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USC Computer Science Technical Reports, no. 823 (2004)

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USC Computer Science Technical Reports, no. 823 (2004)

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Content 1
Analyzing the Transitional Region in Low Power
Wireless Links
Marco Zuniga and Bhaskar Krishnamachari
Department of Electrical Engineering - Systems
University of Southern California, Los Angeles, CA 90089-0781
marcozun@usc.edu, bkrishna@usc.edu
Abstract— The wireless sensor networks community, has now
an increased understanding of the need for realistic link layer
models. Recent experimental studies have shown that real deploy-
ments have a “transitional region” with highly unreliable links,
and that therefore the idealized perfect-reception-within-range
models used in common network simulation tools can be very
misleading. In this paper, we use mathematical techniques from
communication theory to model and analyze low power wireless
links. The primary contribution of this work is the identification
of the causes of the transitional region, and a quantification of
their influence. Specifically, we derive expressions for the packet
reception rate as a function of distance, and for the width of
the transitional region. These expressions incorporate important
channel and radio parameters such as the path loss exponent
and shadowing variance of the channel; and the modulation and
encoding of the radio. A key finding is that for radios using
narrow-band modulation, the transitional region is not an artifact
of the radio non-ideality, as it would exist even with perfect-
threshold receivers because of multi-path fading. However, we
hypothesize that radios with mechanisms to combat multi-path
effects, such as spread-spectrum and diversity techniques, can
reduce the transitional region.
I. INTRODUCTION
Wireless sensor network protocols are often evaluated
through simulations that make simplifying assumptions about
the link layer, such as the binary perfect-reception-within-
range model. Several recent empirical studies [1] [2] [3] have
questioned the validity of these assumptions. These studies
have revealed the existence of three distinct reception regions
in a wireless link: connected, transitional, and disconnected.
The transitional region is often quite significant in size, and is
generally characterized by high-variance in reception rates and
asymmetric connectivity. Particularly, in dense deployments
such as those envisioned for sensor networks, a large number
of the links in the network (even higher than 50%) can be
unreliable due to the transitional region.
Because of its inherent unreliability and extent, the transi-
tional region can have a major impact on the performance
of upper-layer protocols. In [1] it is shown that the dy-
namics of even the simplest flooding mechanism and the
topology of data gathering trees constructed in dense sensor
networks can be significantly affected due to the asymmetric
and occasional long-distance links caused by nodes present
in the transitional region. In [6] also, it is argued that the
This work was supported in part by NSF under grant number 0347621, and
by a gift grant from Ember Corporation.
routing structures formed taking into account unreliable links
can be very different from the structures formed based on
a simplistic model. Similarly, the authors of [7] report that
such unreliable links can have a significant impact on routing
protocols, particularly geographic forwarding schemes. On the
other hand, other works have proposed mechanisms to take
advantage of nodes in the transitional region. For instance,
[5] found that protocols using the traditional minimum hop-
count metric perform poorly in terms of throughput, and that
a new metric called ETX (expected number of transmissions),
which uses nodes in the transitional region, has the best
performance. On the same line of work, by evaluating link
estimator and neighborhood table management, the authors in
[3] found that cost-based routing using a minimum expected
transmission metric has a good performance. Therefore, due to
the significant impact that nodes in the transitional region have
on upper-layer protocols, there is an increased understanding
of the need for realistic link layer models for wireless sensor
networks.
In order to address this need, some recent works [3] [7] [8]
have proposed new link models based on empirical data. While
these empirical models do play an invaluable role in improving
the realism of protocol evaluation, they suffer from some
significant shortcomings. They do not provide fundamental
insight into the root causes of the observed phenomena. And
they do not provide a systematic way to generalize the models
(i.e., extend their validity and accuracy) beyond the specific
radio and environment conditions of the experiments from
which the models are derived.
On the other hand, there exists a rich literature on wire-
less communications, particularly in the context of cellular
telecommunication networks
1
, that provides a set of models
