34 1
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996
A Comparison of Theoretical and Empirical
Reflection Coefficients for Typical Exterior
Wall Surfaces in a Mobile Radio Environment
Orlando Landron, Member, IEEE, Martin J. Feuerstein, Member, IEEE,
and Theodore S. Rappaport, Senior Member, IEEE
Abstract-This paper presents microwave reflection coefficient the electric fields of each multipath component (or ray path)
measurements at 1.9 GHz and 4.0 GHz for a variety of typical that illuminates the receiver.
smooth and rough exterior building surfaces. The measured
As with any radio propagation model, ray-tracing techniques
test surfaces include walls composed of limestone blocks, glass,
need
to be verified and enhanced with actual RF measurements
and brick. Reflection coefficients were measured by resolving
individual reflected signal components temporally and spatially, which are representative of the possible installation scenarios.
using a spread-spectrum sliding correlation system with direc- Propagation studies in microcellular environments have shown
tional antennas. Measured reflection coefficients are compared that significant multipath components arise from reflections off
to theoretical Fresnel reflection coefficients, applying Gaussian
rough surface scattering corrections where applicable. Compar- of building surfaces [ 131-[ 161, [23]. Hence, ray-tracing techisons of theoretical calculations and measured test cases reveal niques must reliably predict the influence of these buildings
that Fresnel reflection coefficients adequately predict the reflec- and other obstructions. For specularly reflected ray paths (i.e.,
tive properties of the glass and brick wall surfaces. The rough reflection for which parallel incident rays remain parallel after
limestone block wall reflection measurements are shown to be reflection), the Fresnel reflection coefficients can be used to
bounded by the predictions using the Fresnel reflection coefficients for a smooth surface and the modified reflection coefficients predict the reflection loss of a building surface, provided its
using the Gaussian rough surface correction factors. A simple, but dielectric properties are known. While there exists a classic
effective, reflection model for rough surfaces is proposed, which body of literature for the electromagnetic properties of various
is in good agreement with propagation measurements at 1.9 GHz materials [17]-[ 181, the actual reflective properties of typical
and 4 GHz for both vertical and horizontal antenna polarizations.
These reflection coefficient models can be directly applied to the external building structures at microwave frequency bands are
estimation of multipath signal strength in ray tracing algorithms just beginning to be explored [19]-[25].
for propagation prediction.
To provide enhanced reflection coefficient models for buildings, measurements at 1.9 GHz and 4.0 GHz have been
made for a variety of typical smooth and rough exterior
I. INTRODUCTION
building surfaces. The measured test surfaces include walls
ITH THE eminent arrival of commercial personal com- composed of limestone blocks, glass, and brick. Reflection
munication services (PCS), wireless service providers coefficients were measured by resolving individual reflected
will need to rapidly deploy their networks to quickly gain signal components temporally and spatially, using a spreadmarketshare. To install and maintain reliable PCS systems, spectrum sliding correlation system with directional antennas.
a thorough understanding of the RF propagation channel The measured reflection coefficients are compared with theis essential. Recent studies on ray tracing techniques for oretical Fresnel reflection coefficients using Gaussian rough
propagation prediction [ 11-[ 121 have shown promising results surface scattering corrections when applicable. The dielectric
in predicting channel parameters such as path loss and delay material properties of the tested building surfaces were taken
spread in complex environments. Ray-tracing approximates from either published data [17], [18], or measurements [191.
electromagnetic waves as discrete propagating rays that un- These comparisons are used to develop simple, and empirically
dergo attenuation, reflection, and diffuse scattering phenomena accurate, reflection models for building surfaces that can be
due to the presence of buildings, walls, and other obstructions. directly applied to ray-tracing algorithms.
The total received electric field at a point is the summation of
Manuscript received March 22, 1995. This work was supported by
DARPAESTO and the MPRG Industrial Affiliates Program at Virginia
Tech.
0. Landron is with AT&T Bell Laboratones, Wireless Communications
Systems Engineering, Holmdel, NJ 07733 USA.
M Feuerstein is with AT&T Bell Laboratories, Radio Technology
Performance Group, Whlppany, NJ 07981 USA.
T. S . Rappaport is with the Mobile and Portable Radio Research Group
(MPRG), Bradley Department of Electrical Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, VA 24061 USA.
Publisher Item Identifier S 0018-926X(96)01818-2.
11.
REFLECTION AND SCATTERING
MODELS
The Fresnel reflection coefficients (r)relate the field reflected from an infinite dielectric slab to the incident field, and
are described in [26], [27] as
0018-926X/96$05.00 0 1996 IEEE
342
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996
h
I\
Fig. 1. Geometry for fresnel reflection coefficient calculation.
A
i
where E , and ET are the incident and reflected fields, respectively. The parallel (perpendicular) subscript refers to the
E-field component that is parallel (perpendicular) to the plane
of incidence, as shown in Fig. 1. The reflection coefficients,
determined by material properties, angle of incidence (Q%), and
frequency, are given by
8, 771
Qt
rl = 77 22 COS
COS 8,+ 7
1 COS Qt
8t
r l l = 7 2 cos 8t
7 2 cos
-
COS
- 171
cos 0,
(2)
+ 111 cos 8,
where the wave impedances (qm) and the transmitted wave
angle (8,) are expressed as
where w is the radian frequency and the wavenumbers (k,)
are
(4)
The properties of each of the dielectric materials at the
interface are characterized by their permittivity (E,), magnetic
permeability ( p m ) ,and conductance ( c T ~ ) .
