A channel model for wireless infrared communication

Abstract

An simple analytic model for the light propagation in indoor
environments is presented. Ray tracing simulations confirm that the
model is applicable to the wireless infrared communication channel in
rooms

Full text

A Channel Model for Wireless Infrared Communication
Volker Pohl, Volker Jungnickel and Clemens von Helmolt
Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH,
Einsteinufer 37, 10587 Berlin, Germany, e-mail:
jungnickel@hhi.de
ABSTRACT
An simple analytic model for the light propagation in
indoor environments is presented. Ray tracing
simulations confirm that the model is applicable to the
wireless infrared communication channel in rooms.
INTRODUCTION
Wireless infrared (IR) communication has attracted
much attention during the last years since it is an
alternative to radio transmission for high-speed indoor
communication. IR systems occupy no radio frequency
(RF) spectrum and they can be used where
electromagnetic interference is critically (clinics,
production halls, air planes). But of course, there are
some peculiarities like the strong background light level,
the transmitter power which is limited due to eye safety
and the relatively poor sensitivity of the IR receivers in
which direct detection of the intensity modulated light is
performed [1, 2].
The basic knowledge on the indoor IR transmission
channel is not yet complete. Unlike at RF transmission,
the light is reflected diffusely at most walls in a room,
and, already for the first reflection, there is a continuum
of possible paths between the transmitter (Tx) and the
receiver (Rx). The light may suffer many of these
reflections, and the channel estimation is not trivial.
Gfeller and Babst [1] estimated the delay spread for a
single diffuse reflection at a wall in terms of a bandwidth
times cell diameter product of 260 Mbit*m/s. Barry et al.
[3] used a numerical approach to simulate the IR impulse
response in rooms. A recursive method was introduced
that was later on used in virtually all simulation work on
the IR channel [4-8]. But because of numerical
complexity, not more than 5 reflections [4] were
considered. Hence, these models overestimate both the
path loss and the channel bandwidth, systematically.
Wireless channels do depend on the Tx and Rx
configuration and on the actual situation in the
environment. Consequently, the complexity of the
simulation was increased from [3] to [8] to include, for
instance, furniture or windows. On the other hand, an
engineer trying to check the basic parameters of the IR
channel rather needs some quick rule of thumb than
specific simulations. But the former is not available at
the moment.
For this reason, an analytical model for the IR channel is
needed, which is simple but includes all reflections. In
this paper it is shown that the essential properties of the
diffuse light propagation in rooms can be described,
already, with a simple analytic formula which is derived
from the integrating sphere. It is also shown how the
sphere formula can be scaled to a specific room. The
model is confirmed by statistical ray tracing simulations
which take all diffuse reflections into account.
THE RAY TRACING TECHNIQUE
The simulation method used here has already been
employed by the authors to describe the diffuse light
propagation in integrating spheres [9, 10]. The path of
individual photons from the transmitter (Tx) through the
room to the receiver (Rx) is tracked in detail (see Fig. 1).
At the Tx, a random start direction is created according
to a generalised Lambertian law
θ
π
θ
m
mP
I cos
2
)1(
)(
+
= (1)
(see Appendix A), where I is the radiant intensity, P is
the total optical power, m is the Lambert exponent, and
θ
is the angle to the direction of maximum power. When
the photon reaches the room surface (wall, ceiling, floor
etc.), either it is absorbed or a random new direction is
created according to a Lambertian distribution (set
m = 1). A large number of photons N
0
is tracked (up to
10
10
), and, occasionally, a photon reaches the Rx. The
optical path loss
a is calculated from the number of
received photons N
Rx
0
log10
N
N
a
Rx
−=
. (2)
It was checked that the sum of N
Rx
and all absorbed
photons is equal to N
0
. No photon is lost during the
entire simulation and the number of reflections is not
limited. During the flight of each photon, the total time
of flight is accumulated. A histogram with a resolution
of 167 ps is created for the overall time of flight
distribution h(t) from the Tx to the Rx. The channel
transfer function H(jf) is obtained from the histogram by
Tx
Rx
LOS signal
diffuse reflections
Fig. 1 Principle of ray tracing in a room.
(LOS = line of sight)

