Model for Site-Specific Indoor Radio Propagation Prediction Based on Geometric
112
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002
A New Statistical Model for Site-Specific Indoor
Radio Propagation Prediction Based on Geometric
Optics and Geometric Probability
Mudhafar Hassan-Ali, Member, IEEE and Kaveh Pahlavan, Fellow, IEEE
AbstractThe ray-tracing (RT) algorithm has been used for ac-
curately predicting the site-specific radio propagation character-
istics, in spite of its computational intensity. Statistical models, on
the other hand, offers computational simplicity but low accuracy.
In this paper, a new model is proposed for predicting the indoor
radio propagation to achieve computational simplicity over the RT
method and better accuracy than the statistical models. The new
model is based on the statistical derivation of the ray-tracing oper-
ation, whose results are a number of paths between the transmitter
and receiver, each path comprises a number of rays. The pattern
and length of the rays in these paths are related to statistical pa-
rameters of the site-specific features of indoor environment, such
as the floor plan geometry. A key equation is derived to relate the
average path power to the site-specific parameters, which are: 1)
mean free distance; 2) transmission coefficient; and 3) reflection
coefficient. The equation of the average path power is then used
to predict the received power in a typical indoor environment. To
evaluate the accuracy of the new model in predicting the received
power in a typical indoor environment, a comparison with RT re-
sults and with measurement data shows an error bound of less than
5 dB.
Index TermsPower coverage, power delay profile, probabilistic
geometry, rat tracing, site-specific channel model, statistical indoor
radio propagation, wireless deployment tool.
I. I
NTRODUCTION
W
E ARE living with ever increasing demand on telecom-
munications speed and ubiquity. The advent of the
Internet and data networks has escalated this demand. The
mobility and ease of installation make wireless communication
networks one of the most important communication systems
to deploy. Personal communications systems (PCS), wireless
local area networks (WLANs), wireless private branch ex-
changer (WPBXs), and Home Phoneline Network Alliance
(HomePNA) are the services that are being deployed in indoor
areas on an increasing scale. The latter application is proving to
have a large market since it will be integrated to the emerging
Digital Subscriber Loop technologies (ADSL, VDSL, etc.). The
market of these services will try to reach out to offices, schools,
hospitals, and factories [10], [12]. Because the indoor radio
Manuscript received December 1, 1999; revised February 1, 2001; accepted
March 7, 2001. The editor coordinating the review of this paper and approving
it for publication is R. Valenzuela.
M. Hassan-Ali is with the Systems Engineering, Alcatel USA, Petaluma, CA
94954 USA.
K. Pahlavan is with the CWINS, Worcester Polytechnic Institute, MA 01609
USA.
Publisher Item Identifier S 1536-1276(02)00185-X.
channel has a tremendous amount of impairment and variability
[1], [5], [6], large-scale deployment of these services provides
a major challenge to the network designers. For this reason, it
is imperative to develop deployment tools, where efficient but
accurate radio channel models are required. The efficiency of a
model is measured by the computational complexity, whereas
accuracy is measured by the estimation error. Ray-tracing
(RT) [1], [14], [20] is one of the most popular techniques for
predicting radio channels used in the deployment tools. The
main characteristic of the RT is the computational intensity,
which is the main reason for the prediction tools to be slow
in spite of its accuracy compared to the tools based on the
statistical model. This has motivated a significant research
effort to pursue alternative methods including the so-called
Fast RT [2], [21] in an attempt to expedite the computation
time. Still these alternative methods require more complex
floor-plan databases and the need to trace all rays regards of
their significance to the received power.
The purpose of this paper is to introduce a new model for
statistically predicting the indoor radio propagation in order to
contrive a more computationally efficient method for predicting
the received power within a building.
The paper is organized as follows. Section II states the theory
behind the new model and presents a key equation for estimating
path power. Section III shows a method whereby the total re-
ceived power can be estimated. In Section IV, the prediction of
indoor radio power using the new model is compared to the pre-
diction of RT software and data collected from measurements
for a typical office environment.