The Fresnel reflection coefficients in (2) account only for
specular reflection, which occurs for smooth surfaces. When
the surface is rough, impinging energy will be scattered in
angles other than the specular angle of reflection (i.e., diffuse
reflection), thereby reducing energy in the specularly reflected
component [26]-[30]. The Rayleigh criterion is commonly
used as a test for surface roughness, giving the critical height
(h,) of surface protuberances as
h, =
x
~
(5)
8 cos 8,
where X is the RF wavelength. The height ( h ) of a given
rough surface is defined as the minimum to maximum surface
protuberance, as shown in Fig. 2. A surface is considered
smooth if h < h, and rough if h > h,. Equation (5) shows
that as the incident angle approaches grazing (i.e., 8,
go"),
--f
the critical height becomes larger, effectively reducing the
scattering effect of the surface protuberances. For the case
of rough surfaces, a scattering loss factor (ps) was derived in
[28] to account for diminished energy in the specular direction
of reflection, given by
where 5 h is the standard deviation of the surface height
about the mean surface height in the first Fresnel zone of the
illuminating antenna. The assumption in (6) is that the surface
heights are Gaussian distributed. In general, incident radiation
on a surface will induce a current density ( J ) which is a
function of both 2 and y directions shown in Fig. 2. Equation
(6) assumes that this surface current density at height y is
always J(y), regardless of whether the surface element at a
particular z is shadowed or illuminated by another part of the
surface. This approximation was made to simplify the integral
equations used to derive (6). When ps is used to modify the
reflection coefficients, we refer to this model as the Gaussian
rough surface scattering model, which is written as
(rl)rough
(7)
(rll)rough = P S r l I .
PSrl
It was reported in 1291 that the scattering loss factor of (6)
gives better agreement with measured results when modified as
ps = e-[ -8
(
"
)
1,
[y (
")
2]
(8)
where l o ( z ) is the modified Bessel function of zeroth order.
When the Bessel function argument is small, (6) and (8) are
approximately equal, since 10 ( 2 ) approaches unity.
The Fresnel models presented here assume the dielectric
slab is infinite in extent. Although this is not true for real
buildings, the dimensions of the tested building reflecting
surfaces are sufficiently large that they may be approximated
as infinite, such that these models can be applied.
111. 1.9 GHz AND 4.0 GHz MEASUREMENT
SYSTEMS
Various techniques for measuring UHF and microwave
reflection coefficients of materials have been reported in the
literature [20]-[25] and [31)-[33]. Of these, wideband measurement systems have the ability to temporally resolve desired
reflections from spurious, unwanted signals. For this research,
a wideband spread-spectrum sliding correlation system was
~
343
LANDRON et al.: COMPARISON OF REFLECTION COEFFICIENTS IN A MOBILE RADIO ENVIRONMENT
reference
-
.. .. , ~
length 32,767 chips
-.:
:
m#e=
LOS Measurement
%
~
IOMHz- 4GHz
Tnggercable
to RX
Transmitter System
239.960MHz
SGA 40
4 GHz hom
m
cable
from Tx
Exthlgger
\59--
RefleeemMesurement
Fig. 4. Two-step technique for reflection coefficient measurement
measured E-plane and H-plane half-power beamwidths of
17.2’ and 14.3’, respectively. The 1.9-GHz system used trapezoidal log-periodic antennas with 60’ half-power beamwidths.
Further specifications of these systems are given in [20]. Due
to the superior spatial resolution of the 4.0-GHz system, most
of the measurements were performed at this band, where the
surface roughness effects are more pronounced.
IV. REFLECTION
COEFFICIENT
MEASUREMENT
The reflection coefficients were measured using a two-step
technique [20], [21] ?hewn in Fig. 4. First, 10 line-of-sight
Receiver System
(LOS) channel-impulse responses were measured with the two
antennas facing each other. Then, the antennas were aimed at
Fig. 3. 4.0-GHz wide band spread spect” sliding correlation system.
the reflection point on the test surface and 10 reflected channelimpulse responses were collected. The LOS measurements
developed, similar to that in [34]. The temporal resolution of provided a reference for comparison with the received channelthese systems is determined by the transmitted RF bandwidth. impulse responses from the reflection measurements. PerformThe 1.9 GHz and 4.0 GHz measurement systems used ing the LOS and reflected path measurements sequentially
slightly different hardware, but were conceptually the same. ensured that variances due to the measurement equipment (e.g.,
Fig. 3 shows the system block diagram of the 4.0 GHz temperature variations, cable losses, connector losses, etc.)
measurement system. At the transmitter, a CW source was were minimized. This two-step method was repeated for each
modulated by the maximal length pseudonoise (PN) sequence, desired incident angle, as well as for different test surfaces.
giving the characteristic (sin(z)/z)’ power spectrum. This
Examples of measured LOS and reflected path impulse
signal was then amplified up to a maximum of 10 W and responses are shown in Fig. 5. In many instances, the reflected
transmitted via the high gain horn antenna. The transmitted path impulse response contained both an LOS and reflected
power at the antenna terminal was monitored using the power peak, where the LOS peak was attenuated by the directional
meter and accounting for the RF coupler and cable loss.
antenna patterns. These multipath components were resolved
At the receiver, the spread-spectrum signal was correlated to temporally by comparing the measured differential delay (i.e.,
the identical PN sequence with a clock rate which was slightly the difference in arrival times of the reflected path with respect
offset from the transmitter. This causes the two sequences to the LOS path) to the calculated differential delay using the
to slide past each other, giving maximal correlation when geometry in Fig. 4. The result of this comparison is shown in
aligned. When multiple incoming signal paths arrive at the Fig. 5(b).
