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In a randomly deployed and large scale wireless sensor network, coverage-redundant nodes consume much unnecessary energy. As a result, turning off these redundant nodes can prolong the network lifetime, while maintaining the degree of sensing coverage with a limited number of on-duty nodes. None of the off-duty eligibility rules in the literature, however, are sufficient and necessary conditions for eligible nodes. Hence redundancy or blind points might be incurred. In this paper we propose a complete Eligibility Rule based on Perimeter Coverage (ERPC) for a node to determine its eligibility for sleeping. ERPC has a computational complexity of ^{2}log(^{3}), where

Wireless Sensor Networks (WSNs) hold the promise of many new applications in the area of environment surveillance and target tracking. In such applications, the user is interested only in the occurrence of a certain event, such as target appearances or status changes. Due to the random distribution or mobility of the targets, a certain level of sensing coverage over the field of interest should be maintained to guarantee that events of interest will be captured with minimal delay. The sensing area of a sensor node is often assumed to be a disk bound by a sensing circle of fixed radius

In WSNs, unattended deployment usually causes asymmetric node density in the field. In some sub-areas of the field, the sensing areas of neighboring nodes might overlap with each other, which results in coverage redundancy. This redundancy can be exploited to design energy-efficient coverage control protocols [

In this paper, we propose a sufficient and necessary condition for a redundant node, Eligibility Rule based on Perimeter Coverage (ERPC). The concept of perimeter coverage was first proposed in [

Since our ERPC is a complete condition to determine an eligible node, the ERPC-based CPP not only eliminates the coverage redundancy completely, but also identifies all the eligible nodes exactly. Therefore, CPP can maximize network lifetime without sacrificing system QoS.

Based merely on local information, CPP is more cost-effective, especially in large scale and multi-hop networks, than the centralized protocols described in [

CPP is capable of maintaining the network to the specific coverage degree requested by an application, while the Ottawa protocol does not support a configurable coverage degree.

The computational complexity of ERPC is ^{2}log(^{3}), CPP is a more lightweight protocol and more suitable for sensors whose computation and storage capabilities are harshly constrained.

The rest of this paper is organized as follows. Section 2 surveys the related work in literature. In Section 3, we describe the network model and problem formulation. Section 4 proposes our method to identify an eligible node and clarifies our advantages over the eligibility rule proposed by [

The most discussed coverage problems in the literature can be classified into two categories: barrier coverage and full coverage. The barrier coverage problem aims to minimize the probability of undetected intrusion through the barrier formed by sensor networks. There has been substantial research on the barrier coverage problem, for example, in [

In this paper, we focus on another type of coverage problem, the so-called full coverage. Full coverage provides the QoS of minimizing the probability of undetected events in the full range of the field. Instrumented with full coverage, the sensor network is vigilant to capture any interested events which take place any time and anywhere. To minimize the power consumption and deployment cost, one kind of energy-efficient full coverage problem is to derive critical conditions for

Many energy-efficient protocols have been proposed to ensure a desired node density by exploiting deployment redundancy. In [

In [

Localized protocols have recently been presented to provide coverage control while maintaining network longevity. One of the most representative protocols is Optimal Geographical Density Control (OGDC) in [

The works most relevant to our approach are the Ottawa protocol in [_{j},_{1}, _{j},_{2} and _{i}_{←}_{j}

In CCP, a coverage-configurable off-duty rule is adopted to determine node eligibility. The CCP rule considers a node to be eligible if all the intersection points inside its sensing area are _{m,t}^{2}log(^{3}), where

Consider a square field _{i},y_{i}

To better state the coverage problem, we give some basic definitions as follows.

The sensing area of node _{i}^{2}+(_{i}^{2}≤^{2}}.

A location point _{i}^{2}+(_{i}^{2}≤^{2} is true.

A location point

The field

For a sensor network with a requested coverage degree of

Unlike the Ottawa protocol, we consider all the nodes with a distance within 2

The neighboring nodes of node _{i}-x_{j}^{2}+(_{i}-y_{j}^{2}≤(2^{2},

Moreover, we assume a simple communication model adopted by [

For any two nodes _{i}-x_{j}^{2}+(_{i}-y_{j}^{2}≤^{2} is true, where

In order to minimize energy consumption caused by communication, we employ a communication radius of

The overlapped sensing areas can result in redundant nodes which are defined in [

Node

As illustrated in

As shown in

Therefore, the energy-efficient coverage problem to be addressed in this paper is formulated as follows:

Given a field

In this section, we describe our novel localized approach to identify redundant nodes, denoted as Eligibility Rule based on Perimeter Coverage (ERPC). Each node runs ERPC locally to compute the coverage degree of each neighbor's sensing circle within the node's sensing area. By checking such information of all the neighboring nodes, the eligibility of a particular node can be determined.

