IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
225
Characteristics’ Prediction in Urban
and Suburban Environments
Nathan Blaunstein, Ran Giladi, and Moshe Levin
Abstract— In this paper, the character of the propagation
in the microcellular urban and suburban environments in the
902–928-MHz frequency band in line-of-sight (LOS) conditions is
investigated both theoretically and experimentally for the purpose
of wireless radio local loop (WRLL) prediction. The path-loss
characteristics and the range of a break point, at which the
polynomial character of field intensity decay along the street level
is changed, are analyzed for various parameters of street widths,
for different average building heights, and for the actual electrical
impedance properties of building walls. A multislit waveguide
with randomly distributed gaps between the sides of buildings is
considered as a model of straight streets. Results of experiments
for VHF/UHF wave propagation along the straight streets in
urban environment in the conditions of direct visibility between
receiver and transmitter are compared with theoretical analysis
of field intensity decay, path-loss distribution, and dependence of
the break point on street topography in LOS conditions.
I. INTRODUCTION
HE PREDICTION of propagation characteristics is an
essential part of radio wireless network planning. The
development of new radio communication systems like the
multigain wireless (MGW) system [1] requires knowledge
of propagation conditions for the operation environments.
To successfully predict the performance of such systems,
detailed experiments and theoretical investigations have been
carried out to examine wideband radio channel characteristics
and their dependence on the various real urban environment
parameters [2]–[9].
The MGW system [1] is a wireless local loop system used
in local networks, serving as an alternative to conventional
loop distribution networks. To design the system successfully,
it is very important to investigate the characteristics of urban
radio channels, define optimal locations of the radio ports, and
make performance predictions for the individual subscribers.
Methods of predicting field intensity attenuation (or path
loss) for line-of-sight (LOS) propagation along the streets and
the range of a break point , at which the characteristic of
energy loss with distance from the transmitter is changed
from the mode
(for
) to the mode
(for
),
were introduced earlier on the basis of the “two-ray” model
[7], [8], [10]–[12]. But as was noted in [13], using the “tworays” model we cannot explain the experimentally observed
changes of the mode of field intensity attenuation from
,
T
Manuscript received June 28, 1996; revised February 12, 1997.
N. Blaunstein and R. Giladi are with the Department of Communication
Systems Engineering, Ben-Gurion University of the Negev, Beer Sheva 84105,
Israel.
M. Levin is with Tadiran Communication Ltd., Petakh-Tikva 49104, Israel.
Publisher Item Identifier S 0018-9545(98)00691-4.
to
,
beyond the break point, , which
m to
m [9], [10], [13]–[15].
varied from
Moreover, the “two-rays” model cannot describe the absence
of a break point, that is, the absence of two-mode law of field
intensity decay, in LOS conditions along narrow streets or
streets with high buildings in urban cells with a range of 1–2
km [13], [16], [17].
A new multislit waveguide model with randomly distributed
slits (gaps between buildings) and screens (walls) for low
antenna heights (in comparison with building heights) along
the street level has been proposed in [13], [15]. This model
considers the multiple reflections on building walls, multiple
diffraction on their corners, and reflections from the road
surface. This is intended for field intensity analysis in LOS
conditions for a regularly planned city with straight streets
and with random intersections between them and between
buildings along each street. It was shown that the total field
is formed basically by the waves reflected from the walls
and ground surface as well as by the waves diffracted from
the edges of buildings. Both the proposed two-dimensional
(2-D) waveguide model [13] and three-dimensional (3-D)
waveguide model [15] correctly (in comparison with other
models and experimental data) described the transformation
with essential
of field intensity attenuation from the mode
intensity oscillations to the smooth exponential attenuation
(which is closed to the experimentally obtained propagation
,
– up to 1–2 km from the source, the
mode
existence of a break point at which this transformation occurs,
–
m.
and the range of this break point,
However, in these works all new effects were analyzed
without taking into account the actual impedance properties
of building walls. Moreover, such an important parameter of
LOS propagation along the streets as a break point, was not examined in detail according to existing numerous experimental
measurements of this parameter.
