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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 3, APRIL 2002 631
A Physical Model of the Wireless Infrared
Communication Channel
Volker Jungnickel, Member, IEEE, Volker Pohl, Stephan Nönnig, and Clemens von Helmolt
Abstract—A simple analytical model of the wireless infrared
communication channel in indoor environments is presented.
The infrared signal is modeled as the combination of a diffuse
component and a line-of-sight (LOS) or direct component. For the
diffuse component alone, the properties of the channel are found
using Ulbricht’s integrating sphere. When a LOS component is
also present, the transfer function depends upon the Rician factor
given by the ratio of the electrical power in the LOS and diffuse
signals after the detector. For small , the transfer function
shows notches down to low frequencies, but due to the nature of
light never for zero frequency. We confirm that a -factor 13
dB is required also in infrared wireless links in order to support
distortionless data transmission beyond 100 Mbit/s. Increasing the
directivity at the receiver and/or at the transmitter improves the
effective value of . Here, we show that a moderate directivity
will be sufficient for high-speed infrared communication in typical
indoor scenarios.
Index Terms—Diversity methods, multipath channels, optical
communication, ray tracing, wireless LAN.
I. INTRODUCTION
RESEARCH on wireless infrared (IR) communication in
indoor environments [1] has recently focused on two op-
tions: the diffuse propagation configuration and tracked directed
links. In the diffuse propagation configuration, a wide-beam
optical transmitter (Tx) is aimed at the ceiling and the diffuse
reflections are used to establish a link to a receiver (Rx) that
also faces the ceiling. Such a scheme simplifies deployment by
eliminating the need for a line-of-sight (LOS) path between the
Tx and Rx. In typical rooms, however, dispersion due to multi-
path propagation limits the data rate to about 50 Mbit/s. More-
over, relatively high optical transmitter power ( 0.5 W) must
be used to illuminate the ceiling [2]. The tracked directed link
overcomes these drawbacks by employing an LOS path. This
permits a smaller field-of-view (FOV) at the Rx which reduces
dispersion due to multipath scattering and reflections. In addi-
tion, a narrow-beam Tx concentrates the power into the region
where the Rx is located. In this way, data rates of more than 100
Mbit/s can be supported at relatively low Tx powers [3]–[5].
Manuscript received February 26, 2001; revised October 8, 2001. This work
was supported by the German Ministry of Research and Education (BMBF)
within the ATMmobil project under Contract 01 BK 611/3. This paper was pre-
sented in part at the 11th IEEE International Symposium on Personal, Indoor and
Mobile Radio Communications (PIMRC) in London, U.K., September 18–21,
2000.
V. Jungnickel, V. Pohl, and C. von Helmolt are with the Heinrich-Hertz-In-
stitut für Nachrichtentechnik Berlin GmbH, D-10587 Berlin, Germany (e-mail:
jungnickel@hhi.de; pohl@hhi.de; helmolt@hhi.de).
S. Nönnig is with Motorola R&D, D-13507 Berlin, Germany (e-mail:
stephan.noennig@motorola.com).
Publisher Item Identifier S 0733-8716(02)03383-8.
Fig. 1. The indoor system concept for wireless infrared communication
motivating this work. Two link modes are combined. The diffuse link is based
on diffuse reflections at the walls so that, in principle, no LOS is required.
When the LOS is clear, the system switches to the tracked directed link which
is more power efficient and allows data rates beyond 100 Mbit/s.
The system concept considered here employs both diffuse and
directed links in order to achieve the advantages of both. A typ-
ical office scenario is depicted in Fig. 1. A base station (BS) is
mounted on the ceiling and the mobile stations (MS) are located
throughout the workplace at tabletop height. In this configura-
tion, the direct path is clear for the majority of MS locations
and thus a tracked directed link can be used for communication.
When, on occasion, the direct path is blocked, a secondary dif-
fuse link can be used to hold the connection at a reduced rate.
The wide-angle transceivers used to detect beacon signals for
position detection and for tracking purposes in a directed link
can be used to pass signals over a diffuse link as well. Array
techniques allow both diffuse and directed links to be realized
with common hardware [6].
This dual-mode approach raises a number of questions con-
cerning the infrared channel. Results for the diffuse configura-
tion alone cannot be applied to this configuration because both
the direct and diffuse signals are usually present. When the di-
rect path is blocked, only the higher order reflections can be used
for communication because the first reflection is outside the
FOV unlike in [2]. In the case of simultaneous diffuse and direct
propagation the transfer function shows deep notches, which is
critical for high-speed data transmission. With increasing direc-
tivity of the Rx and/or Tx, channel quality improves. Accord-
ingly, this paper focuses on determining the degree of directivity
required to achieve very high data rates in indoor environments.