and tools for analyzing the physical layer. In this study,
we make use of these analytical tools to derive expressions
for the packet reception rate as a function of distance for
different settings, and to determine the width of the transitional
region. These expressions do not consider node mobility nor
dynamic objects in the environment; thus, while different links
experience different levels of fading, the fading for each link
is assumed to be constant over time.
The analysis done in this work provides some important
contributions. First, it allows us to delimit the influence of
1
In cellular systems the transitional region is not of interest (except for
modelling inter-cell interference) as cells are designed to fit only the connected
region.
the wireless environment and the radio on the transitional
region; furthermore, the derived expressions show how the
transitional region is impacted by important radio parameters
such as modulation, encoding, output power, frame size and
receiver noise, as well as important environmental parameters,
namely, the path loss exponent and the log-normal shadow
variance. Second, we are able to conclude that, for radios using
narrow-band modulation, the transitional region is present even
with perfect-threshold radios (i.e., that it is not an artifact
of radio non-ideality alone) due to shadowing effects; hence,
radios with mechanisms to combat multi-path may reduce the
transitional region. And third, we bring to the notice of the
community simple analytical models for the link layer that
can be used to enhance simulations.
The rest of the paper is organized as follows. Section II
positions our work in the current literature. The basic frame-
work of the model is derived in section III, it shows how the
channel and radio influence the transitional region. In section
IV, the model is extended for different environments, encoding
schemes, and frames size. This section also introduces the
transitional region coefficient ¡ as a mean to measure the
quality of the link by taking into account the width of the
different regions. Section V shows empirical experiments used
to validate and enhance the correctness of the model, and
provides theoretical models for several scenarios. Finally, we
present our conclusions and future work in section VI.
II. RELATED WORK
Recent experimental studies [1] [2] [3] identify the existence
of three distinct reception regions in the wireless link: con-
nected, transitional, and disconnected. This behavior deviate
to a large extend from the idealized disc-shape model used in
most published results. In [6], Kotz et al. provide data demon-
strating the unrealistic nature of some common assumptions
used in MANET research. In real scenarios, packet losses lead
to different connectivity graphs, and coverage ranges that are
neither circular nor convex, and are often noncontiguous.
Several researchers have pointed out that the use of simple
radio models may lead to wrong simulation results in upper-
layers. In one of the earliest works, Ganesan et al. [1]
presented empirical results from flooding in a dense sensor
network and study different effects at the link, MAC, and
application layers. They found that the flooding tree exhibits
a high clustering behavior, in contrast to the more uniformly
distributed tree obtained with a disc shape model.
Zhao et al. [2] report measurements of packet delivery for
a sixty-node test-bed in different indoor and outdoor environ-
ments. They study the impact of the wireless link in packet
delivery at the physical and MAC layers by testing different
encoding schemes (physical layer) and different traffic loads
(MAC layer).
In [5], De Couto et al. present measurements for DSDV and
DSR, over a 29 node 802.11b test-bed and show that when
the real channel characteristics are not taken into account,
the minimum hop-count metric has poor performance. By
incorporating the effects of link loss ratios, asymmetry, and
interference, they present the expected transmission count
metric which finds high throughput paths. On the same line
of work, Woo et al. [3] study the effect of link connectivity
on distance-vector based routing in sensor networks. By eval-
uating link estimator, neighborhood table management, and
reliable routing protocols techniques, they found that cost-
based routing using a minimum expected transmission metric
shows good performance.
Recently, Zhou et al. [7] reported that radio irregularity has
a significant impact on routing protocols, but a relatively small
impact on MAC protocols. They found that location-based
routing protocols, such as geographic routing perform worse
in the presence of radio irregularity than on-demand protocols,
such as AODV and DSR.
Through empirical studies, the previous works bring to light
the impact that the channel behavior has on protocol perfor-
mance at different layers. However, for large-scale networks,
on-site testing may be unfeasible and models for simulators
will be needed. In order to help overcoming this problem some
tools and models have been recently proposed.
In [3], the authors derive a packet loss model based on
