A Novel Stability Weighted Clustering Algorithm for Multi-Hop Packet Radio Virtual Cellular Network

Abstract

Cooperative communications exploit the spatial diversity inherent in multiuser system by allowing cooperation among users having a wide range of channel qualities. How to search the cluster-head and its member relay nodes to cooperate is important. Since nodes are coming into or out of the clusters time to time, the network topology is perturbed and the reconfiguration of the network is unavoidable. In this paper, we propose a new algorithm called stability weighted clustering algorithm (SWCA) to solve this problem. We define the stability by using a new metric of mobility. In the traditional WCA, the speed of every separate node is considered. However, our proposed algorithm introduces a new weight factor, which uses the relative speed of two nodes to represent the mobility of the network. Simulation results show that the SWCA achieves better stability than the traditional WCA while it performs almost the same performance as the WCA with respect to the dominant set update rate and the load balancing factor (LBF).

Full text

Page 1

A Novel Stability Weighted Clustering Algorithm for
Multi-hop Packet Radio Virtual Cellular Network

Qiyue YU Na ZHANG Weixiao MENG
Department
Communication Engineering,
Harbin Institute
Technology
Harbin, P. R. China
wxmeng@hit.edu.cn


serve its member relay nodes. The selection of the cluster-head
and its member relay nodes is a very important problem.
Fumiyuki ADACHI
Department of Electrical and
Communication
Engineering ,
Tohoku University
Sendai, Japan
adachi@ecei.tohoku.ac.jp
Department
Communication Engineering,
Harbin Institute
Technology
Harbin, P. R. China
julyrain39@yahoo.com.cn
of
of
Department
Communication Engineering,
Harbin Institute
Technology
Harbin, P. R. China
pingpongq@163.com
of
of
of
of
Abstract—Cooperative communications exploit the spatial
diversity inherent in multiuser system by allowing cooperation
among users having a wide range of channel qualities. How to
search the cluster-head and its member relay nodes to cooperate
is important. Since nodes are coming into or out of the clusters
time to time, the network topology is perturbed and the
reconfiguration of the network is unavoidable. In this paper, we
propose a new algorithm called stability weighted clustering
algorithm (SWCA) to solve this problem. We define the stability
by using a new metric of mobility. In the traditional WCA, the
speed of every separate node is considered. However, our
proposed algorithm introduces a new weight factor, which uses
the relative speed of two nodes to represent the mobility of the
network. Simulation results show that the SWCA achieves better
stability than the traditional WCA while it performs almost the
same performance as the WCA with respect to the dominant set
update rate and the load balancing factor (LBF).
Keywords-virtual cellular network;cooperative communications;
clustering; stablity; WCA
I.
INTRODUCTION
Much higher speed data services with peak data rates of
100Mbps-to-1Gbps are required for 4G systems [1]. To support
such high speed transmissions, two important technical issues
need to be addressed: spectrum efficiency and transmission
power problem [2],[3]. To keep the transmit power the same as
in the present system, a fundamental change of the wireless
access network is necessary. One promising solution is to apply
the multi-hop cooperative relay technique as in the multi-hop
virtual cellular network (VCN) [4],[5].
The term “cooperative relay” typically refers to the
technique which allows different relay nodes to share their
resources to enhance transmission quality. With cooperation, a
user who experiences a deep fading in its link towards the
destination can utilize good channels provided by its relay
nodes to achieve the desired quality of service (QoS). Any user
can be a node in the network. A number of relay nodes form a
cluster to cooperate. A relay node with good condition (i.e.,
low path-loss and/or low mobility) can be a cluster-head and
The cluster-head and its member relay nodes are randomly
distributed in the network. The concept of partitioning the
geographical region into clusters (or small cooperative zones)
has been presented in [6]. Any node can be a cluster-head if it
satisfies some necessary conditions (such as the mobility, the
transmission power, etc). After selecting the suitable node as a
cluster-head, the other nodes become its member relay nodes.
Due to the mobility of the network, clusters may change
dynamically [7]. Refs. [7-11] focused on partitioning the
geographical region into clusters. However, most of the
previously proposed approaches [8],[9],[11] for selecting the
cluster-heads do not give an optimal solution. The previously
proposed approaches cannot maximize the life time of clusters
although they perform well in terms of dominant set update
rate and the load balancing factor (LBF).The set of
cluster-heads is known as a dominant set[13]. Dominant set
update rate is defined as the frequency of a dominant set
changing. It is desirable If the nodes can keep cooperate and
communicate with the destination as long as possible (i.e., the
network topology is kept stable as long as possible). Once the
battery of cluster-head is run out, the cooperation is
interrupted; the network topology is perturbed and the
reconfiguration of the network is unavoidable. One of the
well-known clustering algorithms is the lowest-ID heuristic
algorithm [13]; however, it may lead to high battery power
consumption of cluster-heads, leading to shorter life time of the
clusters. The most popular clustering algorithm is the weighted
clustering algorithm (WCA) [12]. It is necessary to keep the
topology stable as long as possible. However, the WCA pays
little attention to the stability of the network. In fact, with the
association and dissociation of nodes into/from the clusters, the
stability of the network topology is perturbed and the
reconfiguration of the network becomes unavoidable.
In this paper, we propose a stability WCA algorithm
(SWCA) which introduces a new stability weight factor.
However, due to the dynamic nature of the network, it is very
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
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difficult to maintain a completely balanced system. A
pre-defined threshold is introduced to achieve the load
balancing and ensures that none of the cluster-heads are
overloaded.
The remainder of the paper is organized as follows. Section
II overviews the previous works. In Sect. III, the proposed
SWCA is described in detail. Section IV evaluates by computer
simulation dominant set update rate, LBF, and the average life
time of the clusters. Finally, Sect. V offers some concluding
remarks.
II.
CLUSTERING ALGORITHMS AND STABILITY PROBLEM
A. Multi-hop network
The multi-hop network is formed by the nodes and the links
connecting them as shown in Fig. 1. Any node can be a
cluster-head if a certain condition is satisfied. The
neighborhood of a cluster-head is the set of nodes which lie
within its transmission range.