The sensing circle of node _{i}^{2}+(_{i}^{2}=^{2}}; An arc segment of the perimeter of node

Suppose a point _{j}^{2}+(_{j}^{2}≤^{2} is true. If

Node

A perimeter coverage lemma is proposed in [

Any arc segment of node i' (i∈S) sensing circle divides two sub-regions in the field A. If this arc segment is k-perimeter-covered, the sub-region that is outside node i's sensing area is k-covered and the sub-region that is inside node i's sensing area (k+1)-covered.

Based on Lemma 1, we can obtain the following lemma.

In a sensor network S with a requested coverage degree k, node i (i∈S) is a redundant node if and only if any neighboring node j (j∈N(i)) is k-perimeter-covered when node i is ignored.

For the “if” part, each sub-region inside the sensing area of node

For the “only if” part, we prove by contradiction. Suppose there exists a neighboring node _{m}_{m}_{m}

Lemma 2 justifies that a node is redundant if and only if no neighboring node is less than

In a sensor network S with a requested coverage degree k, node i (i∈S) is said to be eligible for turning off if and only if for each neighboring node j (j∈N(i)) of node i, the arc segment of node j's sensing circle within the sensing area of node i is k-perimeter-covered other than node i.

The proof is directly from Lemma 2. For the “if” part, since the arc segment of each neighboring node _{m}_{m}_{m}

For the case in which some nodes' sensing areas may exceed the boundary of the field _{q}_{,3}, _{q}_{,4}] and [_{q}_{,5}, _{q}_{,6}] within node

By running ERPC locally, a node can identify its off-duty eligibility only based on the location information of its neighboring nodes. Therefore, ERPC is a localized approach and incurs limited communication overhead to the network.

In [

In a sensor network S with a requested coverage degree k, node i (i∈S) is said to be eligible for turning off if and only if each neighboring node j (j∈N(i)) of node i is still k-perimeter-covered after node i is removed.

However, this eligibility rule, denoted as PSS-ER, does not follow a distributed fashion completely. PSS-ER requires excessive collaborations and communications among neighboring nodes, which is more time-consuming and energy-expensive than ERPC only based on limited local information. The two main advantages of ERPC over PSS-ER are detailed as follows.

In each round of PSS-ER, each node has to evaluate its perimeter coverage for two times: the first time evaluation filters out the candidates of eligible nodes; and then, for the second time, each neighbor of any candidate node ^{2}log(

ERPC and PSS-ER share one thing in common at that both of them require information exchange with neighbors when collecting neighbor information and announcing eligibility. Apart from such communication cost, however, each candidate node in PSS-ER has to broadcast its candidacy to all of its neighbors after the first evaluation phase ends. Therefore, PSS-ER incurs much more communication overhead into the network than ERPC does.

In a word, compared with the macro view of the work in [

The main part of the ERPC algorithm is to determine the perimeter coverage degree of the arc segment of each neighboring node within a node's sensing area. The whole algorithm of ERPC that runs at node

For a node _{j←i}_{j←i,L}, θ_{j←i,R}_{i}-y_{j}_{i}-x_{j}

For node _{j←m,L}, θ_{j←m,R}

Add all the points _{j←m,L}_{j←m,R}

As demonstrated in _{j←i}_{temp}_{j←i,L}, θ_{j←i,R}_{temp}_{temp}_{j←i}_{temp}

For each node

Consider the algorithm in Section 4.2. In a network with ^{2}log(^{2}) and the complexity to calculate the coverage of an intersection point is ^{3}). Therefore, ERPC is a more lightweight off-duty eligibility rule than CCP rule.

After turning off the eligible nodes filtered out by ERPC, the network coverage degree can be preserved by the remaining active nodes. If these on-duty nodes continuously work, however, they may soon run out of battery energy. This working model might not be desirable since the failure of some functional nodes can result in partitioning of the network or isolation of nodes. In this section, we propose a Coverage Preserving Protocol (CPP) to balance energy consumption among the neighboring nodes while maintaining the requested coverage degree. In CPP, a node can work at one of three states: Sleeping (Off-duty), Active (On-duty) and Listening. The operation of each node is divided into rounds. Each round takes the same period of time (_{r}

At the beginning of each round, all nodes are in On-duty state. To obtain the information of neighboring nodes, each node broadcasts a Beacon Message (BM) which contains node ID and its current location. Then, each node enters Listening state to collect the BMs from its neighbors. Finally, a neighbor list is maintained at each node. Since nodes may have some mobility in some mobile ubiquitous applications, it is necessary for each node to update its neighbor list in each round (we assume that each node can obtain its location information by GPS or other self-localization schemes such as DV-hop[

After collection of neighbor information, each node evaluates its eligibility by ERPC. However, blind points may occur due to some neighboring nodes' dependency on each other, as shown in [_{d}_{d}_{d}_{d}

In Sleeping state, the eligible node is turned off to save battery energy. In On-duty state, the node performs the normal sensing and processing tasks. In Listening state, the node 1). first adds one neighbor in case that a BM is received, and then 2). deletes one neighbor upon QM and finally 3). evaluates its eligibility by ERPC after _{d}

The back-off scheme in CPP employs a randomized delay timer _{d}_{r}_{d}_{d}^{2}^{2}, and _{rt}_{rt}