Below we continue to analyze the problem of wave propagation in LOS conditions along straight streets using the
concept of a multislit street waveguide according to [13]
and [15] and consider walls (screens) with actual dielectric
properties. The range of break point is investigated in more
detail, taking into account approximate formulas obtained
both from the waveguide model and from the “two-ray”
model. The field intensity decay and path-loss distribution are
compared with experimental data obtained in [2] and from
the experiments carried out in the suburban environment with
regularly distributed straight crossing streets.
0018–9545/98$10.00 1998 IEEE
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
Fig. 1. The simplified scheme of Kefar-Yona houses built on a rectangular street grid and of the first experiments in LOS conditions along the street.
II. CONDITIONS
OF THE
EXPERIMENT
The first series of measurements were taken in the small
town of Kefar-Yona, Israel, where the MGW system of Tadiran, Ltd. was under trial in conditions of direct visibility along
the street (LOS conditions, see Fig. 1). The omnidirectional
base-station antenna was located at the same (or lower) level
than the buildings’ roofs, at a distance of 4–5 m from the
corner building surface as depicted schematically in Fig. 1.
The mobile omnidirectional radio port antenna changed its
position along the street in the middle of the road in LOS
conditions (Fig. 1). The tested MGW system was operated in
–
MHz and utilized spreadthe frequency band
spectrum (frequency hopping) digital radio communication.
The tested environment is a typical small urban or suburban region of two- and three-storied brick buildings with
– m and with a rightapproximately uniform heights
angle crossing straight street plan (as schematically presented
in Fig. 1). The base-station transmitter antenna was installed at
m; the moving radio port antenna was lower
the height
– m). The tested cell radius of
than rooftop level (
such an area estimated from measurements was approximately
1–2 km. Field intensity measurements in decibels relative to
m (to compare
intensity in free space at the range
km (to compare
with our calculations) and at the range
with experiments carried out by Hughes [2]) were obtained
to estimate the path loss and the field intensity attenuation in
LOS conditions along the street. In these estimations, we take
into account actual dielectric properties of the brick walls of
buildings and the real distribution of buildings along the street
level.
III. LOS PROPAGATION ALONG
THE
STREET
Instead, the “two-ray” model presented in [7], [11], and
[12], which is usually used in LOS conditions, consisting
of the direct and ground-reflected rays and 2-D propagation
model consisting of multiple reflections from the walls [17],
in conditions where both antennas were placed at the street
level in LOS conditions, a new multislit waveguide model was
proposed in [13] and [15] for describing wave propagation in
urban areas with straight streets and with randomly distributed
walls of buildings and gaps between them (slits) as shown in
Figs. 2 and 3.
BLAUNSTEIN et al.: PREDICTION IN URBAN AND SUBURBAN ENVIRONMENTS
227
Fig. 2. A 3-D model of the street waveguide.
Fig. 3. A 2-D diagram of the street waveguide in the zy plane. The coordinates of source are y = 0 and z = d, and “a” is the street width.
Let us now examine the propagation characteristics in
LOS conditions along the street in more detail taking into
account the real dielectric properties of building walls, actual
distribution of street widths, and building heights along the
street level.
A. Waveguide Model
Let us consider that the buildings on the street are replaced
by randomly distributed nontransparent screens with scales
, the electrical properties of which are defined by surface
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
; the distances between the buildings (slits)
impedance
, , ,
(see Figs. 2 and 3). The laws
we define as ,
of their differential distribution are postulated as independent
and
, respectively,
and exponential with mean values
the probability density functions being given by
(1)
The impedance parallel plane waveguide with randomly distributed buildings along the street models a city street with
receiver and transmitter at street level below the rooftops (see
Fig. 2). One waveguide plane is placed at the waveguide side
, and the second one at
(“ ” is the street width,
see Fig. 3). We also assume that a vertical electric dipole as
plane with coordinates
a real transmitter is placed in the
,
, and
, where 0
on the
axis, 0
on the
axis,
is the transmitter
is the average building height. Taking into
height, and
account that all dimensions are much greater than the radiation
wavelength , we use the approximation of the geometrical
theory of diffraction (GTD) [19]–[22] for the rays reflected
from the walls and rays diffracted from the building corners.
