A COST EFFECTIVE COMPRESSIVE DATA AGGREGATION TECHNIQUE FOR WIRELESS SENSOR NETWORKS

International Journal of Ad hoc, Sensor & Ubiquitous Computing (IJASUC) Vol.1, No.4, December 2010
DOI : 10.5121/ijasuc.2010.1411 116
A COST EFFECTIVE COMPRESSIVE DATA
AGGREGATION TECHNIQUE FOR WIRELESS
SENSOR NETWORKS
M.Y. Mohamed Yacoab1
, Dr.V.Sundaram2
and Dr.A.Thajudeen3
1
Research Scholar, Karpagam University, Coimbatore, India
yacoab@yahoo.com
2
Director, MCA Department, Karpagam College of Engineering, Coimbatore, India
dr_vsundaram@yahoo.com
3
Director, Measi Institute of Information Technology, Chennai India
thaj_a2001@yahoo.com
ABSTRACT
In wireless sensor network (WSN) there are two main problems in employing conventional compression
techniques. The compression performance depends on the organization of the routes for a larger extent.
The efficiency of an in-network data compression scheme is not solely determined by the compression
ratio, but also depends on the computational and communication overheads. In Compressive Data
Aggregation technique, data is gathered at some intermediate node where its size is reduced by applying
compression technique without losing any information of complete data. In our previous work, we have
developed an adaptive traffic aware aggregation technique in which the aggregation technique can be
changed into structured and structure-free adaptively, depending on the load status of the traffic. In this
paper, as an extension to our previous work, we provide a cost effective compressive data gathering
technique to enhance the traffic load, by using structured data aggregation scheme. We also design a
technique that effectively reduces the computation and communication costs involved in the compressive
data gathering process. The use of compressive data gathering process provides a compressed sensor
reading to reduce global data traffic and distributes energy consumption evenly to prolong the network
lifetime. By simulation results, we show that our proposed technique improves the delivery ratio while
reducing the energy and delay.
KEYWORDS
Wireless Sensor Network, Data Aggregation And Data Gathering, Compressive Data
Gathering
1. INTRODUCTION
1.1 Wireless Sensor Networks
Wireless sensor networks include the emerging technologies which have received major
attention from the research community. The sensor network which is self organizing ad hoc
system comprises of several small and low cost devices. It observes the physical environment,
collect the information and transmit it to one or more sink nodes. Generally, the radio
transmission range of the sensor nodes are in the orders of magnitude which is smaller than the
geographical extent of the entire network. Therefore, data should be transmitted towards the sink

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node hop-by-hop in a multi-hop manner. By reducing the amount of data which is to be
transmitted, the energy consumption of the network can also be reduced [1]. A large number of
small electromechanical devices with sensing, computing and communication capabilities are
included in the wireless sensor networks. It can be used for collecting sensory information, such
as temperature measurements, from an extended geographic area [2].
The possible uses of the sensor networks have been researched actively. Due to the
characteristics of the wireless sensor network several challenging issues are created. The
following characteristics are mainly focused:
• Sensor nodes tend to fail.
• Sensor nodes utilize a broadcast communication paradigm and have severe bandwidth
constraints.
• Sensor nodes have limited resources [3].
1.2 Data Aggregation and Data Gathering
A common function of sensor networks is data gathering. In data gathering the information
sampled at sensor nodes has to be transported to the central base station for further processing
and analysis. An important topic mentioned by the wireless sensor network community is the in-
network data aggregation while focusing on the severe energy constraints of the sensor nodes
and the limited transport capacity of multi-hop wireless networks. The basic idea for minimizing
the expense of data transmission is to pre-process the sensor data in the network by the sensor
nodes [4].
One of the basic distributed data processing procedures in the wireless sensor networks is data
aggregation. It is used to save the energy and to reduce the medium access layer contention [5].
The idea is to combine the data coming from different sources, eliminating the redundancy and
reduce the number of transmissions, thus saving the energy [6]. By using the in-network data
aggregation, the natural redundancy in the raw data collected from the sensors can be eliminated.
Moreover, such operations are useful for extracting the specific information from the data.
Supporting high frequency of in-network data aggregation is severe for the network in order to
conserve energy for a longer network lifetime.
1. 3 Need of Compressive Data Aggregation technique in WSN
In wireless sensor network (WSN) there are two main problems with conventional compression
techniques.
• The compression performance relies heavily on how the routes are organized. In order to
achieve the highest compression ratio, compression and routing algorithms need to be
jointly optimized.
• The efficiency of an in-network data compression scheme is not solely determined by
the compression ratio, but also depends on the computational and communication
overheads [7].
In this situation, Compressive Data Aggregation technique helps to cope up with these issues. In
this technique, data is gathered at some intermediate node where the data size size is reduced by
applying compression technique without losing any information of complete data. Compressive
Data Aggregation technique requires each node in the WSN to send exactly k packets
irrespective of what it has received, which means, compared with traditional techniques , more
work/load for the nodes which are far away from the sink and less work/load for the nodes that
are close to the sink. Data compression and aggregation technique have the potential to improve
WSN energy efficiency and minimize communication [8].

