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\begin{document}

\title{Lifetime Coverage Optimization Protocol \\
  in Wireless Sensor Networks}  %LiCO Protocol 

\author{Ali Kadhum Idrees,~\IEEEmembership{}
        Karine Deschinkel,~\IEEEmembership{}
        Michel Salomon,~\IEEEmembership{}
        and~Rapha\"el Couturier ~\IEEEmembership{} 
        \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
          Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
          michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}

\markboth{IEEE Communications Letters,~Vol.~XX, No.~Y, January 2015}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}

\maketitle

\begin{abstract}
The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
use of its limited energy provision, so  that it can fulfill its monitoring task
as  long as  possible. Among  known  available approaches  that can  be used  to
improve  power  management,  lifetime coverage  optimization  provides  activity
scheduling which ensures  sensing coverage while minimizing the  energy cost. In
this paper,  we propose  a such approach  called Lifetime  Coverage Optimization
protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
region of interest is first subdivided  into subregions and our protocol is then
distributed among sensor nodes in each  subregion. A sensor node which runs LiCO
protocol  repeats   periodically  four  stages:  information   exchange,  leader
election, optimization decision, and sensing.  More precisely, the scheduling of
nodes activities (sleep/wake up  duty cycles) is achieved in each  subregion by a
leader selected after  cooperation between nodes within the  same subregion. The
novelty of  approach lies essentially in  the formulation of a  new mathematical
optimization  model  based  on  perimeter coverage  level  to  schedule  sensors
activities.  Extensive simulation experiments have been performed using OMNeT++,
the  discrete event  simulator, to  demonstrate that  LiCO is  capable to  offer
longer lifetime coverage for WSNs in comparison with some other protocols.
\end{abstract} 

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
\end{IEEEkeywords}

\IEEEpeerreviewmaketitle

\section{\uppercase{Introduction}}
\label{sec:introduction}

\noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
wireless communication hardware  has given rise to the opportunity  to use large
networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
(WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
communicating with one another through  multihop radio communications. Each node
can send the data  it collects in its environment, thanks to  its sensor, to the
user by means of  sink nodes. The features of a WSN made  it suitable for a wide
range of application  in areas such as business,  environment, health, industry,
military, and  son~\cite{yick2008wireless}.  Typically,  a sensor  node contains
three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
physical,  chemical, or  biological  phenomena observed  in  the environment;  a
processing unit which will process and store the collected measurements; a radio
communication unit for data transmission and receiving.

The energy needed  by an active sensor node to  perform sensing, processing, and
communication is supplied by a power supply which is a battery. This battery has
a limited energy provision and it may  be unsuitable or impossible to replace or
recharge it in  most applications. Therefore it is necessary  to deploy WSN with
high density in order to increase the reliability and to exploit node redundancy
thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
of sensing  areas can be exploited  to schedule alternatively some  sensors in a
low power sleep mode and thus save  energy. Overall, the main question that must
be answered is: how to extend the lifetime coverage of a WSN as long as possible
while  ensuring   a  high  level   of  coverage?   So,  this  last   years  many
energy-efficient mechanisms have been suggested  to retain energy and extend the
lifetime of the WSNs~\cite{rault2014energy}.

%The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.

%From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one.  So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.

%\uppercase{\textbf{Our contributions.}}

This paper makes the following contributions.
\begin{enumerate}
\item We devise a framework to schedule nodes to be activated alternatively such
  that the network lifetime is prolonged  while ensuring that a certain level of
  coverage is preserved.  A  key idea in our framework is  to exploit spatial an
  temporal subdivision.   On the one hand  the area of interest  if divided into
  several smaller subregions and on the other hand the time line is divided into
  periods of equal length. In each subregion the sensor nodes will cooperatively
  choose a  leader which will  schedule nodes  activities, and this  grouping of
  sensors is similar to typical cluster architecture.
\item We  propose a new mathematical  optimization model.  Instead of  trying to
  cover a set of specified points/targets as  in most of the methods proposed in
  the literature, we formulate an integer program based on perimeter coverage of
  each sensor.  The  model involves integer variables to  capture the deviations
  between  the actual  level of  coverage and  the required  level.  So  that an
  optimal scheduling  will be  obtained by  minimizing a  weighted sum  of these
  deviations.
\item We  conducted extensive simulation  experiments, using the  discrete event
  simulator OMNeT++, to demonstrate the  efficiency of our protocol. We compared
  our   LiCO   protocol   to   two   approaches   found   in   the   literature:
  DESK~\cite{ChinhVu} and  GAF~\cite{xu2001geography}, and also to  our previous
  work published in~\cite{Idrees2} which is  based on another optimization model
  for sensor scheduling.
\end{enumerate}

%Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
% the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.

