Effect of Energy-Efficient Routing for Packet Splitting using Chinese
Remainder Theorem (CRT) for Wireless Sensor Networks (WSNS)
ADENIJI OLUWASHOLA DAVID1*, AZEEZ, BUKOLA AKEEM2,
SAMUEL OLADELE ADEYEMI3
1Computer Science Department,
University of Ibadan,
NIGERIA
2Computer Science Department,
University of Ibadan,
NIGERIA
3Department of Human Kinetics and Health Education,
University of Ibadan Ibadan,
NIGERIA
*Corresponding Author
Abstract: - The most popular Wireless Sensor Network (WSN) protocol utilized for energy optimization of
WSN nodes is the Low Energy Adaptive Clustering Hierarchy (LEACH) protocol, which is a basic energy-
efficient routing protocol of hierarchical routing protocol’s family, where the sensor nodes remain static. There
is a need to extend the lifetime with respect to reducing the energy consumption of nodes, and this was
accomplished using the Chinese Remainder Theorem (CRT. In this research large data packets are broken into
smaller packets. The focus of the study is to develop an energy routing for splitting packets in Wireless Sensor
Networks (WSNs) using Chinese Remainder Theorem (CRT) techniques. A further improvement in WSN
lifetime is by utilizing fuzzy logic. Factoring node parameters such as residual energy of nodes, their centrality
within clusters, and their distance to the base station and improving upon the selection of nodes as cluster heads
are required. The developed application can be used to reduce the communication cost of Energy efficiency of
WSN. The forwarding technique for this research is to split the packet sent by the source node of a WSN so
that the maximum number of bits per packet that a node has to transmit is significantly minimized.
Key-Words: - Energy consumption, Adaptability, Localization, Routing, Chinese Remainder Theorem (CRT),
Wireless Sensor Networks (WSNS).
Received: July 2, 2022. Revised: August 27, 2023. Accepted: September 25, 2023. Published: November 28, 2023.
1 Introduction
A Wireless Sensor Network (WSN) is an ad-hoc
network that consists of a set of sensor nodes that
are either randomly fixed or spread out in a given
geographical area and usually communicate through
a wireless link. The area in which these sensor nodes
operate is usually called the area of interest and
where information is collected. Most often, to save
data, a special sensor node is chosen to collect data
from the various other nodes, and this node is called
the sink node. Most often, the transmission of the
collected data is done periodically or may be event-
based, usually dependent on the application. The
sink node usually acts as a bridge between the WSN
and the end-user network, allowing the user to
communicate with the WSN through this node.
Individual sensor nodes have their own
characteristics and energy autonomy, and this
resource is essential to the survival of a WSN
because, in most cases, the sensor’s battery is
irreplaceable. Energy in Wireless Sensor Networks
is controlled with limited power thereby making the
revitalization of resources difficult. Therefore, it is
important to plan WSNs in an energy-efficient
manner because it affects the network lifetime.WSN
energy saving is highly dependent on how long a
sensor node takes to process data packets. WSN
technologies utilize Network coding to achieve this
objective, but can only be efficiently applied to
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sensor nodes for data dissemination, and cannot be
applied to data collection, which is the most
important traffic in WSN.
The main features of WSN are: Energy
consumption: Sensors have energy autonomy, and
they usually use tiny batteries as energy resources.
In most cases, WSNs are deployed in hard-to-reach
areas. This makes it difficult or almost impossible
to recharge or replace the batteries. This difficulty
leads us to deduce that the life time of a sensor is
essentially dependent on the battery. Therefore,
energy-consumption management is a major
constraint in this type of network. An intrinsic
characteristic of these sensors is their low storage
capacity. Although they also have a processor, the
sensors cannot perform very large operations due to
their relatively low processing power. For example,
“mote”-type sensor nodes are composed of an 8-bit
4 MHz microcontroller, 40 KB of memory, and a
radio with a bit rate of about 10 Kbps.
These remain true even for midrange nodes,
such as “UCLA/ROCKWELL’S WINS”, which
have a strong ARM 1100 processor with 1 MB flash
memory, 128 KB of RAM, and a 100 Kbps radio.