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1.4 Adaptive Traffic Aware Data Aggregation Technique
In our previous work [9], we have proposed an adaptive traffic aware aggregation technique for
wireless sensor networks. In this work, a multi path structured tree is constructed in which nodes
are selected based on their residual energy level. A traffic monitoring agent is used to monitor
the load status of the event traffic and each node estimates its traffic load during the data
reception. At the sink, it estimates the total traffic load in the system and sends an
OVERLOADED packet to the sources if it is greater than a threshold level T. Then the
aggregation technique is changed to structure-free lossy aggregation by the sources. If the traffic
load is less than the threshold value T, the sink sends UNDERLOADED packet to the sources
and then sources change the aggregation mode to the structured lossless aggregation. This
technique eventually provides a reliable transmission environment with low energy
consumption, by efficiently utilizing the energy availability of the forwarding nodes to gather
and distribute the data to sink, according to its requirements.
As an extension of our previous work, we provide a compressive data gathering technique to
enhance the traffic load, when structured data aggregation is used. The use of compressive data
gathering provides a compressed sensor reading to reduce global data traffic and distributes
energy consumption evenly to prolong network lifetime. We can also increase the efficiency
level if the correlated sensor readings are transmitted jointly rather than separately.
2. RELATED WORK
Marco F. Duarte et al [11] have introduced a new theory for distributed compressed sensing
(DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit
both intra- and inter-signal correlation structures. They also proposed algorithms for joint
recovery of multiple signals from incoherent projections.
Zainul Charbiwala et al [12] have proposed that if CS is employed for source compression, then
Compressive Sensing (CS) can further be exploited as an application layer erasure coding
strategy for recovering missing data. They showed that CS erasure encoding (CSEC) with
random sampling is efficient for handling missing data in erasure channels, paralleling the
performance of BCH codes, with the added benefit of graceful degradation of the reconstruction
error even when the amount of missing data far exceeds the designed redundancy.
Wenbo He et al [13] proposed a two privacy-preserving data aggregation schemes for additive
aggregation functions. The first scheme – Cluster-based Private Data Aggregation (CPDA) –
leverages clustering protocol and algebraic properties of polynomials. The second scheme –
Slice-Mix AggRegaTe (SMART) – builds on slicing techniques and the associative property of
addition. The goal of this work is to bridge the gap between collaborative data collection by wireless
sensor networks and data privacy.
Maarten Ditzel et al [14] presented the results of a study on the effects of data aggregation for
multi-target tracking in wireless sensor networks. Wireless sensor networks are normally limited
in communication bandwidth. The nodes implementing the wireless sensor network are
themselves limited in computing power and usually have a limited battery life. These
observations are recognized and combined to come to efficient target tracking approaches.
Steffen Peter et al [15] described and evaluated three algorithms that were reported to suit to the
WSN scenario. As result of the evaluation, where emphasize is on the awareness to potential
attack scenarios, a brief overview of strengths and weaknesses of the algorithms is presented.
Since no algorithm provides all desirable goals, two approaches to cope with the problems are