As a consequence of its small wavelength compared to the
surface roughness of most building materials, light tends to be
reflected diffusely in indoor environments. All points of the
room surface illuminated by the Tx and situated within the FOV
0733-8716/02$17.00 © 2002 IEEE
632 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 3, APRIL 2002
of the Rx contribute to the diffuse signal. Not only does the first
reflection consist of a large number of paths, the number in-
creases with higher order reflections.
There are two basic approaches to simulate diffuse light prop-
agation in rooms. Gfeller and Babst [1] decompose the room
surface into a number of reflecting elements. Light is collected
from all directions that the element faces. The element scatters
the light with a Lambertian characteristic and the power inci-
dent upon the Rx from all the elements is summed. Barry et al.
[7] extend this approach by using a recursive algorithm to allow
for higher order reflections. The propagation time between the
elements is taken into account in order to obtain the impulse
response. This method is widely used [8]–[23]. In general, reli-
ability of results improves with the number of reflections taken
into account, but computing time increases exponentially. When
too few reflections are taken into account, path loss and band-
width are systematically overestimated.
A more recent method is based on ray tracing [24]–[29]. The
path of a single photon is tracked during a random flight in the
room until it is absorbed or hits the Rx. The procedure is re-
peated many times and statistical data on the path loss and on
the time-of-flight distribution are collected. While this allows
all reflections to be taken into account, many trials must be con-
ducted in order to obtain good results. Path loss estimation re-
quires about 10 trials while estimating the impulse responses
takes up to 10 trials with subnanosecond time resolution [29].
Ray tracing is preferable in terms of reliability but might be less
efficient than Gfeller and Babst’s technique.
Few measurements on the IR channel have been reported to
date. An empirical study conducted by [30] shows strong spatial
and angular variations of power and bandwidth. Reference [31]
focused on the diffuse configuration but also presented some
data on nondirected LOS links. Reference [32] considered the
reflection properties of indoor materials. More recently, [33] an-
alyzed a large database of measurements in order to determine
the correlation between delay spread and path loss.
This paper introduces an analytical model of the infrared
channel that allows approximate prediction of path loss and
bandwidth. It aims to be more convenient for the system
designer than either simulations or measurements. At the end
of the 19th century, the German engineer Ulbricht invented
the integrating sphere as a model to describe illumination by
electrical lightning in train stations [34]. This model is now
adapted to the IR channel. Simulations and measurements in
this paper are intended to show that the model works well in
many indoor scenarios.
The diffuse propagation model can be extended by taking the
LOS or direct signal into account. It is found that the shape of
the frequency response is steered, in principle, by the Rician
-factor. A conservative estimate for the smallest value of
is found above which high-speed IR transmissions are possible
(100 Mbit/s). The transition from the diffuse to the directed
IR link can also be described in terms of . Rician -factor
increases quickly with directivity, and it is found that moderate
directivity will be sufficient for high-speed communication in
indoor scenarios.
II. RAY TRACING COMPUTER SIMULATION
At the Tx, a random start direction was created according to
a Lambertian distribution
(1)
where is the radiant intensity, the Tx power, is the
Lambert exponent, and is the angle between the initial direc-
tion of flight and the direction of maximum power. The initial
direction of flight ( , ) was obtained by using two random
numbers and uniformly distributed over [0, 1]. They were
inserted into the formulas
and (2)
When a photon reached a surface (wall, ceiling, floor, etc.), a
third random number uniformly distributed over [0, 1] was
used to describe the reflectivity .For the photon was
send to a new random direction according to a Lambertian dis-
tribution ( ) and the path was tracked to the next reflection
point. For , the path was stopped. By tracking the photon
in this way, the number of reflections is random.
A large number of photons was tracked, and, occasion-
ally, a photon reached the Rx. The optical path loss was then
calculated from the number of received photons
(3)
A detector with a diameter of 10 cm was used as a good com-
promise between simulation efficiency and temporal resolution
[29]. Throughout this work, the FOV is defined as the full ac-
ceptance angle at the Rx. A reduced FOV was realized by cal-
culating the angle of incidence for each photon from the
direction of arrival at the detector. Only when
was the photon accepted in the statistics.