Figure 1. Multi-hop network.
The node degree (which will be introduced in detail in Sect.
III), the transmission power, the mobility, and the battery
power are considered to select a cluster-head. In this paper, the
following assumption is used.
•
•
The cluster-head is selected periodically.
The cluster-head is able to communicate with its
neighbors within the transmission range [14].
Each cluster-head supports only δ nodes (where δ is
the pre-defined threshold and a group of the nodes
belonging to each cluster-head is called the member
nodes) to guarantee that the network works efficiently
and the nodes do not have any interruption in
communicating with the destination. The reason for
why the number of member nodes is limited to δ is for
a cluster-head not to consume its battery power
excessively.
•
•
It is necessary to select a slowly moving node as a
cluster-head to avoid frequent cluster-head change.
Otherwise, the cluster-head may change frequently.
•
The cluster-head consumes more battery power than
ordinary nodes since the cluster-head has extra
responsibilities to serve its member nodes.
•
The battery power is determined by the transmission
range (less power is required for a node to
communicate with the one closer to it).
B. Previous popular algorithms
Three popular algorithms (i.e., lowest-ID heuristic
algorithm [12], highest-degree heuristic algorithm [13] and
WCA [12], [13] are overviewed below.
1) Lowest-ID heuristic algorithm: this algorithm assigns a
unique ID to each node and selects the node with the lowest ID
as a cluster-head. The lowest-ID algorithm was proposed by
Baker and Ephremides [6],[7],[10] and is known as an
identifier-based clustering. The cluster-head can delegate its
responsibility to the next node with the lowest ID in its cluster.
It has less frequent cluster-head updating and higher
throughput performance than the highest-degree heuristic
algorithm. However, a drawback of this algorithm is its bias
towards nodes with smaller IDs, which may lead to high
battery power consumption of certain nodes(cluster-head)[12].
2) Highest-degree heuristic algorithm: this algorithm is
known as a connectivity-based clustering algorithm, which
computes the node degree based on its distance from others.
This algorithm was proposed by Gerla and Parekh [12],[13]. In
this algorithm, each node broadcasts its ID to other nodes
within its transmission range. The node with maximum
number of neighbors is selected as a cluster-head. The
computer simulation demonstrates[13] that the highest-degree
heuristic algorithm achieves a low updating rate of
cluster-heads, but provides low throughput.
3) WCA: this algorithm is the most popular algorithm. The
WCA selects the nodes with the smallest combined weight.
The combined weight
v
W for each node is defined as
=Δ ++
1234vvvvv
Ww w Dw Mw P
+
, (1)
where
to handle up to a certain number of nodes in its cluster);
related to the energy consumption (it represents the transmit
power);
v
M is the mobility of the nodes (a node with lower
mobility is a better choice as a cluster-head);
(cumulative) time during which a node acts as a cluster-head
(in another word, it represents the consumed battery power of
the nodes). In equation (1), w1, w2, w3, and w4 are weighting
factors which reflect the relative importance of
and
experience.
v
Δ is the node degree (it is desirable for a cluster-head
v
D is
vP is the total
v
Δ ,
v
D ,
v
M ,
vP , respectively and ; usually they are determined by
It is desirable to keep the network topology stable as long
as possible. The WCA takes into account the mobility of the
nodes which is the average moving speed of every node until
the present time. However, since the relative mobility between
