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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In wireless sensor networks, density control is an important technique for prolonging a network’s lifetime. To reduce the overall energy consumption, it is desirable to minimize the overlapping sensing area of the sensor nodes. In this paper, we study the problem of energy-efficient area coverage by the regular placement of sensors with adjustable sensing and communication ranges. We suggest a more accurate method to estimate efficiency than those currently used for coverage by sensors with adjustable ranges, and propose new density control models that considerably improve coverage using sensors with two sensing ranges. Calculations and extensive simulation show that the new models outperform existing ones in terms of various performance metrics.

A wireless sensor network (WSN) is composed of a large number of sensor nodes that are densely deployed near an area of interest and are connected by a wireless interface. Since each sensor is equipped with a limited power source and, in most applications, it is impossible to replenish power resources, a major constraint of WSN lifetime is energy consumption. Energy savings optimization is thus a major challenge for the success of WSNs. Typical tasks of a sensor node in a sensor network are to collect data, perform data aggregation, and then transmit data. Among these tasks, monitoring and transmitting data require much more energy than processing it [

Coverage is one of the most important issues of the WSN. Since sensors have limited battery life, wireless sensor networks are characterized by high node density. It is not necessary to have all sensor nodes operate simultaneously in active mode and different scheduling methods are used to ensure energy-efficient coverage and connectivity [

In this paper, we suggest a more accurate method for estimating energy efficiency based on coverage of the sensing area by equal, non-overlapping standard figures (

The rest of the paper is organized as follows. Section 2 presents related work. In Section 3, we introduce several coverage models and give theoretical estimates of their energy efficiency. Section 4 contains the simulation and performance evaluation results. Section 5 concludes the paper.

The coverage problem is a key issue for any wireless sensor network, and coverage can be viewed as one measurement of quality of service of the system. Most sensor networks have both high node density and limited node power. The goal is to minimize energy consumption to prolong the system’s lifetime, while maintaining effective coverage. Coverage can be achieved by designing some kind of density control mechanism, that is, scheduling the sensors to work alternatively to minimize the power wastage due to the overlap of active nodes’ sensing areas.

Many topology and density control methods have been proposed for wireless sensor networks. In [

It is proven that if the radio range is at least twice the sensing range, complete coverage of a convex area implies connectivity among the working set of nodes [_{s}

Most density control algorithms assume that the sensing ranges of all sensors are the same. In [

We assume the sensor nodes are randomly deployed over a two-dimensional square area, and that the location of each node is known. The sensing area of a node is a disk of a given radius (sensing range). To guarantee network connectivity, we assume that all the active sensor nodes form a minimal spanning tree, and that each sensor node adjusts its communication range to reach its furthest neighbor on the tree.

Suppose first that the sensing ranges of all sensors are equal, and that it is necessary to cover every point of the monitoring area by at least one disk of radius

To estimate the efficiency of the coverage models, we use regular polygons - tiles that cover the whole monitoring area without overlapping. For model A, the tile is a triangle _{1}A_{2}A_{3}_{1}B_{2}B_{3}B_{4}

For model B-1 the areas and the coverage density are:

Similar to [_{1}, or the power consumption per unit. Then, the _{1} ·

A similar characteristic is calculated in [

This is apparently incorrect, because not all overlap of the disks was considered. In model A-1, each disk intersects with six other disks, but in [

Model B-1 was not considered in [

If every three equal neighboring disks in model A (or four equal neighboring disks in model B) are tangent, then there is a gap between them (see

It is easy to check that for model A-2, the radius of the extra disk is

The coverage density in model A-2 is substantially increased compared to model A-1. Model A-2 was also considered in [_{A-2}_{II}_{A-1}_{I}_{II}

If the energy consumption of a disk of radius ^{n}

In model A-3 we permit equal overlapping of the neighboring disks of radius

In order to minimize the sensing energy consumption per unit area, it is necessary to solve the following optimization problem:

The solution of this problem is

As a result, we have
_{A−3} = 33^{2}/62,
_{A-3}_{1}. The radius ^{n}

In model B-3, the tile is a square with vertices in the centers of four neighboring disks of radius

In order to minimize the SECPA, we need to solve the following problem:

Its solution is

As a result, we have _{B−3} = 16^{2}/5, _{B−3} = 6^{2}/5, _{B−3} = (3_{B-3}_{1}.

Further improvement of the models is possible if one uses more sensing ranges, but sometimes this presents a negative effect. For example, in [^{2}/2. Taking into account that
_{A−1} ≈ 1.2091μ_{1}.

Communication energy consumption depends on the distance between the communicating sensors. In order to estimate the _{2}. Then, CECPA is the part of the sensors’ communication energy used by the nodes inside a tile divided by the tile’s area.

