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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