receiver with different time delays, each will correlate with
The transmitter and receiver locations were constrained
the receiver PN sequence at the corresponding time. The by a number of factors, including desired specular refleccorrelation process effectively converts the wideband signal tion angles, temporal resojution of the sliding correlator,
into the RF channel impulse response, where it was filtered, far-field criteria, and environment topography. For example,
down-converted, and detected using a spectrum analyzer set to the temporal resolution of the measurement system dictates
zero span. The baseband output was displayed in real time on the minimum resolvable differential delay, and hence, the
the digital storage oscilloscope (DSO) and stored on a portable allowable transmitter and receiver positions. In addition, the
computer for later processing.
transmitter distance ( d l in Fig. 4) was selected to ensure that
The temporal resolution of these systems allowed easy iden- incident waves striking the test surface could be approximated
tification of desired reflected multipaths from other spurious as plane waves. For these reasons, the dimensions shown in
signals. In particular, the 240-MHz PN sequence clock gave Fig. 4 varied over the following ranges: 3 m < d l < 27 m, 3
an RMS system resolution of approximately 4.2 ns. For spatial m < dz < 40 m, and 3 m < dLos < 65 m. For a particular
resolution, the 4.0-GHz measurement system used 18.6-dB incident angle, d l remained fixed while the receiver distance
was selectively varied.
standard gain horns (at the transmitter and receiver) with (d’), and hence,
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO 3, MARCH 1996
344
0.3
-
0.2
"0.1
limestone wall 0 4 GHz
LOS component <--> 0.25 V Q t = 1.0 ns
3
B 0.0
n
2a -0.1
8
-0.2
v)
-0.3
-0.4
0
-50
100
50
150
200
Time (ns)
effect, the receiver distance (d2 in Fig. 4) was selectively
varied for most measured incident angles (Q%). These results
are discussed in Section VII.
The post-processing task began with the conversion of
the individual impulse responses into corresponding measured
power delay profiles, using the calibration characteristics of
the receiving system. Then for each transmitter and receiver
location, the ensemble average of the 10 raw power delay
profiles was calculated. The averaged LOS power from the
averaged LOS delay profile was taken to be the free space
value, i.e.,
(a)
m
>
limestone wall Q 4 GHz
LOS component <--> 0.22 V Q t = -19.7 ns
Reflected component <--> 0.24 V Q t = 1.O ns
.
-0.4l
-50
calculated differentialdelay = 20.3 ns
measured differentialdelay = 20.7 ns
.
'
0
.
'
'
50
'
100
.
'
150
200
Time (ns)
(b)
Fig. 5. Examples of (a) LOS channel-impulse response and (b) reflected path
channel impulse response at 4.0 GHz (time axis has arbitrary zero reference).
During the measurements, the antennas were kept stationary
for two reasons. The first was that moving the directional
antenna over a local area would induce artificial multipath
fluctuations caused by directional antenna patterns, pointing
errors, etc. The second was that it was observed in the field that
the magnitudes of individual multipaths faded only slightly
with small linear movements (i.e., a few wavelengths) of the
receiving antenna. This observation agrees with the reasoning
that signal fading in local neighborhoods is mainly due to
the constructive and destructive interference of multipaths,
rather than variations on the individual multipath amplitudes.
This phenomena was also shown to be true for indoor factory
channels containing an LOS path [35]. Individual multipath
amplitudes should vary significantly within a small area only
when a path is composed of a number of subpaths or when
a path suddenly becomes shadowed by some obstacle in
the environment. Since there w5re no obstacles in the test
environments, the main cause of fades on any individual
multipath is due to clusters of subpaths forming that multipath.
Since the sliding correlation system can resolve individual
multipath components 4.2 nanoseconds apart, the subpath
clusters can possibly affect the wideband measurements in two
ways. The first is in the LOS measurement where the ground
reflection generally exceeds the system temporal resolution
due to the physical geometry (discussed further in Section V).
The second is in the reflected path measurements, where wall
surface protuberances can induce interference effects that are
also irresolvable by the wideband system. To observe this
The averaged power delay profile for the reflected path measurements was calculated in an identical manner. The averaged
reflected power was taken to be the free space value for the
unfolded path length multiplied by the square of the voltage
reflection coefficient (I?), or
The use of the Fresnel reflection coefficient in (10) is an
approximation since rigorous electromagnetic image theory
requires perfect conductivity [36]. Equation (10) also assumes
that the reflecting boundary is infinitely large, which is approximately true, when the wall dimensions are much larger than
distances dl and dz in Fig. 4 and the wall surface area is much
larger than the illuminated area. Assuming these conditions are
satisfied, taking the ratio of (9) and (10) and solving for the
reflection coefficient yields
Therefore, the empirical reflection coefficient is the square
root of the ratio of the reflected and LOS power measurements,
weighted by the difference in measurement distances (i.e.,
accounting for the path loss difference in the two measurements).
v.
EFFECTSOF GROUNDREFLECTION
In the LOS measurements, a ground-reflected multipath
may interfere with the direct LOS path. These ground reflected multipaths are irresolvable from the LOS path because
they generally exceed the temporal and spatial resolution
capabilities of the measurement system. The severity of this
interference depends on the antenna patterns and the distance
between the transmitter and receiver.
