Path coverage enhancement in wireless sensor networks based on CVT model

Abstract

In order to overcome the problems of low detection probability, low coverage uniformity and low coverage of current path coverage enhancement methods in wireless sensor networks, a new path coverage enhancement method based on CVT model is proposed in this paper. Firstly, the node perception model and network coverage model are constructed. On the basis of the node awareness model and network coverage model, CVT model is used to adjust the connection mode, density and location of nodes in wireless sensor networks, so as to improve the coverage performance of nodes in the detection area in wireless sensor networks, and realize the effective enhancement of path coverage in wireless sensor networks. Experimental results show that, compared with the traditional methods, the proposed method has high detection probability, high coverage uniformity and coverage rate, and the highest coverage rate reaches 97%, which has higher practical application performance.

Keywords

CVT model wireless sensor network node awareness coverage performance

1. Introduction

In recent years, with the development of micro electromechanical technology, wireless communication technology, sensor technology and embedded computing technology, wireless sensor network has been widely studied and concerned [1]. Wireless sensor network is a kind of self-organized network, which is composed of multi-functional sensor nodes with low energy consumption, low cost and small volume. Each sensor node has the functions of short distance communication, environment detection, data processing and signal acquisition in the network [18]. A large number of sensor nodes can be set in the geographic location of interest through the methods of deterministic deployment and random deployment to form a wireless sensor network. Each sensor node has limitations in communication, memory, computing, signal processing and battery power, and can only perceive a small part of the environment, and can complete tasks through a large number of nodes cooperating with each other, so as to sense most of the environment [2]. In the sensing environment, the sensor nodes can collect and process the original data. The nodes communicate with each other, collect and process the data, transmit it to the base station, and use the Internet or satellite to transmit the final data to the outside world [16]. Low deployment cost is the main sensor network of wireless sensor network. Generally, the working environment of the sensor network is relatively poor. The nodes are deployed in the detection area by the way of random distribution. The nodes cannot be supplemented, the energy is limited, and the distribution is uneven. In order to extend the life of wireless sensor network, the network coverage ability needs to be enhanced [15]. At present, there are some problems in the path coverage enhancement methods of wireless sensor networks, such as low detection probability, low coverage uniformity and low coverage.

Reference [4] proposes a path coverage enhancement method for wireless sensor networks based on mobile distance and patching radius. This method establishes the relationship model between patching radius and mobile distance, and maintains the connected patching position of mobile nodes in the patching circle. On the basis of the hole area and moving distance, the mobile node creates the corresponding priority of the hole, and determines the order of hole repair according to the priority, so as to enhance the path coverage of wireless sensor networks. In wireless sensor networks, the probability of using this method to detect the target point is low, and the detection probability is low. Reference [20] proposes a path coverage enhancement method for directional heterogeneous sensor networks. The nodes are deployed in the target path through the cooperation between the virtual gravity of the specified path and the virtual force of the neighbor nodes, and the node position is fine tuned under the combined virtual force through autonomous movement and rotation, so as to enhance the network path coverage. The coverage area of the nodes in this method is small in wireless sensor networks, and the coverage rate is low. Reference [5] proposes a path coverage enhancement method based on connectivity for wireless sensor networks. This method determines the corresponding working direction of wireless sensor, maximizes the coverage area of each Voronoi unit, adjusts the maximum overlapping coverage neighbor node, and improves the optimal coverage contribution rate of node. The sensing direction of boundary nodes is adjusted to enhance the path coverage of wireless sensor networks. The standard deviation of node distance is large, and the coverage uniformity is low. In reference [6], a path coverage enhancement method based on particle swarm optimization (PSO) algorithm is proposed in wireless sensor networks. In this method, the sensing model of wireless sensor networks is established, and the sensing direction of sensor nodes in the network is determined by PSO algorithm. The simulated annealing operation is introduced into the algorithm to solve the local optimal problem and enhance the path coverage of wireless sensor networks. The coverage area of this method is relatively small, and the coverage rate is low.

In order to solve the problems in the above methods, a path coverage enhancement method based on CVT model is proposed. The overall scheme of this method is as follows:

The node perception model and network model are constructed.

CVT model is used to enhance the path coverage of wireless sensor networks.