numerical Fourier transform. The cut-off frequency f
½
is
determined at |H(jf
½
)| =
√
0.5
⋅
|H(0)|
1
.
The simulation becomes faster when a large detector is
used. On the other hand, the time resolution is limited by
the detector diameter d (Fig. 2). When a light pulse from
a far source is incident, the detector signal is broadened
by
∆
t. In a diffuse IR link, the light may arrive from all
directions. When the figure
∆
t is averaged with respect
to the cosine-like detector characteristic, an overall time
resolution <
∆
t>=2d/3c is obtained where c is the speed
of light. According to the sampling theorem, the transfer
function is valid below f
max
=3c/4d. Consequently, a cut-
off near 200 MHz was observed in early simulation runs
with d = 1 m (see dashed line in Fig. 3). In order to
obtain reliable results below 1 GHz, a smaller detector
(d = 10 cm) was generally used.
The simulation results were carefully checked against
previous work. A comparison with the data of Barry et
al. [3] is shown in Fig. 3. The open circles mark their
results. The same scenario (configuration A, Table 1 in
Ref. [3]) was investigated with the ray tracing technique.
For comparison, the magnitude data in Fig. 3 were
normalised to the same Rx area. In general, the ray
tracing technique creates similar results like Barrys
approach. The results agree very well with each other,
when the simulation is stopped after 3 reflections, like in
[3] (dotted line). The complete ray tracing (full line)
creates better results, especially at low frequencies, since
the higher order reflections are properly taken into
account.
1
|H(jf)| is related to the received optical power, and the
electrical power after the photodiode scales with |H(jf)|
2
.
BASIC SIGNALS IN THE IR CHANNEL
The impulse response corresponding to the data in Fig.
3 is shown in Fig 4. It consists of a discrete, Dirac-like
pulse due to the LOS signal followed by a continuous
signal due to the diffuse reflections. Both components
are well separated from each other so that it is useful to
distinguish them in the following investigations. The
channel model used from now on is thus decomposed
into the two components h
LOS
(t) and h
diff
(t) which are
due to the LOS signal and the diffuse reflections,
respectively (see insert in Fig. 4).
THE SPHERE MODEL
The time response of the diffuse signal is very similar to
that of an integrating sphere. Some more or less
pronounced peaks with varying shape are observed
which are related to the first reflections in the room. The
time response then becomes smooth and a nearly perfect
exponential decay is observed. The exponential decay
results from the superposition of the higher order
reflections. Due to the exponential decay, an IS in an
optical transmission line is equivalent with a first order
low-pass in the electrical domain [10].
Because the corresponding transfer function of the IS is
a simple low pass, it shall now be adapted to the diffuse
IR channel to obtain an approximate channel model. The
transfer function reads
0
diff
f
f
j1
(jf)H
+
=
η
with
πτ
2
1
f
0
= (3)
where the optical power efficiency








−
=
ρ
ρ
η
~
1
~
room
Rx
A
A
(4)
is related to the path loss by a = -10·log(
η
). Note that the
leading term in (4) is the ratio of the detector area A
Rx
and to the total area of the room surface A
room
. The
average reflectivity ρ
~
is given by
∑
=
=
N
i
ii
room
A
A
1
1
~
ρρ
(5)
d
photodiode
light from
far source
Θ
∆
t
Fig. 2
The time resolution is limited by the detector size
0,1 1 10 100 1000
-122
-120
-118
-116
-114
-112
-110
magnitude response [dB]
frequency [MHz]
Fig. 3
Comparison with previous results [3] (open circles).
0 20406080100
10
5
10
6
10
7
10
8
10
9
diffuse reflections
line-of-sight signal
number of photons
time [ns]
h (t)
LOS
h (t)
diff
Fig. 4 Impulse response corresponding to the full line in
Fig.3. Inset: The channel model used in this work.

