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Abstract—The propagation characteristics of indoor
multi-floor environments have been studied extensively and
empirical models for many scenarios are available. These studies
usually do not concern about stair structures. In this paper we
study radio propagation in four typical stairwells through
measurement at two frequencies (2.4 GHz and 5.8 GHz). Values of
path loss exponent n have been derived for vertical and horizontal
polarizations. These n-values for stairwells are found to be higher
than the n-values for multi-floor environments. We also propose a
new path loss model based on the so-called “accumulative
distance” the receiver has traveled, in addition to the conventional
separation distance between transmitting and receiving antennas.
The new path loss model has lower n values and, most
importantly, smaller standard deviation and can thus be
considered a better model fitting the measurement data. The
results in this study can be useful for designers of small cell
wireless communications system such as pico- and femto-cells.
Index Terms—Indoor propagation, path loss model, stairwell.
I. INTRODUCTION
ROPAGATION modeling is important for successful
planning and implementation of wireless communications
systems [1]. Propagation models are formulas for calculating
large scale path loss (or gain) and are usually established
empirically based on measurements [2]. Since path loss is
dependent mainly on environment, frequency, and height of
antennas, a propagation model can only be applied to sites
similar to the one where the model is developed. The evolution
of wireless systems in recent years tends to have reduced cell
sizes, increased operation frequencies and wider bandwidth,
and lowered height of base station antennas. These trends
indicate that some existing models need to be revised and/or
new models have to be established to accommodate the new
challenges.
A propagation model expresses the mean path loss (or gain)
Manuscript received February 20, 2012; revised October 1, 2013; accepted
November 27, 2013. This research was supported in part by NSF under Grant
ECCS08-24095.
S. Y. Lim is with the University of Nottingham Malaysia Campus, and she is an adjunct faculty with the Hawaii Center for Advanced Communications,
College of Engineering, University of Hawaii at Manoa, Honolulu, HI 96822
USA. (email: Grace.Lim@nottingham.edu.my). Z. Yun and M. F. Iskander are with the Hawaii Center for Advanced
Communications, College of Engineering, University of Hawaii at Manoa,
Honolulu, HI 96822 USA (emails: zyun@hawaii.edu, magdy@hawaii.edu).
as a function of the separation distance between the
transmitting (Tx) and receiving (Rx) antennas. The simplest
propagation model is for free space where the path gain is a
function inversely proportional to the square of the separation
distance between Rx and Tx. For other propagation
environments, the inverse-square law has to be modified due to
the multipath effect. In general, a propagation model can be
expressed as a function of (path gain) or (path loss)
where is the path-loss exponent. When expressed in dB, the
path loss is a linear function of and , which indicates how
fast the path gain drops (or the path loss increases). Based on
many measurements, it is well known that path loss can be
treated as a random variable distributed log-normally about the
values predicted by the mean path loss [3].
Typical values of n for various indoor and outdoor
propagation environments as reported in [3] ranges from 2, that
of free space to a value of between 3 to 5 for shadowed urban
cellular radio, and to a value of between 4 to 6 for obstructed in
building. Specifically, for indoor environment, the typical
n-values for a wide range of locations in many buildings across
different floors are reported in [4]. The n-values vary in the
range of 2 to 6 for propagation on the same floor as well as
across-floors. It was observed that when signal propagates
across multiple floors the value of n increases as the number of
floors increases. For instance, n has a value of 4.19 for
propagation through one floor; and this value increases to 5.04
and 5.22 for propagation through two and three floors
respectively.
The purpose of this study is to propose a new path loss model
for indoor stairwell, which is very important for emergency
applications (law enforcement and fire-fighting purposes) as
well as to help develop effective indoor communications
systems. Results from this study are not particularly intended
for base station location determination.
In this paper, we have examined four types of stairwells that
are often encountered in two general categories of “stairwell
around a square well” and “dog-leg stairwell”, on the campus of
University of Hawaii at Manoa (UH). A series of measurement
campaigns were conducted at two frequencies, i.e., 2.4 GHz
and 5.8 GHz which are common in the deployment of wireless
local area network (WLAN).