Here, we present the full field as a superposition of a direct
wave field from the source, fields reflected from the road and
walls, and fields diffracted from the building edges [15]. As
was shown by [7] and [8], we can exclude in our derivations
the twice reflected waves, that is, “road-wall-road” and “wallroad-wall” reflected rays. In this approximation, the resulting
field can be considered as a sum of the fields arriving at
, from the virtual image
the receiver, placed at height
sources as schematically presented in Figs. 2 and 3. In most
measurements for VHF/UHF waves, this condition is true for
– km [7], [8], [10], [11], [16].
distances
According to the approach proposed in [15], we also introand
,
duce here the “telegraph signal” functions
which equal one when reflection or diffraction from the walls
(screens) takes place and zero when rays pass through the
spaces between the buildings, i.e., fall into the slits of the
represent screens
waveguide. Thus, segments with
represent
including their edges, but segments with
slits (see Fig. 3). The real electric properties of screens (walls)
,
are defined by the surface electric impedance
, where is the dielectric permittivity of
the dielectric constant of vacuum, the
the wall surface,
the angular
electric conductivity of the wall surface, and
, where
frequency of the radiated wave with
denotes the frequency of the radiated wave.
The full field inside the street waveguide can be presented
as a sum of the direct field from the source and rays reflected
and diffracted from the building walls and corners. In order to
calculate the full field from the source, we substitute for each
reflection from the walls an image source
(for the first
reflection from the left-hand walls of the street waveguide)
and
(for the first reflection from the right-hand walls),
where is the number of the reflections (see Fig. 3).
B. Average Field Along the Street
To calculate the average total field along the street waveguide we, as in [13] and [15], take into account the exponential
screens and slits distributions (1), treat the transmitter antenna
as a vertical electric dipole with field
,
and the simple evaluations from the GTD in which the formulations of diffracted waves are similar with those obtained for
reflected waves and in which the reflection coefficient
of
each reflected wave from the screen (wall) is simply replaced
with a diffraction coefficient
for each diffracted ray from
the wall’s edge [19]–[22]. Here,
is distance from the
source
,
is the electric momentum of a
vertical electric dipole,
is the wave number, and
is the wavelength
.
Using the procedure of averaging arbitrary order moments
of “telegraph signal” functions
according to [15] and
combining the reflected and diffracted waves with the direct
wave (LOS component) from the source and introducing the
Fourier transform, direct and inverse, we obtain the total
average field in the broken impedance waveguide given in
(2) at the bottom of the page. Here,
is the parameter of brokenness,
, and
is the constant introduced above. The coefficient
of reflection for each reflected waveguide mode
will be
presented below. The difference between (2) and that obtained
earlier in [15] [see (18), p. 318] lies in the existence of
reflection coefficient
in the integrand. As was obtained
for the perfectly conductive multislit waveguide (when
1), (2) consists of two terms: the first term is obtained from
integration of integral (2) along contour in the complex
plane, and the second one can be obtained after integration
of (2) along path in the complex
plane (see Fig. 4). We
will now examine these terms for the case of an impedance
multislit waveguide.
1) Discrete Spectrum of the Total Field: The first term in
(2) represents the discrete waveguide mode spectrum of the
total field inside the broken waveguide. It can be obtained
from (2) for the case
as
(3)
(2)
BLAUNSTEIN et al.: PREDICTION IN URBAN AND SUBURBAN ENVIRONMENTS
Fig. 4. A scheme of integration paths for (2) in the complex
Here,
K
229
plane.