where N is the number of different areas A
i
of the room
surface with the individual reflectivities
ρ
i
. The cut-off
frequency f
0
in (3) is calculated using the decay time
ρ
τ
~
ln
><
−=
t
(6)
where <t> is the average time between two reflections in
the actual room. A simple procedure to obtain <t> for
rectangular rooms is described in Appendix B.
RESULTS ON THE DIFFUSE SIGNAL
In Fig. 5 it is shown how the properties of the diffuse IR
channel without LOS depend on
ρ
~
. For comparison,
plots according to (3) are also shown (dashed lines). A
rectangular room with uniform reflectivity
ρ
is
investigated
2
(see Fig. 6 for the scenario). Note the
logarithmic axes in Fig. 5 which were scaled for better
comparison with (3). The abscissa is multiplied with <t>
given in the figure while the ordinate is divided by
A
Rx
/A
room
.
In general, the simulation results (full lines) can be well
fitted using (3) when the same parameters are used like
in the simulation. Obviously, formula (3) provides a
good quantitative approximation both for the path loss
and for the frequency response of the diffuse IR signal.
As for the IS, significant deviations are observed only at
high frequencies.
2
No significant changes are observed, when the walls have
individual reflectivities with the same
ρ
~
.
When the reflectivity is increased, more optical power is
received. At
ρ
= 0.9, the power is 10 times larger than
for ρ = 0.5. This is explained by the increased light
accumulation in the room
3
. On the other hand, the cut-off
frequency f
½
is 1.9 MHz for
ρ
= 0.9, but it is 13 MHz for
ρ = 0.5. Apparently, the variations of the received power
and of the available bandwidth are almost inverse to
each other. This can also be shown analytically. When
the gain factor g=ρ
ρρ
ρ
~
/(1-ρ
ρρ
ρ
~
)
in (4) is multiplied with the
bandwidth f
0
in (3)
><
≈
><−
=⋅
tt
fg
ρ
ρ
ρ
ρ
~
~
ln
~
1
~
0
(6)
a nearly constant product is obtained for (1-
ρ
~
)
〈〈
1. Note
that g·f
0
still depends on
ρ
~
so that the dashed curves in
Fig. 5 do not really merge together at high frequencies.
Eq. (4) predicts a constant power distribution in the
room. This is a basic property of the IS, which is
approximately applicable to the diffuse IR signal in
rooms, too. But, of course, there are spatial variations
when the Rx is moved (typically less than 5 dB
opt
).
The variations become extraordinary large in a corridor
scenario recently introduced by Gfeller et al. [11] which
was again investigated with the ray tracing technique. As
in [11], the LOS is blocked. The path loss as a function
of the Rx position is plotted in Fig. 7. Along the corridor,
a spatial variation of more than 20 dB is observed
consistent with the measurements in [11]. Note that the
sphere model still gives a reasonable estimate for the
bandwidth in this environment. This is shown in Fig. 8
where |H
diff
| is plotted for two Rx positions in the room.
While a cut-off frequency of f
½
=12.9 MHz is found at
10 m, it is reduced to 8.8 MHz at 15 m. The estimate
according to (3) is 11.1 MHz.
SUPERPOSITION WITH THE LOS
In practical IR systems, the diffuse signal and the LOS
component may be present, simultaneously. The two
signals add at the Rx, and noticeable superposition
effects are observed. This is investigated in a scenario
3
This is a familiar phenomenon: Highly reflective walls
considerably brighten a room.
0,01 0,1 1
0,01
0,1
1
10
<t> = 8.5 ns
ρ
ρρ
ρ
= 0.3
ρ
ρρ
ρ
= 0.5
ρ
ρρ
ρ
= 0.75
ρ
ρρ
ρ
= 0.9
|H(jf)| [A
Rx
/ A
room
]
frequency [<t>
-1
]
Fig. 5 Frequency response of the diffuse signal for
different values of the wall reflectivity. The dashed
lines are theoretical curves according to Eq. (3).
z
y
x
5 m
4 m
3 m
Tx Rx
1 m 4 m
Fi
g
. 6 The scenario investi
g
ated in Fi
g
. 5.
0 5 10 15 20 2
5
60
65
70
75
80
85
sphere
model
Tx position
path loss [dB
opt
]
Rx position [m]
z
y
x
35 m
2 m
2.4 m
Tx
Rx
1 m
y
x
z
45°
25°
x
y
z
Rx Tx
m = 7
d=3 mm
Fig. 7 Path loss variation in a long corridor.