Experimental results and analysis verify the overall effectiveness of path coverage enhancement method based on CVT model in three aspects: detection probability, coverage uniformity and coverage.

Conclusions.

Through the whole scheme, the path coverage of wireless sensor network is effectively enhanced.

2. Path coverage enhancement in wireless sensor networks

2.1. Node perception model

The coverage ability of wireless sensor networks is usually determined by the sensor nodes’ perception model and location in wireless sensor networks. Probability perception model and binary perception model are the main sensor nodes’ perception models at present [10].

2.1.1. Probability perception model

In the environment, the uncertainty of the detection ability of nodes to the surrounding environment is the precondition of the probabilistic perception model, which has strong practicability in the practical application environment. The probabilistic perception model can be divided into obstacle model, statistical model and exponential model according to different actual situations [9,14].

(1) Obstacle model: when there are obstacles in the practical application of the above-mentioned node perception model, it is difficult to realize the real perception ability of the node for the target. When the obstacle exists in the connection between the target and the node, the perception ability of the node is 0 for the target point. As shown in Fig. 1, for two targets, the perception ability of the sixth node is 0. If the target seven can be covered by the perception range of node six, the application requirements can be met, indicating that target seven can be sensed by node six. The perception ability of node six for one target is 0.

Fig. 1.

Networks with obstacles.

Let $p^{'} (s, a)$ represent the perception probability of the node for the target; $p^{'} (s, a)$ represents the perception probability of the node for the target when there is no obstacle environment. The expression of the obstacle model is as follows: $\begin{matrix} (1) & p^{'} (s, a) = \{\begin{matrix} P (s, a) & if there is no obstacle between s and a \\ 0 & else \end{matrix} \end{matrix}$

(2) Statistical model: after investigation, it is found that the sensing range of nodes in wireless sensor networks will show irregular shape, which is not always the same, as shown in Fig. 2.

Fig. 2.

Statistical model of sensor nodes.

If the distance between the sensor node s and the target point a is less than $r - r_{e}$ , the sensing ability of the node is 1 for the target point; if the distance between the sensor node and the target point is less than or equal to $r + r_{e}$ and greater than or equal to $r - r_{e}$ , the sensing ability of the node is the exponential function corresponding to the distance; if the distance between the sensor node and the target point is greater than $r + r_{e}$ , the sensing ability of the node is the exponential function corresponding to the distance. For the target point, the perception ability of the node is 0, and the expression of the statistical model is obtained through the above analysis: $\begin{matrix} (2) & P (s, a) = \{\begin{matrix} 0 & if r + r_{e} ⩽ d (s, a) \\ e^{- λ α^{β}} & if r - r_{e} ⩽ d (s, a) ⩽ r + r_{e} \\ 1 & if r - r_{e} ⩾ d (s, a) \end{matrix} \end{matrix}$

In the formula, $r_{e}$ represents the measurement of uncertainty in the detection process; α describes the corresponding attenuation coefficient of perception quality in the range of $r - r_{e}$ . β describes the corresponding attenuation coefficient of perception quality in the range of $r + r_{e}$ .

(3) Exponential model: the accuracy of node acquisition information is usually determined by the distance between the target and the node. The accuracy of node acquisition information increases with the decrease of the distance between the node and the target. The expression of exponential perception model is as follows: $\begin{matrix} (3) & P (s, a) = e^{- α d (s, a)} \end{matrix}$

2.1.2. Binary perception model

To determine the ability of nodes to detect events is the precondition of binary perception model. If there is a detection target within the coverage of the node, it indicates that the ability of the node is 1 for the target. Binary perception model is omnidirectional when the sensing direction of the node is omnidirectional. The perception range of binary perception model is a circular plane with r as the radius and node as the center.

Let $s (x_{s}, y_{s})$ and $a (x_{a}, y_{a})$ describe the nodes and any point in the two-dimensional plane sensing range, and the corresponding sensing ability of node s for any point a can be obtained, whose expression is as follows: $\begin{matrix} (4) & P (s, a) = \{\begin{matrix} 1 & if d (s, a) ⩽ r \\ 0 & other \end{matrix} \end{matrix}$

Where $d (s, a)$ represents the Euclidean distance between any point a and node s, and its calculation formula is as follows: $\begin{matrix} (5) & d (s, a) = \sqrt{{(x_{s} - x_{a})}^{2} + {(y_{s} - y_{a})}^{2}} \end{matrix}$

If the binary perception model is a directed perception model when the node has a directed perception direction, the sector plane with an angle of σ, a radius of r and a node as the center is its perception range, then the schematic diagram of the plane of the directed binary perception model and the omnidirectional binary perception model is shown in Fig. 3.