Quality is defined by the ability to interpret the
information collected by the sink. Even though the
QoS requirements vary according to the different
WSN applications, the two main measures of QoS
are data reliability and latency. Usually, a successful
data-exchange rate between the sensor nodes and the
sink must be above a certain threshold to ensure
network reliability and functionality. Reliability can
be further maximized, but this could be at the cost of
increased energy consumption. It is therefore
necessary to design robust and lightweight
algorithms for data encryption, authentication
mechanisms for privacy protection, and secure
routing for data relays to protect the entire network
against passive and active attacks, and denials of
external service providers.
2 Theoretical Foundation
The Architecture used in WSNs is commonly based
on five layers of the OSI Model. However,
Transmission Control Protocol (TCP) is not suitable
for WSNs because of multi-hop communication.
Different layers used in WSNs are application,
transport, network, data link, and physical.
Additionally, the special functions of a WSN such as
power management, mobility management, and task
scheduling, to improve the effectiveness of the
network are generally managed by three cross layers
which are: Application layer: it supervises
movement and offers software for several usages
which transfer queries to obtain information.
Transport layer: this layer is usually essential for
internetwork communication. There have been
numerous protocols designed to offer consistency
and avoid congestion. Generally, because of multi-
hop communication, TCP is not appropriate for
WSNs. Network Layer: this layer provides a
function for routing which is a difficult mission in
WSNs. As a result of low energy and inadequate
memory, routing protocol has to provide consistent
and redundant paths, for which many protocols are
available according to the desired metric. To
guarantee consistency in case of hub failure,
redundant hubs are deployed which results in the
production of a lot of redundant information. The
information can be processed as a processing unit
that utilizes less energy co Data link layer: this
layer guarantees consistency from point-to-point or
point-to-multipoint. Error control and multiplexing
of information streams are also achieved in this
layer. In WSN, Medium Access Control (MAC) has
a significant part to play. It offers higher efficiency,
consistency, low delay, and higher rates of
transmission. Physical layer: this layer makes
available an interface to convey streams of
information over a physical medium. It also deals
with the choice of frequency, generation of a carrier
frequency for modulation, signal detection, and
security, [1]. Also the research in, [2], The
correctness of information has incredible impact on
the performance of the network.
2.1 Wireless Sensor Network Operating
Systems
LiteOS is a newly developed OS for wireless sensor
networks, which provides UNIX-like abstraction
and support for the C programming language.
Contiki is an OS that uses a simpler programming
style in C while providing advances such as
6LoWPAN and proto-threads, [3]. Clustering
Routing schemes are expected to make efforts to be
scalable given the vast collection of motes in WSNs.
WSNs should be able to talk back to the events
taking place in the environment effectively, [4]. The
number of sensor nodes deployed in the sensing area
may be on the order of hundreds, thousands, or
more. Any routing scheme must be able to work
with this huge number of sensor nodes. Because
there is no global addressing scheme like IP IP-
based network, the location of a sensor node in
WSN is estimated by calculating the signal strength
between two specific nodes. This technique will not
realize the coordinates of the neighboring node. The
realistic alternative is to use GPS (Global
Positioning System). Also, there is a need for
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scalable and energy-efficient routing, data gathering,
and aggregation protocols in these WSN
environments, [5]. However, using GPS will add
significant power consumption to the sensor node
which is already energy-constrained, [6].
A number of redundant data are sent to the BS,
this is not desirable in WSN because such
unnecessary data add a significant burden to the
network thus reducing the lifespan of the network.
This drawback is evident in the flat routing
protocols as all nodes send data to the BS directly.
Reducing redundant data is part of the requirements
of WSN; it is desirable to divide sensors into groups
(clusters) so that not only cluster heads (CH) are
allowed to send data out of the network.
2.2 Classification of WSN Routing Protocol
According to Network Operations
These are protocols based on the overall goal or kind
of operation performed by the network. Several
paths are discovered between the source and the
destination and are used to provide a backup route.
When the primary path fails, the backup is used and
this increases the network performance at the
expense of increasing the cost of energy
consumption and traffic generation. E.g. Ad hoc On-
demand Multipath Distance Vector routing
(AOMDV), [7], the Destination node sends queries
requesting certain data from the nodes in the
network. If a node has the data that matches the
query, it sends it back to the requested node. This
process is known as Directed Diffusion. The main
idea is to suppress duplicate information and prevent
redundant data from being sent to the next sensor or
the base station by conducting a series of negotiation
messages before the real data transmission begins.