The rest  of the paper is  organized as follows.  In the next section  we review
some related work in the  field. Section~\ref{sec:The LiCO Protocol Description}
is devoted to the LiCO protocol  description and Section~\ref{cp} focuses on the
coverage model  formulation which is used  to schedule the activation  of sensor
nodes.  Section~\ref{sec:Simulation  Results and Analysis}  presents simulations
results and discusses the comparison  with other approaches. Finally, concluding
remarks   are  drawn   and  some   suggestions   given  for   future  works   in
Section~\ref{sec:Conclusion and Future Works}.

% that show that our protocol outperforms others protocols.
\section{Related Literature}
\label{sec:Literature Review}

\noindent  In  this section,  we  summarize  some  related works  regarding  the
coverage problem and  distinguish our LiCO protocol from the  works presented in
the literature.

The most  discussed coverage problems in  literature can be classified  in three
categories~\cite{li2013survey}   according   to  their   respective   monitoring
objective.  Hence,  area coverage \cite{Misra}  means that every point  inside a
fixed area  must be monitored, while  target coverage~\cite{yang2014novel} refer
to  the objective  of coverage  for a  finite number  of discrete  points called
targets,  and  barrier coverage~\cite{HeShibo}\cite{kim2013maximum}  focuses  on
preventing  intruders   from  entering   into  the   region  of   interest.   In
\cite{Deng2012}  authors  transform the  area  coverage  problem to  the  target
coverage one taking into account the  intersection points among disks of sensors
nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
\cite{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
sensors are sufficiently  covered it will be  the case for the  whole area. They
provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
each  sensor,  where  $d$  denotes  the  maximum  number  of  sensors  that  are
neighboring  to  a  sensor and  $n$  is  the  total  number of  sensors  in  the
network. {\it In LiCO protocol, instead  of determining the level of coverage of
  a set  of discrete  points, our  optimization model is  based on  checking the
  perimeter-coverage of each sensor to activate a minimal number of sensors.}

The major  approach to extend network  lifetime while preserving coverage  is to
divide/organize the  sensors into a suitable  number of set covers  (disjoint or
non-disjoint), where  each set completely  covers a  region of interest,  and to
activate these set  covers successively. The network activity can  be planned in
advance and scheduled  for the entire network lifetime or  organized in periods,
and the set  of active sensor nodes  is decided at the beginning  of each period
\cite{ling2009energy}.  Active node selection is determined based on the problem
requirements (e.g.   area monitoring,  connectivity, or power  efficiency).  For
instance, Jaggi {\em et al.}~\cite{jaggi2006}  address the problem of maximizing
the lifetime  by dividing sensors  into the  maximum number of  disjoint subsets
such  that each  subset  can ensure  both coverage  and  connectivity. A  greedy
algorithm  is applied  once to  solve  this problem  and the  computed sets  are
activated  in   succession  to  achieve   the  desired  network   lifetime.   Vu
\cite{chin2007},  Padmatvathy  {\em   et  al.}~\cite{pc10},  propose  algorithms
working in a periodic fashion where a  cover set is computed at the beginning of
each period.   {\it Motivated by  these works,  LiCO protocol works  in periods,
  where each  period contains a  preliminary phase for information  exchange and
  decisions, followed by a sensing phase where one cover set is in charge of the
  sensing task.}

% MICHEL TO BE CONTINUED FROM HERE
Various approaches, including centralized,  or distributed algorithms, have been
proposed    to     extend    the     network    lifetime.      In    distributed
algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},       information      is
disseminated  throughout  the  network   and  sensors  decide  cooperatively  by
communicating with their neighbors which of them will remain in sleep mode for a
certain         period         of         time.          The         centralized
algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
provide nearly or close to optimal  solution since the algorithm has global view
of the whole network.  But such a method has the  disadvantage of requiring high
communication costs,  since the node  (located at  the base station)  making the
decision needs information from all the sensor  nodes in the area and the amount
of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
  network, in  the LiCO protocol, the  area of interest is  divided into several
  smaller subregions, and in each one, a node called the leader is in charge for
  selecting the active sensors for the current period.}