Fig. 3.

Binary perception model.

Through the construction of node perception model, the distance between wireless sensor network nodes is accurately calculated, which lays the foundation for the following wireless sensor network path coverage enhancement.

2.2. Network coverage model

According to the sensing information provided by the nodes, the wireless sensor network uses the network coverage model to determine the detected physical data [23,24]. At present, single node model is the most widely used model, but in some cases, single node model can not meet the needs of the perceived target. So a $(k, ε)$ information coverage model is proposed.

Single node model

There are uncertain factors in the environment and network application. For any point in the detection area, the perception ability of network nodes can not be 1.

Assuming that $c_{th}$ is the minimum threshold, if the perception probability of a single node is higher than the minimum threshold $c_{th}$ , it is considered that for the target, the coverage of the network is 1, otherwise it is 0 [21]. Let $P (s)$ represent the coverage corresponding to the single node model, and its calculation formula is as follows: $\begin{matrix} (6) & P (s) = \{\begin{matrix} 1 & if P (s, a) ⩾ c_{th} \\ 0 & else \end{matrix} \end{matrix}$

$(k, ε)$ information coverage model

The information provided by a single sensor node in the case of node failure or node sparsity can not meet the requirements of the minimum threshold $c_{th}$ . A $(k, ε)$ information coverage model is proposed, and k nodes are selected. The rate of missing detection is less than ε, which meets the application requirements of wireless sensor networks. The value of K is directly determined by the actual application requirements, but the practical application experience can usually determine k, ε [3].

3. Path coverage enhancement in wireless sensor networks based on CVT model

CVT model is the abbreviation of centroidal varoni tessellation model. It is an effective target coverage area adjustment model. It has the characteristics of high coverage efficiency and high precision of boundary range. Therefore, CVT model is used to enhance the path coverage of wireless sensor networks.

When using CVT model to enhance path coverage of wireless sensor network, the specific network definition is as follows:

The static network is composed of n nodes in the plane in network S, and its expression is as follows: $\begin{matrix} (7) & S = {s_{1}, s_{2}, \dots, s_{n}} . \end{matrix}$

In wireless sensor networks, nodes use binary sensing detection model. Let $S_{i}$ describe the sensing range of node $s_{i}$ in the network, C describe the total sensing range of wireless sensor networks, that is, the union of sensing ranges of all nodes in wireless sensor networks [7,11], and its expression is as follows: $\begin{matrix} (8) & C = ⋃_{i = 1}^{n} S_{i} . \end{matrix}$

The communication radius of sensor nodes in the network is R. when the communication radius is greater than or equal to the distance between two nodes, direct communication can be realized.

Neighbor set $N (i)$ is composed of node $s_{i}$ whose communication radius R is equal to or whose distance is less than the communication radius R, and its expression is as follows: $\begin{matrix} (9) & N (i) = {s_{j} ∣ d (s_{j}, s_{i}) ⩽ R, j \neq i} . \end{matrix}$

The undirected graph $G = (V, E)$ is used to represent the wireless sensor network composed of nodes, where V describes the set of nodes, $V = S = {s_{1}, s_{2}, \dots, s_{n}}$ ; E describes the set of connected edges, when $d (s_{j}, s_{i}) ⩽ R$ , $e_{ij} = (s_{j}, s_{i}) \in E$ . The corresponding communication graph of sensor network S is undirected graph G. Let $P = {s_{1}, s_{2}, s_{3}, \dots}$ represent the communication path existing in the undirected graph, which is composed of multiple nodes relaying and forwarding in the network. When the distance between adjacent nodes in the undirected graph is less than R, they are communication neighbors [25]. If the communication link between any two points in undirected graph G is connected, it is said that undirected graph G is connected.

Let the area detected by wireless sensor network be as R, and S represents the set of nodes. If the sensing circle of at least one node in the set S covers every node in the detected target region R, it indicates that the set S of nodes is the covering set of region R [8,17]. If set S constitutes a connected communication graph, then set S is the connected covering set of region R.