Previous studies regarding propagation in stairwells [5]-[7]
have served different purposes, such as analyzing the antennas,
frequency-selected surfaces, absorbers, and radio wave
propagation. In [5], a hybrid approach that combines ray tracing
Propagation Measurement and Modeling for
Indoor Stairwells at 2.4 and 5.8 GHz
Soo Yong Lim, Member, IEEE, Zhengqing Yun, Member, IEEE, and Magdy F. Iskander, Fellow, IEEE
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method with a periodic moment method was developed to
examine the wave propagation, penetration, and scattering by
periodic structures inside a building. In [6], propagation
measurements were reported for a stairwell structure, and a
three-dimensional propagation model was proposed and
validated by the measurement results. Our group has
investigated the propagation characteristics in one multi-floor
stairwell through measurement and simulation [7]. An
image-based ray tracing scheme was used to identify the
fundamental propagation mechanisms such as reflection from
stairwell walls and transmission through the stair steps. We
found that the stairwell walls in the studied case do not reflect
much of the incoming energy but the transmission through the
stairs has significant contributions to the total received power.
In [7], the convergence of ray tracing results was reached by
continually including additional rays until the path loss result
does not change appreciably (within 1 to 5%).
The research objective in this paper is different from the
work in [5-7]: we will establish the path loss model in stairwells
based on extensive measurements at 2.4 GHz and 5.8 GHz with
various antenna polarizations. Thus, in this paper, only
measured results are reported and readers are referred to [7-9]
for more details regarding our measurement procedure and
associated accuracy comparisons with ray tracing and
computational modeling techniques. We also propose a path
loss model using the so-called accumulative distance traveled
by Rx instead of the conventional separation distance between
Tx and Rx. The new model has lower standard deviations and is
thus a better model compared with the conventional separation
distance model.
The path loss models developed in this paper can be useful in
the design of small cells such as pico-cells and the recently
proposed femto-cells which have great potential in increasing
the capacity and in reducing the operational cost for wireless
communication systems [10].
II. STAIRWELL STRUCTURES
There are six general categories of stairwell structures
according to a building handbook [11]. We found two of them,
“stairwell around a square well” and “dog-leg stairwell,” are
common in office and/or lab buildings on UH Manoa Campus.
Three dog-leg stairwells and one stairwell around a square well
are selected for the measurement campaigns based on their
accessibility and convenience. They are located inside the
Pacific Ocean Science & Technology (POST) Building, the
Hamilton Library, the Marine Sciences Building (MSB), and
the Holmes Hall. We label these stairwells as PO, HA, MS, and
HL. The top view of a dog-leg stairwell structure is depicted in
Fig. 1. All three dog-leg stairwells have the similar structure
with different number of stair steps and sizes. For the stairwell
around a square well, Fig. 2 shows its top view. All the
dimensions of the stairwells are listed in Table I.
Fig. 1. Top view of the dog-leg stairwell structure.
Fig. 2. Top view of the stairwell around a square well structure. Note that
Sections S1, S2, S3, and S4 form the first round of stairs; and S5 is right above
S1, S6 above S2, S7 above S3, and S8 above S4.
The modeling of the indoor stairwells in this work
incorporates a series of measurement campaigns conducted at
four different indoor stairwells for various antennas
polarizations over a period of three years. The traits of these
stairwells are recorded and summarized in Table I. All the stairs
have several sections, as indicted in Figs. 1 and 2. Each section
may have different number of steps. In Table II, the number of
steps for all four stairwells is listed. Since these stairwells are
Rx
W
W
L
Tx
G
a
p
Tread
Riser
Soffit
S2, S4
L G W W
Rx
Tx (MS)
Tx (PO)
Tx (HA)
S1
S5
S3
S7
S1, S3,
S5
Sections of the
staircases are marked
S1, S2, S3, S4, …, upward started from
ground. Note that S3
is right above S1, S4 above S2, and S5
above S3.
S2, S6
S4, S8
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common and can be found easily in modern offices and
buildings, the path loss model for indoor stairwell derived from
this work is beneficial and may be considered for broader
applications in a variety of similar stairwell structures. Fig. 3
shows the photos of two common stairwells.
TABLE I
THE TRAITS OF EACH STAIRWELL
Stairwell W (m) G (m) L (m) T (m) R (m)
PO 1.10 0.20 1.53 0.27 0.16
HA 1.22 0.15 1.30 0.28 0.18
MS 1.63 0 2.00 0.31 0.18
HL 1.89 0.78 1.89 0.26 0.18
Fig. 3. Two stairwells: dog-leg (left, HL) and stairwell around a square (right,
HO).