,
,
,
,
is the constant describing the electric properties of the vertical
is the coefficient of reflection from the
electric dipole, and
impedance walls inside the waveguide
(4)
is its modulus, and
is its phase given in (5) at the
bottom of the page. For the case of a perfectly conductive
,
, and
, we obtain
waveguide, when
from (3)
(6)
which is the same expression obtained in [15] for the case
of a perfectly conductive multislit waveguide. In the broken
waveguide, as follows from (3) and (6), the wave modes attenuate inside it exponentially. But in the case of the impedance
waveguide, their lengths of extinction
attenuate inside the multislit waveguide very quickly;
the corresponding lengths of extinction
are decreased. In
both cases of perfectly conductive and impedance waveguides,
an increase in parameter
(
), i.e., a decrease
in the gaps between buildings along the street, leads to a
decreased attenuation of the reflected waves and to an increase
of the extinction lengths [see (7)]. In the limit of an unbroken
waveguide (
,
), the normal waves
with numbers
(the main modes) propagate without
appreciable attenuation at large distances (depending on the
actual dielectric properties of walls’ surface). In the case of a
perfectly conductive unbroken waveguide (
,
),
the process of wave propagation inside it continuously limits to
the classical one when
and normal modes propagate
without attenuation [19], [20].
2) Continuous Spectrum of Total Field: The second term
represents the continuous part of the total field spectrum
,
which for the case
can be presented in the following
form [15]:
(8)
(7)
depend not only on the number of reflections “ ,” on the
waveguide (street) width “ ,” and parameter of brokenness
. It also depends on the actual electric properties of the
or, as
waveguide walls, which are defined by the parameter
. Thus, with
follows from (5), by the dielectric impedance
(
), as follows from
an increase in parameter
(3)–(7), the extinction lengths become smaller, and the normal
waves in the impedance multislit waveguide attenuate faster
than in the case of a perfectly conductive multislit waveguide.
The same picture is observed with an increase in the number
of reflections . The normal reflected modes with numbers
where
is the constant describing the real properties of
electric dipole. As can be seen from (8), in the case of
a broken waveguide the continuous part of the total field
propagates as a spherical wave and reduces to the case of
an unbroken waveguide in the limit
. But, whereas
inside the perfectly conductive unbroken waveguide for the
large distances (
) the continuous part of total field
is canceled by the source field, that is,
[15], in the
unbroken impedance waveguide this term does not vanish.
As can be seen from (8), for the case
(unbroken
waveguide), but
, the term
differs from
zero, i.e., in calculations of field intensity and path loss we
(5)
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
must take into account both field spectra, the continuous and
discrete, which exist in the unbroken impedance waveguide.
This is a new principal result, which is absent in the case of
an ideal conductive unbroken waveguide.
obtain the normalized average intensity for the numerical
calculations
C. Field Intensity Attenuation
Let us consider as above that the term
is the field
reflected from the wall with coordinate
and the term
is the field reflected from the wall with coordinate
(see Fig. 3). Then, the average total field intensity inside the
waveguide can be presented in following form:
(12)
(9)
where
and
are wave impedances. The sign (*) denotes
the inverse complex field values.
Using the differential distribution (1) and the results of the
procedure of averaging for the one- and two-order moments
of “telegraph” functions
presented in [15], we finally
obtain the expression for the average intensity inside the
multislit waveguide
Here
(10)
Using the Fourier representation of the field
(13)
and introducing it in (10), we can calculate the average field
intensity
(11)
Here, the polar coordinates
,
,
and new parameters
and
were
introduced, where
and
.
is the coefficient of reflection from the road surface, which
is considered also as an impedance (in [15] it was assumed
that the ground surface is perfectly conductive, i.e.,
1);
all other parameters were introduced above.
