PERFORMANCE ANALYSIS OF DISTRIBUTED CLUSTERING ALGORITHMS FOR SENSOR NETWORKS

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PERFORMANCE ANALYSIS OF DISTRIBUTED CLUSTERING ALGORITHMS FOR SENSOR
NETWORKS
Brian McDaniel,Matt Oswald and Peter Sholander
Sandia National Laboratories, Albuquerque, NM, USA
{bmcdani, mtoswal, peshola}@sandia.gov
ABSTRACT

There has been extensive research on clustering
algorithms for sensor applications. Those algorithms
allow tradeoffs between energy consumption, convergence
time, and adaptability to changing network topologies.
However, many of these algorithms may not function well
in deployed UGS networks because previous analyses of
those algorithms used simplified radio and channel
models. For example, the communications between node
pairs is often assumed to be “time-invariant” and based
on a fixed communications range. Hence nodes either can
or cannot communicate. This time-invariant assumption
allows the protocol designer to show “proof of concept”
operation,since the clustering algorithms converge with
probability 0 or 1.In contrast, this research extends
previous analyses of Distributed Clustering Algorithms
(DCAs) to include more realistic wireless channel and
radio models to include the effects of both RF propagation
and the Media Access Control (MAC) protocols.
INTRODUCTION
Previous research on Unattended Ground-based Sensor
(UGS) networks has focused on the energy-usage of
individual protocols and functions within each sensor, as
well as the cross-layer optimization of those protocols and
functions in an overall sensor network. Examples include
research on networking protocols, Media Access Control
(MAC) protocols, adaptive clustering techniques,
Adaptive Power Control (APC) algorithms, sleep-mode
operation, service discovery protocols,sensor fusion
algorithms, RF waveforms, and the underlying low-power
sensor/radio/compute hardware [1]. However, there has
been less research on how to optimally “task” a wireless
UGS network to accomplish a user-specified goal, such as
detecting a user-specified target set within a user-specified
operational area, while subject to constraints on that