119
proposed. The first is the successive combination of two algorithms. It increases security, while
the additional efforts can be minimized by carefully selected parameters. For the second
approach, specific weaknesses are faced and so mechanisms are engineered that solve the
particular issues.
3. STRUCTURED TREE CONSTRUCTION
Initially we will describe the structured tree construction algorithm presented in our previous
paper.
We consider the wireless sensor network M as a directed graph G (N, E). Let the set of nodes N
consists of sensors and (a, b) ∈E if a and b are residing inside the transmission range of each
other. The fundamental idea of the proposed algorithm is, when a data gathering request is
arrived, then using the greedy algorithm a data gathering tree for the request is constructed. The
greedy algorithm maximizes the minimum residual energy among the nodes. Then the nodes are
included in the tree one by one but in the beginning only the sink node is included. A node b is
selected to be included into the tree if the causes to maximize the minimum residual energy
among the trees are included.
In our algorithm, we use the following notations
• N is the total number of nodes
• NT is the set of nodes in the tree,
• stop is a Boolean variable,
• newnode is the node that will be added to the tree.
• q is the size of the sensed data by newnode.
• wα
a,b is the weight assigned to the edge.
• R is the set of nodes that are not in the tree.
• RE is the residual energy.
• s is the sink node
• mremax is the maximum value of minimum residual energy at each node of the tree.
• tp is the temporary parent node.
• Pa,s is the unique path in T from node a to node s
• p(a) is the parent of a in T
• Let node v ∈ N - NT be the considered node.
3. 1. 1. Tree Construction Algorithm
Algorithm.1
1. NT = {s}
2. Stop = “false”
3. R = N - NT
4. RE(s) = ∞
5. mremax = 0
6. for each i ∈ R
6.1 Compute mremax (i) and tp
6.2. If mremax (i) > mremax, then
6.2.1. mremax = mremax(i)
6.2.2. Newnode = i
6.3 End if
7. End for
8 If mremax > 0, then
8.1. P (newnode) = tp(newnode)

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8.2. For each j ∈ Pnewnode, s do
8.2.1. RE (j) = RE (j) - qwα
j,p(j)
8.3 End for
8.4. NT = NT ∪ {newnode}
8.5 R = R - newnode
9 Else
9.1 stop = “True”
10. End if
11. If (R ≠φ ) or stop=”false” then
11.1 repeat from 5
12. End if
13. End
4. ADAPTIVE COMPRESSIVE DATA GATHERING AND RECOVERY
4. 1. Compressive Data Gathering
The intuition behind CDG is that higher efficiency can be achieved if correlated sensor readings
are transmitted jointly rather than separately. We have given a simple example in Section I,
showing how sensor readings are combined while being relayed along a chain-type topology to
the sink. In practice, sensors usually spread in a two-dimensional area, and the ensemble of
routing paths presents a tree structure. Fig. 4(a) shows a typical routing tree in which the sink
has four children. Each of them leads a sub tree delimited by the dotted lines. Data gathering and
reconstruction of CDG are performed on the sub tree basis.
The perception behind CDG is that joint transmission of the correlated sensor readings instead of
transmission of the readings separately will increase the efficiency to a higher level. The
combining of the sensor readings when it is being transmitted to the sink along the chain type
topology is shown as an example in section 1. Generally sensors spread in the two dimensional
area and the structure represented by the routing paths is a tree structure. A routing tree with four
children at the sink is shown in the Fig. 4(a). A sub tree delimited by the dotted lines is lead by
each of them. On the sub tree basis data gathering and reconstruction of the CDG are performed.
In order to combine sensor readings while relaying them, every node needs to know its local routing
structure. That is, whether or not a given node is a leaf node in the routing tree or how many
children the node has if it is an inner node. To facilitate efficient aggregation, we have made a
small modification to standard ad-hoc routing protocol: when a node chooses a parent node, it
sends a “subscribe notification” to that node; when a node changes parent, it sends an
“unsubscribe notification” to the old parent.
Each node should know its local routing structure so as to combine the sensor readings when it is
being transmitted. That is, if the given node in the routing tree is a leaf node or not or if the node
is an inner node then how many children does it have. To the standard routing protocol, a small
modification is

121
fig. 1
done so as to facilitate proficient aggregation: when a parent node is chosen by the node, it
transmits a “subscribe notification” to that node and an “unsubscribe notification” is sent to the
old parent, when the node changes the parent.
The data gathering process of CDG is illustrated through an example shown in Fig. 4(b). It is the
detailed view of a small fraction of the routing tree marked in Fig. 4(a). After all nodes acquire
their readings, leaf nodes initiate the transmission.
The example shown in fig. 1 illustrates the data gathering process of CDG. The leaf nodes will
initiate the transmission only after all nodes receive their readings.
In this example, S2 generates a random number αi2, computes αi2v2, and transmits the value to S1.
The index i denote the ith
weighted sum ranging from 1 to M. Similarly, S4, S5 and S6 transmit
αi4v4, αi5v5, and αi6v6 to S3. Once S3 receives the three values, it computes αi3v3, adds it to the
sum of relayed values and transmits ∑=
6
3
ij
j
jvα to S1. Then S1 computes αi1v1 and
transmits ∑=
8
1
1j
j
jvα . Finally, the message containing the weighted sum of all readings in a sub
tree is forwarded to the sink.
In this example, a random number αi2 is generated by S2 and it computes αi2v2 and then the
value is sent to S1. The ith weighted sum is denoted by the index i which ranges from 1 to M.
Likewise αi4v4, αi5v5, and αi6v6 is transmitted to S3 by S4, S5 and S6. After the three values are
received by S3 it will compute the value αi3v3 and then it adds to the sum of the relayed value.
It then transmits to S1 the value ∑=
6
3
ij
j
jvα . Next αi1v1 is computed by the node S1 and
S1
S2 S3
S6
S7
S8
S5
S4