2.3 Development of Chinese Remainder
Theorem
This is an ancient theorem that gives the conditions
necessary for multiple equations to have a unique
simultaneous integer solution. It states that if one
knows the remainders of the Euclidean division of
an integer n by several integers, then one can
determine uniquely the remainder of the division of
n by the product of these integers, under the
condition that the divisors are pairwise coprime or
relatively prime. The theorem can be widely used
for computing with large integers, as it allows
replacing a computation for which one knows a
bound on the size of the result by several similar
computations on small integers.
CRT can be formulated as follows: Let
be integers greater than 1, which
are often referred to as moduli or divisors. Let M
denote the product of the The theorem asserts
that if the are pairwise coprime, and if
are integers such that
then there is one and only one
integer X, such thatand the remainder of
the Euclidean division of X by n is for every i.
This may be restated as follows in terms of
congruences. If the are pairwise coprime, and if
are any integers, then there exist integer
X such that
X
.
.
.
STEP 1:
STEP 2:
STEP 3: Find the inverse using Euler's or
Fermat’s theorem
.
.
STEP 4: X
For instance, consider the system below:
X
X
X
Using the methods and equations above, X = 23.
The review in [8], presents a new energy-aware
algorithm named Minimum Residual Hop Capacity
(MRHC). The algorithm is incorporated into the
most commonly used protocol called Low Energy
Adaptive Clustering Hierarchy (LEACH) in the
transmission process within clusters. This reduces
energy utilization in the transmission process,
extends network lifetime, and improves the amount
of data delivered to the base station, [9],
investigating an application of the Chinese
Remainder Theorem (CRT) for novel privacy-
preserving routing in Wireless Sensor Networks
(WSNs). The distinctive nature of their proposed
technique is to gather data, aggregate, and then slice
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the aggregate. t-out-of –n secret sharing scheme
(based on CRT) and then route the final aggregate
with just t shares using CRT. The multi-objective of
their proposed technique is to provide data privacy,
identity privacy, source location privacy, and route
privacy. Their proposed approach can be modified
to cover Energy saving in Wireless Sensor Networks
(WSNs). Different methods have been employed to
secure and protect the shared and sensitive data.
However, the significant roles of encryption
algorithms are numerous and essential in
information security, [10], in the Comparative Study
of Symmetric Cryptography Mechanisms. The
prediction of incoming attacks is achieved promptly
which enables security professionals to install
defense systems to reduce the possibility of such
attacks in Zero-Day Attack Prediction with
Parameter Setting Using Bi Direction Recurrent
Neural Network in Cyber Security, [11]. Applying
the Chinese remainder theorem to data aggregation
in wireless sensor networks in, [12], provides data
aggregation. Work on comparison of Modified
LEACH (MODLEACH) and Mobile sink improved
energy-efficient PEGASIS-based routing protocol
(MIEEPB). Simulation results of the two protocols
using MATLAB showed that MIEEPB performs
better than MODLEACH. They noted with interest
that wireless sensors that are powered by ambient
energy are promising technology for many wireless
sensor applications. Immune Inspired Concepts
Using Neural Networks for Intrusion Detection in
Cybersecurity will detect and prevent such intrusive
attacks, [13].
3 Methodology
The Wireless Sensor Network (WSN) model utilized
in the methodology is based on the novel Low
Energy Adaptive Clustering Hierarchy (LEACH)
protocol, which is a basic energy-efficient routing
protocol of the hierarchical routing protocol’s
family, where the sensor nodes remain static.
LEACH protocol algorithm contains the set-up of
clusters and stable data transmission. As for the
selection of cluster heads, LEACH adopts an equal
probability method, selecting cluster heads in a
circle and random manner and distributing the
energy of the whole network evenly on each node.
During the set-up stage of clusters, nodes will
generate a number randomly between 0 and
1(including 0 and 1). If the random number is
smaller than the threshold T(n), then the node will
be a cluster head in this round. The calculation
method of T(n) is based on the following formula:
In the above formula, p represents the
percentage of cluster nodes accounting for the total
number of nodes, that is probability of nodes
becoming cluster heads; r refers to the current
number of rounds (periods), and N is the total
number of nodes; G is the set of nodes that did not
become cluster heads in the 1/p round.
