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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}}
%\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
%\thanks{Manuscript received April 19, 2005; revised December 27, 2012.}}
 
\markboth{IEEE Communications Letters,~Vol.~11, No.~4, December~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}


\maketitle


\begin{abstract}


 One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered by a wireless sensors so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The network is logically divided into subregions using divide-and-conquer method. LiCO protocol is distributed in each sensor node in the subregion. The lifetime coverage is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. The optimization decision is made at each subregion, by a leader, who his election comes from the cooperation of the sensor nodes within the same subregion of WSN. A new mathematical optimization model is proposed to optimize the lifetime coverage in each subregion. Extensive simulation experiments have been performed using OMNeT++,  the discrete event simulator,  to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible 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 great development in  Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover,  the energy needed by the sensor node is supplied by a power supply, to accomplish the Scheduled task. This power supply is composed of a battery with a limited lifetime. Furthermore, it maybe be unsuitable or impossible to replace or recharge the batteries, since sensor nodes may be deployed in a hostile or unpractical environment. 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.}} 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 remainder of the paper is organized as follows. The next section reviews  the related  work  in  the field.  Section~\ref{sec:The LiCO Protocol Description} is devoted to the LiCO protocol Description. Section~\ref{cp}  gives the coverage model
formulation which is used to schedule the activation of sensors.
Section~\ref{sec:Simulation Results and Analysis} shows the simulation results.  Finally, we give concluding remarks and some suggestions for
future works in Section~\ref{sec:Conclusion and Future Works}.

\section{\uppercase{Related Literature}}
\label{sec:Literature Review}
\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) is 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 Our protocol is used the perimeter-coverage model which stated 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. 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. 

\subsection{The Main Idea}
\noindent The area  of  interest can  be  divided using the
divide-and-conquer strategy 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 intersection 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 in the subregion respectively.
Initially, the sensor node checks its remaining energy 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 $RE_k$, sensor node id, and the number of its one-hop live neighbors during the information exchange. 
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 intersection 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 are mathematically formulated, 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 will use the intersection points which are produced by using the perimeter coverage model~\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. We also consider the intersection points as targets.   


\noindent In this paper, let us define some parameters, which are used in our protocol.
%the set of intersection 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 $J :$ the set of all sensors in the network.\\
\noindent $K :$ the set of alive sensors within $J$.\\
%\noindent $I :$ the set of intersection points.\\
\noindent $I_j :$ the set of intersection points for sensor $j$.\\

\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 intersection point $i$ of sensor $j$.

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



\noindent For an intersection point  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the intersection point $i$ 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{intersection point $i$ of sensor $j$}, \\
  0 & \mbox{Otherwise.}\\
\end{array} \right.
%\label{eq12} 
\notag
\end{equation}

\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 J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\textrm{subject to :}&\\
\sum_{k \in K} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq 1 \\
%\label{c1} 
\sum_{k \in K} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq 1 \\
% \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 K
\end{array}
\right.
\end{equation}

The first group  of constraints indicates that some intersection points $i$
should be covered by at least one  sensor node and, if it is not always the
case, overcoverage and undercoverage variables help balancing the
restriction equations by taking positive values. There are two main         
objectives. First, we limit the overcoverage of intersection points in order to
activate a minimum number of sensors.  Second, we prevent the absence of monitoring on
some parts of the subregion by minimizing the undercoverage. The
weights $\alpha$ and $\beta$ must be properly chosen so as to
guarantee that the maximum number of intersection points are covered during each round.


\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 focused on the performance of LiCO protocol, which is distributed in each sensor node in the sixteen subregions of WSN. We used the same energy consumption model which are 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.

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{$A_r^p$}}{\mbox{$S$}} \times 100 .
\end{equation*}
Where: $A_r^t$ is the number of active sensors in the subregion $r$ during period $p$ 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.
 
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}, which is improved version on the work in ~\cite{idrees2014coverage}. 

\subsubsection{\textbf{Coverage Ratio}}
In this experiment, Figure~\ref{fig333} shows the average coverage ratio for 150 deployed nodes. 
 