The total time of flight from the Tx to the Rx was accumulated
in each trial. A histogram with a time resolution of 167 ps was
obtained from these data which is equivalent with the impulse
response . The complex transfer function was ob-
tained by Fourier transform of . The cutoff frequency
was taken at .1
Results were checked against previously published data. Con-
figuration A in [2, Table 1] was studied again with ray tracing.
Magnitude data were normalized to the same Rx area. The two
results agree perfectly with each other, when the ray tracing
is exceptionally stopped after three reflections (dotted line in
Fig. 2), which compares to the method used in [2] (open circles
mark the results taken over from [2]). When the path of each
photon is fully tracked, results are more reliable, especially at
low frequencies (full line).
III. MEASUREMENT SETUP
The collimated beam of a monolithic master-oscillator
power-amplifier (MOPA) laser diode (SDL-5762-A6) oper-
ating at a wavelength of 993 nm was directed to the white
painted ceiling where the light was diffusely reflected with a
1Note that
j
H
(
f
)
j
is related to the received optical power, and the electrical
power after the photodiode scales with
j
H
(
f
)
j
.
JUNGNICKEL et al.: PHYSICAL MODEL OF WIRELESS INFRARED COMMUNICATION CHANNEL 633
Fig. 2. Comparison of ray tracing results including all (solid line) and only
three reflections (dotted line) with the results of [2] which considered three
reflections, too (open dots).
nearly Lambertian beam characteristics. For measurements of
the resulting power profile in the room, the MOPA was used
in continuous mode at a power of 1 W. The received power
was measured with a wavelength-calibrated optical power
meter with a sensor diameter of 5 mm and an FOV of 90 (HP
81 524A). Measurements were done in rooms with darkened
windows to reduce the background light. This is not expected to
alter results since the reflectivity of glass is low except of large
angles of incidence and, to a first approximation, windows can
be regarded as absorbers.
Frequency response was recorded using the -parameter test
set (HP 85046A) of a network analyzer (HP 4396A). A 50-
bias tee was built into the MOPA to allow direct high-frequency
modulation of the master oscillator section by the output of the
network analyzer. The modulated light was then on-chip opti-
cally amplified in the power amplifier section driven by a dc
current of 3 A. The IR receiver used a silicon avalanche photo-
diode (APD) with 3-mm diameter (EG&G C30872). After am-
plification, the signal was fed back into the network analyzer.
Calibration was done at a Tx-to-Rx distance of 2 m with the Rx
tracked toward the Tx spot. The Rx FOV was limited for cal-
ibration to less than 1 with a pin hole. The useful frequency
range was between 300 kHz and 300 MHz and the acquisition
bandwidth was 3 kHz.
IV. DECOMPOSING THE INFRARED CHANNEL
The impulse response corresponding to the complete ray
tracing in Fig. 2 is shown in Fig. 3. Note the logarithmic scale
on the vertical axis. An initial Dirac-like pulse due to the LOS
is observed followed by a continuous signal due to the diffuse
reflections. These two components are well separated from
each other in the time domain and, obviously, they should be
distinguished. The impulse response of the IR channel is thus
written as a parallel combination
(4)
with contributions due to the LOS signal and
due to diffuse reflections, as suggested by the
insert in Fig. 3. The figure is the gain of the LOS signal
Fig. 3. Impulse response corresponding to the solid line in Fig. 2. Inset: The
channel is modeled as a parallel circuit of the LOS and diffuse signals.
and describes the delay between the LOS signal and the
onset of the diffuse signal. In Sections V and VI, the properties
of the diffuse signal are studied, separately. The LOS signal is
added in Sections VII and VIII.
V. A SPHERE MODEL FOR THE DIFFUSE SIGNAL
The impulse response of the diffuse signal in Fig. 3 shows
some initial peaks with varying shape and intensity due to the
first reflections in the room. The response then becomes smooth
and a nearly perfect exponential decay is observed due to su-
perposition of higher order reflections. This long lasting decay
has great impact on the low-frequency part of the transfer func-
tion which is relevant for base-band transmission via an IR link.
Consequently, one must find a model relating the parameters of
this exponential decay (path loss, decay time) to the room prop-
erties.
The impulse response of the diffuse signal in Fig. 3 is very
close to that of an integrating sphere. At low frequencies, the
transfer function of the sphere can be approximated with a first-
order low pass filter depending on a small set of parameters [35].
In the following, this simple transfer function is taken over as a
model for the diffuse signal in rooms.