Sandia National Laboratories is a multiprogram laboratory
operated by Sandia Corporation,a Lockheed Martin Company,
for the United States Department of Energy’s National Nuclear
Security Administration under contract DE-AC04-94AL85000.
SAND
2005-5643C
approved for public release; further
dissemination unlimited.
network’s minimum operational lifetime, allowed sensor
locations, minimum detection error-rates and the
network/radio characteristics.
- “Lower” transmit power
- “Higher” transmit power
- “Cluster” Controller
Road
Junction
#1
Road
Junction
#3
Road
Junction
#2
- “Lower” transmit power
- “Higher” transmit power
- “Cluster” Controller
- “Lower” transmit power
- “Higher” transmit power
- “Cluster” Controller
- “Higher” transmit power
- “Cluster” Controller
Road
Junction
#1
Road
Junction
#3
Road
Junction
#2
Figure 1. Netted Sensor System
The “netted” sensor systems shown in Figure 1 have
several key characteristics. First, they may be self-
forming and self-healing. A routing protocol may allow
for both peer-to-peer communications between sensors, as
well as automated routing between the sensor nodes and
the gateway nodes. Second, the sensor nodes may have
more on-board processing.This allows individual nodes
to perform multi-sensor data fusion operations – as well as
advanced sensor modalities such as beam-forming. Third,
the embedded sensor radios may implement advanced
energy-saving techniques (such as sleep-mode operation,
automated clustering, and adaptive power-control) that
extend the overall lifetime of the entire UGS field. Finally,
the individual nodes may be “taskable”.Advanced robotic
nodes may be able to change their positions. Sensor nodes
with multiple embedded sensors may be able to change
their effective sensor modality based on the expected
target mix. If the sensors are air-dropped then some
sensors may go into a “sleep mode” if their capabilities are
redundant with their neighbors’ roles. Nodes may also
rotate their “roles” (e.g., sensor node, relay node and
gateway node) or tasks in order to improve the overall
energy usage and/or performance characteristics of the
network.
70 Texas Wireless Symposium 2005
Application Overview and Design Tradeoffs
Many papers assume that the UGS field’s task is to detect
and classify one or more targets as those targets pass
through the UGS field. In this application, a randomly-
deployed (e.g., air-dropped) UGS field is tasked to wake
up, actively sense the local environment for a period of T
seconds, and then exfiltrate that entire data-set back to a
Mission Operations Center (MOC) over a limited number
of SATCOM channels. The delay constraints for the bulk-
data upload preclude the use of one central exfiltration
point, so that a clusterhead-based approach is required.
However, the available RF spectrum requires the
assignment of non-overlapping frequency / time-slot /
code assignments to each pair of adjacent clusters.
There are three different roles that a given node may have
in this data exfiltration application. They are:
 Sensor nodes.
 Relay nodes that enable ground-based
communications between other nodes, such as
sensor nodes and uplink nodes.
 Uplink nodes that enable communications from
the UGS field to the MOC.
A given node may have multiple roles – such as being
both a sensor node and a relay node.
Many previous research studies have not fully accounted
for overhead associated with adaptively selecting node
roles in large UGS fields.A relevant example would be
the energy required to selected clusterheads in a large
UGS field.
This paper includes detailed simulations of the energy
costs associated with adaptive role sets and the
tradeoffs/design considerations of dynamically performing
role selection during network formation. In particular, the
assignment of node roles occurs during network formation
using a weighted leader-election DCA.
A related paper [2] examines the tradeoffs between delay,
connectivity and frequency re-use constraints based on
graph-theoretic techniques. These two basic design
constraints – namely having peer-to-peer connectivity
between all of the UGS nodes and having frequency re-use
between clusters – conflict with each other and hence
provide one limit on the possible UGS design solutions.
This paper’s simulation-based analysis provides further
insight into the design constraints related to dynamically
assigning role sets in UGS networks.
Radio and Channel Model
In this paper’s simulations, all DCA packets are
broadcasted using a Time Division Multiple Access
(TDMA) scheme over an 802.11b physical layer. Because
the DCA messages are broadcasted the 802.11b MAC
layer becomes essentially Carrier Sense Multiple Access
(CSMA),which produces a large number of collisions.
Therefore a TDMA scheme is used above the MAC layer
to ensure that the DCA messages do not collide. This
assumption allows the analysis to focus on the RF layer
effects such as bit errors and fading.Future work will
consider more realistic (e.g., distributed) MAC protocols
that minimize the collisions (e.g., [3]) between the
broadcast DCA messages.
Since this paper is concerned with understanding and
extending the tradeoff analyses of distributed clustering
algorithms, simulation results for DCA performance are
given based on both deterministic and non-deterministic
radio and channel models. The difference between the
deterministic and non-deterministic radio and channel
models is that Bit Error Rate (BER) effects are added to
the radio model and a shadowing term 

is added to
channel model. In particular, the log-normal channel
model [4,5] is of the following form:











0
100
log10)()(
d
d
ndPLdPL
(1)
Where d is the transmitter-receiver distance,d
0
is the
reference distance,n is the path loss exponent, and X

is a
zero-mean Gaussian RV (in dB) with standard deviation
that accounts for the shadowing effects.For this paper,
the following parameters are used in the log-normal
channel model:
 A path-loss exponent of 3.
 A shadowing standard deviation of 1.0 dB.
 A maximum transmitter power of 10W.
 A noise floor (N) of -100.0 dBm.
 A reference loss and distance of PL(d
0
) = 102 dB at
d
0
= 50 m.
The BER effects for DPSK (Differential Phase-Shift
Keying) modulation are assumed to have the following
Probability of Bit Error (P
b
):
SNR
2
1
b
eP