any two nodes is not considered, frequent reconfiguration of
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the network is unavoidable and hence, the association and
dissociation of nodes into/from clusters perturb the stability of
the network topology. The relative speed between the
cluster-head and its neighbors must be considered. It is
desirable to select a node, whose neighbor nodes do not move
very quickly against that node, as a cluster-head. This paper
focuses on this stability problem.
III.
STABILITY WCA
The stability WCA consists of nine steps. Step 1 is used to
search the possible cooperative nodes; steps 2 to 6 compute the
factors which affect the selection of a cluster-head; and steps 7
and 9 select a cluster-head. Each step is described in detail
below.
• Step 1: Find the neighbor nodes ν’ which are within its
transmission range of each node v as
{
⎣
()
}
'
_
Numberdistance,
vtx range
Rd v v
⎡⎤
⎦ , (2)
=<
where
neighbor nodes whose distances are shorter than the
transmission range
_tx range
R
.
vd denotes the degree defined as the number of
• Step 2: For each node v, compute the degree difference
as
v
δ Δ =−
, where δ is the pre-defined threshold to
ensure that nodes have high throughput [12]. The
cluster-head should not handle a large number of nodes
as its member nodes because of the resource limitation
(i.e., the limited battery power) even if all of them lie
within its transmission range. This is because high
power consumption is necessary if the cluster-head
communicate with too many nodes. In the computer
simulation, we assume δ=2.
vd
• Step 3: Compute the sum of the distances associated
with all of its neighbors as
{
'
v v
≠
()
}
'
distance,
v
Dv v
=∑
, (3)
which represents the differences in degree of nodes.
Larger transmit power is required as the
communication range is increased. The received signal
power is attenuated inversely proportionately to the
2~4th power of the distance in urban areas [3]. The
battery power consumption of a node in a cluster is
determined by the distance between the cluster-head and
the node. The cluster-head consumes more battery
power than its member nodes.
• Step 4: Calculate the relative speed of each node as
(
'
v
vC
∈
where (
,',
V v t are the speed vectors of node
v and v’, respectively, at time t. Both the speed and the
direction (0o~360o) of the node must be considered. The
mobility of a node is determined by the average relative
speed over a period of time T as
)
()
()
{}
''
, ,,,
V v v tV v tV v t
=−
∑
, (4)
)
V v t and ()
()
'
1
T
, ,
t
v
t T
−
MV v v t
= ∑
. (5)
• Step 5: Compute the cumulative time
the node v acts as a cluster-head.
much battery power have been consumed and is much
larger for a cluster-head than for an ordinary node.
vP during which
vP implies how
• Step 6: Compute the stability of the network. The link
connecting the two nodes is regarded stable if the
relative mobility
)(ν′
v
M
' v meet the following condition
rel
between node v and node
If
( ) 'v < ，then 0
rel
v
M
( )
v
min
'
rel
v
Threshold
MM
<
(6)
If
( ) ' v0
rel
v
M
>
，then
( )
v
max
'
rel
v
Threshold
MM
<
, (7)
where
the relative mobility, which are predetermined system
parameters .If
( ) '0
v
Mv
<
are moving in opposite
( ) '0
v
Mv
>
, node v and node
the same directions.
min
M
minimum and maximum values of
respectively.
min
Threshold
Mand
max
Threshold
M are two thresholds of
rel
, node v and node
directions
' v are moving in
' v
if while
rel
Threshold
and
max
Threshold
M are the
)(ν′
rel
v
M
,
The HELLO message (the neighbor nodes broadcast
this message to other nodes [20]) is exchanged more
than 3 times between two nodes (node
v) [21] when they are cooperating.
' v and node
The relative mobility
and node ' v is defined as
)(ν′
rel
v
M
between node v