In order to obtain the path loss, it is assumed that the first
diffuse reflection of a wide-beam optical source creates a ho-
mogeneous intensity across the entire room surface
given by
(5)
where is the reflectivity of the region initially illuminated by
the Tx and is the Tx power.The contribution of the second
reflection is reduced by the average reflectivity defined as
(6)
where the individual reflectivities of walls, windows, book-
shelves, and other objects in the room are weighted by their in-
dividual areas . The light undergoes an infinite number of
634 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 3, APRIL 2002
reflections, at least in principle. Hence, the total intensity can
be calculated by summing up a geometrical series
(7)
in which the index counts the number of reflections. The re-
ceiver is now considered as a small part of the room surface and
the received power is obtained by multiplying (7) with the
receiver area . Hence, the power efficiency for the diffuse
signal is given by
(8)
and it is related to the optical path loss by .
A detailed derivation of the impulse response for the sphere
was given in [35]. The corresponding result for the diffuse IR
signal is
with (9)
where is the cutoff frequency. The exponential decay time
is given by
(10)
The figure can be considered as the average time between
two reflections and the term is the average number
of reflections until a photon is likely to be absorbed.
In the following, the figure is obtained from the sphere
model. Assume that a certain amount of light is homogeneously
accumulated inside a cavity and, suddenly, the light is switched
off. The energy in the cavity is then proportional to the cavity
volume while the energy loss , which is assumed to
be homogeneously distributed across the surface , is propor-
tional to . Therefore, we can write
(11)
Now, in the case of the integrating sphere, an analytical formula
for the loss rate is known [35]. The exact result is
(12)
where and are the sphere diameter and the speed of light,
respectively. As expected, the unknown figure can
be related to the volume-to-surface ratio . We can apply this
relation for a rectangular room as follows:
(13)
where , , and are the length, the width, and the height, re-
spectively. The ray tracing procedure was slightly modified to
check the validity of (13). A single photon was sent to a flight in
a synthetic room where the surface reflectivity was set to unity.
It was assumed that the different reflection points at the surface
are randomly reached after a large number of reflections as often
as predefined by the room geometry. A histogram for the time
between two reflections was created during the flight. After 10
reflections, typically, the resulting distribution converged
Fig. 4. Average time between two reflections as a function of the room
dimensions. Full dots refer to simulation results (see text) and the solid curves
are obtained from (13).
Fig. 5. Comparison between measured (solid line), simulated (dashed line),
and modeled frequency responses (short dashed line) for the diffuse signal
without LOS. Curves are normalized at low frequency. The scenario is shown in
principle in the inset.
j
S
j
values include amplifier gain and do not represent
the path loss.
and the random flight was stopped. The figure was then cal-
culated as the mean value of . Results for a large number of
room dimensions are shown as full dots in Fig. 4 and the solid
lines refer to (13). Obviously, (13) is an excellent approxima-
tion for in rectangular rooms. Patel et al. [36] recently found
a formula which is similar but not identical to (12). They as-
sumed . But this is not consistent since depends on
wall reflectivity as shown above.
Equations (6), (8)–(10), and (13) now form a complete set
by which an approximate transfer function for the diffuse signal
can be calculated by using the room dimensions, the
average reflectivity and the Rx area if we assume .
Fig. 5 compares frequency responses obtained by measure-
ment and ray tracing with the sphere model. Measurements were
done in an empty lab in which windows and floor were covered
with wallpaper so that reflectivity is more homogeneous. The
first-order low-pass response (dotted line) predicted by (9) was
fitted to the low-frequency part of the measured frequency re-
sponse. From the resulting cutoff frequency , an average re-
flectivity of was obtained according to (10) and (13)
which was next used in the simulation. Ray tracing was started
with a rough model of the measurement scenario (see inset in
Fig. 5). The sphere model works well over more than a decade
of power reduction in the 1 10 MHz range. At high frequen-
cies, additional ripple is observed both in measurements and in
JUNGNICKEL et al.: PHYSICAL MODEL OF WIRELESS INFRARED COMMUNICATION CHANNEL 635
Fig. 6. Measured power (left) and bandwidth (right) profiles of the diffuse signal with the receiver pointing up (top figures) and down (bottom figures) in a
furnished lab with the same size as indicated in the inset of Fig. 5. Tx power is 1 W.
simulation. But the ripple is not relevant for data transmissions
in narrowband diffuse links and it can be neglected in the model.
VI. PROPERTIES OF THE DIFFUSE SIGNAL
Simulations and measurements in this section are intended to
show that basic properties of light propagation in a sphere are
also found for the diffuse signal in rooms, namely the homo-
geneous and isotropic intensity distribution and the relatively
constant gain-bandwidth product.