In Fig. 3, stair rails of two stairwells are shown. Although the
materials of the stair rails could influence the measurement
results, their effects should be less important in comparison to
the large appearance of the surrounding walls, the stair steps,
and ceilings of the stairwell since the main reflection and
transmission occur there. From our observations, most stair
steps are made of reinforced concrete, and the stairwell walls
are composed of gypsum panels/concrete. As for the
ceilings/floors, they are mostly made of concrete in modern
offices and buildings. This similarity of the structures and
materials of stairwells in modern office building ensures that
the proposed path loss models may be applied to many, if not
all, of the indoor stairwell propagation environments in modern
buildings (with similar stairwell structures to the two types
discussed in this paper).
TABLE II
NUMBER OF STAIR STEPS FOR EACH SECTION OF STAIRWELL
Stairwell Section
S1 S2 S3 S4 S5 S6 S7 S8
PO 9 10 11 12 12 12 12 -
HA 10 10 10 10 10 - - -
MS 8 12 12 12 12 - - -
HL 10 3 5 3 5 3 10 10
III. MEASUREMENT SYSTEM
We use the same data acquisition system in [7] to collect
measurement data with slight modifications. A low noise
amplifier (LNA) of 10 dB gain is added to the front end of the
receiver for extending the measurement dynamic range. The
operating frequency of this LNA is 20-7000 MHz.
At 2.4 GHz, we employed the 8 dBi high performance
omnidirectional wireless LAN antennas (HyperLink
Technologies HGV-2409U); and at 5.8 GHz, we utilized the 8
dBi ISM/UNII band omnidirectional wireless LAN antenna
(HyperLink Technologies HG5808U). For these antennas
manufactured by the HyperLink Technologies, their radiation
patterns are obtained from the accompanying datasheets. At 2.4
GHz, the vertical beam width is 15˚ and the horizontal beam
width is 360˚; while at 5.8 GHz, the vertical beam width is 16˚
and the horizontal beam width is 360˚. Fig. 4 shows the block
diagram of our measurement system.
Fig. 4. Block diagram of the measurement system.
Two sets of omnidirectional dipole antennas at 2.4 GHz have
been used. There was no specific reason for using different
antennas at 2.4 GHz and the records of the two sets of
omnidirectional antennas at 2.4 GHz simply reflected the
historical aspects of the measurement campaigns. Since the
results are presented in terms of path loss, the different sets of
antennas do not affect the results as they are independent of the
antennas gains. In other words, path loss is normalized with
respect to the incident power. Hence, the use of two different
omnidirectional antennas in the 2.4 GHz measurements will
have no effect on the developed models. As for 5.8 GHz
measurements, only one set of dipole antennas is used. Table III
summarizes the various antennas polarizations and the heights
of Tx and Rx.
TABLE III
ANTENNA POLARIZATION AND TX & RX HEIGHT
Stairwell Polarization Height (m)
Tx Rx
PO
VV 1.63 1.33
HH 1.53 1.23
VH 1.63 1.23
HH (Set II) 1.57 1.63
HA VV 1.65 1.65
HH 1.65 1.55
MS VV 1.78 1.65
HH 1.57 1.60
HL VV 1.63 1.33
HH 1.53 1.23
Three different transmit/receive antenna polarizations are
considered in the measurements: vertical/vertical (VV),
Rx
Rx
Antenn
a
Tx Tx Antenna
Signal
Generator PA
LNA
10
dB
Spectrum
Analyzer Laptop
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horizontal/horizontal (HH), and vertical/horizontal (VH). From
the work done in [7], we have already found that the effect of
cross-polarization (VH) is only significant in the first section of
the stair. For higher stair sections, depolarization occurs due to
multiple reflections and leads to all three Tx/Rx polarizations to
produce similar received power. Consequently, in this work,
the primary attentions are only given to VV and HH
polarizations at 2.4 and 5.8 GHz.
IV. MEASUREMENT RESULTS
Different techniques exist for measuring the local mean
signal strength, such as averaging the power measured in an
area, along a line segment, and along a circular line [12-13]. In
our measurements, the Tx antenna is fixed at one location and
the Rx antenna is rotated 360 around a supporting post in a
circular track. The Rx antenna is mounted on a wooden
horizontal arm which is taped on a plastic post. The length of
the wooden arm is about 2.5 wavelengths at 2.4 GHz.