aggregate statistical measures such as mean and standard
deviation of packet reception rate (PRR). The model assumes a
gaussian distribution of the PRR for given transmitter-receiver
distance, which is not accurate.
Using the SCALE tool [4], Cerpa et al. [8] identify other
factors for link modelling. They capture features of groups
of links associated with a particular receiver, a particular
transmitter, a particular radio, and links associated with a
group of radios that are geographically close. Using several
statistical techniques, they provide a spectrum of models of
increasing complexity and increasing accuracy.
A most recent model, called the Radio Irregularity Model
(RIM), was proposed in [7]. Based on experimental data,
RIM takes into account both the non-isotropic properties of
the propagation media and the heterogeneous properties of
devices.
While these models are important steps towards a realistic
channel model, their main drawback is that they are valid only
for the parameters used in the deployment; among those we
have: modulation, encoding, packet size, environment char-
acteristics, noise floor and output power. If these parameters
are modified the empirical model is either not valid or not
accurate.
On the other hand, years of research in wireless commu-
nications, particularly cellular networks, provide a rich set of
models and tools for analyzing the physical layer [13]. Two
of these tools are of significant importance to understand the
transitional region, the log-normal shadowing path loss model
(to model the environment) and the bit-error performance of
various modulation and encoding schemes with respect to the
signal to noise ratio (to model the radio).
The research done so far has identified the channel mod-
elling problem and its impact on upper-layer protocols, it
also has proposed some realistic channel models. However,
what is missing is a clear understanding of the causes of
the link behavior. Our work presents an in-depth analysis of
the transitional region and provides theoretical models for
the link layer showing how PRRs vary with distance for
0 5 10 15 20 25 30 35 40
−110
−100
−90
−80
−70
−60
−50
distance (m)
P
r
(dBm)
Analytical Channel Model
Fig. 1. Channel Model, n=4, ¾ =4, P
t
=0dBm
different radios and environments. The model presented in
this work does not consider interference, which is part of our
future work. Nevertheless, in scenarios where the traffic and
contention are relatively light; a very reasonable assumption
for many classes of data-centric sensor networks, our model
provides an accurate estimate of the links’ quality.
III. DELIMITING RESPONSIBILITIES: THE CHANNEL AND
THE RADIO
The transitional region is the result of placing specific de-
vices, for example MICA2 motes, in an specific environment,
like the aisle of a building. With the intend of analyzing how
the channel and the radio determine the transitional region;
first, we define models for both elements, to subsequently
study their interaction.
A. The Wireless Channel
When an electromagnetic signal propagates, it may be
diffracted, reflected and scattered. These effects have two
important consequences on the signal strength. First, the
signal strength decays exponentially with respect to distance.
And second, for a given distance d, the signal strength is
random and log-normally distributed about the mean distance-
dependent value.
Due to the unique characteristics of each environment, most
radio propagation models use a combination of analytical
and empirical methods. One of the most common radio
propagation models is the log-normal shadowing path loss
model [13]
2
. This model can be used for large and small
[11] coverage systems; furthermore, empirical studies [12]
have shown the the log-normal shadowing model provides
more accurate multi-path channel models than Nakagami and
Rayleigh for indoor environments. The model is given by:
PL(d)=PL(d
0
)+10nlog
10
(
d
d
0
)+X
¾
(1)
2
The model is valid only for the transmission frequency and environment
where the data was gathered.
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
PRR
Analytical Radio Model
Zero Packet
Reception
Perfect Packet
Reception
Fig. 2. Radio Model: Non-Coherent FSK, NRZ radio, f =50bytes
Where d is the transmitter-receiver distance, d
0
a reference
distance, n the path loss exponent (rate at which signal
decays), and X
¾
a zero-mean Gaussian RV (in dB) with
standard deviation¾ (shadowing effects)
3
. In the most general
case, X
¾
is a random process that is a function of time, but,
since we are not assuming dynamic environments, we model
it as a constant random variable over time for a particular link.
The received signal strength (P
r
) at a distance d is the
output power of the transmitter minus PL(d). Figure 1 shows
an analytical propagation model for n=4, ¾ =4, PL(d
0
)=
55 dB and an output power of 0 dBm.
B. The Radio
To facilitate the explanation of the radio model, this sub-
section assumes NRZ encoding. Section IV provides models
for other encoding schemes.
The steps followed to derive the radio model are similar