A large  variety of coverage scheduling  algorithms has been developed.  Many of
the existing  algorithms, dealing with the  maximization of the number  of cover
sets, are heuristics.  These heuristics involve  the construction of a cover set
by including in priority the sensor  nodes which cover critical targets, that is
to  say   targets  that  are   covered  by   the  smallest  number   of  sensors
\cite{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
and dedicated  techniques (solving with a  branch-and-bound algorithms available
in optimization solver).   The problem is formulated as  an optimization problem
(maximization of the lifetime or number of cover sets) under target coverage and
energy  constraints.   Column  generation   techniques,  well-known  and  widely
practiced techniques for  solving linear programs with too  many variables, have
also                                                                        been
used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In LiCO
  protocol, each leader,  in each subregion, solves an integer  program with the
  double   objective  consisting   in  minimizing   the  overcoverage   and  the
  undercoverage of the perimeter of each sensor.
}


%\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored  after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so,  some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.

%The problem of k-coverage in WSNs was addressed~\cite{ammari2012centralized}. It mathematically formulated and the spacial sensor density for full k-coverage determined, where the relation between the communication range and the sensing range constructed by this work to retain the k-coverage and connectivity in WSN. After that, a four configuration protocols have proposed for treating the k-coverage in WSNs.  

%In~\cite{rebai2014branch}, the problem of full grid coverage is formulated using two integer linear programming models: the first, a model that takes into account only the overall coverage constraint; the second, both the connectivity and the full grid coverage constraints have taken into consideration. This work did not take into account the energy constraint.

%Li et al.~\cite{li2011transforming} presented a framework to convert any complete coverage problem to a partial coverage one with any coverage ratio by means of executing a complete coverage algorithm to find a full coverage sets with virtual radii and transforming the coverage sets to a partial coverage sets by adjusting sensing radii.  The properties of the original algorithms can be maintained by this framework and the transformation process has a low execution time.

%The authors in~\cite{liu2014generalized} explained that in some applications of WSNs such as structural health monitoring (SHM) and volcano monitoring, the traditional coverage model which is a geographic area defined for individual sensors is not always valid. For this reason, they define a generalized coverage model, which is not need to have the coverage area of individual nodes, but only based on a function to determine whether a set of
%sensor nodes is capable of satisfy the requested monitoring task for a certain area. They have proposed two approaches to divide the deployed nodes into suitable cover sets, which can be used to prolong the network lifetime. 
 
%The work in~\cite{wang2010preserving} addressed the target area coverage problem by proposing a geometric-based activity scheduling scheme, named GAS, to fully cover the target area in WSNs. The authors deals with small area (target area coverage), which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explained that GAS is capable to monitor the target area by using a few sensors as possible and it can produce as many cover sets as possible.

%Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications
%and increase network lifetime via putting in sleep mode some redundant nodes. In this work, the effective sensing area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node and by compute it's ESA can be determine whether it will be active or sleep. The suggested  work permits to sensor nodes to be in sleep mode opportunistically whilst fulfill the needed sensing coverage.
 
%In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The
%maximum observed area fully covered by a minimum active sensors. In this work, the major property is to getting rid from the redundant sensors  in high-density WSNs and putting them in sleep mode, and choosing a smaller number of active sensors so as to be sure  that the full area is k-covered, and all events appeared in that area can be precisely and timely detected. This algorithm minimized the total energy consumption and increased the lifetime.

%A novel method to divide the sensors in the WSN, called node coverage grouping (NCG) suggested~\cite{lin2010partitioning}. The sensors in the connectivity group are within sensing range of each other, and the data collected by them in the same group are supposed to be similar. They are proved that dividing n sensors via NCG into connectivity groups is a NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed.
%For some applications, such as monitoring an ecosystem with extremely diversified environment, It might be premature assumption that sensors near to each other sense similar data.

%In~\cite{zaidi2009minimum}, the problem of minimum cost coverage in which full coverage is performed by using the minimum number of sensors for an arbitrary geometric shape region is addressed.  a geometric solution to the minimum cost coverage problem under a deterministic deployment is proposed. The probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region is suggested. The authors are clarified that with a random deployment about seven times more nodes are required to supply full coverage.

%A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{dong2012distributed}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.

%Liu et al.~\cite{liu2010energy} formulated maximum disjoint sets problem for retaining coverage and connectivity in WSN. Two algorithms are proposed for solving this problem, heuristic algorithm and network flow algorithm. This work did not take into account the sensor node failure, which is an unpredictable event because the two solutions are full centralized algorithms.

