propagation measurement and modeling for indoor stairwells at 2.4 and 5.8 ghz

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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

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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: [email protected]). 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: [email protected], [email protected]).

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

P



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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


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


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


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


Pa

th L

oss (

dB

)

VV Polarization

HH Polarization

0 10 20 30 40 50-60

-50

-40

-30

-20

-10

0

10


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

)



AP1305-0701.R1

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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

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0.3

0.35

x (dB)

Pro

ba

bili

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Measurement

Gaussian Distribution

-20 -10 0 10 200

0.05

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Gaussian Distribution



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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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[1] M. F. Iskander, Z. Yun, “Propagation Prediction Models for Wireless

Communication Systems,” IEEE Trans. Microwave Theory and Tech.,

vol. 50, no. 3, pp.662-673, March 2002.

[2] IEEE Vehicular Technology Society Committee on Radio Propagation,

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[3] T. S. Rappaport, Wireless communications: principles and practice,

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[4] S. Y. Seidel, and T. S. Rappaport, “914 MHz path loss prediction models

for indoor wireless communications in multifloored buildings,” IEEE

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[5] C. F. Yang, B. C. Wu, “A Ray-Tracing/PMM Hybrid Approach for

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[6] C. H. Teh, H. T. Chuah, “Propagation Measurement in a Multi-Floor

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[7] S. Y. Lim, Z. Yun, J. M. Baker, N. Celik, H. Youn, and M. F. Iskander,

“Propagation modeling and measurement for a multi-floor stairwell,”

IEEE Antennas and Wireless Propag. Letters, vol. 8, pp. 583-586, 2009.

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“Radio propagation in stairwell: measurement and simulation results,”

IEEE Antennas and Propagation Society International Symposium,

APSURSI’09, pages: 1-4, 2009. (Access through IEEE Xplore at

ieeexplore.ieee.org.)

[9] S. Y. Lim, Z. Yun, and M. F. Iskander, “Radio propagation measurements

in multifloor indoor stairwells,” IEEE International Conference on

Wireless Information Technology and Systems, ICWITS’10, pages: 1-4,

2010. (Access through IEEE Xplore at ieeexplore.ieee.org.)

[10] V. Chandrasekhar, and J. G. Andrews, “Femtocell networks: a survey,”

IEEE Commun. Magazine, vol. 46, no. 9, pp. 59-67, September 2008.

[11] D. Adler, Metric handbook: planning and design data, 2nd ed,

Architectural Press, Oxford, pp. 2-16 – 2-17, 1999.

[12] R. A. Valenzuela, O. Landron, and D. L. Jacobs, “Estimating local mean

signal strength of indoor multipath propagation,” IEEE Trans. Veh.

Technol., vol. VT-46, pp. 203-212, 1997.

[13] H. L. Bertoni, Radio propagation for modern wireless systems, Prentice

Hall PTR, Upper Saddle River, pp. 15-39, 2000.

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



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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.

propagation measurement and modeling for indoor stairwells at 2.4 and 5.8 ghz

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