(2)
71
Performance Metrics
The performance metrics of interest include the average
number of non-convergent nodes, average algorithm
convergence-time, average energy consumed by each node
and the average cluster-size.
A non-convergent node is a node whose particular portion
of the DCA did not complete because the node was unable
to choose whether it should join a cluster or become an
uplink.
The average energy consumed by each node was the sum
of the energy consumed during three different states –
namely the “radio transmit”, “radio idle” and “radio
receive” states. For this paper, the power needed to
receive or be able to receive (idle state) was set to be 1/2
and 1/10 of the transmit power,respectively.
The next section’s results show the variation of the
aforementioned performance metrics as more realistic
wireless channel models and MAC behavior are
introduced into the simulated UGS networks. This
approach provides further insight into the design
limitations and tradeoffs of DCAs in UGS applications.
DCA IN UGS APPLICATIONS
Given a multi-channel transceiver, system performance for
this paper’s data exfiltration application can be enhanced
by forming multiple subnets of clustered sensors. The
following subsections analyze the system performance
when a weighted leader-election DCA is used to form
those clusters.
This section’s scenarios assume a lay down of 120 nodes
that are equally able to assume either the uplink or sensor
node roles.An Independent, Identically Distributed (iid)
uniform distribution on a square 1000m
2
area is chosen for
the nodes. Since “average” performance metrics are of
concern the results are based on 25 simulations for every
value of transmit power (P
TX
) and the SNR Threshold
described below. Each simulation had a different starting
random seed value. These results illustrate the tradeoffs
and design considerations associated with using this
weighted leader-election DCA prior to performing the data
exfiltration application in an UGS network.
This section begins with a brief summary of a particular
DCA algorithm. Baseline results are then presented for
that DCA given ideal radio and channel models. Next this
paper shows how DCA performance degrades when the
radio model includes BER effects. To fix this problem, an
SNR Threshold parameter is introduced into the DCA
during the neighbor selection process.However, the DCA
still has trouble with fading channels. This section
concludes with a discussion of a “cost function” that helps
a UGS system designer visualize the parameter sets
(transmit power and SNR Threshold) that provide
acceptable system performance.
DCA Summary
Weighted DCAs determine which nodes are best suited to
become uplinks. The DCA simulated in this section is
similar to the weighted leader-election DCA presented in
[6] and is implemented in OPNET as follows.
In a leader-election clustering algorithm nodes choose
either to be sensors or uplinks only after their neighbors
with lower weights have made their decisions. First every
node announces its existence with an “announcement
message” that includes its x and y coordinates.After those
initial messages have been received the nodes calculate
their respective weights. To optimize the sensor network’s
performance, each node’s weight calculation can include
many parameter such as available energy, number of
neighbors and the distance to neighbors [7]. For this
application each node’s weight is calculated to be the sum
of the distances to its neighbors as shown in Equation 2.
This heuristic approach is used because dense clusters with
centrally-located uplink nodes have been shown to
perform well in this paper’s data exfiltration application
[2].