Intensity Distribution: Measured intensity and bandwidth
profiles are shown in Fig. 6 for a furnished and fully equipped
lab with the same dimensions as shown in the inset in Fig. 5.
The Rx was placed at a height of 1 m. The origin of the ( , )
coordinates is the front-left corner in the lab.
When the Rx points up and the LOS is blocked, a nearly
homogeneous intensity profile with a min-to-max variation of
less than 3 dB is observed. Frequency responses were also
recorded at these points. The corresponding bandwidth profile
is plotted on the right side in Fig. 6. As expected, little variation
of the bandwidth is observed for the diffuse signal alone.
With the data in the upper figures, the consistency of the
sphere model is checked. According to (13), is 9.8 ns. From
MHz, can be estimated using (9) and (10).
With the sensor area of cm , m ,
reducing the power of diffuse light by a factor of
2 according to [1] and , all inserted in (8), a path loss
of 70.7 dB is estimated which corresponds to a received power
of 85 nW at 1 W Tx power. The measured values for the dif-
fuse power range between 60 and 120 nW. Obviously, model
and measurement agree reasonably well with each other taking
into account that the furniture increases and reduces
compared to .
Fig. 7. Measured frequency responses for various orientations of the receiver
without LOS in an empty lab. The scenario is shown in principle in the inset.
j
S
j
values include amplifier gain and do not represent the insertion loss.
When the Rx points down (bottom in Fig. 6), the first reflec-
tion is inside the FOV. The power profile is not as homogeneous
as above and there are some points in the room where a band-
width significantly larger than 10 MHz is observed. Note that
the bandwidth profile is not always correlated with the power
profile eventually due to furniture.
Measured frequency responses for various Rx directions are
plotted in Fig. 7. Data were recorded in the empty lab described
in Section V but with uncovered windows and floor. When ei-
ther the LOS is not available or it is blocked by hand, about
the same power is received from each direction. Anisotropy of
optical power is only 1.6 dB at the particular measurement lo-
cation. Note that the measured diffuse power and transmission
bandwidth is dependent on the distance to the main first re-
flection plane, yielding higher values for the north, west, and
636 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 3, APRIL 2002
Fig. 8. Frequency response as a function of average reflectivity in the room.
Solid curves are simulation results while dashed curves show the analytic results
obtained from the sphere model. The scenario is shown in the inset.
downward direction ( m) than for the other directions
(m).
Gain-Bandwidth Product: Equations (8)–(10) predict that
gain and bandwidth depend on . Note that the
product for approaching unity is independent of
(14)
When gets larger, the average number of reflections
is increased. More light is accumulated in the
room (i.e., the gain is larger), but at the same time the
exponential decay time (10) is increased. According to (9), the
bandwidth is therefore reduced.
Simulation results for varying are shown in Fig. 8.
The scenario is shown in the inset. Notice the logarithmic
axes, scaled by and , respectively. The dashed
curves mark the frequency responses obtained from the sphere
model. In general, the larger the reflectivity is the more the
first-order low-pass response is pronounced. At the same time
the received power increases and the bandwidth decreases. This
is confirmed also by measurements in the empty lab with and
without wallpaper covering the windows and floor.
As concluding results of this section, the basic properties of
an integrating sphere can be found also in rooms, and the sphere
model can be used to estimate the basic channel parameters for
the diffuse signal.2
VII. SUPERPOSITION WITH THE LOS SIGNAL
In this section, the LOS signal is added to the diffuse signal.
The LOS signal creates a short Dirac pulse (see Fig. 3) which is
little broadened when light arrives inclined on a small detector.
2Note a striking exception where the sphere model fails to calculate the path
loss. When one dimension in the room differs significantly from the two others,
like in a long corridor, path loss variations up to 20 dB are observed while
the sphere model predicts a constant power, in general. On the other hand, the
bandwidth profile was almost homogeneous, and it was correctly estimated by
the model [29].
For this reason, the LOS channel is distortionless up to very high
frequencies.
The received power from the LOS channel can be calculated
from the current geometry. With a Lambertian Tx at the ceiling
pointing downwards, for instance, the received power is ob-
tained by multiplication of the radiant intensity (1) with the solid
angle covered by the Rx. The gain reads
(15)
where denotes a scalar product, , , and
are unit vectors of the LOS direction from Tx to Rx, the Tx max-
imum power direction and the Rx maximum sensitivity direc-
tion, respectively, and is the distance between Tx and Rx. Note
that when or .