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∑=
8
1
1j
j
jvα is transmitted. Lastly, to the sink, the message which contains the weighted sum of all
readings in a sub tree is forwarded.
Assume that there are N nodes in a particular tree, and the sink intends to collect M
measurements. Then all nodes send the same number of O (M) messages regardless of their hop
distance to the sink. The overall message complexity is O (NM). When M << N, CDG transmits
less messages than the baseline data collection whose worst case message complexity is O (N2
).
More importantly, the transmission load is spread out uniformly so that the lifetime of bottleneck
sensors and the entire network is greatly extended.
In a specific tree, if it is assumed to have N nodes and M measurements are intended to be
collected by the sink. Then regardless of the hop distance of the node to the sink, all nodes will
send the same number of O (M). O (NM) will be the overall message complexity. If M << N,
then less messages are transmitted by CDG when compared with the baseline data collection
when O (N2
) is the worst case message complexity. More importantly, for the extension of the
lifetime of the bottleneck sensors as well as the entire network, the transmission load is spread
uniformly.
The ith
weighted sum can be represented by:
∑
=
=
N
j
ji vA
1
ijα (1)
The sink obtains M weighted sums {Ai}, i = 1, 2 ...M.
Mathematically, we have:
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(2)
In this equation, each column of {αij} contains the series of random numbers generated at a
corresponding node. In order to avoid transmitting this random matrix from sensors to the sink,
we can adopt a simple strategy: before data transmission, the sink broadcasts a random seed to
the entire network. Then each sensor generates its own seed using this global seed and its unique
identification. With a pre-installed pseudo random number generator, each sensor is able to
generate the corresponding series of coefficients. These coefficients can be reproduced at the
sink given that the sink knows the identifications of all sensors.
In the above equation, series of random numbers are placed in each column of {αij} which is
produced at the corresponding node. A simple strategy is used for preventing the transmission of
the random matrix from sensors to the sink: a random seed is broadcasted to the entire network
before transmission. Using this global seed and its unique identification, each sensor will
generate its own seed. Each sensor generates a corresponding series of coefficients from a pre-
installed pseudo random number generator. Given that the sink knows the identifications of all
sensors, the coefficients can be reproduced at the sink.
In (2), vi (i = 1, 2 ...N) is a scalar value. In a practical sensor network, each node is possibly
attached with a few sensors of different type, e.g. a temperature sensor and a humidity sensor.
Then sensor readings from each node become a multi-dimensional vector. In this case, we may