The radio communication energy consumption
model used is defined as:
According to the radio communication energy
consumption model, we know that when sending
kbit data, sensor nodes will consume the following
energy:
Such that:
where:
: Energy consumed when sending kbit data
by sensor nodes from d distance
: Energy consumed by the transmitter
distributor
: Energy consumed by the transmit
power amplifier
: The length of the data package sent
: Data transmission distance
: Energy consumed by radiating circuit when
processing 1-bit data
: Energy consumed by the transmit power
amplifier when sending 1-bit data to the unit area in
the free space channel model
: Energy consumed by transmit power
amplifier when sending 1-bit data to the unit area in
multipath fading channel model
Where
: Energy consumed by the interface
circuit
: Energy consumed by the interface circuit
when processing 1-bit data
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The definition of is given by:
Where
: energy consumed by transmission
: height of receiving antenna
: height of transmit antenna
: wavelength
Refined formula for is established as:
The results obtained are compared with LEACH
and based on the equation:
And
It can be seen that the length of the data packet,
, ultimately affects the amount of energy consumed
and ultimately the lifetime of sensor nodes. Their
CRT helps to reduce , and hence energy
consumption.
Using the Fuzzy map, the chance of a node
becoming a cluster head is now reviewed in the
below procedure.
Where
represents normally distributed random
number
represents fuzzy map
RE represents node residual energy
NC represents Node Centrality
DBS represents distance from base station
The flowchart in Figure 1 show shows the
LEACH protocol:
START
Initialise Network
Selection of Cluster Heads using Eq.3.1
Divide into clusters
Compute Energy of each node:
Etx (Eq.3.3), Erx (Eq.3.5), and Etotal
(Eq.3.2)
Lifetime
Reached?
STOP
One Round
No
Yes
Fig. 1: LEACH Protocol
The flowchart also is depicted for LEACH-CRT
and is shown in Figure 2:
START
Initialise Network
Selection of Cluster Heads using Eq.3.1
Divide into clusters
Compute Energy of each node:
Etx (Eq.3.3), Erx (Eq.3.5), and Etotal
(Eq.3.2)
Lifetime
Reached?
STOP
One Round
No
Yes
Packet Reduction using CRT
Fig. 2: LEACH-CRT Protocol
The WSN LEACH protocol with and without
CRT were all modeled in Python. The data utilized
for modeling is given in Table 1 below:
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Table 1. WSN Model Parameter
4 Discussion of Results
This data in the model parameter was applied to the
LEACH protocol with and without CRT and the
result is shown below: Table 2 shows the status of
the network at the beginning of LEACH with and
without CRT.
Table 2. LEACH vs LEACH-CRT for Energy
Dissipated
Number of Rounds
LEACH
LEACH-CRT
10
0
0
1000
9
0
2000
97
0
3000
99
0
4000
99
0
5000
100
0
6000
100
0
7000
100
0
7500
100
14
7900
100
99
8000
100
100
This data when simulated and applied to the
LEACH protocol. This data when simulated and
applied to the LEACH protocol with and without
CRT, the result in Figure 3 shows that without CRT
the number of rounds was 2800 while with CRT the
number of rounds was 3000 with both energy
dissipation stable. When some of the nodes on the
network are dead i.e. exhausted their residual
energy.
Fig. 3: Energy dissipated
However, another result in Figure 4 shows that
without CRT the number of rounds was 900 while
with CRT the number of rounds was 0 with both
numbers of dead nodes stable.
Fig. 4: Number of dead nodes
The number of clusters was also investigated to
see its effect on the lifetime of the network. The
following results were obtained for 2, 5, 10, 30, 60.
Number of dead nodes for different clusters for
LEACH without CRT and Number of dead nodes
for different clusters for LEACH with CRT are
provided in Figure 5, Figure 6, Figure 7, Figure 8,
Figure 9, Figure 10, Figure 11, Figure 12, Figure 13,
Figure 14 and Figure 15.
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Fig. 5: Number of dead nodes for different clusters
for LEACH without CRT
Fig. 6: Number of dead nodes for different clusters
for LEACH with CRT
The effect of base station location was also
investigated on the lifetime of the network as the
results are shown below. The effect of the Number of
dead nodes for LEACH without CRT with BS as
(50km,50km) and (0km,0km) position was
investigated.
Fig. 7: Number of dead nodes for LEACH without
CRT with BS at (50km,50km) and (0km,0km)
positions.
Several dead nodes for LEACH with CRT with
BS as (50km,50km) and (0km,0km) position are
shown below.
Fig. 8: Number of dead nodes for LEACH with
CRT with BS BS at (50km,50km) and (0km,0km)
positions.