To determine whether ground reflection would have a significant effect on the reflection coefficient measurements, a series
of LOS measurements were made. The transmitter and receiver
separation was varied along a linear path while the wideband
delay profiles were measured. These impulse responses were
converted into their equivalent powers and plotted versus
predictions with a two-ray model [20]. The two-ray model
computes the received power as the magnitude squared of
345
LANDRON et al.: COMPARISON OF REFLECTION COEFFICIENTS IN A MOBILE RADIO ENVIRONMENT
-
-15
-20 -
-20
-15
! %-25' -
-
-25 .
zl
,"
-30
-30
0
2
g -35 ,
,$l
-40
G,=G,= 18.6dB
perfect gnd . r = -1
soil gnd er= 30, a = 0 02
-45
-35 ' G t = G r = 1 8 6 d B
-40
-45'
perfect gnd r = -1
Soil gnd : Er = 30,D = 0 02
'
'
I
Fig. 7. Measured LOS power versus two-ray model at 4 GHz (horizontal
antenna polarization).
the vector sum of the LOS and ground reflected electric field
components, whose magnitudes and phases were computed
theoretically. The ground reflected component was multiplied
by the reflection coefficient of the ground and the elevation
patterns of the antennas. The ground was modeled as either
being moist soil or a perfect reflector. The moist soil reflection
coefficients were calculated using (2) with tabulated dielectric
parameters [26] (E, = 30, c = 0.02 S/m). The perfect
reflector was simply modeled as having a unity reflection
coefficient (I? = -l), regardless of incident angle. The
elevation patterns of the directional antennas were modeled
as (sin(z)/z) functions. The two-ray model assumed antenna
3-dB beamwidths of 20" and two meter antenna heights (above
ground). Figs. 6 and 7 show the results of the wideband LOS
measurements and the various ground reflection models. The
measurements show that there are minor variations around
the free space LOS power, which loosely agrees with the
predictions of the two-ray model. In general, the measurements
agree well with the free space prediction, with the exception
of one measurement point near 16 meters.
Let the LOS error (ELOS)
be defined as
expressed as
Er = Ir[(PR)MEAS]I- lr[(pR)LOS]I
-
For the measurements presented in this paper, the distance ratio
in (13) is less than two for more than 85% of the transmitter
and receiver positions used. Therefore, a conservative error
estimate can be written as
where E L ~ isS now the linear power ratio (not in dB). As
the reflected to LOS power ratio decreases, the effect of LOS
errors decreases. Typical reflected to LOS power ratios for the
measurements reported here were less than -15 dB, although
occasionally were above -10 dB. Therefore, if 94% of the
measured LOS variations were less than 4 dB, the typical
reflection coefficient errors should be no worse than 0.2 (in
magnitude of field ratio). In general, the errors will be much
smaller than that, so these measurements should give adequate
results for the reflection characteristics of the test surfaces.
VI. MEASUREMENT
SITES
where (PR)LOS
is the ideal free space LOS power (in mW)
and (PR)MEAS
is the measured LOS power (in mW) including
ground reflections. For each measurement point in Figs. 6 and
7, the LOS error was computed. From the ensemble of LOS
errors, the mean error and standard deviation are less than
1.3 dB and 1.9 dB, respectively. The positive mean error
of 1.3 dB could be easily caused by measurement system
losses (such as cables, connectors, aperture efficiencies, etc.)
which are not included in the free space model. Therefore, the
significant parameter is the 1.9-dB standard deviation, which
gives an indication of the variability of the measured LOS
power. Assuming these errors are Gaussian distributed, 94%
(i.e., two standard deviations) of the variations due to ground
reflection are expected to be within 4 dB.
To quantify the effects of these LOS errors on the computed
reflection coefficients, the reflection coefficient error ( E r ) is
Two buildings were carefully selected for the reflection
coefficient measurements. These buildings had exterior walls
made of rough limestone, smooth metallized glass, and brick.
These walls were chosen since they were representative of
typical building surfaces in a mobile radio environment. The
chosen sites had homogenous surface characteristics (i.e., free
of clutter, windows, doors, etc.) and were relatively isolated
from objects which could induce additional reflection and
scattering. The variation of surface roughness at these sites
ranged from very rough stone to smooth glass.
The rough stone wall was located toward the rear of a sixstory office building constructed of large rectangular limestone
blocks. The sizes of the limestone blocks varied, with the
average block being approximately 0.5 meters wide and 0.3
meters high. The outer surfaces of these blocks exhibited
random roughness features, with a roughness height up to 12.7
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996
346
TABLE I
ROUGHNESS
AND DIELECTRIC
PARAMETERS FOR THE
LIMESTONE
AND BRICKWALLSURFACES
AT 4.0 GHZ
Wall
h(cm)
oh (cm)
E,
P?
Limestone
12.7
2.5
7.51
0.95
0.03
Brick
1.3
0.5
4.44
0.99
0.01
Limestone wall
freq = 1.9 GHz, Perpendicular (1)
Polarization
,
0
?
cm. The metallized glass wall was located on the same building
and separated an interior lounge area from a parking lot. The
glass wall measurements were conducted at 4.0 GHz only,
while both frequencies were measured at the limestone wall.
The brick wall was located in the rear of a multilevel recreational facility constructed of concrete and red masonry brick
common in residential homes, as well as older urban buildings.
Table I lists the estimated surface roughness parameters and
the measured dielectric properties [19] of the limestone and
brick surfaces at 4.0 GHz. The roughness parameters for
these surfaces are the same for both frequencies, and the
dielectric properties are approximately the same. The dielectric
properties for the glass wall were not measured in [19].
5 0.4 .
% 0.3 -
0
0
0.0 1
0
.+
.!!",..-.-.p..'
-.-,
,e.
-.-.
.
c
,..'...<.'
.
.,.'
0
0
15
30
45
60
75
90
8, (degrees)
Fig. S. Measured reflection coefficients for limestone wall at 1.9 GHz
(perpendicular polarization).
Limestone wall
freq = 1.9 GHz, Parallel (11) Polanzation
1.0
S
.g
0.9
f
0.8
E
Gaussianrough surface
Moddiedgaussian rough surface
Measureddata
0.7
0.6
VII. MEASUREMENT
RESULTS
Measurement and prediction comparisons were performed
for perpendicular and parallel polarizations for each test wall
surface. The predicted reflection coefficients are simply the
Fresnel formulas of (2) versus incident angle, using the rough
surface scattering corrections when appropriate. Each measured reflection coefficient was obtained by averaging 10 LOS
and 10 reflected path power delay profiles, then using (11)
with the corresponding transmitter and receiver distances. For
the receiver distance (d2 in Fig. 4) is
most incident angles
selectively varied to observe overall measurement variations
due to surface protuberances.