%The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in
%an integrated way. The network lifetime is divided in a fixed number of rounds. A coverage bitmap of sensors of the domain has been generated in each round and based on this bitmap,  it has been decided which sensors
%stay active or turn it to sleep. They checked the connection of the graph via laplacian of adjancy graph of active sensors in each round.  the generation of coverage bitmap by using  Minkowski technique, the network is able to providing the desired ratio of coverage. They have been defined the  connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution.

%Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}. 

%\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the  full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.

%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. LiCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.


\section{ The LiCO Protocol Description}
\label{sec:The LiCO Protocol Description}
\noindent In this section, we describe our Lifetime Coverage Optimization Protocol which is called LiCO in more detail.
% It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion;  the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period.  Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently. 
%Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.

\subsection{ Assumptions and Models}
\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The  wireless sensors  are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of  communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The  location  information is available to the  sensor node  either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.  We consider a boolean  disk coverage model which is the most widely used sensor coverage model in the literature. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.

\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
%According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node $0$. On this figure, sensor $0$ has $9$ neighbors. We report for each sensor $i$ having an intersection with sensor $0$, the two intersection points,  $iL$ for left point and $iR$ for right point. These intersections points subdivide the perimeter of the sensor $0$ (the perimeter of the disk covered by the sensor)  into portions called segments.

\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{pcm.jpg}  
\caption{Perimeter coverage of sensor node 0}
\label{pcmfig}
\end{figure} 

Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed  that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. 

The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}. 
% to determine the level of the perimeter coverage for each left and right point of a segment.
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{twosensors.jpg}  
\caption{Locating the segment of $u$$\rq$s perimeter covered by $v$.}
\label{twosensors}
\end{figure} 


\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{expcm.pdf}  
\caption{ Coverage levels for sensor node $0$.}
\label{expcm}
\end{figure} 









%For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.

\iffalse

\begin{figure}[ht!]
\centering
\includegraphics[width=90mm]{ex2pcm.jpg}  
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\label{ex2pcm}
\end{figure} 

\fi

 \begin{table}[h]
 \caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\  Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\  Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
0.0291    & L                                                                         & 1                                                         & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
0.104     & L                                                                         & 2                                                         & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
0.3168    & R                                                                         & 3                                                         & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
0.6752    & R                                                                         & 4                                                         & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
1.8127    & R                                                                         & 1                                                         & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
1.9228    & L                                                                         & 5                                                         & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
2.3959    & L                                                                         & 6                                                         & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
2.4258    & R                                                                         & 2                                                         & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
2.7868    & L                                                                         & 7                                                         & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
2.8358    & L                                                                         & 8                                                         & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
2.9184    & R                                                                         & 5                                                         & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
3.3301    & R                                                                         & 7                                                         & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
3.9464    & L                                                                         & 9                                                         & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
4.767     & R                                                                         & 6                                                         & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
4.8425    & L                                                                         & 3                                                         & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
4.9072    & R                                                                         & 8                                                         & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
5.3804    & L                                                                         & 4                                                         & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
5.9157    & R                                                                         & 9                                                         & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \hline
\end{tabular}

\label{my-label}
\end{table}


%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.

In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.

In the case of sensor node, which has a part of its sensing range outside the border of the WSN sensing field as in figure~\ref{ex4pcm}, the coverage level for this segment is set to $\infty$, and the corresponding interval will not be taken into account by the optimization algorithm.
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{ex4pcm.jpg}  
\caption{Part of sensing range outside the the border of WSN sensing field.}
\label{ex4pcm}
\end{figure} 
%Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
%\begin{figure}[ht!]
%\centering
%\includegraphics[width=75mm]{ex5pcm.jpg}  
%\caption{Coverage intervals and contributing sensors for sensor node 0 having a  part of its sensing range outside the border.}
%\label{ex5pcm}
%\end{figure} 


\subsection{The Main Idea}
\noindent The area  of  interest can  be  divided into smaller areas called subregions and
then our protocol will be implemented in each subregion simultaneously. LiCO protocol works into periods fashion as shown in figure~\ref{fig2}.
\begin{figure}[ht!]
\centering
\includegraphics[width=85mm]{Model.pdf}  
\caption{LiCO protocol}
\label{fig2}
\end{figure} 