The diffuse component arrives with delay . The two com-
ponents have a frequency-dependent phase offset and
with (4) and (9) the combined transfer function is given by
(16)
The total frequency response depends on
(17)
on , and on the phase offset . The -factor in (17)
is intentionally associated with the electrical power ratio at the
output of the detector. Comparison with the Rician -factor
widely used in radio communications is easier in this way.
Measured power and bandwidth profiles in the furnished lab
are shown in Fig. 9. Optical power varies by more than a decade
when the LOS is present. In corners and nearby walls, power
and bandwidth are similar to the diffuse signal (see Fig. 6).
Note a transparent region near the Tx spot where the band-
width ( 300 MHz) is by orders of magnitude larger than in the
corners. The LOS signal is more dominant in this region and,
hence, the response is almost flat.
The surprisingly steep onset of the transparent region was in-
vestigated in a separate experiment. The Rx was placed on a ro-
tary stage at a fixed distance to the Tx and frequency responses
were recorded with and without LOS at different angles between
LOS and . From the electrical power data ( ,
) at low frequency, the -factor was obtained ac-
cording to
(18)
The 3-dB bandwidth was taken from each curve with LOS
and results are shown in Fig. 10 as a function of (full cir-
cles). For comparison, theoretical data were obtained from the
frequency-dependent amplitude of (16) in order to illustrate the
influence of . In the measurements, dB was
sufficient for a bandwidth larger than 300 MHz. In the worst
theoretical data ( ns), transparency is given for
dB. A similarly sudden transition to transparency was also
JUNGNICKEL et al.: PHYSICAL MODEL OF WIRELESS INFRARED COMMUNICATION CHANNEL 637
Fig. 9. Measured power (left) and bandwidth (right) profiles like in Fig. 6 (top) when the LOS signal is added.
Fig. 10. Measured (filled dots) and analytical results (open symbols) for the
cutoff frequency as a function of the Rician
K
-factor. Note the sudden transition
to transparency for
K
13
dB.
Fig. 11. The scenario investigated in the simulations in Fig. 12. Rician
K
-factor is set by changing the angle
at the receiver having an FOV of 180 .
found for the 19-GHz indoor radio channel at dB [37].3
When is increased, characteristic changes in the frequency
response are observed. This is demonstrated by simulation of the
scenario given in Fig. 11 in which the angle was reduced to
increase .At , no LOS is available and the low-pass
response due to the diffuse signal is observed (see Fig. 12 and
note the linear frequency axis). When is now reduced by only
3The transparency point depends in addition on
f
and on the targeted band-
width
B
. Precisely, a value of
K
13
dB is needed for
f
B
, which is true
when data rates
>
100 Mbit/s are targeted in typical rooms where
f
is about
10 MHz. There are still distortions of amplitude and phase at
K
13
dB. But
they are so small that “the eye is open,” i.e., digital communication at high data
rates is possible and the penalty reduces when
K
is increased.
Fig. 12. Typical frequency responses when the Rican
K
-factor is changed. A
dashed line marks the separate response due to the LOS and a dotted line refers
to the diffuse signal for each
.
1 , the frequency response changes, dramatically. A deep notch
is created at about 200 MHz followed by some ripple at higher
frequencies. When the angle is further reduced ( ), the
notch is shifted down to 50 MHz. At , the LOS signal
predominates and the response is almost flat. Note that the notch
is always close to the crossing point of the separate responses
due to the LOS and the diffuse signal also shown in Fig. 12.
Very similar results are obtained when the beam-width at the
Tx is reduced (see Section VIII).
Unlike for radio base-band signals in fading channels, a notch
like in Fig. 12 never occurs at zero frequency for IR channels.
The two conditions and
(19)
hold at the notch frequency where, in principle, the two
photo currents due to and interfere destructively.
The smallest notch frequency may be observed at in
(19) for maximum , i.e., when Tx and Rx are close to each
other in a corner pointing toward the center of the room. Then
is given, approximately. When and
cross in a far point, a weak LOS signal is received for which
shall be assumed. Within the sphere
model, is obtained from
638 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 3, APRIL 2002
Fig. 13. Normalized optical power of the diffuse signal as a function of the
FOV. The theoretical curve is given as a full line and two extreme fit curves are
indicated by dashed lines.
(19). Consistently, no notch below 25 MHz is observed in our
measurements since is roughly 10 ns in common rooms.