(e,),
c?.
Be
0.5
0.4
0.3
3
c
'2
0.2
9 0.1
0.0
0
15
30
45
60
75
90
8, (degrees)
Fig. 9. Measured reflection coefficients for limestone wall at 1.9 GHz
(parallel polarization).
Figs. 10 and 11 show the 4.0 GHz comparison results for
the limestone wall for perpendicular and parallel polarizations,
respectively. Again, the measurements are compared with the
theoretical Fresnel reflection formulas for smooth surfaces
A. Limestone Wall Results at 1.9 GHz and 4.0 GHz
and for rough surfaces using the scattering corrections of
Figs. 8 and 9 show the 1.9 GHz comparison results for (6) and (8). The theoretical models show that the smooth
the rough limestone wall for perpendicular and parallel polar- surface reflection coefficients at 1.9 GHz and 4.0 GHz are
izations, respectively. The measurements are compared with nearly equivalent. This is an expected result since the reflection
the theoretical Fresnel reflection formulas for smooth surfaces coefficients in (2) become frequency independent when cr -+0.
and for rough surfaces using the scattering correction of However, the scattering corrections are a strong function of
(6) and (8). The Fresnel model using (6) is referred to as frequency.
From the 4.0-GHz results in Figs. 10 and 11, over 92%
the Gaussian rough surface, while using (8) is referred to
as the modified Gaussian rough surface. For this surface, of the measured reflection coefficients are bounded by the
the measured data shows significant variability as a function Fresnel formulas for smooth and rough surfaces. Similar to
of the receiver distance (dz). This variability can be the the 1.9-GHz measurements, the 4.0-GHz measured data shows
result of a number of factors, including ground reflection significant variability when varying the receiver distance (dz),
effects and interference of the reflected multipath due to although the variations tend to be more clustered. In addition,
surface protuberances. Regardless, over 90% of the measured the Gaussian rough-surface model (with either scattering loss
reflection coefficients are bounded by the Fresnel formulas for factor) tends to give pessimistic predictions of the measured
smooth and rough surfaces. In almost all cases, Figs. 8 and 9 reflection coefficient values, although (8) does provide some
show that using the Gaussian rough surface model alone gives improvement over (6).
The observation that the scattering loss factor overestimates
pessimistic predictions to the measured reflection coefficient
values. The comparison between the scattering loss factors the scattering loss for many of the measurements may be
in (6) and (8) shows that (8) gives better agreement with attributed to a number of simplifying assumptions (e.g., Gaussian distribution of surface heights, sharp edge effects, etc.).
measured values.
LANDRON et al.: COMPARISON OF REFLECTION COEFFICIENTS IN A MOBILE RADIO ENVIRONMENT
TABLE 11
ERRORSTATISTICS FOR COMPARISONS OF MEASURED
REFLECTION
COEFFICIENTS AT LIMESTONE
WALL WITH MODELOF (15)
Limestone wall
Polarization
freq = 4 GHz, Perpendicular (I)
1.0
C
~
.$
0.9
5
0.8
8
0.7
2
0.6
d
$
3
.F
m
.$
347
Freq.(GHz)
Gaussianrough surface
Modifiedgaussian rough surface
Measureddata
0
0.5
0.4
"
0.3 .^
0.2
,.,.'.:..
I .
0
0
15
0
30
90rh %
S
I
1.9
Parallel
4.03
0.06
4.0
Perpendicular
-0.07
0.16
0.29
0.10
4.0
Parallel
-0.07
0.09
0.15
.e'
.
e
.
.
.
.
_
.
0
Eays
0
0
0.1
0.0
~
Polanzauon
45
.
60
75
90
0, (degrees)
TABLE I11
ERRORSTATISTICS
FOR COMPARISONS
OF MEASURED
1.9 GHZAND 4.0 GHZ REFLECTION
COEFFICIENTS AT
LIMESTONE
WALL WITH VARIOUS REFLECTION
MODELS
Reflection model
Fig. 10. Measured reflection coefficients for limestone wall at 4.0 GHz
(perpendicular polarization).
Symbolic notation
E,
smooth surface
rL 11
-0.23
Gaussian rough surface
prrL
4.18
averagedmodel of (15)
r,,,
-0.03
s
1
Wrh%
0.16
0.42
0.13
0.31
0.13
0.19
Limestone wall
freq = 4 GHz, Parallel(11) Polarization
0
15
30
45
60
75
90
0, (degrees)
Fig. 11. Measured reflection coefficients for limestone wall at 4.0 GHz
(parallel polarization).
This was then repeated using the modified Fresnel formulas
in (7), accounting for roughness effects. Table 111 details the
error statistics comparing all of the 1.9 GHz and 4.0 GHz
measured data with each of the three model combinations
(i.e., r A v G , r l , l l , and psrl,ll). This table shows that using
the smooth surface Fresnel coefficient alone gives overly
optimistic results, while the rough surface model gives overly
pessimistic results. The average error improvement of r A V G
over the smooth and rough surface models is approximately 0.2
in both cases. The impact of this difference will be discussed
in the next section.