II. P
OWER OF A
P
ATH
W
ITH A
G
IVEN
L
ENGTH
RT approximates the radio propagation in a finite number of
rays originated from the transmitter. Each ray encounters reflec-
tion and transmission upon intersecting with an obstacle (such
as walls, doors, windows, etc.) The pattern of ray propagation
is dictated by the geometry of the floor layout and the materials
from which these obstacles are made. Hence, as an alternative,
the statistical characterization of radio propagation can be re-
lated explicitly to the statistics of these patterns [4]. The statis-
tical features of the propagation can be deduced directly from
the layout and the materials of the floor under consideration.
The purpose of this section is to relate the path power to the key
site-specific propagation parameters. The path power relation-
ship will be used in Section III to predict the received power.
15361276/02$17.00 © 2002 IEEE HASSAN-ALI AND PAHLAVAN: STATISTICAL MODEL FOR SITE-SPECIFIC INDOOR RADIO PROPAGATION PREDICTION
113
A. Path Power and the Number of Reflections and
Transmissions
When a path arrives at a point, it has already gone through
many reflections and transmissions (object-intersections). Con-
sequently, the path power tends to decay rapidly with distance
more than the inverse-square distance law for the free-space.
Each path is traced throughout its entire trip from the transmitter
to the receiver. Each time there is an object-intersection the ray
loses a certain amount of power while the propagation loss in
between intersections will maintain the free-space rate, i.e., in-
verse-square distance law. The intersection loss is either due
to reflection or transmission, since other mechanism, such as
diffraction and diffused scatter, can be ignored in indoor prop-
agation [9]. Each loss can be expressed in power formulation
as a multiplication by a loss coefficient. Hence, after traveling
meters from the transmitter (Tx) and undergoing
intersections
(
reflections and
transmissions), the path power is ex-
pressed
(1)
where
and
are the mean voltage reflection and transmis-
sion coefficients, respectively,
is the free-space power at dis-
tance 1 meter, which is expressed by
Where
and
(
for isotropic antenna) are gain of
transmit and receive antennas, respectively,
is the speed
of light in free space, and
is the frequency of the radio
signal, which is 900 MHz in this paper. For rest of this paper,
the assumption is that the transmit and receive antennas are
isotropic; i.e., omni-directional propagation.
The mean path power can be expressed as follows:
(2)
where
is the PDF of a path that intersects
objects
after traveling distance with
reflections and
trans-
missions. In the following section, this PDF will be discussed
in detail.
B. Calculation of
One can think of the process of hitting
obstacles as a com-
bination of reflections and transmissions. These two events are
independent and exclusive in one path at one instance. Hence,
can be decomposed as a multiplication of two func-
tions
(3)
where
is the PDF for a path that has undergone
in-
tersections after traveling distance . In [13], it has been demon-
strated through a Monte Carlo simulation that this function is a
Poisson distribution for the indoor environment. Hence
(4)
Fig. 1.
The rectangular model used to find PDF of
q and p.
where
is the mean free distance between two intersections,
which depends on the floor layout Mean Free Distance. It is de-
fined as the mean distance a ray can travel before it intersects
with an object. This parameter is estimated within a given shape,
which is assumed to be rectangular due to the adoption of the
rectilinear model. In Section III-C, a method for estimating this
parameter will be presented using probabilistic techniques. The
method estimates
from knowing the width and length of the
rectangles of the floor plans. The second function
,
on the other hand, gives the probability of having exactly
re-
flections and
transmissions in path length . As men-
tioned earlier, these are independent and exclusive, hence bino-
mial PDF fits these conditions [18]. Then
(5)
where
and
are the probabilities of reflection and trans-
mission, respectively, for a path of length . Note that
. After a few manipulations on (2) we obtain the fol-
lowing results (see Appendix A for derivation):
(6)
This equation gives an explicit relationship between the av-
erage power of a path with site-specific details and the building
layout via
, and the floor materials via (
and
). By esti-
mating the values of these parameters based on the location of
both transmitter and receiver, (6) can be applied to predict the
power of a path versus distance.
C. Calculation of
and
To use (6) for predicting the power of a multipath arrival
knowing the location of the transmitt