( )
v
( )
2
'
1
'
v
rxP
rxP
( )
→
( )
3
'
2
'
v
( )
→
( )
'
v
m
v
→
()
1
v
'
'10 l g
⋅
10 l g
⋅
10 l g
⋅
rel
v
vvvv
vv
m
→
v
rxP
rxP
rxP
rxP
Moo
o
→→
−
=++
+
?
, (8)
where
m-th link when node v’ transmits its signal to node
v .
( ) '
v
Mv
small in order to ensure both the stability and low
battery power. The overall degree of the relative
mobility between the node vand its neighbor nodes
is defined as
( )
'v
m
v
rxP→is the received signal power in the
The value of
rel
needs to be relatively
( )
v
M
' 1
=
'
rel
v
K
v
v
M
M
=∑
, (9)
where K is the number of neighbor nodes belonging to
node v and
min
MM
=
( ) '0
v
Mv
< (0
v
Mv
≥ ).
Threshold
(
max
Threshold
MM
=
) if
rel
( ) '
rel
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Page 4

In this paper, we define the stability as the ratio of
the relative mobility and the number of stable links as
link
v
v
N
M
e
S
=
, (10)
where
link
N
N is the number of stable links. Instead of
link
N
the denominator becomes 0 when
,
link
eis heuristically introduced to avoid that
0
link
N
=
.
•
Step 7: Calculate the final weight
as
v
W for each node v
12345vvvvvv
Www Dw Mw Pw S
=Δ ++++
(11)
where w1, w2, w3, w4, and w5 are the weighting factors
reflecting the importance of the corresponding system
parameters. Eq.(11) is similar to Eq.(1), but, the
stability
v
S is added as a new factor. In this paper, we
use fixed values of w1, w2, w3, w4, and w5 which are
determined by experience [13].
•
Step 8: The node with the smallest
the cluster-head. All the member nodes belonging to
the cluster-head are no longer necessary to proceed to
Step 9.
v
W is selected as
•
Step 9: Repeat steps 2-8 for the remaining nodes which
are not yet selected as a cluster-head or not yet selected
as a member of the cluster-head.
IV.
SIMULATION RESULTS
Simulations are done to compare the cluster-head updating
rate, LBF, and the average life time of clusters. The simulation
conditions are shown in Table 1.
Table 1.
SIMULATION CONDITIONS
Pre-defined threshold δ
(number of nodes)
Number of nodes in the
network
Network tracking time
2
30
1000 s
Nodes are uniformly distributed in an area
of 100m×100m
Random over [0-5 m/s]
Random over [0o-360o] and the moving
direction of each node changes every five
seconds
Initial consumed battery power 0-5 mw
Position of nodes
Speed of nodes
Directions of nodes
Consumed battery power
Received power between
the neighbor nodes
M
to determine relative
mobility
M
to determine relative
mobility
Random over [0-100 mw)
Threshold
min
Threshold

3 (dB)
Threshold
max
Threshold

5 (dB)
Weights (w1, w2, w3, w4,
w5)
(w1, w2, w3, w4, w5)=(0.5, 0.0, 5, 0.05,
0.05, 0.35) by experience following to
[13]
Transmission range R 0-100 m