B. Glass Wall Results at 4.0 GHz
Figs. 12 and 13 show the comparisons between the measured glass wall reflection coefficients and the Fresnel formulas
for smooth surfaces for perpendicular and parallel polarizations, respectively. Since the glass wall was electromagnetically smooth, the rough surface scattering corrections were not
applied. For this particular glass wall, the dielectric properties
were unknown. The dielectric properties of clear, nondoped
glass are typically quoted as: E, = 5 , U
, , = 1 and U = lo-"
where rl,li is either the perpendicular or parallel polarization S/m [26]. Since the glass wall was metallized, the conductivity
reflection coefficient given in (2) and ps is the scattering loss was higher than lop1' S/m. Because the conductivity was
factor given in (6). To assess the accuracy of the simple model unknown, several Fresnel reflection coefficient curves with
in (15), r A V G was compared to each measured reflection various conductivities (10-l' to 10 S/m) are plotted in Figs. 12
coefficient in Figs. 8-11. From the resulting ensemble of and 13. A material having a conductivity of 10.0 S/m would
errors, the error statistics, including average error (Eavg), be considered a semiconductor, similar to seawater or intrinsic
standard deviation (s), and the 90th percentile are given in germanium. A good conductor would typically exhibit n >
Table 11. From this table, r A V G tends to underestimate the lo6 S/m.
reflection coefficient at 1.9 GHz and overestimate the reflection
Figs. 12 and 13 show that the measured reflection coefcoefficient at 4.0 GHz (on average). The overall fit of r A V G ficients exhibit a dependence on incident angle similar to
to the measured reflection coefficients was slightly better for that predicted by the Fresnel formulas. In addition, these
parallel polarization, as seen by the smaller standard deviations measurements exhibit significantly less variability than that
and 90th percentiles. Over the ensemble of measured results seen in the rough limestone wall for a particular incident angle
at both frequencies and polarizations, the model of (15) gives ( B i ) , indicating much less interference effects from surface
a 90th percentile of error of 0.19.
protuberances.
To quantify the improvement of r A V G over using only
The measured reflection coefficients of Fig. 12 closely agree
rl,ll for smooth surfaces, the error statistics comparing the with the theoretical Fresnel reflection coefficients using cr w 5
measured data with the Fresnel formulas in (2) were computed. S/m. For many of the measurements where 0, 2 45", the
Regardless, Figs. 8-1 1 suggest that in the absence of measured
data, an adequate model for rough building surfaces can be
computed by averaging the Fresnel reflection coefficients for
smooth and rough surfaces, as a function of incident angle, i.e.,
348
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996
0
:
E 0.8 .-5 0.9
o.7
._
0 o,6
c
$ 0.5
2
0
%
0.4
0.3
-
.....
-.-.-----8 ........
'
8c
0
.................. ..........
.
.
90th %
..
0.W
/..*' ,.e'
,,_...<...-'"
<..._...
.......
-...-."-"-'
.g 0.2 Y.V
TABLE IV
ERRORSTATISTICS
FOR COMPARISONS
OF MEASURED
4.0 GHZ
REFL.ECTION
COEFFICIENTS
WITH IDEAL
SMOOTH
SURFACE
MODELS
Glass wall
freq = 4 GHz, Perpendicular (I)
Polarization
1.0 -
a = 2.5 Slm
a = 5.0 wrn
G = 10.0 S/m
Measureddata
0
15
30
45
60
75
Brick
Perpendicular
Brick
Parallel
_----;--
g
0.9
1.o
0
8
.....
.......
0.8 E
0.7
0.6
$
0.5
2
0.4
0
XI
0.3
o=io.OS/m
....................
..........................
-,..
....
5
0.1
0.0
-.-
....1)......-.-.2'.
,,<,;:I
........ '.'. ::!
............-3
......a.......
.< 0.2
B
a = 2.5 Slm
_---. o = 5.0 Sim
0
.... ....
15
30
a.01
1
0.10
0.16
I
0.18
8
06
e?
e
$
0.5
-
04-
03/8-----+f
!;I
,
0
..f
15
30
45
60
75
90
6, (degrees)
.. ..
%..
'..
Glass : E~ = 5.0
0
0.10
0
+
'
-.., ....
0.32
-0.05
Ideal smoolh surface
Gaussianrough sutface
Modifiedgaussianrough sutiace
Measureddata
Glass wall
freq = 4 GHz, Parallel (11) Polarization
s
0.38
0.08
Brick wall
Polarization
freq = 4 GHz, Perpendicular (1)
Fig. 12. Measured reflection coefficients for glass wall at 4.0 GHz (perpendicular polarization).
._ 0.9
0.06
4.26
90
6, (degrees)
4-
1
0.07
45
'. . '.. I.,:
60
.*
75
90
Fig. 14. Measured reflection coefficients for brick wall at 4.0 GHz (perpendicular polarization).
8, (degrees)
Fig. 13. Measured reflection coefficients for glass wall at 4.0 GHz (parallel
polarization).
measured reflection coefficients are even greater than that
predicted using F = 10 S/m. In Fig. 13, the comparisons
indicate that the measured reflection coefficients are well
approximated by the Fresnel reflection coefficients using 0 M
2.5 S/m. For modeling the glass wall, the conductivities
of 5 S/m and 2.5 S/m were used for perpendicular and
parallel polarizations, respectively. For each measured reflection coefficient, the modeling error was computed. From the
resulting ensemble of errors, the error statistics, including
average error (Eavg),standard deviation (s), and the 90th
percentile are given in Table IV. The overall fit of the Fresnel
reflection formulas to the measured data shows excellent
agreement when using the appropriate dielectric properties.
Over the ensemble of all measured results at the glass wall,
the theoretical models give a 90th percentile of error of 0.13.