Fig. 4.

Connected coverage diagram of detection area.

In Fig. 4, the dotted line area describes the target detection area in the network. The nodes $s_{1}$ , $s_{2}$ , $s_{3}$ , $s_{4}$ , and $s_{5}$ can cover the detection area, but they can not form a connected wireless sensor network. The nodes $s_{6}$ , $s_{7}$ and $s_{8}$ are added to the appropriate location, and the eight nodes above constitute a connected wireless sensor network, covering the whole target area, where the black dot describes the first enabled and selected network node; the bar dot describes the enabled and selected network node for the second time, and the hollow dot describes the nodes of wireless sensor network not selected and enabled.

Let S represent the sensor network deployed in the detection area R, and look for a subset $S^{'} \subseteq S$ that meets the following conditions:

Subset $S^{'}$ can completely cover detection region R, which satisfies the following formula: $\begin{matrix} (10) & R \subseteq ⋃_{s_{i} \subseteq S^{'}} S_{i} \end{matrix}$

The connected communication graph $G^{'}$ constituted by the node set $S^{'}$ ;

Set $S^{'}$ is the smallest subset in S and satisfies the above conditions.

Through the above analysis, we can use the minimum covering connected set question to replace the subset $S^{'}$ question.

Voronoi partition is a very important and useful structure partition, which can effectively describe the proximity between points, and is widely used in various fields [13,19]. Let point set $2 < n < \infty$ , and $\forall i, j \in {1, 2, \dots, n}$ , if the values of i and j are not equal, then the values of $p_{i}$ and $p_{j}$ are not equal. The path coverage enhancement method of wireless sensor network based on CVT model uses $d (p_{i}, q)$ to represent the distance between point $p_{i}$ and point q.

Let $B (p_{i}, p_{j})$ represent the vertical bisector between point $p_{i}$ and point $p_{j}$ , and its expression is as follows: $\begin{matrix} (11) & B (p_{i}, p_{j}) = {q \in R^{2} ∣ d (p_{i}, q), i \neq j} \end{matrix}$

Plane $R^{2}$ can be divided into two half planes $H (p_{i}, p_{j})$ by line $B (p_{i}, p_{j})$ . The expression is as follows: $\begin{matrix} (12) & H (p_{i}, p_{j}) = {q \in R^{2} ∣ d (p_{i}, q) ⩽ d (p_{i}, q), i \neq j} \end{matrix}$

A half plane $H (p_{i}, p_{j})$ is called the dominatregion of a point $p_{i}$ about the point $p_{i}$ , let $V (p_{i}) = ⋂_{j \in I_{n} / {i}} H (p_{i}, p_{j})$ be the Voronoi region associated with the point $p_{i}$ , $V (P) = {V (p_{1}), V (p_{2}), \dots, V (p_{n})}$ describes the Voronoi graph corresponding to the point set P, let $\partial V (p_{i})$ describe the boundary corresponding to $V (p_{i})$ . Because $⋃_{i = 1}^{n} V (p_{i}) = R^{2}$ , and the following formula exists: $\begin{matrix} (13) & [\frac{V (p_{i})}{\partial V (p_{i})}] \cap [\frac{V (p_{j})}{\partial V (p_{j})}] = Φ \end{matrix}$

Through the above analysis, we can use $V (P) = {V (p_{1}), V (p_{2}), \dots, V (p_{n})}$ to get the corresponding partition of $R^{2}$ , that is, Voronoi partition. $V (P)$ is divided by Voronoi to get point set P.

If $V (p_{i}) \cap V (p_{j}) \neq Φ$ , then $V (p_{i}) \cap V (p_{j})$ is Voronoi edge, which constitutes partition. Generally, $e_{ij}$ is used for description, and its expression is as follows: $\begin{matrix} (14) & e_{ij} = V (p_{i}) \cap V (p_{j}) \end{matrix}$

If $e_{ij} \neq Φ$ , then $p_{i}$ and $p_{j}$ are Voronoi neighbors in the process of partition. Voronoi vertex describes the end point and start point of Voronoi edge $e_{ij}$ .

Figure 5 shows a Voronoi partition in the $R^{2}$ plane.

