 and
15. The match between the modified Poisson/log-normal
simulation and the empirical results is significantly better
than that provided by the Poisson/Rayleigh simulation.
The weakness of the Poisson/Rayleigh simulation is more
obvious in the manufacturing floor environment.
5
Summary and conclusions
Multipath profiles obtained from radio propagation measurements at 910 MHz were analysed to determine a suitable method for computer simulation of the indoor radio
channels. In the manufacturing floors there is plenty of
open space usually without any presence of walls, most of
the received power is therefore concentrated in the initial
paths. The college office areas have a wider spread of
power in delay, because of less open space and the frequent obstruction of the signal between the transmitter
and the receiver by one or more walls. The statistical
parameters required for computer simulation of multipath profiles in each environment were also determined.
160
deviation of the log-normal distribution were shown to fit
decaying exponentials. The simulation procedure was
detailed and the parameters determined from the modified Poisson process and log-normal distribution were
used to regenerate the indoor radio channel multipath
profiles. The distribution of the RMS delay spreads computed from simulation was shown to closely fit the
empirically obtained distribution. Channel profiles were
also simulated with Poisson arrivals and Rayleigh
amplitudes and the distribution function of the RMS
delay spreads computed from such simulated profiles had
a weaker fit to the empirical data. The modified Poisson/
log-normal combination was shown to provide a better
model for simulation.
Although additional research is required for confirmation, it is anticipated that this simulation technique can
be extended to other kinds of environment by adjusting
the value of its parameters. As with any other simulation
model, it can be effectively used in the design and testing
of communication systems as a substitute for costly hardware experiments. System designers can use it for performance predictions and comparative study of various
alternatives. Alexander [l5] has shown the effect of different types of building construction on the distance/
power law gradient. The relationship of the parameters in
this simulation model with the building construction
materials is a subject worth exploring.
6
Acknowledgments
We wish to thank T. Hotaling for help on the implementation of the measurement set-up and K. Zhang for
assistance in conducting the experiments. This work was
supported in-part by the National Science Foundation
(USA) under contract NCR-8703435. A short version of
this paper was presented at IEEE GLOBECOM 89.
IEE PROCEEDINGS-I, Vol. 138, NO. 3, J U N E 1991
7
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