Another experiment was conducted for the
Number of dead nodes for LEACH with CRT with
BS as (50km,50km) and (0km,0km) position with an
extended number of rounds of 5000. The result of
the simulation is presented below.
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Fig. 9: Number of dead nodes for LEACH with CRT
with BS as (50km,50km) and (0km,0km) position
extended number of rounds of 5000.
The effect of packet size on the lifetime of the
network was also investigated by increasing the
original packet size by 25%, 50%, 75%, and 100%.
The results gathered after the simulation were
presented as follows.
Fig. 10: Number of dead nodes for LEACH without
CRT for varied Packet Size Increase
Fig. 11: Energy Dissipation for LEACH without
CRT for varied Packet Size Increase
The Number of dead nodes for LEACH with
CRT for varied Packet Size increase was simulated
and the figure below presents the result.
Fig. 12: Number of dead nodes for LEACH with
CRT for varied Packet Size Increase
The result of Energy Dissipation for LEACH
with CRT for varied Packet Size increase is
presented below.
Fig. 13: Energy Dissipation for LEACH with CRT
for varied Packet Size Increase
The improved LEACH-CRT algorithm
incorporating fuzzy demonstrates the effectiveness
of considering node factors in electing cluster heads
and the results obtained from the mathlab simulation
are compared to the LEACH-CRT algorithm
without incorporating fuzzy in Table 3 and Table 4
provide the WSN energy dissipation, and the WSN
number of dead nodes.
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Table 3. LEACH-CRT vs. LEACH-CRT-Fuzzy for
Energy Dissipated
Rounds
LEACH-CRT
LEACH-CRT-Fuzzy
10
0.496
0.499
1000
0.108
0.418
2000
0.002
0.344
3000
0
0.277
4000
0
0.215
5000
0
0.159
6000
0
0.108
7000
0
0.059
7500
0
0.037
7700
0
0.029
8000
0
0.023
Table 4. LEACH-CRT vs LEACH-CRT-FUZZY for
the number of dead nodes
Rounds
LEACH-CRT
LEACH-CRT-FUZZY
10
0
0
1000
7
0
2000
96
0
3000
100
0
4000
100
0
5000
100
0
6000
100
0
7000
100
0
7500
100
1
7700
100
27
8000
100
60
The simulated Energy Dissipated Comparison
between LEACH-CRT with and without Fuzzy
results is presented below.
Fig. 14: Energy Dissipated Comparison between
LEACH-CRT with and without Fuzzy
The Number of dead nodes comparison between
LEACH-CRT with and without Fuzzy is presented
below.
Fig. 15: Number of dead nodes comparison between
LEACH-CRT with and without Fuzzy
5 Contributions to the Research
It was observed that including CRT increases the
Wireless Sensor Network lifespan, and at the same
time reduces the overall energy dissipation of the
nodes in the network, and this also shows the
relationship between the life of a node and its energy
consumption. Though the LEACH and LEACH-
CRT show similar sensitivity to parameter changes,
the LEACH-CRT showed an extended number of
rounds for each parameter change. Finally, it was
observed that factoring node factors in the election
of cluster heads using fuzzy logic showed further
improvement in network performance.
6 Conclusion
In this research work, Wireless Sensor Network
(WSN) was modeled using LEACH protocol and
CRT was incorporated into the WSN model using
Python to improve on network lifespan. The
performance of the improved model was tested over
the number of network node clusters, the location of
the Base Station (BS), and the size of packets used
in the network. The LEACH-CRT showed improved
performance across all parameter changes (Number
of Clusters, location of Base Station, and Packet
Size). It was further shown that utilizing fuzzy logic
to map node networks to elect CHs showed further
network performance.
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Acknowledgments:
The authors wish to thank the Department of
Computer Science, University of Ibadan for the
support in this research work.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Adeniji oluwashola david, Azeez, bukola akeem
carried out the simulation and the optimization.
- Azeez, Bukola Akeem has implemented the
Algorithm on mathlab.
- Adeniji oluwashola david, Azeez, bukola akeem
and Samuel Oladele Adeyemi organized and were
responsible for the Statistics.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
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WSEAS TRANSACTIONS on COMMUNICATIONS
DOI: 10.37394/23204.2023.22.14
Adeniji Oluwashola David,
Azeez Bukola Akeem, Samuel Oladele Adeyemi
E-ISSN: 2224-2864
151
Volume 22, 2023