After integrating (11) and taking into account the intensity
from a vertical electrical dipole in free space, we finally
In (12), the two first terms describe the multiray reflection from
the walls and diffraction from the walls’ edges. They present
normal modes generated in the multislit waveguide, which
transform into normal waves in the unbroken waveguide (when
) and propagate along the waveguide with exponential
attenuation at large distances. The third term describes the
reflection from the ground and then the reflection from the
buildings’ walls. The last term describes the direct wave and
then reflections from the road surface and from the walls. In the
case of the real impedance unbroken waveguide, when
,
but
, this term does not vanish (as was obtained
in [15] for a perfectly conductive waveguide). Thus, in the
case of impedance waveguide, we must take into account all
waves, direct from the source, reflected from the ground, and
then both reflected from the walls (as schematically presented
in Fig. 2). On the other hand, for
we tend to the case of
free space propagation above the ideal conductive flat surface.
In this case, the last term is much larger than other terms
and describes the interference between the direct waves and
those reflected from the road, which is described by the term
. The field intensity attenuates as a spherical wave
. This case is close to the two-rays model presented, for
example, in [11], where the plane wave propagates above the
flat ideal conductive surface. Moreover because earlier in [13],
BLAUNSTEIN et al.: PREDICTION IN URBAN AND SUBURBAN ENVIRONMENTS
[15] it was shown that both the 2-D and 3-D waveguide models
give sufficiently accurate results of field intensity attenuation,
it is very important for the prediction of experimental data to
obtain the approximative expression of average field intensity
inside the impedance multislit waveguide. Taking into account
that the average intensity can be approximately presented as
and after integrating (2) for field
in the
limits of
,
, and
using the
same procedure as in [15], we finally obtain the approximate
expression for the average field intensity at a large range from
the source
231
which continuously limits to the approximate formula
only for the case of
,
,
.
In fact, let us determine the “break point” range as the
range at which the first term in (14) is equal to the
second one, i.e.,
(15)
(14)
and
. We do
not present here the expression of the reflection coefficient
because it is sufficiently fully described in the literature for
different kinds of radiated field polarization (see, for example,
[19]–[21]). Let us now examine expression (14) for various
actual experimental situations in the urban street scene.
1) Let us consider that the street width is larger than the
average building heights and both antenna heights, that
is,
,
,
. In this case, at distances less than
the “break point” in the approximate formula (14), the
second term, which describes the direct wave and the
waves reflected from the ground and which attenuates
as a spherical wave
, is larger than the first term,
which describes the attenuation of the normal reflecting
modes along the multislit street waveguide. Beyond the
“break point,” conversely, the first term in (14) is larger,
and field intensity attenuates exponentially. This law
of attenuation is close to that obtained experimentally
in most measurements, where the attenuation mode of
field intensity beyond the “break point” was
,
– . According the “two-ray” model [10]–[12], one can
obtain only two modes of field intensity decay:
before and
beyond the “break point.” Moreover,
no clear physical explanation of such a rapid (with
– ) field intensity attenuation in the farthest zones
from the transmitter existed until now. This effect can
be clearly understood using the waveguide street model
and following from it the exponential attenuation of field
intensity (which is close to mode
,
– ) at
the distances beyond the “break point.” As was shown
in [15], the waveguide model continuously tends to the
“two-rays” model in the case of wide streets. We can
also show that the “break point” range presented in [11],
, can be used to estimate the “break point”
range only for urban areas with wide streets (avenues).
Moreover, the 3-D waveguide model allow us to obtain
a stricter expression for “break point” range estimation,
Here,
After the expansion of the exponent in the right hand of
(15) into the series
for
and
and taking into account the fact
that because
,
and
1 all terms with their product are smaller than one, we
finally obtain the approximate formula of “break point”
range for the waveguide street model
(16)
which continuously (with constant
in
order with one for
and
)
tends to
presented, for example, in [11]
for the case when
and
, i.e., for the
case of wide streets.