Each period is divided into 4 stages: Information (INFO) Exchange, Leader  Election, Optimization Decision,  and  Sensing.  For  each  period there  is exactly one set cover responsible for the sensing task. LiCO is more powerful against an unexpected node failure because it works in periods. On the one hand, if the node failure is discovered before taking the decision of the optimization algorithm, the sensor node would not involved to current stage, and, on the other hand, if the sensor failure takes place after the decision,  the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts, since a new set cover will take charge of the sensing task in the next period.  The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period.  However,   the  pre-sensing  phases   (INFO  Exchange,  Leader Election, and  Decision) are energy  consuming for  some sensor nodes,  even when they do not join the network to monitor the area. 

We define two types of packets to be used by LiCO protocol.
%\begin{enumerate}[(a)]
\begin{itemize} 
\item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
\item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}

There are five status for each sensor node in the network :
%\begin{enumerate}[(a)] 
\begin{itemize} 
\item LISTENING: Sensor is waiting for a decision (to be active or not)
\item COMPUTATION: Sensor applies the optimization process as leader
\item ACTIVE: Sensor is active
\item SLEEP: Sensor is turned off
\item COMMUNICATION: Sensor is transmitting or receiving packet
\end{itemize}
%\end{enumerate}
%Below, we describe each phase in more details.

\subsection{LiCO Protocol Algorithm}
The pseudo-code for LiCO Protocol is illustrated as follows:


\begin{algorithm}[h!]                
 % \KwIn{all the parameters related to information exchange}
%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
  \BlankLine
  %\emph{Initialize the sensor node and determine it's position and subregion} \; 
  
  \If{ $RE_k \geq E_{th}$ }{
      \emph{$s_k.status$ = COMMUNICATION}\;
      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
      \emph{Update K.CurrentSize}\;
      \emph{LeaderID = Leader election}\;
      \If{$ s_k.ID = LeaderID $}{
         \emph{$s_k.status$ = COMPUTATION}\;
         
      \If{$ s_k.ID $ is Not previously selected as a Leader }{
          \emph{ Execute the perimeter coverage model}\;
         % \emph{ Determine the segment points using perimeter coverage model}\;
      }
      
      \If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
      
      	 \emph{ Use the same previous cover set for current sensing stage}\;
      }
      \Else{
            \emph{ Update $a^j_{ik}$ and prepare data to Algorithm}\;
            \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
            \emph{K.PreviousSize = K.CurrentSize}\;
           }
      
        \emph{$s_k.status$ = COMMUNICATION}\;
        \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
        \emph{Update $RE_k $}\;
      }	  
      \Else{
        \emph{$s_k.status$ = LISTENING}\;
        \emph{Wait $ActiveSleep()$ packet from the Leader}\;
        \emph{Update $RE_k $}\;
      }  
  }
  \Else { Exclude $s_k$ from entering in the current sensing stage}
  
 
\caption{LiCO($s_k$)}
\label{alg:LiCO}

\end{algorithm}

\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes still alive in the subregion respectively.
Initially, the sensor node checks its remaining energy $RE_k$, which must be greater than a threshold $E_{th}$ in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensors inside a same region cooperate to elect a leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.  


%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.

% The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.


\section{Lifetime Coverage problem formulation}
\label{cp}
In this section, the coverage model is mathematically formulated.
For convenience, the notations are described first. 
%Then the lifetime problem of sensor network is formulated. 
\noindent $S :$ the set of all sensors in the network.\\
\noindent $A :$ the set of alive sensors within $S$.\\
%\noindent $I :$ the set of segment points.\\
\noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\
\noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.
\noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:

\begin{equation}
a^j_{ik} = \left \{ 
\begin{array}{lll}
  1 & \mbox{if the sensor $k$ is involved in the } \\
  	&	\mbox{coverage interval $i$ of sensor $j$}, \\
  0 & \mbox{Otherwise.}\\
\end{array} \right.
%\label{eq12} 
\notag
\end{equation}
Note that $a^k_{ik}=1$ by definition of the interval.\\
%, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
%We defined some parameters, which are related to our optimization model. In our model,  we  consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .   
\noindent We  consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely  satisfied, to reach a coverage level as close as possible that the desired one.



%A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized. 

%\noindent In this paper, let us define some parameters, which are used in our protocol.
%the set of segment points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.