On each stair step, the Rx antenna will be rotated around the
post an entire revolution while 550 sampling signals are
recorded over a 30-second period. These sampling signals are
then averaged offline to obtain the mean power. Three typical
received signals taken at three different steps of a stair are
shown in Fig. 5.
Fig. 5. Typical received signals at different steps when the Rx antenna rotates a
complete revolution.
The path gain results for four stairwells at 2.4 GHz are shown
in Fig. 6 (VV) and Fig. 7 (HH). As for the results for 5.8 GHz,
we only have three stairwells measured (we were unable to
work on the HA stairwell due to safety reasons) and the results
are plotted in Fig. 8 and Fig. 9. Note that the path gain plotted in
Figs. 6 to 13 are all relative to the first stair step. The absolute
path loss should include the path loss from Tx to the first step
(see next two sections for more details).
From Fig. 6 and Fig. 7, we can observe that at 2.4 GHz, there
is a clear power drop at the junctions between the consecutive
stair sections regardless of the antenna polarizations, whether
VV or HH polarizations. The large power drop is especially
obvious at the first junction (around stair step 10 for PO, HA,
and MS stairwells) because in every measurement, line-of-sight
(LoS) scenario exists for the entire first section of the stairwells.
When Rx turns at the junction to proceed to the next section of
the stair, the LoS ray is lost and a significant power drop
happens. For other junctions, the power drop is due to multiple
reflections and transmissions as explained in greater detail in
[7].
Fig. 6. Path gain at four stairwells for VV polarization at 2.4 GHz.
Fig. 7. Path gain at four stairwells for HH polarization at 2.4 GHz.
At the frequency of 5.8 GHz, the power drop phenomenon at
junctions is not obvious for VV polarization as shown in Fig. 8.
However, for HH-polarization the power-drop phenomenon
still exists, as shown in Fig. 9. Figs. 10 and 11 compare the path
loss for the PO stairwell at two different polarizations VV and
HH. Fig. 10 is for measurement at 2.4 GHz while Fig. 11 is for
measurement at 5.8 GHz. As may be noted from these figures
that, while the VV and HH polarizations are expected to have
different path loss exponents (as will be explained later), the
difference in the values of n is particularly significant at 5.8
GHz as shown in Fig. 11. It is particularly interesting to note in
Fig. 11 that the path loss for the HH polarization is less than that
for the VV polarization. This can be possibly explained in terms
of the orientation of the electric field with respect to the
stairwell structure. For the HH polarization, the electric field is
parallel to the stair structure hence stronger reflection and
0 100 200 300 400 500 600-80
-60
-40
-20
0
Sampling Points
Re
ce
ive
d P
ow
er/
dB
m
Step 2
Step 20
Step 50
0 10 20 30 40 50 60-60
-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
PO Stairwell
HA stairwell
MS Stairwell
HL Stairwell
0 10 20 30 40 50 60-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
PO Stairwell
HA stairwell
MS Stairwell
HL Stairwell
Path
Gain
(dB
) P
ath
Gain
(dB
)
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diffraction effects are expected. This resulted in a reduced path
loss (or increased path gain) value at 5.8 GHz. Similar effect
but at a lesser magnitude may also be observed in Fig. 10 at 2.4
GHz.
Fig. 8. Path gain at three stairwells for VV polarization at 5.8 GHz.
Fig. 9. Path gain at three stairwells for HH polarization at 5.8 GHz.
Fig 10. Path gain for PO stairwell at 2.4 GHz.
Fig. 11. Path gain for PO stairwell at 5.8 GHz.
V. VALUES OF PATH LOSS EXPONENT
In this section we extract the values of path loss exponent n
for each measurement. Path loss is an indication of power loss
in the channel [3]:
(1)
where is the transmitted power; is the received power
which is proportional to and is the separation distance
between Tx and Rx and is the path loss exponent. Note that
path gain is the negative of .
It is well understood that the mean power predicted by (1) is
a random variable, which can be characterized by adding an
extra term, , a log-normal distribution for both outdoor and
indoor propagation environments. Thus, modification can be
made to equation (1) to obtain equation (2), as shown below:
(2)
where is the mean path loss/gain in dB and represents
the log-normal distribution which has zero mean and is thus
solely determined by its deviation ( ). The mean path loss/gain
can be explicitly expressed in terms of a reference path
loss/gain and the distance to the source ( ). Thus, (2)
becomes:
(3)
where is the reference path loss at a distance from
Tx.