123
separate readings of each dimension and process them respectively. Alternatively, since the
random coefficients αij are irrelevant to sensor readings, we may treat vi as a vector. The
weighted sums Ai become vectors of the same dimension too.
In (2), vi (i = 1, 2 ...N) is a scalar value. Each node is possibly attached with a few sensors of
different type, e.g., temperature sensor and a humidity sensor in a practical sensor network. Then
from each node, the sensor readings become a multi dimensional vector. In this case, in each
dimension we may separate the readings and process them. Alternatively, since for the sensor
readings, the random coefficients αij are irrelevant, vi is treated as a vector. Ai which is a
weighted sum become vectors of the same dimension too.
When M < N, solving a set of M linear equations with N unknown variables is an ill-posed
problem. However, sensor readings are not independent variables. In most cases, the sensor field
follows a certain structure because of the spatial or temporal correlations. Hence, there exists a
transform domain in which the signal is sparse. Under this assumption, we will explain in the
following subsection whether the set of linear equations are solvable, what requirements M
should meet to solve them, and how these equations can be solved.
When M < N, with N unknown variables, solving a set of M linear equations is an ill-posed
problem. But sensor readings are no where independent variables. In most cases, a certain
structure is followed by the sensor field due to the spatial or temporal correlations. So, a
transform domain is used wherever the signal is sparse. Based on this assumption in the
following subsections we explain: whether linear equation set is solvable, to meet them what are
the requirements M and these equations can be solved.
4.2 Data recovery
According to compressive sampling theory, a K-sparse signal can be reconstructed from a small
number of measurements with a probability close to one. The weighted sums obtained in (2) are
a typical type of measurements. Signal sparsity characterizes the correlations within a signal. An
N-dimensional signal is considered as a K-sparse signal if there exists a domain in which this
signal can be represented by K (K _ N) non-zero coefficients. Fig. 5(a) shows a 100-dimensional
signal in its original time domain. Obviously, it is not sparse at all in this domain. Because of the
signal correlation, it can be described more compactly in transform domains such as wavelet and
DCT.
A K-sampling signal according to the compressive sampling theory can be reconstructed based
on the small number of measurements having a probability nearly one. The weighted sum from
(2) is measurements of typical type. Within a signal, signal sparsity characterizes the
correlations. An N-dimensional signal is called as a K-sparse signal when there is a domain
where signal can be presented as K(K_N) non zero coefficients. Fig.5(a) represents a 100-
dimensional signal in its real time domain. Due to signal correlation, in transform domains such
as wavelet and DCT, it can be described more compactly.
In a densely deployed sensor network, sensors have spatial correlations in their readings.
Sensors have spatial correlations in its readings in a densely deployed sensor networks.
Let N sensor readings form a vector v = [v1 v2 ... vN] T
, then v is a K-sparse signal in a particular
domain λ. Denote λ = [λ 1 λ 2 ... λ N] as the representation basis with vectors {λ i} as columns,
and X = [X1, X2 ...XN] T
are the corresponding coefficients. Then,
v can be represented in the λ domain as:
i
N
i
iXv λ∑=
=
1
Or v = λX (3)
Compressive sampling theory tells that a K-sparse signal can be reconstructed from M
measurements if M satisfies the following conditions [6]:
M ≥ β. ∆2
(α, λ). K.log N (4)

124
where β is a positive constant, α is the sampling matrix as defined in (2), and ∆ (α, λ) is the
coherence between sampling basis α and representation basis λ. The coherence metric measures
the largest correlation between any two elements of α and λ, and is defined as:
∆ (α, λ) = √N. Max | < αi, λj> |, 1≤ i, j ≥N (5)
From (5), we can see that the smaller the coherence between α and λ is, the lesser measurements
are needed to reconstruct the signal. In practice, using random measurement matrix is a
convenient choice, since a random basis has been shown to be largely incoherent with any fixed
basis and M = 3K ~ 4K is usually sufficient to satisfy (4).
From eq. (5), we get to know that lesser is the coherence in between α and λ, reduced
measurements are required for the signal reconstruction. In practice, a convenient choice is to
use random measurement matrix, since with any fixed basis a random basis is shown to be
largely incoherent and M = 3K – 4K is sufficient to satisfy eq. (4).
With sufficient number of measurements, the sink is able to reconstruct sensor readings by
solving an l1-minimization problem:
1
min
l
XNX ℜ∈
s.t. A = αv, v = λX (6)
In addition, for sparse signals whose random projections are contaminated with noise,
reconstruction can be achieved by solving a relaxed l1-minimization problem, where is a
predefined error threshold:
1
min
l
XNX ℜ∈
s.t. ||A – αv||
2
l < ε, v = λX (7)
Suppose is the solution to this convex optimization problem, then the proposed reconstruction
of the original signal is ũ = λ . It has been shown that the above l1-minimization problem can
be solved with linear programming (LP) techniques. Although the reconstruction complexity of
LP based decoder is polynomial, it goes pretty high when N is too large. While there is a large
body of on-going work looking for low-complexity reconstruction techniques, this topic is
beyond the scope of our paper. With the current LP based decoder, we would suggest that the
size of N does not exceed one thousand.
Suppose for the convex optimization problem if is the solution, then for the original signal the
proposed reconstruction is ũ = λ . The linear programming (LP) techniques can be used for
solving the above mentioned l1-minimization problem. When N is too large the reconstruction
complexity of LP based decoder goes pretty high even though initially it is a polynomial
function. This topic is beyond the scope of our paper, when there is a large body of on going
work looking for low complexity reconstruction technique. We would suggest, for the current
LP based decoder that the size of N does not exceed one thousand.
In (6) and (7), the λ matrix describes the correlation pattern among sensor readings. It is utilized
only in data recovery process, and is not required to be known to sensors. In this way, most of
the computations are shifted from sensors to the sink. Such asymmetry of computation
complexity makes CDG an appealing choice for WSNs.
In (6) and (7) the correlation pattern among the sensor reading is described by the λ matrix. It is
not required to be known to the sensors since it is utilized in data recovery process. Likewise,
most of the calculations are transferred from the sensors to the sink. As a result of the
asymmetry of computation complexity, CDG is an appealing choice for WSN’s.
5. MINIMIZING COMPRESSION COST
Our objective is to minimize both the computation and communication costs rather than
minimizing communication cost only, as done in the prior works. To perform the compression
over the data gathering tree (given in the last section), we propose a flow based technique where
data from each source is compressed and transmitted as a traffic flow over the corresponding
path from the source to the sink.