depicted in Fig. 9. The distance between the Tx and the
Rx is held fixed, and the Rx is tilted by an angle
θ
to
modify the ratio between the two signal amplitudes A
diff
and A
LOS
. A uniform reflectivity of ρ = 0.6 is assumed.
Results for different angles θ are plotted in Fig. 10.
When the Rx is directed to the ceiling (θ = 90°), |H(jf)| is
due to the diffuse signal, only. At θ = 89°, a weak LOS
signal is received having about 20 times less power than
the diffuse signal. Although the direction of the Rx is
nearly the same, the total frequency response is
markedly changed. A distinct notch is observed near
210 MHz followed by some ripple at high frequencies.
For θ = 85°, the LOS signal is lifted by a factor of 5, and
the notch is now obtained near 52 MHz. The individual
curves for |H
diff
(jf)| (dotted curve) and |H
LOS
(jf)| (dashed
curve) are also plotted in Fig. 10. Note that the notches
occur near the crossing point of these two signals. At
θ = 45°, the frequency response is mainly determined by
the LOS signal which has about 2 times more power than
the diffuse light. A nearly flat response is then obtained.
The notches are critical, when they should fall into the
transmission band. In the following it is shown that there
is a lower bound for the notch frequency f
crit
. A
diff
(f) is
used to describe the diffuse signal amplitude and the
LOS signal A
LOS
is added by taking a certain delay
∆
T
between both signals into account, which is clearly
evident in Fig. 4. The total amplitude reads
]2cos[)(2)(
||
22
diffLOSdiffLOSdiff
LOSdiff
TfAfAAfA
HH
Φ+∆++
=+
π
. (7)
The second term
Φ
diff
= -arctan(f/f
0
) in the cosine
argument arises from the low pass behaviour of the
diffuse signal. A zero sum signal requires both identical
amplitudes and opposite phases of the two signals. It is
relatively unlikely that both conditions are fulfilled,
simultaneously. But also when the amplitudes are about
the same, a deep notch is created when the phase
condition
)/arctan()12(2
0
ffnTf
critcrit
+−=∆
π
π
(8)
is fulfilled, where n is an integer. This is a transcendent
equation depending both on ∆T and f
0
. In a worse case
∆T = <t> can be assumed. The lowest possible notch
frequency (n = 1) then varies from 0.5·<t>
-1
to 0.75·<t>
-1
.
0,01 0,1 1 10
0,01
0,1
1
10
sphere model
Rx at 10 m
Rx at 15 m
<t> = 7.1 ns
|H
diff
(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
Fig. 8 Frequency response at two positions in the corridor.
The dotted line indicates the theoretical curve.
012345
0,01
0,1
1
<t> = 9.6 ns
θ
θθ
θ = 90°
A
LOS
= 0
|H(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
012345
0,01
0,1
1
θ
θθ
θ = 89°
A
LOS
/A
diff
= 0.043
<t> = 9.6 ns
|H(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
012345
0,01
0,1
1
θ
θθ
θ = 85°
A
LOS
/A
diff
= 0.22
<t> = 9.6 ns
|H(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
012345
0,01
0,1
1
θ
θθ
θ = 45°
A
LOS
/A
diff
= 2.13
<t> = 9.6 ns
|H(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
Fig. 10 Frequency response for different angles θ
between the transmitter and the receiver. The dashed
and dotted lines indicate the LOS signal and the diffuse
component, respectively. The amplitude ratios of the
two components are also given.
z
y
1 m 5 m
Tx
Rx
1 m
3 m
l = 6 m
m = 3
θ
θθ
θ
w = 5m
Fig. 9 The scenario investigated in Fig. 10.