To calculate the values, we adapt a method as follows. We
first assume the -values are between 1 and 15, with an interval
of 0.01. Then we search the best n-values by minimizing the
standard deviation (dB) (which is different from in )
between the measured path loss and the one predicted by (2).
These results are shown in Table IV.
0 10 20 30 40 50 60-70
-60
-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
PO Stairwell
MS Stairwell
HL Stairwell
0 10 20 30 40 50 60-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
PO Stairwell
MS Stairwell
HL Stairwell
0 10 20 30 40 50 60 70-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
VV Polarization
HH Polarization
0 10 20 30 40 50-60
-50
-40
-30
-20
-10
0
10
Stair Steps: From the Ground Up
Pa
th L
oss (
dB
)
VV Polarization
HH Polarization
Path
Gain
(dB
)
Path
Gain
(dB
) P
ath
Gain
(dB
) P
ath
Gain
(dB
)
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TABLE IV
PATH LOSS EXPONENT VALUES
Freq. Stairwell/Pol Path Loss
Exponent
2.4
GH
z
1) HL/VV 8.93 7.23
2) HL/HH 7.48 6.39
3) PO/VV 9.64 7.62
4) PO/HH 8.57 5.83
5) PO/VH 7.77 5.82
6) HA/VV 8.76 5.16
7) HA/HH 7.62 5.77
8) MS/VV 8.17 5.06
9) MS/HH 7.33 4.37
10) PO/HH (II) 8.75 5.66
Average 8.30 5.89
5.8
GH
z
11) HL/VV 10.12 6.28
12) HL/HH 7.49 6.64
13) PO/VV 12.94 9.59
14) PO/HH 8.74 6.63
15) MS/VV 10.96 7.72
16) MS/HH 8.16 5.88
Average 9.74 7.12
From Table IV, we observe that the n-values for stairwells
fall in the range between 7 to 10 at 2.4 GHz and 7 to 13 at 5.8
GHz which are significantly higher than the values reported in
the literature for various propagation environments (see Section
I). Fig. 12 shows the measured path gain and its linear fit as a
function of separation distance between Tx an Rx antennas for
VV-polarization at MS stairwell at 2.4 GHz. Comparing with
Fig. 6, it can be seen that path gain/loss has different apperances
when plotted as function of stair steps and function of
separation distances. It is obvious that when plotted as a
function of separation distance, path gain/loss varies about the
predicted more significantly than plotted as a function of stair
steps.
Fig. 12. Measured and fitted path gain for MS stairwell at 2.4 GHz with
VV-polarization
This observation prompts us to introduce the accumulative or
walking distance which is the distance traveled by the Rx
antenna and is proportional to the number of steps. This
walking distance concept has been used for propagation
modeling for indoor bent corridors and outdoor cross roads
where the total distance is the sum of the distances of corridor
or road sections. Using this walking distance the n-values are
recalculated for all measurement cases and the results are
shown in Table V where the results using separation distance
are also listed for comparison. It can be seen from Table V that
the -values are about 35% (5.39/8.30) and 34% (6.42/9.74) of
the values using separation distances for 2.4 GHz and 5.8 GHz,
respectively.
Fig. 13. Measured and fitted path gain for MS stairwell at 2.4 GHz with
VV-polarization: walking distance being used.
In Fig. 13, the measured and modeled path gains are plotted
as a function of walking distance. Comparison with Fig. 12
shows that the overall variation of path gain around the
modeled is less severe than the variation using separation
distance. This fact is clear because the standard deviation of
the walking distance model is smaller, as shown in Table V. It
can be seen that the average standard deviation values drop to
56% (from 5.89 to 3.29 dB) and 40% (from 7.12 to 2.86) of the
values when separation distance is used for 2.4 GHz and 5.8
GHz, respectively. Note that in Tables V, VI and VII, “S. Dist.”
and “W. Dist.” represent separation and walking distance,
respectively.