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5. 1. Network Model
The underlying wireless network is modeled as a connected weighted graph
G = < N, L, W >,
Where the vertex set N represents the set of n sensor nodes; the edge (link) set L represents the
wireless connection between nodes and associated with each edge li Є L, its weight Wli is the
energy cost of sending a data packet of unit size over li. The link weight is determined by the
distance between the two adjacent nodes, the radio device, and the communication environment.
We also use (u, v) to denote an edge connecting u and v.
Let si Є N denote the sink node and S ⊂ N, denote the set of source nodes. In each period, each
source node generates a raw data of one unit size that needs to be transported to the sink,
possibly via multi-hop communication.
A data gathering tree is a sub-tree of G rooted at sink and containing S, denoted as
T = < N’, L’ >,
where S ⊂ N’ ⊂ N and L’ ⊂ L. Let Mn denote the number of source nodes in the sub-tree
rooted at n Є N. Given a data gathering tree, let Ps denote the path in the tree that connects s to si.
Also, for two edges l1, l2 on the same path, let l1 l2 denote the fact that l1 is a predecessor of l2.
We define a pre-defined system parameter, costcomp ≥ 0, to represent the energy cost of
compressing one unit of data (using (1) and (2) in section 4) normalized by the cost of
communicating one unit of data. The energy cost of compressing source information of size z to
an output of size o is represented as a function
F (o) = Costcomp * z * CR (8)
Where CR =
o
z is the compression ratio.
From (1), it can be seen that the energy cost is
• Proportional to the input size z since it has to process the whole input at least once,
• Proportional to the compression ratio CR.
If. l = (u, v) denote a one-hop link, where u generates a data packet of one unit size that needs
to be transmitted to v after appropriate compression by u, then z=1 and Eq. (1) can be modified
as.
F (o) =
o
Costcomp
Let Wl denote the cost of transmitting one unit of data over the link l. The overall energy costs,
denoted as Costenergy(o) can then be modeled as follows
Costenergy(o) =
o
Costcomp
+ o. Wl (9)
5. 2. Cost Effective Data Gathering
Given a data gathering tree (as described in section 3) over a sensor network, we model data
transmission over the tree as a composition of different data flows from each source node to si.
That is, each path from a source node to si in the tree corresponds to a data flow over the path.
The flow size may change along its corresponding path due to data compression performed by
intermediate nodes. Also, the energy cost of the system is the sum of the computation and
communication costs of all paths in the tree.
Consider an arbitrary path Ps in the tree from a source node n to si. Let fl
n
denote the flow over l
Є Ps and qs denote the last edge in Ps, i.e., the edge incident on si in Ps. We assume that the total
energy spent on data compression over the path Ps is determined by the flow on qs, i.e., the total
energy cost for data compression over Ps is calculated as