%\noindent \begin{equation}
%X_{k} = \left \{ 
%\begin{array}{l l}
 % 1& \mbox{if sensor $k$  is active,} \\
%  0 &  \mbox{otherwise.}\\
%\end{array} \right.
%\label{eq11} 
%\notag
%\end{equation}

%\noindent $M^j_i (undercoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.

%\noindent $V^j_i (overcoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.





\noindent Our coverage optimization problem can be mathematically formulated as follows: \\
%Objective:

\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\textrm{subject to :}&\\
\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
%\label{c1} 
\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
% \label{c2}
% \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
% U_{p} \in \{0,1\}, &\forall p \in P\\
X_{k} \in \{0,1\}, \forall k \in A
\end{array}
\right.
\end{equation}


\noindent $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
relative importance of satisfying the associated
level of coverage. For example, weights associated with coverage intervals of a specified part of a region
may be given a relatively
larger magnitude than weights associated
with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. 


\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}  
\label{sec:Simulation Results and Analysis}
%\noindent \subsection{Simulation Framework}

\subsection{Simulation Settings}
%\label{sub1}
In this section, we focus on the performance of LiCO protocol, which is distributed in each sensor node in the sixteen subregions of WSN. We use the same energy consumption model which is used in~\cite{Idrees2}. Table~\ref{table3} gives the chosen parameters setting.

\begin{table}[ht]
\caption{Relevant parameters for network initializing.}
% title of Table
\centering
% used for centering table
\begin{tabular}{c|c}
% centered columns (4 columns)
\hline
Parameter & Value  \\ [0.5ex]
   
\hline
% inserts single horizontal line
Sensing  Field  & $(50 \times 25)~m^2 $   \\

Nodes Number &  100, 150, 200, 250 and 300~nodes   \\
%\hline
Initial Energy  & 500-700~joules  \\  
%\hline
Sensing Period & 60 Minutes \\
$E_{th}$ & 36 Joules\\
$R_s$ & 5~m   \\     
%\hline
$\alpha^j_i$ & 0.6   \\
% [1ex] adds vertical space
%\hline
$\beta^j_i$ & 0.4
%inserts single line
\end{tabular}
\label{table3}
% is used to refer this table in the text
\end{table}
Simulations with five  different node densities going from  100 to 250~nodes were
performed  considering  each  time  25~randomly generated  networks,  to  obtain
experimental results  which are relevant. All simulations are repeated 25 times and the results are averaged. The  nodes are deployed on a field of interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio.

Each node has an initial energy level, in Joules, which is randomly drawn in the
interval  $[500-700]$.  If  it's  energy  provision reaches  a  value below  the
threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
active during one period, it will no more participate in the coverage task. This
value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by
multiplying the energy consumed in active  state (9.72 mW) by the time in seconds
for one period (3600 seconds), and  adding the energy for the pre-sensing phases.
According to  the interval of initial energy,  a sensor may be  active during at
most 20 rounds.

The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN.  We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.

In the simulations,  we introduce the following performance  metrics to evaluate
the efficiency of our approach:

%\begin{enumerate}[i)]
\begin{itemize}
\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
  $50\%$). We assume that the sensor  network can fulfill its task until all its
  nodes have  been drained of their  energy or it  becomes disconnected. Network
  connectivity  is crucial because  an active  sensor node  without connectivity
  towards a base  station cannot transmit any information  regarding an observed
  event in the area that it monitors.
  
    
\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to 
  observe the area of interest. In our case, we discretized the sensor field
  as a regular grid, which yields the following equation to compute the
  coverage ratio: 
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
where  $n$ is  the number  of covered  grid points  by active  sensors  of every
subregions during  the current  sensing phase  and $N$ is  total number  of grid
points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
\times 26 = 1326$ grid points.


\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
in  order to  minimize  the communication  overhead  and maximize  the
network lifetime. The Active Sensors Ratio is defined as follows:
\begin{equation*}
\scriptsize
\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
\end{equation*}
Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.

 

\item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
  $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
  of EC can be expressed as follows:
  \begin{equation*}
    \scriptsize
    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  
      + E^{a}_m+E^{s}_m \right)}{M},
  \end{equation*}

where $M$  corresponds to the number  of periods. The total energy consumed by
the sensors (EC) comes through taking into consideration four main energy factors. The  first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represent the
energy consumption  spent by  all the nodes  for wireless  communications during
period $m$.   $E^{\scriptsize \mbox{list}}_m$,  the next factor,  corresponds to
the  energy consumed by  the sensors  in LISTENING  status before  receiving the
decision to  go active or  sleep in period $m$.  $E^{\scriptsize \mbox{comp}}_m$
refers to the energy needed by all the leader nodes to solve the integer program
during a period.  Finally, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
by the whole network in the sensing phase (active and sleeping nodes).