These error calculations were then repeated using the tabulated
conductivity for clear, nondoped glass (i.e., F =
S/m) for comparison purposes. Table IV clearly shows that
modeling this glass wall using the clear glass conductivity
was pessimistic (as seen by the large positive Eavg).The
average error improvement of using a conductivity which
fits the measured data over using the published value for
clear glass is approximately 0.31 and 0.26 for perpendicular
and parallel polarizations, respectively. The impact of these
differences will be discussed further in the next section. These
results demonstrate that metallization and other impurities can
have significant effects on the reflectivity of glass surfaces
commonly used in building construction.
C. Brick Wall Results ut 4.0 GHz
Figs. 14 and 15 show the brick wall reflection coefficient
results for perpendicular and parallel polarizations,
respectively. For these comparisons, the Fresnel reflection
formulas for smooth surfaces and rough surfaces were used.
These formulas used the measured dielectric properties for
brick [19] and the estimated roughness parameters from
Table I. For this brick wall surface, there is little difference
between the scattering loss factors of (6) and (8), because
the small standard deviation of height (oh)causes the Bessel
function in (8) to approach unity.
Similar to the glass wall measurements, the brick wall data
points are clustered together for particular incident angles (e,).
This indicates little variability in the measured coefficients as
the receiver distance ( d 2 ) is varied and, therefore, are relatively
insensitive to interference effects from surface protuberances.
The differences between the theoretical models of the
smooth versus rough surface for the brick wall are much
smaller than in the rough limestone case. Hence, the measured
reflection coefficients of the brick wall are not well bounded
by the smooth and rough surface predictions, in general.
The roughness of the brick surface is such that the critical
heights (h,)are greater than the maximum protuberances for
many of the incident angles. Because of this, the Rayleigh
criterion predicts that the surface appears smooth to the
incident radiation and the reflection will be predominantly
~
349
LANDRON et al.: COMPARISON OF REFLECTION COEFFICIENTS IN A MORILE RADIO ENVIRONMENT
Brick wall
Power difference due to reflectioncoefficient error
(on single specular ray path)
freq = 4 GHz, Parallel (11) Polanzation
10-
40
6i-
S 30
Gaussian rough surface
-U-
8
truer =0.5
20
$
t
B
10
O
-10
0
15
30
60
45
75
90
9, (degrees)
Fig. 15. Measured reflection coefficients for brick wall at 4.0 GHz (parallel
polarization).
specular. To some degree, this is seen in Figs. 14 and 15 since
the measurements are distributed about the predicted Fresnel
reflection coefficients for smooth surfaces. To quantify the
differences between the predicted reflection coefficients and
the measured data, the modeling error is calculated for each
measured data point. From the resulting ensemble of errors,
the error statistics, including average error (Eavg),standard
deviation (s), and the 90th percentile are given in Table IV.
The overall fit of the smooth surface reflection formulas to
the measured data shows excellent agreement when using
the known dielectric properties. Over the ensemble of all
measured results at the brick wall, the theoretical models give
a 90th percentile of error of 0.18.
In comparing the glass and brick wall measurements, both
are accurately described using the smooth surface Fresnel
formulas of (2).These formulas give slightly better agreement
with the glass wall (using 0 = 2.5 5 S/m) than the brick
wall. This is noted by the larger standard deviations and
90th percentiles in Table IV for the brick surface. Over the
ensemble of measured results at the glass and brick walls,
the smooth surface model of (2) gives a 90th percentile of
error of 0.14. These error statistics indicate that (2) gives
an empirically accurate model for surfaces with roughness
features smaller than the critical height of (5).
N
VIII. IMPLICATIONS FOR PROPAGATION PREDICTION
When discussing ray-tracing in urban environments and reflection properties of building surfaces, the following question
typically arises, “How accurate must reflection coefficients
be to obtain an accurate prediction?“ While the question is
straightforward,the answer is, unfortunately, that it depends on
the situation. On one hand, there is potentially a large number
of variables which can have a significant impact on accuracy,
in which reflection properties are but one (e.g., LOSIOBS
topography, reflection properties, diffraction modeling, terrain
effects, accuracy of building database, local scattering effects,
etc.). On the other hand, ray-tracing algorithms are fairly sensitive to the reflective properties of the environmental objects,
and if not adequately modeled, can give large prediction errors.
As an example, let the true reflection coefficient of a building surface be represented by I‘. Now, assume the reflection
-1.0 -0.8 -0.6 -0.4 -0.2
0.0 0.2
0.4 0.6 0.8
reflection coefficient error (Er)
Fig. 16. Effects of reflection coefficient error on a first-order, specularly
reflected-ray path.
+
coefficient was actually modeled as I’ E r , where Er is the
reflection coefficient error. Using (10) to calculate the reflected
ray powers using the true reflection coefficient versus the
modeled coefficient, the power difference (A) in dB of the
two rays is
A = 2010g
(----)
r
r+Er
[dB].
Fig. 16 shows the magnitudes of A for various reflection
coefficient values. A positive power difference (A > 0)
implies that the true reflected power is greater than the
predicted power, and vice versa. As an example, the glass
wall measurements in Section VI1 showed that average error
improvement of the fitted reflection models over the predictions using published conductivities was approximately 0.3 1
for perpendicular polarization. Assuming the true reflection
coefficient for this case was 0.75 for all incident angles, the
predicted power error on a single reflected path would be
approximately 4.6 dB.
IX. CONCLUSION
Microwave reflection coefficient measurements were presented at 1.9 GHz and 4.0 GHz for a variety of typical smooth
and rough exterior building surfaces. The measurement test
cases included walls made of limestone blocks, glass, and
brick. The reflection coefficients were measured by resolving
individual reflected signal multipaths temporally and spatially,
using a wideband spread spectrum system and directional
antennas. The measurement results were compared to the
theoretical Fresnel reflection coefficients using Gaussian rough
surface scattering corrections when applicable.