126
Ps = s
q
comp
s
f
Cost
(10)
Given a node in the tree, the number of incoming flows equals the number of source nodes in its
sub-tree. The output size required for compressing each incoming packet is lower bounded by
the joint entropy of these source nodes. We assume that the joint entropy of any i source nodes,
Ei is a non-decreasing and concave function of i with E1 = ED, where ED Є (0, 1) is the entropy of
one unit of data. We assume that the compression of i incoming data flows at node n can be
performed in such a way that the lower bound for compressing each data flow equals LBi =
i
Ei
,
with LB1 = E1 = ED. In other words, we assume that when maximal compression is performed on
i pieces of source information, the fraction of compressible data of each piece is the same.
Thus, for any l = (a, b) Є Ps, we impose the constraint on fl
n
such that
l
nf ≥ nMLB =
nM
nME
(11)
Let λi = nMLB , where Mn is the number of source nodes in the sub-tree rooted at n∈N. Also, we
have λi ≥λi+1, for i = 1. . . k − 1.
Given a data gathering tree and an arbitrary source node s Є S, consider the path from s to si. Let
Ps = {s1, s2. . . sk} denote the path, where s1 = s, sk = si, and k is the number of nodes along Ps.
We need to compress and transmit a packet of unit size from s1 to si with the minimal
computation and communication energy costs.
Let f denote a vector with flow along Ps, i.e., f = { l
n
f
1
, …., l
nk
f
1−
}.
For any optimal flow f over a path Ps, if fi+1 < fi, we have fi = λi.
6. SIMULATION RESULTS
6. 1. Simulation Setup
The performance of our cost effective compressive data aggregation (CECDA) technique is
evaluated through NS2 [13] simulation. A random network deployed in an area of 500 X 500 m
is considered. We vary the number of nodes as 20, 40….100. Initially the nodes are placed
randomly in the specified area. The base station is assumed to be situated 100 meters away from
the above specified area. The initial energy of all the nodes is assumed as 3.1 joules. In the
simulation, the channel capacity of mobile hosts is set to the same value: 2 Mbps. The
distributed coordination function (DCF) of IEEE 802.11 is used for wireless LANs as the MAC
layer protocol. The simulated traffic is CBR with UDP source and sink. The number of sources
is varied from 1 to 5.
Table 1 summarizes the simulation parameters used
TABLE 1: SIMULATION PARAMETERS
No. of Nodes 20,40,….100
Area Size 500 X 500
Mac 802.11
Simulation Time 50 sec
Traffic Source CBR
Packet Size 512
Transmit Power 0.660 w

127
Receiving Power 0.395 w
Idle Power 0.335 w
Initial Energy 3.1 J
Transmission
Range
75m
6. 2. Performance Metrics
The performance of CECDA technique is compared with our previous ATAA [9] protocol. The
performance is evaluated mainly, according to the following metrics.
Average end-to-end Delay: The end-to-end-delay is averaged over all surviving data packets
from the sources to the destinations.
Average Packet Delivery Ratio: It is the ratio of the number of packets received successfully
and the total number of packets transmitted.
Energy Consumption: It is the average energy consumed by all the nodes in sending, receiving
and forwarding operations
The simulation results are presented in the next section.
6. 3. Simulation Results
A. Dense
In our initial experiment, we vary the number of nodes as 20, 40, 60, 80 and 10 in which the
sources are densely deployed.
No. Of Nodes vs Delay
0
1
2
3
20 40 60 80 100
Nodes
Delay(s)
ATAA
CECDA
Fig 1: Nodes Vs Delay
No. of Nodes Vs Delivery Ratio
0
0.2
0.4
0.6
0.8
1
20 40 60 80 100
Nodes
Del.ratio
ATAA
CECDA
Fig 2: Nodes Vs DelRatio

128
No. Of Nodes Vs Energy
0
0.5
1
1.5
2
2.5
20 40 60 80 100
Nodes
Energy(J)
ATAA
CECDA
Fig 3: Nodes Vs Energy
Since the aggregation involves compressed data, the delay incurred in sending the data from
sensors to the sink, will be significantly reduced. Fig 1 gives the average end-to-end delay when
the number of nodes is increased. From the figure, it can be seen that the average end-to-end
delay of the proposed CECDA technique is less when compared with ATAA.
Fig 2 presents the packet delivery ratio when the number of nodes is increased. The compressed
data aggregation eliminates the packet drops at the intermediate nodes and hence increases the
packet delivery ratio. So CECDA achieves good delivery ratio, compared to ATAA.
Compressing the data during data aggregation reduces the number of data packets to be
aggregated at the aggregator nodes. Hence the total energy consumption involved in the
aggregation process will also be reduced. Fig 3 shows the results of energy consumption when
the number of nodes is increased. From the results, we can see that CECDA technique has less
energy consumption when compared with ATAA, since it has the energy efficient tree.
B. Sparse
In our second experiment, we vary the number of nodes as 20, 40, 60, 80 and 10 in which the
sources are sparsely deployed.
No.of Nodes Vs Delay
0
5
10
15
20
20 40 60 80 100
Nodes
Delay(s)
ATAA
CECDA
Fig 4: Nodes Vs Delay