neighborsofnumber
1j
iji
DistanceWeight
(3)
After each node calculates its weight, it then transmits
another announcement message. This allows every node
to learn all of its neighbors’ weights.At this point, the
node that has the smallest weight compared to its
neighbors proceeds to announce itself to be an uplink.
Once a node has the lowest weight among its undecided
neighbors then that node announces that it is either joining
the uplink closest to itself, or if none of its neighbors are
uplinks then it announces itself to be an uplink.
DCA Performance
Initially only deterministic elements were included in the
channel and radio models. In particular BER and a
shadowing variable were left out of the radio and channel
models respectively. The DCA’s performance with this
idealized channel and radio model provided baseline
values for the average number of non-convergent nodes,
average cluster-size, average convergence time and
average node energy consumed.
72
When the channel characteristics were deterministic then
all inter-nodes links were symmetrical. As a result there
were not any non-convergent nodes. Average cluster size
increased as a function of P
TX
as shown in Figure 2. The
tradeoff associated with P
TX
and average cluster size was
expected and was consistent with results found in
reference [5]. An increase in P
TX
resulted in a larger
coverage area for each node. This increased the number of
neighbors at each node, which in turn created a smaller
number of uplink nodes.
-15
-10
-5
0
5
10
0
20
40
60
80
100
120
Power (dBW)
Cluster Size
Figure 2.Average Cluster Size as a Function of P
TX
.
As figure 3 shows the average convergence time and
average node energy consumed were highly correlated
since they both increased similarly as PTX was increased.
The longer convergence time for greater transmit powers
is not surprising because, on average, having more
neighbors forces nodes to receive more decision messages
before deciding their own roles. Also,having to receive
more decision messages also increases energy
consumption because the radio spends more time in its idle
and receive states. (Note:Increasing P
TX
does cause the
node to consume more energy in the transmit state.
However, the energy consumed during the radio transmit
state is relatively small, compared to the energy consumed
during radio idle and radio receive states, because the
implemented DCA requires that each node only transmit 3
messages.)
-15
-10
-5
0
5
10
0
5
10
Power
(
dBW
)
Convergence Time (s)
-15
-10
-5
0
5
10
0
2
4
6
Energy (mJ)
C
o
n
v
e
r
g
e
n
c
e
T
i
m
e
E
n
e
r
g
y
The next step in the analysis of this particular DCA was to
add the BER effects for DPSK modulation and a 1Mbps
data rate to the radio model. The inclusion of BER effects
in the radio model created substantial degradation of DCA
performance. Figure 4 shows that the DCA did not
converge for a large number of nodes. (A node could not
converge when a neighboring node’s decision message
was received erroneously.)
Figure 3.Average Node Energy Consumed and Average
Convergence Time as Functions of P
TX
.
-15
-10
-5
0
5
10
0
10
20
30
40
50
Power (dBW)
Number ofNon-Converged Nodes
Figure 4.The Confidence Interval (90%) for the Number
of Isolated Nodes when P
b
is included in the radio model.
The performance of DCA’s is dependent on the reliability
of the communications links. All nodes converge in
previous analyses of DCA execution where simple 0 or 1
channel behavior were assumed [6]. In this paper the
addition of an SNR threshold parameter in the receiver
model is used to make the wireless channels arbitrarily
reliable.This improves the DCA’s performance.
73
The SNR Threshold parameter is added to the DCA by
measuring each neighbor’s SNR during its announcement
broadcasts, and then choosing neighbors with SNRs above
some predetermined threshold. Figure 5 shows the
benefits of adding the SNR Threshold parameter into the
DCA.Its inclusion results in the average number of non-
converged nodes tending to zero as the SNR Threshold
parameter is increased. Increasing the SNR threshold has
the negative effect of reducing communications capacity
though since the clustering algorithm now ignores packets
from some links (whose quality is below the SNR
threshold) even if some packets from those links could be
received correctly.
Figure 5.The Average Number of Non-Convergent Nodes
as a function of P
TX
and SNRThreshold with BER model.
If the UGS radio can perform SNR measurements then a
useful design tool is a “cost function” that utilizes
simulation results to weigh the two design parameters,
SNR Threshold and P
TX
, against the desired performances
of each metric (average convergence time, average cluster
size and average number of isolated nodes). Figure 6
shows the results for the following cost function.
6)max(4
10
2
AVG
AVG
AVGAVG
NC
E
ECS
C 