VIII. TRACKED DIRECTED LINKS
It is well known that high-speed transmission with directed
links is almost trouble-free when the LOS is clear. But transmis-
sion is distorted when the diffuse IR signal becomes too strong
[38]. A system designer may be interested in the degree of di-
rectivity which is required to achieve a particular transmission
bandwidth in indoor scenarios.
In principle, the required directivity can be calculated with
the sphere model by selecting the beam-width at the Tx
and the FOV at the Rx at which is beyond the 13-dB threshold
found in the last section. Finding a general rule for the directivity
is quite simple for the Tx but it proves to be difficult at the Rx
in rectangular rooms.
In order to reduce the full beam-width at the Tx, one
can increase the Lambert exponent in (1) and (15) according
to
(20)
Power is then more concentrated onto the Rx. When the Tx is
directed to the Rx, with (15) increase of power is given by
(21)
Note that the numerator in the -factor (17) becomes larger
when is increased.
Vice versa, only the diffuse signal being the denominator
in (17) is reduced when a smaller FOV is used. Gfeller and Babst
[1] derived the formula
(22)
for the diffuse signal as a function of the FOV. They assumed
a homogeneously shining surface with diffuse reflectivity in
the Rx FOV. In Fig. 13, simulation data are shown which were
obtained for various scenarios with different room parameters.
Obviously, the exponent 2 in (22) is only a rough approxima-
tion. Especially at low FOVs, deviations of up to 3 dB from
Fig. 14. Measured frequency responses with a nearly Lambertian transmitter
when the FOV at the Rx is reduced. The scenario is detailed in the text. The
signal at
FOV
=
180
without the LOS is also given.
j
S
j
values include
amplifier gain and do not represent the insertion loss.
Fig. 15. Diffuse (dotted line) and LOS signal (full line) when the beam-width
2
at the transmitter and the FOV at the receiver areequal and simultaneously
increased (simulation data). The transparency point (see text) is indicated by an
arrow.
the theoretical curve are observed. Deviations are attributed to
residual anisotropy of the diffuse signal which is expected to be
increased with a small FOV. The Rx or the Tx may be then di-
rected to parts in the room where reflectivity differs from
. Data for a given scenario can be modeled empirically by
changing the exponent in (22) from 1.3 to 3 (see Fig. 13). Due
to these uncertainties it is difficult to derive the directivity for
rectangular rooms using the sphere model. The required direc-
tivity depends on the scenario and results are not useful for other
configurations.
Fortunately, it is obvious from Fig. 9 that the directivity must
be increased only when the Rx is located outside the transparent
region. In addition, the -factor depends upon the square of the
path gains and for an optical link. In order to increase
above the required threshold for high data rate transmissions,
therefore, moderate directivity will be sufficient.
This is illustrated by measurements and ray tracing results
in Figs. 14 and 15. The diffuse spot was located at the ceiling
for the measurement at the position (4 m, 3 m) in the furnished
lab depicted in principle in the inset of Fig. 7. The receiver was
JUNGNICKEL et al.: PHYSICAL MODEL OF WIRELESS INFRARED COMMUNICATION CHANNEL 639
placed in the front-left corner (0, 0) at a height of 1 m. Only
the FOV was reduced by using a number of preformed tubes in
front of the Rx. Fig. 14 indicates that the bandwidth is larger
than 300 MHz in the curves for and that the re-
sponse is almost flat at . Similar results were ob-
tained by simulation in [29]. Simulation results for the powers
received from the LOS and from the diffuse signal are depicted
in Fig. 15. The scenario is given inthe inset. The values for FOV
and are set equal and they were simultaneously changed.
The LOS signal is significantly increased when is reduced
since light is more concentrated onto the Rx now. At the same
time, also the diffuse signal is reduced. Transparency is there-
fore achieved at even larger FOV compared to Fig. 14 which is
indicated by an arrow in Fig. 15.
IX. CONCLUSION
An analytical model for the indoor infrared communication
channel has been presented. The IR channel is the parallel com-
bination of LOS (or direct) and diffuse (or scattered) paths. Sim-
ulations and measurements indicate that formulas derived from
the integrating sphere can be applied to estimate path loss and
bandwidth for the diffuse signal using only a few physical pa-
rameters associated with the room. When the LOS is added,
deep notches may occur in the frequency response and they are
likely to reduce the useful bandwidth to approximately 25 MHz.
Similar to radio links, a Rician factor of dB is needed
for a bandwidth larger than 300 MHz. Tracked directed links
can reduce the transmitter power and increase the channel band-
width when the receiver is far from the transmitter. The effects
of a reduced FOV at the receiver and of a narrow beam at the
transmitter were investigated. It was found in principle and ver-
ified by measurement and simulation that moderate directivity
will be sufficient for indoor infrared communication at data rates
beyond 100 Mbit/s.