129
No. of Nodes Vs Delivery Ratio
0
0.2
0.4
0.6
0.8
1
20 40 60 80 100
Nodes
Del.ratio
ATAA
CECDA
Fig 5: Nodes Vs DelRatio
Nio. of Nodes Vs Energy
0
0.5
1
1.5
2
2.5
20 40 60 80 100
Nodes
Energy(J)
ATAA
CECDA
Fig 6: Nodes Vs Energy
Since the aggregation involves compressed data, the delay incurred in sending the data from
sensors to the sink, will be significantly reduced. Fig 4 gives the average end-to-end delay when
the number of nodes is increased. From the figure, it can be seen that the average end-to-end
delay of the proposed CECDA technique is less when compared with ATAA.
Fig 5 presents the packet delivery ratio when the number of nodes is increased. CECDA
achieves good delivery ratio, compared to ATAA. The compressed data aggregation eliminates
the packet drops at the intermediate nodes and hence increases the packet delivery ratio.
Fig 6 shows the results of energy consumption when the number of nodes is increased.
Compressing the data during data aggregation reduces the number of data packets to be
aggregated at the aggregator nodes. Hence the total energy consumption involved in the
aggregation process will also be reduced. From the results, we can see that CECDA technique
has less energy consumption when compared with ATAA, since it has the energy efficient tree.
7. CONCLUSION
Compressive Data Aggregation technique helps to solve the issues of traditional compression
techniques. In this technique data is gathered at some intermediate node where size of the data
need to be sent is reduced by applying compression technique without losing any knowledge of
complete data. In our previous work, we have developed an adaptive traffic aware aggregation
technique in which the aggregation technique is adaptively changed to structured and structure-
free, depending on the load status of the traffic. In this paper, as an extension of our previous
work, we have provided a compressive data gathering technique to enhance the traffic load,
when structured data aggregation is used. We have also designed a technique that effectively
reduces the computation and communication costs involved in the compressive data gathering
process. The use of compressive data gathering provides a compressed sensor reading to reduce
global data traffic and distributes the energy consumption evenly to prolong network lifetime.

130
By simulation results, we have shown that our proposed technique improves the delivery ratio
while reducing the energy and delay.
References
[1] Dorottya Vass and Attila Vidacs, “Distributed Data Aggregation with Geographical Routing in
Wireless Sensor Networks”, Proc., IEEE International Conference on Pervasive Services (ICPS), Istanbul,
Turkey, 15-20 July, 2007.
[2] Jukka Kohonen, “Data Gathering in Sensor Networks”, Helsinki Institute for Information Technology
in Finland, Nov-2004.
[3] Gregory Hartl, Baochun Li, “Loss Inference in Wireless Sensor Networks Based on Data
Aggregation”, IPSN 2004.
[4] Tao Cui, Lijun Chen, Tracey Ho, Steven H. Low, and Lachlan L. H. Andrew, “Opportunistic Source
Coding for Data Gathering in Wireless Sensor Networks”, Proceedings of the 2007 conference on
Diversity in computing Orlando, Florida, 2007.
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Aggregation in Wireless Sensor Networks”, Draft Infocom2007 Paper.
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Wireless Sensor Networks”, Proceedings of the 22nd International Conference on Distributed Computing
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[7] Chong Luo and Feng Wu, “Compressive Data Gathering for Large-Scale Wireless Sensor Networks”,
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China, 2009.
[8] Hengyu Long et al, “Energy-Efficient Spatially-Adaptive Clustering and Routing in Wireless Sensor
Networks”, Proceedings of Design, Automation & Test in Europe Conf, 2009.
[9] M.Y. Mohamed Yacoab and Dr. V. Sundaram, “An Adaptive Traffic Aware Data Aggregation
Technique for Wireless Sensor Networks”, American Journal of Scientific Research Issue 10, 2010.
[10]Riccardo Masiero et al, “A Bayesian Analysis of Compressive Sensing Data Recovery in Wireless
Sensor Networks”, IEEE SASN 2009, Saint Petersburg, Russia, Oct. 12-14, 2009.
[11]Dror Baron et al, “An Information-Theoretic Approach to Distributed Compressed Sensing”,
Proceedings of the 43d Allerton Conference on Communication, Control, and Computing, Monticello, IL,
September, 2005.
[12]Zainul Charbiwala et al, “Compressive Oversampling for Robust Data Transmission in Sensor
Networks”, IEEE INFOCOM, San Diego, CA, March 2010.
[13] Wenbo He, Xue Liu, Hoang Nguyen, Klara Nahrstedt and Tarek Abdelzaher, “PDA: Privacy-
preserving Data Aggregation in Wireless Sensor Networks”, 2007.
[14] Maarten Ditzel, Caspar Lageweg, Johan Janssen and Arne Theil, “Multi-target Data Aggregation and
Tracking in Wireless Sensor Networks”, JOURNAL OF NETWORKS, VOL. 3, NO. 1, JANUARY 2008.
[15] Steffen Peter, Krzysztof Piotrowski and Peter Langendoerfer, “On Concealed Data Aggregation for
Wireless Sensor Networks”, 2007.

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