TABLE V
PATH LOSS EXPONENT: SEPARATION VS. WALKING DISTANCE
Freq. Stairwell/
Pol
-Values
S. Dist. W. Dist. S. Dist. W. Dist.
2.4
GH
z
HL/VV 8.93 5.75 7.23 3.94
HL/HH 7.48 4.83 6.39 3.71
PO/VV 9.64 5.79 7.62 3.22
PO/HH 8.57 4.97 5.83 2.20
PO/VH 7.77 4.62 5.82 2.28
HA/VV 8.76 5.73 5.16 4.21
HA/HH 7.62 5.01 5.77 4.80
MS/VV 8.17 6.53 5.06 3.25
MS/HH 7.33 5.82 4.37 3.20
PO/HH (II) 8.75 4.83 5.66 2.13
Average 8.30 5.39 5.89 3.29
5.8
GH
z
HL/VV 10.12 6.36 6.28 2.72
HL/HH 7.49 4.89 6.64 3.66
PO/VV 12.94 7.45 9.59 2.84
PO/HH 8.74 5.06 6.63 2.08
MS/VV 10.96 8.58 7.72 1.77
MS/HH 8.16 6.16 5.88 4.11
Average 9.74 6.42 7.12 2.86
5 10-60
-50
-40
-30
-20
-10
0
10
Separation Distance (m)
Path
Loss (
dB
)
Measurement
Fitted
5 10 15 20-60
-50
-40
-30
-20
-10
0
10
Walking Distance (m)P
ath
Loss (
dB
)
Measurement
Fitted
Path
Gain
(dB
)
Path
Gain
(dB
)
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We can see from Table V that the path loss exponent n
calculated with walking distance are lower than those given
with separation distance as the former distance is always
greater than or equal to the latter for a stairwell. As for the
log-normal distribution of path loss about its mean, i.e., , we
calculate the standard deviation of for the four stairwells.
These results are presented in Table VI, for both VV and HH
polarizations.
TABLE VI
-VALUES FOR 2.4 GHZ AND 5.8 GHZ
Freq. Pol. Stairwell (dB)
S. Dist. W. Dist.
2.4 GHz
VV
PO 11.62 5.32
HA 1.00 7.08
MS 6.24 12.73
HL 9.28 2.04
HH
PO 3.57 2.63
HA 4.10 5.08
MS 1.00 5.65
HL 9.42 4.25
5.8 GHz
VV
PO 13.84 4.80
MS 2.66 3.29
HL 10.87 3.15
HH
PO 2.83 33.077
MS 12.31 2.20
HL 1.83 1.00
The log-normal distribution describes the random shadowing
effects, which occur over a large number of measurement
locations that have the same transmitter-receiver separation. To
meet the criteria of a large number of measurement locations,
we have further combined all the measured results into two
large groups for VV and HH polarizations at 2.4 and 5.8 GHz
respectively instead of calculating the values of each
individual stairwell (as shown earlier in Table VI), and the
results are plotted in Figs. 14 and 15, and also shown in Table
VII.
Fig. 14. Measured and modeled distribution of the excessive mean path loss for
VV polarization at 2.4 GHz: Separation Distance.
Fig. 15. Measured and modeled distribution of the excessive mean path loss for
VV polarization at 2.4 GHz: Walking Distance.
In Figs. 14 and 15, we plot the log-normal distribution for
measured path loss together with the theoretic predictions. It is
evident that walking distance gives rise to a narrower width of
the Gaussian curve and a better fit between measurement and
theory. Keeping in mind the role a stairwell plays in emergency
situations, accuracy of the developed models is of prime
importance. The fact that the developed models may be related
to those based on the displacement/separation distance is
recognized and yet, it is a worthwhile attempt to extend the
concept of accumulative/walking distance to improve the
accuracy of the developed stairwell propagation models.
It should be noted from Fig. 13 that the ‘walking distance’
model matches the first section of stairs very well and varying
accuracy can be observed in other sections. But the overall
accuracy of the ‘walking distance’ model is better than the
‘separation distance’ model, as evidenced by the smaller values
of in Table V of the walking distance model
VI. EMPIRICAL PATH LOSS MODEL FOR INDOOR STAIRWELLS
Based on the measurement and modeling results, we derive a
path loss model for indoor stairwells characterized by the -
and -values in (3). These values are the average of the four
stairwells and are presented in Table VII.
TABLE VII
- and -VALUES FOR 2.4 GHZ AND 5.8 GHZ
Freq.
(GHz) Pol.
(dB)
S. Dist. W. Dist. S. Dist. W. Dist.
2.4
VV 8.88 5.95 5.72 3.89
HH 7.95 5.15 4.67 3.25
Average 8.30 5.39 5.20 3.57
5.8
VV 11.34 7.46 6.23 2.11
HH 8.13 5.37 2.53 1.64
Average 9.74 6.42 4.38 1.88
It can be seen from Table VII that the standard deviation
drops when walking distance is used for modeling the path loss.