to the ones in [9]. Let P
i
be a Bernoulli random variable,
where P
i
is 1 if the packet is received and 0 otherwise. Then,
for r transmissions, the packet reception rate is defined by
1
r
P
r
i=1
P
i
. Since P
i
s are i.i.d. random variables, by the weak
law of large numbers PRR can be approximated by E[P
i
],
where E[P
i
] is the probability of successfully receiving a
packet.
If NRZ is used and 1 Baud = 1 bit, the probability p of
successfully receiving a packet is:
p =(1¡P
e
)
8`
(1¡P
e
)
8(f¡`)
=(1¡P
e
)
8f
(2)
Where f is the frame size
4
, ` is the preamble (both in
bytes), andP
e
is the probability of bit error.P
e
depends on the
modulation scheme, for non-coherent FSK (modulation used
in MICA2 motes), P
e
is given by:
P
e
=
1
2
exp
¡
®
2
(3)
3
n and¾ are obtained through curve fitting of empirical data;PL(d
0
) can
be obtained empirically or analytically.
4
A frame consists of: preamble, network payload (packet) and CRC
0 5 10 15 20 25 30 35 40
−110
−100
−90
−80
−70
−60
−50
distance (m)
P
r
(dBm)
Analytical Method to Determine Regions in Wireless Links
μ μ+2σ μ−2σ
noise floor (P
n
)
P
n
+ γ
U
P
n
+ γ
L
Beginning of
Transitional Region
End of
Transitional Region
Fig. 3. Analytical Observation of the Transitional Region
Where ® is the
E
b
N0
ratio. Hence, the PRR p is defined as:
p=(1¡
1
2
exp
¡
®
2
)
8f
(4)
Nevertheless, most commercial radios do not provide the
E
b
N0
metric, but the RSSI (Received Signal Strength Indicator)
of the received signal. The RSSI measurements can be used
to determine the SNR (Signal-to-Noise ratio); henceforth, in
this work, the expression based on
E
b
N
0
are converted to SNR.
The relation between SNR and
E
b
N0
is given by:
SNR =
E
b
N
0
R
B
N
(5)
Where R is the data rate in bits, and B
N
is the noise
bandwidth. For MICA2 motes, R = 19.2 kbps and B
N
= 30
kHz. Finally, the PRR p in terms of the SNR (°) is given by:
p=(1¡
1
2
exp
¡
°
2
1
0:64
)
8f
(6)
The curve in figure 2 shows equation 6 (receiver response)
for a frame size of 50 bytes. As we shall see later, this curve
plays an important role in determining the different regions.
C. The Noise Floor
Another important element that determines the transitional
region is the noise floor, which depends on both, the radio
and the environment. The temperature of the environment in-
fluences the thermal noise generated by the radio components
(noise figure), the environment can further influence the noise
floor due to interfering signals. When the receiver and the
antenna have the same ambient temperature the noise floor is
given by [13]:
P
n
=(F +1)kT
0
B (7)
Where F is the noise figure, k the Boltzmann’s constant,
T
0
the ambient temperature and B the equivalent bandwidth.
MICA2s use the Chipcon CC1000 radio [14], which has a
noise figure of 13 dB and a system noise bandwidth of 30
0 5 10 15 20 25 30 35 40
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
distance (m)
PRR
Analytical PRR vs Distance
connected
region
transitional
region
disconnected
region
Fig. 4. Analytical PRR vs Distance, obtained through equation 9
kHz. Considering an ambient temperature of 300
±
K (27
±
C,
75
±
F) and no interference signals, the noise floor is -115 dBm.
The noise figure provided in [14] is only for the chip,
and does not include losses due to board implementations.
Hence, the noise figure of the final hardware will be higher.
In section V, the noise floor is redefined based on empirical
measurements.
D. Putting all Together
Given a transmitting power P
t
, the SNR ° at a distance d
is:
°(d)
dB
=P
t dB
¡PL(d)
dB
¡P
n dB
(8)
Henceforth, the PRR at a distance d for the encoding and
modulation assumed in this section is:
p(d)=(1¡
1
2
exp
¡
°(d)
2
1
0:64
)
8f
(9)
With the aim of obtaining the radius of the different regions,
let us bound the connected region to PRRs greater than 0.9,
and the transitional region to values between 0.9 and 0.1. If
we let °
U dB
and °
L dB
be the SNR values for PRRs of 0.9
and 0.1 respectively, then from equation 9 we obtain:
°
U dB
=10log
10
(¡1:28 ln(2(1¡0:9
1
8f
)))
°
L dB
=10log
10
(¡1:28 ln(2(1¡0:1
1
8f
)))
(10)
The previous equations determine the bounds of the regions
in the radio model. Now, let us analyze how these bounds
interact with the channel model to define the radius of the
different regions at the link layer.
Due to the gaussian characteristic of log-normal shadowing
in the path loss model, the received signal strength P
r
can be
bounded within§2¾, i.e. P(¹¡2¾

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Description

Marco Zuniga, Bhaskar Krishnamachari. "Analyzing the transitional region in low power wireless links." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 823 (2004).

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Creator Krishnamachari, Bhaskar (author), Zuniga, Marco (author)

Core Title USC Computer Science Technical Reports, no. 823 (2004)

Alternative Title Analyzing the transitional region in low power wireless links (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

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Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)