ACKNOWLEDGMENT
The authors would like to thank Dr. F. Gfeller (IBM Zurich)
for a fruitful discussion on the simulation technique, Dr. T.
Hermes and Dr. U. Krüger for valuable comments on the
efficiency of ray tracing and on the manuscript, and R. Ziegler
for assistance in building the measurement setup.
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Volker Jungnickel (M’00) was born in Großenhain,
Germany, in 1964. He received the Dipl.-Phys. and
Dr. rer. nat. degrees in physics, in 1992 and 1995,
respectively, from Humboldt-University, Berlin, Ger-
many.
In 1984, he became a certified optician with Carl
Zeiss, in Jena. In 1995, he was concerned with pho-
toluminescence properties of quantum dots and the
mechanism of electron–phonon coupling in strongly
confining zero-dimensional semiconductors, and he
joined ILS GmbH in Stahnsdorf working in the field
of medical laser technology. In 1997, he came to the broadband mobile com-
munication networks department at Heinrich-Hertz-Institute in Berlin where he
developed a high-speed wireless system for indoor communication based on in-
frared. In particular, he was engaged in the system design, infrared channel mod-
eling, and building a 155-Mbit/s experimental demonstrator with an imaging
infrared receiver. At present, his scientific interests include multiple-input mul-
tiple-output (MIMO) radio systems for high-speed wireless communications.
He has authored and coauthored more than 30 conference and eight journal pa-
pers and holds a patent.
Dr. Volker is a member of the German Physical Society
Volker Pohl was born in Dresden, Germany, in 1972.
He became a certified technician for electrome-
chanics with Mertik Regelungstechnik, in 1992. He
received the Dipl.Ing. in electrical engineering from
Technical University Berlin, Berlin, Germany, in
2000.
He joined the Heinrich-Hertz-Institut (HHI) in
1998 as a Student Research Associate. Initially,
he was involved in the development of electro-lu-
minescence color displays. Later, he changed to
the broadband mobile communications networks
department where he was concerned with the development of wireless infrared
systems. In particular, he developed the ray tracing simulation tool used
in the present paper. At present, he is a Research Associate at HHI. While
working toward his Ph.D., he is concerned with modeling and measurements of
multiple-input multiple-output (MIMO) radio channels in indoor and outdoor
environments. He has authored six conference and two journal papers and
holds a patent.
Stephan Nönnig was born in New York, NY, in 1971.
He received the Dipl.-Ing. from the College of Elec-
trical Engineering at the Berlin Technical University,
Berlin, Germany, in 2000.
He became a Certified Technician for communica-
tion systems with the Bosch Telecom Group, in 1993.
He joined HHI in the broadband mobile communica-
tion networks department, where he set up a Linux-
based ATM network and prepared his thesis in mea-
surements of the wireless indoor infrared channel. At
present, he is a Software Engineer at Motorola R&D,
Berlin, working with embedded systems in the TETRA Engineering Depart-
ment. He is interested in wireless communication systems and communication
networks. Presently, he is involved in software development for TETRA sub-
scribers.
Clemens von Helmolt was born in Berlin, Germany,
in 1952,. He received the Dipl. Ing. and the Dr.-Ing.
degrees, in 1979 and 1985, respectively, both in elec-
trical engineering from the Technische Universität
Berlin, Germany.
From 1979 to 1984, he was a Research Associate
at the Institut für Hochfrequenztechnik, Technische
Universität, Berlin, where he worked in the field of
acousto–optic interaction in optical strip waveguides.
In 1984, he joined the Heinrich-Hertz-Institut (HHI)
where he was engaged in research on LiNbO
devices for coherent receivers until the end of 1987. From 1988 to 1998, he
worked in the field of optical frequency stabilization of of optical heteroyne and
WDM broadband communication systems, respectively, where he coordinated
the HHI research activities related to the European projects “RACE-1010,”
“RACE-2065,” and “ACTS-084.”From 1996 to 2000, he was responsible for a
national research project related to broadband mobile indoor communication
based on infrared. Since November 2000, he has been managing research
projects related to multiple-input multiple-output (MIMO) techniques and
systems for RF multielement antenna mobile communication. He has authored
and coauthored more than 40 journal publications and conference presentations
each, has made several contributions to books, and holds several European and
U.S. patents.