\parskip 0pt    
\begin{figure}[h!]
\centering
 \includegraphics[scale=0.5] {R/CR.pdf} 
\caption{The coverage ratio for 150 deployed nodes}
\label{fig333}
\end{figure} 

It is shown that DESK,  GAF, and LiCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.25\% against 99.02\% produced by DiLCO-16 for the lowest number of rounds. 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 nodes are active in the case of DESK and GAF, and a little higher in comparison with the optimization algorithm used by LiCO.
Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO-16 protocol maintains almost a good coverage from the round 31 to the round 50 and it is close to LiCO protocol. This is because it optimizes the coverage and the lifetime in WSN based on the primary points by selecting the best representative sensor nodes for the sensing stage. The coverage ratio of LiCO Protocol seems to be better than other approaches starting from the round 50 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.

Figure~\ref{figCR200} represents the average coverage ratio provided by
DiLCO-16, DESK, GAF, and LiCO for 200 deployed nodes while varying the number of periods. The same observation is made as in Figure~\ref{fig333}, i.e. DiLCO-16 showed a good coverage in the beginning then 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.
 
\parskip 0pt    
\begin{figure}[h!]
\centering
 \includegraphics[scale=0.5] {R/CR200.pdf} 
\caption{The coverage ratio for 200 deployed nodes}
\label{figCR200}
\end{figure} 


\subsubsection{\textbf{Active Sensors Ratio}} 
It is important to have as few active nodes as possible in each period, in order to minimize the energy consumption and maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 150 deployed nodes. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/ASR.pdf}  
\caption{The active sensors ratio for 150 deployed nodes }
\label{fig444}
\end{figure} 

We can observe that DESK and GAF have 37.62 \% and 44.77 \% active nodes for the first fourteen rounds and DiLCO-16 and LiCO protocols competes perfectly with only 24.82 \% and 29.70 \% active nodes for the first 14 rounds. Then as the number of rounds increases our LiCO protocol has a lower number of active nodes in comparison with DiLCO-16, DESK and GAF, especially from the round $15^{th}$ because it optimizes the lifetime coverage into the subregion based on the perimeter coverage model, which made LiCO improves the coverage ratio in comparison with other approaches. 

The variation of average active sensor nodes
against the number of periods for 200 deployed sensors is illuminated in figure~\ref{figASR200}. Observe that the number of active nodes, which are provided by DiLCO-16 is lower than the case of LiCO protocol (17.92 of active nodes against 21.8 respectively, for first $17^{th}$ periods). After that, LiCO protocol generates a lower number of active sensors using our optimization algorithm that contributed in extend the lifetime coverage as long as possible. 


\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/ASR200.pdf}  
\caption{The active sensors ratio for 200 deployed nodes }
\label{figASR200}
\end{figure} 


%We see that the DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many nodes are died due to the high energy consumption by the redundant nodes during the sensing phase. 

\subsubsection{\textbf{The Energy Consumption}}
In this experiment, 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 with other approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/EC95.pdf} 
\caption{The Energy Consumption per period with $Lifetime_{95}$}
\label{fig3EC95}
\end{figure} 
                                           
\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/EC50.pdf} 
\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 Figures~\ref{fig3EC95} and ~\ref{fig3EC50}, LiCO consumes less energy  especially when the network size increases because it puts in sleep mode less active sensor number as possible in most periods of the network lifetime. The optimization algorithm, which used by our LiCO protocol,  was optimized 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 redundant nodes as well as the energy consumed during the different modes of sensor nodes. 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}}
In this experiment, we are observed the superiority of LiCO and DiLCO-16 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.pdf}  
\caption{The Network Lifetime for $Lifetime_{95}$}
\label{fig3LT95}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{R/LT50.pdf}  
\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, with our LiCO and DiLCO-16 protocols that leads to maximize the lifetime of the network compared with other approaches. 

By choosing the best suited nodes, for each round, 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 between LiCO and DiLCO-16 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.

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


Comparison shows that our LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one 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. 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:  the first, 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.
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.

Our future work is four-fold: the first, we plan to extend a lifetime coverage optimization problem in order to computes all active sensor schedules in only one step for many periods;
the second, we focus on extend our protocol and optimization algorithm 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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