2) In the inverse case of urban areas with narrow streets
(
) the approximate waveguide model (14) can be
successfully used to describe the field intensity attenuation along the street in LOS conditions (see Fig. 5, curve
2). In fact Fig. 5 depicts the field intensity attenuation
relative to the intensity in free space at the distance 100
m from the source, using the approximate model according to (14) (curve 2), and the strict model according to
(12) (curve 1) for
,
, and
0.8 for the case of a wide street (
m,
m,
m, and
m). As can be seen from
the illustration presented in Fig. 5, both models [strict
(12) and approximate (14)] predict two modes of field
intensity attenuation from
to exponential and the
existence of a break point at the range
–
m
[according to (16)] for
–
MHz. Additional
estimations have showed that for the case of narrow
streets, the range of the break point is farther from the
transmitter than in the case of wide streets. For example,
for the case of a narrow street with
m,
m,
m, and
–
MHz, the break
point has been observed at the range
–
m
for
m and
–
m for
m
according to (16).
Thus, as can be seen from illustrations and as follows from
(16) for
and
, the range of the “break
point” tends to infinity for the observed wavelength band
–
m with a decreasing street width or with an
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
Fig. 5. The total field intensity attenuation along the street waveguide for M = 0:5 and a = 50 m. The curve 2 represents the calculations according to
the approximate model (14), and the curve 1 represents the calculations according to the strict model (12).
increasing building height. In the inverse case of a wide street,
the approximate model (14) tends to the “two-rays” model, and
(16) transforms into that presented in [7]–[12]. So we have a
good transition from the waveguide model to the “two-ray”
model in the particular case of wide avenues or canyons with
building heights less than the street width. On the other hand,
the waveguide multislit model, more generally than the “tworay” model, predicts the propagation characteristics in LOS
conditions along straight streets.
Because the approximate waveguide model gives closed
results with the strict waveguide model (see Fig. 5), we can
use the simple formula (14) to obtain the path loss in the LOS
conditions along straight streets with great accuracy
(17)
This formula is more general than the approximate formula
obtained in [13] for the case of the 2-D waveguide model
without taking into account the reflection from the road and
actual dielectric properties of building walls.
IV. COMPARISON
WITH
EXPERIMENTAL DATA
Let us now compare the theoretically obtained (17) with
Tadiran’s experimentally measured path loss along straight
streets in the urban area investigated.
As was mentioned above, the first experiments were carried
out in LOS conditions when the transmitter and receiver
antennas were placed at the street level with direct visibility
below the roof tops, and the moving radio port changed its
distance from the stationary base station in the range 10–300
m (see Fig. 1). In Fig. 6 the normalized average field intensity
decay in decibels (relative to the intensity of the vertical
electric dipole in free space) is presented versus the distance
“ ” from the transmitter along the street waveguide for the
same conditions as presented in Fig. 5 by curve 1 only for the
strict model (12). The solid points correspond to experimental
measurements at 920 MHz. As can be seen, the 3-D impedance
waveguide model (strict and approximate, because there is not
sufficient difference between them, as follows from Fig. 5)
gives close results with experimental data and can be used for
predicting the path-loss distribution and the range of the break
point along the street in LOS conditions.
The influence of real electric properties of building walls
can be seen in more detail from numerical calculations of
(14) presented as a family of curves in Fig. 7 for parameters
,
,
,
, and
, respectively, and
, where
is the field intensity normalized to the wave
BLAUNSTEIN et al.: PREDICTION IN URBAN AND SUBURBAN ENVIRONMENTS
233
Fig. 6. The field intensity (in decibels) versus the distance r from the transmitter (in meters). The solid curve represents the numerical calculations according
the strict model (12) for the same case, as in Fig. 5, and the solid circles represent the experimental data of signal attenuation (its maximum and minimum values).