The measured reflection coefficients at the limestone wall
showed significant variability, which can be attributed to
several factors, including ground reflection effects and interference of the reflected multipath due to surface protuberances.
In any case, over 92% of the measured reflection coefficients
at 1.9 GHz and 4.0 GHz were bounded by the Fresnel formulas for smooth and rough surfaces. An averaged reflection
coefficient (FAVG) was proposed to improve the prediction
accuracy. Over the ensemble of measured results at both
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996
350
frequencies and polarizations, r A V G was shown to give a
90th percentile of error of 0.19. This was an average error
improvement of approximately 0.2 over the smooth and rough
surface models alone.
The measured reflection coefficients at the metallized glass
wall exhibited very little variability for particular incident angles
This indicated significantly less interference effects
(from surface protuberances) as that seen in the limestone
wall. The measurements were compared with smooth surface
Fresnel reflection models with various conductivities. Over
the ensemble of all measured results at the glass wall, the
theoretical models give a 90th percentile of error of 0.13 when
using o = 5 S/m and 2.5 S/m for perpendicular and parallel
polarizations, respectively. The average error improvement of
using a conductivity which fits the measured data over using
S/m) is
the published value for clear glass (i.e., o =
approximately 0.31 and 0.26 for perpendicular and parallel
polarizations, respectively.
Similar to the glass wall measurements, the measured reflection coefficients for the brick wall showed little variability
as the receiver distance was varied and, therefore, were also
insensitive to interference effects from surface protuberances.
The differences between the theoretical models of the smooth
versus rough surface for the brick wall were small due to the
small standard deviation of surface protuberances (oh).Because of this, the measured reflection coefficients of the brick
wall were not well bounded by the smooth and rough surface
predictions, in general. Using the Fresnel reflection formulas
for smooth surfaces, the comparison gave a 90th percentile of
error of 0.18 over the ensemble of all measurements at the
brick wall.
These comparisons show that the actual reflective properties of various external building surfaces can be adequately
modeled using the Fresnel reflection coefficients and rough
surface scattering corrections when applicable. These results
can be directly applied to ray-tracing algorithms for the purpose of propagation prediction in microcellular environments.
The simple models presented here are defined by physical
roughness features and material dielectric properties of the
reflecting wall surface in question.
(e,).
ACKNOWLEDGMENT
The authors would like to thank J. Don Moore, V. Erceg, A.
Rustako, R . Valenzuela, M. Keitz, and D. Sweeney for many
valuable discussions on this topic. For their help with the data
collection and processing they would also like to thank C K
Sou, A . M. Landron, H. Meng, B. Rele and P. Koushik.
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351
Martin J. Feuerstein (S’83-M’90) received the
B.E. degree from Vanderbilt University, Nashville,
TN, in 1984, the M.S. degree from Northwestern
University, Evanston, IL, in 1987, and the Ph.D.
from Virginia Tech, Blacksburg, in 1990, all in
electrical engineering.
He worked for Northern Telecom developing
hardware and software for testing of telecommunications terminals from 1984-1985. During
the 1991-1992 academic year, he was a Visiting
Assistant Professor with the Mobile and Portable
Radio Research Group at Virginia Tech, where his research focused on
propagation modeling. From 1992-1995, he was employed by US WEST on
the design and modeling of digital cellular and PCS radio systems. He is
currently with the Radio Technology Performance Group at AT&T Bell Labs,
Whippany, NJ, where he is working on simulation of CDMA systems.
Dr. Feuerstein is a member of Tau Beta Pi, Eta Kappa Nu, and Phi Kappa
phi.
Theodore S. Rappaport (S’83-M’ 84-S ’85-M’ 87-
Orlando Landron (S’90-M’92) was born in Washington, DC, in 1967. He received the B.S. and
M.S. degrees in electrical engineering from Viginia
Tech, Blacksburg, VA, in 1990 and 1992, respectively.
From 1990-1992, he was a member of the Mobile
and Portable Radio Research Group (MPRG) at Virginia Tech where he studied microwave reflection
and scattering characteristics from typical building
surfaces found in urban environments. As part of
this work. he helued develou an RF channel imuulse
response measurement system using spread-spectrum techniques. In 1992, he
joined the Wireless Communications Systems Engineering Group at AT&T
Bell Laboratories, Holmdel, NJ. He has been involved with a number of
projects, including the AT&T PCN trial and the development of installation
techniques for indoor wireless PBX systems. His work has primarily involved
the characterization and modeling of radiowave propagation for personal
communication systems design.
SM’90) received the B.S.E.E., M.S.E.E., and Ph.D.
degrees from Purdue University, West Lafayette, IN,
in 1982, 1984, and 1987, respectively.
Since 1988, he has been on the faculty of Virginia
Tech, Blacksburg, where he is Professor of Electrical Engineering. In 1990, he formed the Mobile
and Portable Radio Research Group (MPRG) of
Virginia Tech, and founded TSR Technologies, Inc.,
a cellular radio/PCS manufacturing company that
was purchased by Grayson Electronics (a subsidiary
of Allen Telecom) in 1993. He has authored and edited technical papers and
books in the field of wireless communications, including the textbook Wireless
Communications, Priciples & Practice (Prentice-Hall), and serves on the ediON SELECTED
AREAS
IN COMMUNICATIONS,
torial boards of the IEEE JOURNAL
IEEE Personal Communications Magazine, and the Intemational Journal on
Wireless Information Networks (Plenum: NY).
Dr. Rappaport is CEO of Wireless Valley Communications, Inc., a technical
training and consulting firm.He was awarded the Marconi Young Scientist
Award in 1990 and the NSF Presidential Faculty Fellowship in 1992. He is a
registered Professional Engineer in the state of Virginia and is a Fellow and
Member of the Board of Directors of the Radio Club of America.