TRACKED DIRECTED LINKS
It is well known, that the IR channel response can be
markedly improved with tracked directed links. High
speed transmissions at 140 Mbit/s [12] or even at
1 Gbit/s [13] have been reported. The transmitter power
can be lowered by orders of magnitude, and a bandwidth
limited by the Tx and Rx components is available. On
the other hand, these links are based on the LOS and
they are susceptible to shadowing and blocking. In the
following, the ray tracing is used to study the
improvements of the IR channel in a directed link.
Two typical scenarios shown in Fig. 11 are investigated.
An average reflectivity of 0.62 was assumed. In scenario
1, which is referred to as spot diffusing with directed
links [12], a collimated beam is sent to the ceiling where
it is diffusely reflected. The spot is observed by the Rx
which is aligned with respect to the LOS. For the Rx, a
“sharp-cut” field of view (FOV) was assumed. A photon
is only accepted, when the angle between the final
direction of flight and the direction of maximum Rx
sensitivity is smaller than the FOV. In scenario 2, the
spot is replaced by a base station which sends a
generalised Lambertian Tx beam to the Rx. Scenario 2
can be compared with the adaptive array system in [14].
In Fig. 12 the results for scenario 1 are plotted for
different FOV angles at the Rx. At a FOV of 90° the Rx
signal is mainly due to the diffuse component. When the
FOV is reduced, the diffuse signal is suppressed while
the LOS component remains unchanged. At a FOV of
5°, the response becomes almost flat.
For scenario 2 similar response data were obtained so
that only the path loss (2) and the delay spread
σ
∑
∑
=
=
−
=
M
i
i
M
i
ii
th
tht
0
2
0
22
)(
)()(
µ
σ
with
∑
∑
=
=
=
M
i
i
M
i
ii
th
tht
0
2
0
2
)(
)(
µ
(9)
were extracted from the data. M is the number of time
slots in the histogram. The results are depicted in
Fig. 13. Both the path loss and the delay spread are
reduced with a narrow Tx beam.
Assuming a 1 Gbit/s IR system, a FOV below 15° is
required in scenario 1. Also a relatively precise tracking
system is needed. In scenario 2, a Tx cone with m = 4
(half width ≈ 30°) and a FOV of 30° at the Rx will be
sufficient to obtain a flat response. These demands
increase when the diffuse signal is stronger.
CONCLUSIONS
An analytic model for the diffuse IR indoor channel was
proposed based on the integrating sphere. The model
provides a quick rule of thumb for the path loss and for
the bandwidth of the diffuse IR signal in rectangular
rooms.
The model was verified with a new ray tracing
simulation technique which overcomes the limited
number of reflections in previous works. A characteristic
gain times bandwidth product of the diffuse IR indoor
channel was revealed.
z
y
1 m
4 m
Tx
Rx
0.5 m
3 m
5 m
w = 4 m
FOV
scenario 2
scenario 1
Fig. 11
The two scenarios investigated in Figs. 12 and 13
(floor: ρ = 0.4, ceiling: ρ = 0.9, wall: ρ = 0.6).
0 20406080
25
30
35
40
m=45
m=7
m=1.5
m=1 (scenario 1)
optical path loss [dB]
FOV [°]
0 102030405060708090
10
-4
10
-3
10
-2
10
-1
10
0
m=45
m=7
m=1.5
m=1
delay spread [ns]
FOV [°]
Fig. 13 Path loss (top) and delay spread (bottom) in
scenario 2 (Fig. 11) as a function of the FOV in the Rx.
The Lambert exponent m of the Tx beam is indicated on
the curves. The open symbols refer to scenario 1.
0,01 0,1 1 10
1
FOV = 20°
FOV = 40°
FOV = 5°
FOV = 90°
<t> = 8.5 ns
|H(jf)| [A
Rx
/A
room
]
frequency [<t>
-1
]
Fig. 12 Frequency response for different FOV angles at
the Rx in scenario 1.