Moreover, we take the remained energy at each node into account. Suppose that all nodes have different energy levels at the very beginning. Let _{r}_{m}_{r}/E_{m}_{r}/E_{m}

As for the length of each round, it has little impact on the total working time of each node in all rounds. However, frequent round switch would result in much energy drain. Hence, _{r}_{i}_{d}_{r}

In this section, we evaluate the performance of CPP in simulation experiments. Two of the best-known protocols, the Ottawa protocol and the CCP protocol, are introduced for comparison. We implement CPP in Matlab 7.0[

In this experiment, we compare CPP to the Ottawa protocol in the performance of the achieved network coverage degree which reflects protocol efficiency. To evaluate coverage, we divide the entire field into grids with the size of 1m×1m. The coverage degree of each gird can be measured by checking the number of on-duty nodes that cover the center of the grid. Hence, the achieved coverage degree of the field can be approximately calculated by averaging the coverage degrees of all grids.

In a surveillance sensor network, full coverage is expected to ensure real-time monitoring of the interested events. Therefore, blind points should be avoided to improve system alertness and reliability. Since the blind points caused by random deployment can not be controlled, this experiment evaluates the number of the blind points incurred only by protocols.

The number of the blind points caused by the three protocols is demonstrated in

While comparing to the Ottawa protocol, CPP needs much less active nodes when

In this experiment we evaluate the ability of CPP to configure the network to the requested coverage degrees.

In this experiment, we evaluate the time taken by each protocol to filter out eligible nodes. At the beginning of each round, all nodes are active and then they perform the specific eligibility rule to decide whether to turn off itself. As this eligibility evaluation proceeds, the number of on-duty nodes decreases until all the exact eligible nodes are identified. We define convergence time (_{c}_{r}

It can be observed that Ottawa has the best convergence time performance. This can be expected since the computational complexity of Ottawa is the lowest among all the protocols and, moreover, each node in Ottawa broadcasts at most twice. At the end of the eligibility evaluation, however, Ottawa results in the most on-duty nodes due to its unnecessary eligibility rule. CCP, PSS and CPP perform closely in the number of on-duty nodes since all of them adopt a necessary eligibility rule. PSS spends the most time in filtering out all the eligible nodes. The reason is that, as discussed in Section 4.2, the 2-phase eligibility evaluation and 3-times broadcasting are time-consuming indeed. Since the proposed CPP reduces the computational complexity to ^{2}log(

This experiment evaluates CPP's ability to prolong network lifetime. The metric used in evaluation is the α-coverage lifetime which is defined by [

In this simulation, 100 nodes are randomly deployed in the field of 50 m × 50 m and each of them starts with an initial energy of 200 Joules. In addition, we follow the energy model in [

^{3})-complicated eligibility rule and consequently stays awake longer than in CPP. Moreover, we can observe that the network lifetime in CPP rises more than 20% when comparing with the PSS proposed in [

In summary, we draw the key results from our experiments as shown in

In this paper we investigate the coverage control protocol which reduces energy consumption by turning off redundant nodes. We propose an off-duty eligibility rule, denoted as ERPC, to determine redundant nodes. To the best of our knowledge, ERPC is the first work to provide a sufficient and necessary condition of off-duty eligible nodes. Moreover, ERPC has a lower computational complexity than the most well-known CPP rule. A Coverage Preserving Protocol is developed to schedule the work states of candidate eligible nodes. The localized CPP is more self-adaptive and energy-efficient in a large scale and multi-hop sensor networks. Moreover, CPP supports configurable coverage degree to meet various application requirements. Simulation results indicate that CPP can preserve the network coverage efficiently and accurately. Moreover, CPP can extend the network lifetime up to 4 times without sacrificing system reliability. Most studies including our CPP require that each node knows its own location. To relax such deployment restrictions, we will investigate the possibility of deriving a location-independent coverage control protocol in the future.

This work has been financially supported by National Natural Science Foundation of China (60803120) and Graduate Innovation and Practice Foundation of BUAA. In addition, the authors wish to thank the members of Research05 Group of Computer Application Institute, Beihang University for their many technical suggestions.

(a) Unnecessary condition of of Ottawa. (b) Insufficient condition of CCP.

An example of coverage redundancy.

Examples of ERPC.

Calculation of the perimeter coverage degree of an arc segment in the ERPC algorithm.

State transition in CPP.

Achieved coverage degree.

Blind points incurred by protocols.

On-duty nodes used by protocols.

Achieved coverage degree by CPP.

Dynamic coverage ratio.

Network α-coverage lifetime.

Convergence time.

Ottawa | 1324 | 48.2 | 2 | ||

CCP | 2578 | 20.8 | ^{3}) |
2 | |

PSS | 3659 | 21.1 | 2^{2}log( |
3 | |

Our CPP | 2108 | 21 | ^{2}log( |
2 |

Comparison among protocols.

Ottawa | Much redundancy | No blind points | 1-coverage | 661 | |

CCP | No redundancy | Blind points | 818 | ||

Our CPP | No redundancy | No blind points | 848 |