The average drop is about 33% to 70%. This significant
decrease of the -values again shows that using walking
-20 -10 0 10 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
x (dB)
Pro
ba
bili
ty
Measurement
Gaussian Distribution
-20 -10 0 10 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
x (dB)
Pro
ba
bili
ty
Measurement
Gaussian Distribution
0018-926X (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TAP.2014.2336258, IEEE Transactions on Antennas and Propagation
AP1305-0701.R1
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distance has advantages over the separation distance in that the
predicted path loss has smaller variations.
The developed path loss models represent an important
contribution for designing effective wireless communications
and emergency systems in stairwell. The developed models,
however, are based on 2.4 and 5.8 GHz measurement
campaigns and hence, applies within this frequency band.
While polarization effects were carefully examined, other
considerations such as the antenna beam width and types of
rails materials were not considered. This represents some of the
limitations on the broader applications of the developed models
but leads the way to future examination of these other related
issues. Furthermore, only two general categories of stairwells
were modeled while selecting the four diverse architectures,
avenues are still available for modeling other architectures that
may not particularly be the chosen ones.
VII. CONCLUSION
In this paper we have developed an empirical path loss model,
Equation (3), for indoor stairwell at 2.4 GHz and 5.8 GHz based
on measurements in four stairwells with various antenna
polarizations. The path loss exponent values ( -values) and the
associated standard deviation and are extracted. It is found
that when the conventional separation distance is used in the
path loss model, the -values are significantly higher than the
values for urban and other indoor propagation environments,
indicating faster power drop in stairwells. We also introduced
“walking distance” for the calculation of -values and found
that the n-values drop to the similar level as other indoor
scenarios. More importantly, the standard deviation ( )
between the model and the measurement values is smaller than
that when separation distance is employed. Furthermore, the
standard deviation ( ) of the log-normal distribution of the
excess path loss is also smaller. These smaller standard
deviation values indicate that the path loss model based on
walking distance predicts more accurately than the one based
on separation distance.
The results reported in the paper are beneficial for
understanding radio propagation in indoor stairwell
environment, which is crucial for emergency applications (law
enforcement and fire-fighting purposes). Besides, they can also
help to develop effective indoor communications systems, and
may be useful for the design and simulation of small cell
wireless communication systems such as pico- and femto-cells.
ACKNOWLEDGEMENT
We sincerely thank the reviewers and the associate editor for
their many valuable comments and suggestions that improved
the quality of this paper.
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Soo Yong Lim (Grace) (M’07–SM’13) received the
BEng (Hons) degree in electronics majoring in
telecommunications from Multimedia University, Malaysia, in 2003 and the Ph.D. degree in electrical
engineering from the University of Hawaii at Manoa,
USA, in 2010.
From 2004 to 2006, she was a Research Officer with
the Centre for Applied Electromagnetic, Multimedia
University, Malaysia; from 2007 to 2010 she was a Graduate Assistant at the University of Hawaii at
Manoa; and from 2011 to 2013, she was a faculty member with the Department
of Computer Science and Networked System, Sunway University, Malaysia. She is now an Assistant Professor with the Department of Electrical and
Electronic Engineering, Faculty of Engineering, University of Nottingham
Malaysia Campus. Since January 2013, she has also been appointed as an adjunct faculty with the Hawaii Center for Advanced Communications
(HCAC), College of Engineering, University of Hawaii at Manoa. Her current
research interest includes radio propagation modeling, channel measurements, and ray tracing.
Dr. Lim was a recipient of the Award for Achievement in Research for Early
Career Researchers, Sunway University, in 2012. Also in 2012, she received a
Bronze Medal for her research achievement at the Malaysia Technology Expo,
awarded by the Malaysian Association of Research Scientists. She is a
registered engineer both with the Boards of Engineers Malaysia (BEM) and
with the Institution of Engineers Malaysia (IEM).
Zhengqing Yun (M’98) received his PhD in electrical
engineering from Chongqing University, Chongqing,
China, in 1994. He is Associate Professor with Hawaii Center for
Advanced Communications (HCAC), College of
Engineering, University of Hawaii at Manoa (UH), Honolulu, Hawaii. He was an assistant researcher from
2002 to 2005 in HCAC and became assistant professor
in 2006. He also did postdoctoral work in University of Utah and Southeast University in China before he joined
UH.