When the diffuse component is accompanied by a line-
of-sight signal, notches may appear in the frequency
response which are critical for data transmissions. A
lower bound for the notch frequency was derived.
Finally, remarkable improvements both of the path loss
and of the delay spread can be obtained with tracked
directed links. Quantitative data for these improvements
in a specific indoor environment were reported.
ACKNOWLEDGEMENTS
The authors wish to thank Dr. Gfeller (IBM Zurich) for a
fruitful discussion on the different simulation techniques
and Dr. Hermes (HHI Berlin) for his comments on the
computer program. This work was supported in the
ATMmobil project of the German ministry of research
and education under contract No. 01 BK 611/3.
APPENDIX A: RANDOM DIRECTION
GENERATOR
The random generator for the transmitter and for the
diffuse reflections is similar to Ref. [10]. When
α
,
β
and
γ
are three independent random numbers equally
distributed over [0, 1], the new direction is
π
α
α
φ
2)( = and )arccos()(
1+
=
m
ββθ
(10)
where m is the Lambert exponent (m = 1 for reflections).
Number
γ
is only used to describe absorption at surfaces.
When γ is larger than ρ, the random path is stopped.
APPENDIX B: AVERAGE TIME BEWTEEN
TWO REFLECTIONS IN ROOMS
The average time between two reflections <t> is a basic
parameter in the IS model. For the sphere, it is calculated
in [10]. In an arbitrary room, however, the time of flight
distribution depends on the position on the surface.
Instead of analytical calculations, a numerical approach
based on the ray tracing technique is used here. A single
photon is sent to a random flight through an rectangular
room in which the surface reflectivity is unity. During its
flight, a histogram is created for the time of flight
between two reflections. After about 10
8
reflections the
normalised distribution converges. The various positions
at the room surface have then been reached, frequently,
and a numerical estimate for the time of flight
distribution
χ
(t) is obtained. As an example, Fig. 14 (top)
displays the distribution for a rectangular 3x4x5 m³
room. Note that the distribution for the sphere is a linear
function which stops at D/c. The average time between
two reflections <t> is given by
∑
=
>=<
M
i
ii
ttt
1
)(
χ
(11)
where i is the index in the histogram. In order to allow a
quick estimate of <t> for a wide variety of rectangular
rooms, the diagram in Fig. 14 (bottom) was prepared.
Normalised values are used based on the room height h.
For example, when h = 3 m, width w = 4 m and length
l = 6 m, the curve for w/h = 4/3 is used and a value of 2.9
ns/m is obtained at l/h = 2. Hence <t> reads
3m ⋅2.9 ns/m = 8.7 ns. This value is inserted in (6) and
(3) to estimate the cut-off frequency for the actual room.
REFERENCES
[1] F.R. Gfeller and U.H. Bapst “Wireless in-house data
communication via diffuse infrared radiation”, Proc. IEE,
67, 11 (1979), pp. 1474-1486
[2] J.M. Kahn, J.R. Barry “Wireless Infrared Communica-
tion”, Proc. IEEE, Vol.
58, 1997, pp.
265 -298
[3] J.R. Barry, J.M. Kahn, W.J. Krause, E.A. Lee and D.G.
Messerschmidt “Simulation of the multipath impulse
response for indoor wireless optical channels”, IEEE J.
sel. areas in comm., Vol.
11, No. 3, 1993, pp. 367-378
[4] C.R. Lomba, R.T. Valadas and A.M. deOliveira Duarte
“Propagation losses and impulse response of the indoor
optical channel: A simulation package”, Proc. Int. Zurich
Sem. 1994, pp. 285-297
[5] M. Abtahi and H. Hashemi “Simulation of indoor
propagation at Infrared frequencies in furnished office
environments”, Proc. 6
th
IEEE PIMRC 1995, pp. 306-310
[6] M.R. Pakravan and M. Kaverhad “Design Considerations
for broadband indoor infrared wireless communication
systems”, Int. Journ. of Wireless Information Networks,
Vol.
2, No. 4 (1995), pp. 223-237
[7] R. Perez-Jimenez, V.M. Melian and M.J. Betancor
“Analysis of multipath impulse response of diffuse and
quasi-diffuse optical links for IR-WLAN”, Proc. 14
th
Annual Joint Conf. Of the IEEE Computer and
Communications Societies 1995, pp. 924-930
[8] J.B. Carruthers and J.M. Kahn "Modeling of Nondirected
Wireless Infrared Channels", IEEE Trans. on Commun.,
vol.
45
, no. 10 (1997), pp. 1260-1268
[9] V. Pohl, V. Jungnickel, R. Hentges and C. von Helmolt
“Integrating Sphere Diffuser for Wireless Infrared
Communication", Proc. IEE Colloquim "Optical Wireless
Communications", London, June 22, 1999, pp.4/1-4/6
0 5 10 15 20
0,0
5,0x10
7
1,0x10
8
l = 5 m ; w = 4 m ; h = 3 m
<t> = 8.56 ns
σ
σσ
σ = 5.03 ns
distribution density
time [ns]
012345678910
2,0
2,5
3,0
3,5
4,0
4,5
5,0
w
l
h
w/h=3
w/h=2
w/h=4/3
w/h=2/3
w/h=1
<t>/h [ns/m]
l/h
Fig. 14 Top: Distribution of the time of flight between two
reflections <t> in a rectangular room. Bottom: This
diagram allows a quick estimate for <t> in rectangular
rooms. The dot refers to the example in the text.

[10] V. Pohl, V. Jungnickel, R. Hentges and C. von Helmolt
“Integrating Sphere Diffuser for Wireless Infrared
Communication", accepted for publication in IEE Proc.
Opt., Special issue on Optical Wireless Communications,
Aug. 2000
[11] F. Gfeller and W. Hirt “Advanced Infrared (AIr):
Physical Layer for Reliable Transmission and Medium
Access”, preprint Int. Zurich Seminar Feb. 15, 2000
[12] V. Jungnickel, C. v. Helmolt and U. Krüger “Broadband
wireless infrared LAN architecture compatible with the
ethernet protocol”, Electronics Letters, vol. 34 (1998),
pp. 2371-2372
[13] D.R. Wisely: “A 1 Gbit/s optical wireless tracked
architecture for ATM delivery”, IEE Coll. Opt. Free
Space Com. Links, UK, Feb. 1996, pp.14/1-7
[14] V. Jungnickel, C. von Helmolt, T. Haustein, U. Krüger
"Wireless Infrared Communication using Adaptive
Arrays", Proc. 4th ACTS Mobile Communications
Summit, Sorrento, Italy, June 8-11, 1999, pp. 979-984