(4)
C is the Weighted Cost, CS
AVG
is the average cluster size,
E
AVG
is the average node energy and NC
AVG
is the average
number of non-convergent nodes.As can be seen in
Equation 4, the regions for minimum cost occur where
CS
AVG
is near 10 nodes and E
AVG
and NC
AVG
are both
small. Notice the steep changes on both sides of the
regions of minimal cost. For this particular data
exfiltration application a minimal number of non-
convergent nodes, energy efficiency, and an average
cluster size of 10 nodes are the desired results from the
DCA.Under those assumptions, the design space has
become limited to the region of:
 SNR threshold > -2 dB
 SNR threshold – 8 dB < P
TX
< SNR threshold – 4 dB.
Figure 6. Cost Function
In addition to improving DCA performance when BER
effects are included in the radio model, the SNR Threshold
parameter also had a positive impact on DCA performance
over fading channels. Figure 7 shows that a large enough
SNR Threshold was able to mitigate the effects of bit
errors in a fading channel.In this example, the channel
model was log-normal fading with a shadowing standard
deviation of 1.0 dB.
Figure 7.The Average Number of Isolated Nodes as a
function of P
TX
and SNRThreshold when BER and Log-
Normal Fading are included in the radio and channel
models.
74
However, it should be noted that in channels with large
fading (>1 dB) DCA may not perform well enough (e.g.,
there will be too many non-convergent nodes).As such
future work should focus on what other possible
parameters could be added to the design space to provide a
more viable solution for fading channels. One option
might be a Distance Threshold parameter that relates inter-
node distances to a desired Packet Reception Rate (PRR).
However, there may be limits on the quality of the channel
estimation given the limited number of DCA messages
exchanged between each pair of nodes.
CONCLUSIONS and FUTURE WORK
This paper presented and analyzed a DCA for dynamically
assigning roles during the formation of a UGS network.
Results demonstrated that properly modeling realistic RF
and MAC effects with the OPNET simulation tool led to a
better understanding of the performance tradeoffs and
design constraints associated with DCAs.
This paper demonstrated that additional mitigation
techniques for fading channels are needed for a weighted
DCA. The proposed SNR Threshold parameter helped
mitigate against bit errors. However,given the limited
number of DCA messages, the SNR Threshold parameter
became less useful when time-variant fading channels
were included in the analysis.
Future work will analyze the effective costs of other
popular clustering algorithms for UGS networks such as
the Low-Energy Adaptive Clustering Hierarchy (LEACH)
algorithm [8] and the Weighted Clustering Algorithm
(WCA). Those algorithms’ performance may also be
degraded when realistic RF and MAC effects are included
in the analyses.
Finally, this paper used a simplified TDMA-based MAC
protocol that eliminated collisions between the DCA
messages. Future analyses need to include more realistic
MAC layers and evaluate their impact on the clustering
algorithms’ performance.
REFERENCES
[1] “Special Issue on Energy-Aware Ad Hoc Wireless
Networks”, IEEE Wireless Communications, Aug.2002.
[2] M. Oswald, B. McDaniel, P. Sholander, J. Rohwer and
D.Kilman, “Data Exfiltration From Sensor Networks
subject to Delay, Connectivity and Frequency Re-Use
Constraints”, MILCOM 2005, October 2005.
[3] Y. C. Tay, Kyle Jamieson, and Hari Balakrishnan,
“Collision-Minimizing CSMA and Its Applications to
Wireless Sensor Networks”, IEEE Journal on Selected
Areas in Communications, Vol. 22, No. 6, August 2004.
[4] Theodore S. Rappaport,Wireless Communications:
Principals and Practice,Prentice Hall, 1996.
[5] Marco Zuniga and Bhaskar Krishnamachari,
“Analyzing the Transitional Region in Low Power
Wireless Links”, IEEE SECON Conference,Oct.2004.
[6] Stefano Basagni, “Distributed Clustering for Ad Hoc
Networks”,International Symposium on Parallel
Architectures, Algorithms,and Networks,June 1999.
[7] Mainak Chatterjee, Sajal K.Das and Damla Turgut,
“WCA: A Weighted Clustering Algorithm for Mobile Ad
Hoc Networks”, Cluster Computing 5, 193–204, 2002.
[8] Wendi Rabiner,Anantha Chandrakasan and Hari
Balakrishnan, “An Application-Specific Protocol
Architecture for Wireless Microsensor Networks”, IEEE
Transactions on Wireless Communications,Vol. 1, No.4,
October 2002.
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