Dr. Yun served as the Technical Program Co-Chair of the IEEE Antenna and Propagation Society International Symposium, Honolulu, 2007 and the
0018-926X (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TAP.2014.2336258, IEEE Transactions on Antennas and Propagation
AP1305-0701.R1
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9
Technical Program Chair of the IEEE International Conference on Wireless
Information Technology and Systems, in 2010 (Honolulu) and 2012 (Maui, Hawaii). He was an associate editor of the IEEE Transactions on Vehicular
Technology and is currently an associate editor of the IEEE Transactions on
Antennas and Propagation and an associate editor of the IEEE Access. Dr. Yun’s current research interest includes radio propagation in complex
environments such as urban, indoor and mountainous areas, and ocean surface
and atmospheric ducts. He developed a ray tracing software package which has been included in AREPS (Advanced Refractive Effects Prediction System),
SPAWAR Systems Center Pacific.
Magdy F. Iskander (IEEE S’72–M’76–SM’84–F’93–
LF’12) is the Director of the Hawaii Center for
Advanced Communications (HCAC), College of Engineering, University of Hawaii at Manoa,
Honolulu, HI, USA. He is Co-Director of the NSF
Industry/University Cooperative Research Center with four other universities. From 1997–1999, he was
a Program Director in the Electrical Communications and Cyber Systems Division, at the National Science
Foundation, where he formulated a “Wireless
Information Technology” Initiative in the Engineering
Directorate. He was a member of the 1999 WTEC panel on “Wireless
Information Technology-Europe and Japan”, and chaired two International
Technology Institute Panels on “Asian Telecommunication Technology” sponsored by NSF/DoD in 2001 and 2003. He was also a member of the 1994
National Academy of Science Panel on “Microwave Processing of Materials.”
He was the 2002 President of IEEE Antennas and Propagation Society (AP-S) and a Distinguished Lecturer for the IEEE AP-S (1994–1997).
He authored the textbook Electromagnetic Fields and Waves (Prentice Hall, 1992, and Waveland Press, 2001; second edition 2012); edited the CAEME
Software Books, Vol. I, II 1991–94; and edited four books on Microwave
Processing of Materials (Materials Research Society, 1990–1996). He edited two special issues of the IEEE Transactions on Antennas and Propagation on
Wireless Communications Technology in 2002 and 2006 and co-edited a
special issue of the IEICE Journal in Japan in 2004. He has published over 230 papers in technical journals, holds nine patents, and has made numerous
presentations at national and international conferences. He is the founding
editor of the Computer Applications in Engineering Education (CAE) journal, published by Wiley (1992–present) and the founder of MiWa Technologies,
LLC for medical devices.
Much of his research is funded by the National Science Foundation, the U.S.
Army CERDEC, ARO, the Office of Naval Research, National Institute of
Health, as well as several corporate sponsors. As a result of an NSF Major Research Instrumentation grant, he established wireless testbeds, indoor
antenna ranges, microwave network analysis labs, and an RF fabrication and
characterization lab at the University of Hawaii at Manoa. His center, HCAC, has an ongoing ten-year grant (2005–2014) for partnership in the NSF
Industry/University Cooperative Research Center in Telecommunications with
the University of Arizona, Arizona State University, RPI, and The Ohio State University. His research is in computational electromagnetics with focus on
antenna design, propagation modeling for wireless communications and radar
systems as well as in the area of biological effects and medical applications of electromagnetics.
Dr. Iskander received many teaching excellence and research awards, including the 2013 University of Hawaii Boardof Regents’ Medal for Excellence in
Research and the 2010 Board of Regents’ Medal for Teaching Excellence. In
2012, he received the 2012 IEEE AP-S Chen-To Tai Distinguished Educator Award and the 2013 the IEEE MTT-S Distinguished Educator Award. He also
received the 2010 Northrop Grumman Excellence in Teaching Award, and the
2011and 2014 Hi Chang Chai Outstanding Teaching Award which is voted by the graduating senior class. In 2000, he received the University of Utah
Distinguished Teaching Award. In 1985, he received the American Society for
Engineering Education (ASEE) Curtis W. McGraw National Research Award, and in 1991 the ASEE George Westinghouse National Education Award. In
1992, he received the Richard R. Stoddard Award from the IEEE EMC Society.
In 2014, his company MiWa Technologies won the 1st place prize in the University of Hawaii Business Plan Competition, for the “CP Stethoscope”
project.