\end{itemize}
%\end{enumerate}

\subsection{Simulation Results}
In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz)  processor (2 cores) and the MIPS (Million Instructions  Per Second) rate equal to 35330. To be consistent  with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and  a MIPS rate  equal to 6,  the original execution time on the laptop is multiplied by  2944.2 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$  so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. 
 
We compared LiCO protocol to three other approaches: the first, called DESK and proposed  by ~\cite{ChinhVu}  is a fully distributed  coverage  algorithm;  the second, called GAF  ~\cite{xu2001geography}, consists in dividing the region
into fixed  squares.  During the decision  phase, in each square,  one sensor is
chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).

\subsubsection{\textbf{Coverage Ratio}}
Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
 
\parskip 0pt    
\begin{figure}[h!]
\centering
 \includegraphics[scale=0.5] {R/CR.eps} 
\caption{The coverage ratio for 200 deployed nodes}
\label{fig333}
\end{figure} 

DESK,  GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).

%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.

%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches. 


\subsubsection{\textbf{Active Sensors Ratio}} 
Having active nodes as few as possible in each period is essential in order to minimize the energy consumption and so maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/ASR.eps}  
\caption{The active sensors ratio for 200 deployed nodes }
\label{fig444}
\end{figure} 

We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.

\subsubsection{\textbf{The Energy Consumption}}
We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and \ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/EC95.eps} 
\caption{The Energy Consumption per period with $Lifetime_{95}$}
\label{fig3EC95}
\end{figure} 
                                           
\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/EC50.eps} 
\caption{The Energy Consumption per period with $Lifetime_{50}$}
\label{fig3EC50}
\end{figure} 

The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and \ref{fig3EC50}, LiCO consumes much less energy  than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
%The optimization algorithm, which used by LiCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.

 %The other approaches have a high energy consumption due to activating a larger number of sensors. In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 


%\subsubsection{Execution Time}

\subsubsection{\textbf{The Network Lifetime}}
We observe the superiority of LiCO and DiLCO protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/LT95.eps}  
\caption{The Network Lifetime for $Lifetime_{95}$}
\label{fig3LT95}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/LT50.eps}  
\caption{The Network Lifetime for $Lifetime_{50}$}
\label{fig3LT50}
\end{figure} 

As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, and it is clearly larger with DiLCO and LiCO protocols compared with the two other methods. For instance, for a network of 300 sensors, the coverage ratio is greater than 50\% about two times longer with LiCO compared to DESK method.

%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to  DiLCO-16 protocol for $95 \%$.  
Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios for LiCO and DiLCO protocols. 
We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ respectively. Indeed there are applications that do not require a 100\% coverage of the surveillance region. LiCO might be an interesting  method  since it achieves a good balance between a high level coverage ratio and network lifetime.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/LTa.eps}  
\caption{The Network Lifetime for different coverage ratios}
\label{figLTALL}
\end{figure} 


%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.


\section{\uppercase{Conclusion and Future Works}}
\label{sec:Conclusion and Future Works}
In this paper we have studied the problem of lifetime coverage optimization in
WSNs. We designed a protocol LiCO that schedules node activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.

 


%To cope with this problem, the area of interest is divided into a smaller subregions using  divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques:  network
%leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the  most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
%in the subregion. 
%The network lifetime coverage in each subregion is divided into
%periods, each period consists  of four stages: (i) Information Exchange,
%(ii) Leader Election, (iii) a Decision based new optimization model in order to
%select the  nodes remaining  active for the last stage,  and  (iv) Sensing.
We carried out severals simulations to evaluate the proposed protocol.  The  simulation results show that LiCO is  is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. 
%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily.

We have identified different research directions that arise out of the work presented here. 
We plan to extend our framework such that the schedules are planned for multiple periods in advance.
%in order to compute all active sensor schedules in only one step for many periods;
We also want to improve our integer program to take into account the heterogeneous sensors, which do not have the same energy, processing,  sensing and communication capabilities;
%the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.

\section*{\uppercase{Acknowledgements}}
\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.

 


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%\begin{IEEEbiographynophoto}{Jane Doe}


 

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