Fig. 7. The normalized field intensity versus the normalized distance r=a
from the base station for M = 0:8, a = 20 m, and j0n j = 0:1, 0:2, 0:4, 0:6,
and 0:8. Signs “+” represent measured data in a city region with multistoried
ferroconcrete buildings; signs “o” represent measured data in a city region
with moderate-storied brick buildings.
from illustrations presented in Fig. 7, the curves with
are closer to experimental data measured in a city
area with multistory ferroconcrete buildings (depicted as “o”
in Fig. 7). The curves with
are closer to
the experimental data measured in an area with buildings of
moderate height usually constructed from bricks (depicted as
“ ” in Fig. 7). Both theoretically and experimentally obtained
results give exponential attenuation of radio waves in the
farthest zones from the source in LOS conditions along the
straight streets in regularly straight street planned urban areas
up to 2–3 km. Moreover, for experimentally observed ranges
in the conditions of direct visibility, when both receiver and
transmitter antennas are placed at the street below the rooftop
level, we can use the nonregular multislit waveguide model
and with great accuracy approximate formulas (14), (16), and
(17) to estimate the propagation loss and “break point” range
at street level.
V. CONCLUSIONS
intensity in free space at the distance
1 km from the
transmitter, at frequency
MHz versus to normalized
distance
(
m) along the street. In Fig. 7, signs
“ ” and “o” correspond to experimental measurements carried
out in [2] at frequency 936 MHz, using two mobile station
moving in two different areas of city center. As can be seen
The strict and approximate 3-D multislit waveguide models
constructed above are generalized waveguide models obtained
earlier in [13] and [15] in the case of building walls along the
street and road surface with the actual dielectric properties.
They give a good explanation of experimentally observed twomode VHF/UHF wave attenuation with the transformation of
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 1, FEBRUARY 1998
to exponential attenuation,
field intensity attenuation from
the existence of a break point at which this transformation
takes place, and the range of this break point
–
m.
Moreover, these models can explain the essential changes of
break point location relative to the transmitter, and the absence
of this point in some urban conditions observed experimentally. Using simple formulas (14)–(17), we can with great
accuracy predict the radio-wave-propagation characteristics,
that is, field intensity decay, path-loss distribution along the
street and the break point range, which defines a microcell size
in LOS conditions along straight streets.
[18]
[19]
[20]
[21]
[22]
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L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves.
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Nathan Blaunstein received the B.Sc. and M.Sc.
degrees in radiophysics from Tomsk University,
Tomsk, Russia, in 1972 and 1976, respectively,
and the Ph.D. and D.Sc. degrees in radiophysics
from the Institute of Geomagnetism, Ionosphere,
and Radiowave Propagation (IZMIR), Academy of
Science USSR, Moscow, Russia, in 1985 and 1990,
respectively.
Since 1993, he has been a Senior Scientist of
the Department of Electrical and Computer Engineering and a Visiting Professor in the Wireless
Cellular Communication Program at the Ben-Gurion University of the Negev,
Beer Sheva, Israel. His research interests include problems of radio-wave
propagation, problems of diffraction and scattering in various media for
purpose of mobile-satellite, and terrestrial and mobile communication systems
performance and services.
Ran Giladi received the B.Sc. degree in physics and the M.Sc. degree in
biomedical engineering from the Technion, Israel Institute of Technology,
Israel, in 1980 and 1983, respectively, and the Ph.D. degree in management
information systems from Tel-Aviv University, Tel-Aviv, Israel, in 1992.
He is the Head of the Department of Communication Systems Engineering
at the Ben-Gurion University of the Negev, Beer Sheva, Israel. He cofounded
a multinational data communications firm and is involved in the Israel data
and telecommunications industry. His research interests include computer and
communications systems performance, data networks and communications,
and network management systems.
Moshe Levin received the B.Sc. degree in electrical
engineering from the Technion, Haifa, Israel, in
1981, and the M.Sc. and Ph.D. degrees in electrical
engineering from Tel Aviv University, Tel Aviv,
Israel, in 1986 and 1989, respectively.
From 1986 to 1989, his research at Tel Aviv
University focused on signal processing in radar
systems. From 1989 to 1992, he worked at the EltaIsraeli Aircraft Industries in signal and radar system.
He is currently Chief Scientist of Wireless Systems
at Tadiran Telecommunications, Ltd., Petakh-Tikva,
Israel. His research interests include signal processing, radar system, and
wireless communication systems.