As for the estimation of coverage density, we ignore the edge effect and calculate CECPA for the case of infinite grid. Since in model A-1 the communication energy is used by the nodes of tile triangles, and the total number of tiles in the infinite triangular grid is twice the number of centers of disks of radius _{2} is independent of distance. In model B-1, the communication energy is used by the nodes of the tile square, and the total number of square vertices in the infinite square grid is equal to the number of squares, and so in that case CECPA is equal to the communication energy of one node divided by the tile’s area. The distance between any two adjacent nodes in MST in model B-1 is

In model A-2, during the construction of MST, every vertex of a tile triangle will choose the center of an extra disk to connect, and the center of that extra disk can choose either the center of a larger disk or the center of a smaller one. All these edges have the same length:

In model B-2 all the edges in MST have the identical length

In model A-3 every vertex of a tile triangle will choose the center of an extra disk to connect, and the center of the extra disk will choose either the center of a larger disk or the center of a smaller one. Since all these edges have the identical length

Finally, in model B-3, every vertex of a square tile will choose the center of an extra disk to connect, and the center of the extra disk will choose the center of a larger disk. The length of each edge is

We have summarized the results for the considered models in

As one can see, model A-3 is the best with respect to the sensing energy consumption per unit area, while the B series of models are the best ones with respect to the communication energy consumption per unit area. Since sensing is a permanent duty and communication occurs occasionally, we can conclude that models A-3 and B-3 are the best among the considered models.

For evaluation of our proposed models, we customize a simulator similar to that in [^{2} area. In order to ignore the edge effect, we use the middle (50 − ^{2} of the area to calculate the coverage ratio. We assume the sensing energy consumption of each sensor is proportional to the square of its sensing range. To estimate transmission energy, we first construct a minimal spanning tree among the working nodes. We assume that the energy consumed by communication for a working sensor is proportional to the

For randomly deployed sensors we cannot guarantee that we will find a sensor at any desirable position, so in the simulation we choose the sensor node

We use the same performance metrics as in [

Total energy consumption is shown in

To provide 100% coverage in the case of randomly deployed sensors, we modify all the models as follows. Each selected sensor node stretches its sensing range to its distance

From this simulation we conclude the following:

The coverage ratio of all considered models is proportional to the corresponding sensor energy consumption per unit area.

Whereas models A-3 and B-3 exhibit slightly worse performances with respect to the coverage ratio, they provide necessary gains in terms of energy consumption. The modified version of the algorithm provided 100% coverage, and it also demonstrates the superiority of these two models. For example, for simulation parameters chosen based on the hardware of Crossbow MicaZ nodes the models show that energy consumption is reduced up to 28% for an indoor scenario (communication range is 8 m) and up to 19% for an outdoor scenario (communication range is 20 m).

A larger path lost exponent yields greater energy savings in the proposed models.

In this paper, we considered two types of sensor covers: model A and model B. In model A, the centers of three neighboring disks of equal radius are placed at the vertices of an equilateral triangle. In model B, the centers of four neighboring disks of equal radius are at the vertices of a square. For each type of cover, we considered three models: A-1, A-2, and A-3, and B-1, B-2, and B-3. Newly introduced models A-3 and B-3 bring about a significant improvement in coverage efficiency. We have proposed an accurate calculation of sensing and communication energy consumption per unit area by disks of two different radii. We formulated a correction for performance evaluation of models A-1 and A-2 from [

Since the qualitative leap in models A-3 and B-3 was obtained by optimal overlapping of neighboring disks of radius

In the case of three or more sensing ranges, one can get noteworthy results by separating the disks of radius

In the paper, we assumed that all nodes in a sensor network have circular sensing regions. However, this assumption may not be accurate in real world networks. The considered models can be extended for the case when the shape of the covered region is an ellipsoid instead of a circle. If the ratio between corresponding semimajor and semiminor axes of the ellipsoids is the same for different power levels, and it is possible to give the same orientation to all sensors, we can extend our models using simple affine transformation. Optimality condition (the ratio between big and small radii) for models A-3 and B-3 remains the same. In case where the sensors cannot be oriented properly or nodes may have irregular sensing regions, the analysis of the presented models needs to be reexamined based, for example, on the values of minimum and maximum sensing ranges of a node [

Our paper focuses on area coverage in random deployed WSN, where the density of static sensor nodes compensates for the lack of exact positioning. The primary goal of the paper is to estimate a potential of adjustable sensing ranges in terms of energy efficiency. In the future, we will consider other applications (target coverage, mobile sensors or targets). Finally, we want to set up experimental testbeds for further validation of our results.

This research was supported by MKE (Ministry of Knowledge Economy), Korea under ITRC (Information Technology Research Center) IITA-2009-(C1090-0902-0046), by MEST, Korea under WCU Program supervised by KOSEF (No. R31-2008-000-10062-0), and by the RFBR (grant 08-07-91300-IND_a).

Coverage with uniform sensing range.

Coverage with two sensing ranges.

Optimal coverage with two sensing ranges.

Model III [

Coverage variations with different node density and sensing range.

Energy variations with different sensing range (

Total energy consumption with various ratios

Modified model and sensing energy consumption with 100% coverage (

Separation of big disks.

Coverage with three sensing ranges.

Energy consumption per area for different models.

SECPA | 1.20_{1} |
1.51_{1} |
1.10_{1} |
1.57_{1} |
1.57_{1} |
1.17_{1} |

CECPA | 1.15_{2} |
1.15_{2} |
1.15_{2} |
_{2} |
_{2} |
_{2} |