The dominant set update rate is a very important measure to
compare different clustering algorithms [11]. The dominant set
update rate (times/sec) are shown in Fig. 2 for different
algorithms. It can be seen from Fig. 2 that as the transmission
range increases, the cluster-head updating rate increases at
beginning and reaches the maximum when the transmission
range approaches around 15m; however, as the transmission
range increases beyond 15m, the dominant set update rate starts
to decrease and gradually approaches. According to [3],
According to [3], the received signal power is given by
α−
×∝
dPP
tr
, where
path loss exponent ranging between 2 and 4, depending on the
propagation environment. Therefore, the transmission range
should be
∝
/(
r
Pd
for the given required receive
power. However, in the computer simulation, the transmit
power is assumed to be 1.5mW for the transmission range of
15m.
tP is the transmit power and α is the
α
/ 1)
t P
When the transmission range is 30m, the dominant set
update rate is 0.365 times/s for SWCA while it is 0.325 times/s
for the highest-degree algorithm, 0.352 times/s for WCA, and 1
times/s for the lowest-ID algorithm. The SWCA has less
updating rate than WCA and the highest-degree algorithm has
the highest updating rate while the lowest-ID has the lowest
rate. The reason for this is that the SWCA takes into account
the stability in the weight computation. Using the lowest-ID
algorithm, since all cluster-heads are those nodes with smaller
IDs, the cluster changes quite rarely and hence the dominant set
update rate is extremely small. For example, the node with the
smallest ID will be a cluster-head forever and it will not change
at all.
020406080 100
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8


Dominant set update rate (times/s)
Transmission range(m)
Lowest-ID
Highest-degree
WCA
SWCA

Figure 2. Cluster-head updating rate.
The LBF is plotted in Fig. 3. The LBF is defined as
()
2
_
1
LBF
cluster
∑
cluster
N
i memebermember
i
N
NN
=
=
−
, (12)
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Page 5

where
N
of the i-th cluster,
average number of neighbor nodes over all cluster-heads with
N
being the total number of nodes in the network. It is
obvious that the larger the LBF becomes the better the loading
balance is.
It can be seen from Fig. 3 that the LBF is large if the
transmission range is either too short or too long. If the
transmission range is between 10 to 60m, the LBFs of SWCA
and WCA are similar, while it is significantly lower for the
highest-degree heuristic algorithm (the highest-degree heuristic
algorithm often results in the uneven distribution of member
nodes in each cluster, resulting in a lower LBF). When the
transmission range is longer than 70m, the LBF of the
highest-degree heuristic algorithm is higher than other
algorithms. This is because the number of cluster-heads is close
to 1, thereby increasing the LBF dramatically.
cluster
(1
N is the number of clusters in the network，
≤ ≤
) is the number of the member nodes
(
memeber total
NN
=
_i memeber
cluster
iN
)
clustercluster
NN
−
is the
total
020 40 60 80100
1E-3
0.01
0.1
1
10
100
1000


LBF
transmission range(m)
Lowest-ID
Highest-degree
WCA
SWCA

Figure 3. LBF.
The average life time of clusters is plotted in Fig. 4. The
lowest-ID heuristic algorithm has the longest life time;
however, the SWCA provides a better stability than WCA
since SWCA introduces a new factor representing the stability
S
(see Eq.(11)) to make the life time longer. If the
transmission range is 40m, the average life time is 610s for the
SWCA while it is 802s, 610s, and 583s for the lowest-ID
heuristic algorithm, highest-degree heuristic algorithm, and
WCA, respectively. In the case of the lowest-ID heuristic
algorithm, the node with smaller ID is selected as a
cluster-head, so it has a relatively longer life time than other
algorithms.
ν
020 406080 100
500
600
700
800
900


the average life time of clusters(sec)
transmission range(m)
Lowest-ID
Highest-degree
WCA
SWCA

Figure 4. Average life time of clusters.
V.
CONCLUSIONS
This paper proposed the stability weighted clustering
algorithm (SWCA), which takes into account the network
stability in the weight computation. The simulation results
show that the SWCA can achieve a better stability than
traditional WCA while it provides the cluster-head updating
rate and the LBF comparable to the WCA. Note that in this
paper, we assumed the constant number of arrival users as
assumed in [12],[13]. It is left an interesting future study to
adapt the weight factors to changing number of coming users.
ACKNOWLEDGMENT
This study was supported by China National Science
Foundation under Grand No. 60872016 and Program for New
Century Excellent Talents (NCET-08-0157) in University.
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.