Fig. 5.

Voronoi partition of detection area.

The area in Fig. 5 is divided by 20 points. All the points in the plane are randomly distributed. According to the analysis of Fig. 5, there are both rays and line segments in the Voronoi partition process, resulting in some polygons being bounded and closed in Voronoi partition, but some Voronoi polygons are unbounded and not closed [12].

Let $P = {p_{1}, p_{2}, \dots, p_{n}}$ be the point set existing on $R^{2}$ ., $V (P)$ describes the Voronoi partition corresponding to $R^{2}$ generated by the point set. Let $Q = {v_{1}, v_{2}, \dots, v_{n}}$ , then set Q is composed of all Voronoi vertices.

Let $x_{i 1}, x_{i 2}, \dots, x_{i k_{i}}$ be the space coordinate, and be the vector with the same Voronoi vertex, then the triangle $T_{i}$ and the set D are defined, respectively $\begin{array}{l} (15) & T_{i} = {x | x = \sum_{j = 1}^{k_{i}} λ_{j} x_{ij}, \sum_{j = 1}^{k_{i}} λ_{j} = 1, λ_{j} ⩾ 0, j \in I_{k_{i}} = {1, 2, \dots, k_{i}}} \\ (16) & D = {T_{1}, T_{2}, \dots, T_{n_{v}}} \end{array}$

Combining formula (15) and formula (16), the following formula is obtained: $\begin{array}{l} (17) & ⋃_{i = 1}^{n_{v}} T_{i} = CH (P) \\ (18) & [\frac{T_{i}}{\partial T_{i}}] \cap [\frac{T_{j}}{\partial T_{j}}] = Φ \end{array}$

Let $P = {p_{1}, p_{2}, \dots, p_{n}} \subset R^{m}$ , $x_{i}$ describe the corresponding coordinate vector of point $p_{i}$ , $x_{i} \neq x_{j}$ , $\forall i \neq j$ , $i, j \in I_{n}$ , then region $V (p_{i})$ is a m-dimensional polyhedron associated with $p_{i}$ , and its expression is as follows: $\begin{matrix} (19) & V (p_{i}) = {x ∣ ‖ x - x_{i} ‖ < ‖ x - x_{j} ‖, \forall j \neq i, j \in I_{n}} \end{matrix}$

According to the above formula, in m-dimensional space, the region $V (p_{i})$ in $R^{m}$ is the Voronoi partition generated by set P.

Let $V (P)$ describe the Voronoi partition formed by the point set $P = {p_{1}, p_{2}, \dots, p_{n}}$ ; $Q = {v_{1}, v_{2}, \dots, v_{n}}$ describes the Voronoi vertex of the point set; $T_{i}$ describes the m-dimensional convex shell of $p_{i 1}, p_{i 2}, \dots, p_{i k_{i}}$ . If $\forall i \in I_{n}$ , $k_{i} = m + 1$ , it shows that $D (P) = {T_{1}, T_{2}, \dots, T_{n_{v}}}$ is m-dimensional Delaunay triangulation in the process of shell $CHP$ forming of P [22].

The path coverage enhancement method based on CVT model calculates the coverage blind area of Voronoi triangle according to the coordinates of vertices $v_{ij}^{1}$ , $v_{ij}^{2}$ and nodes $s_{i}$ , and enhances the coverage of wireless sensor network path according to the calculated coverage blind area.

If the distance comparison formula $d (s_{i}, v_{ij}^{2}) ⩽ R$ and the formula $d (s_{i}, v_{ij}^{1}) ⩽ R$ are all valid, that is, there is a vertex $v_{ij}^{1}$ , $v_{ij}^{2}$ in the sensing circle $S_{i}$ of node $s_{i}$ , which can be processed by Voronoi triangle $T_{ij}$ in the sensing circle $S_{i}$ , and node $s_{i}$ can completely cover Voronoi triangle $T_{ij}$ . According to the above analysis, there is no triangle $T_{ij}$ in the coverage blind area of the network, that is: $\begin{matrix} (20) & area (b a_{ij}) = 0 \end{matrix}$

In the sensing circle $S_{i}$ of node $s_{i}$ , there is a vertex $v_{ij}^{1}$ or a vertex $v_{ij}^{2}$ , and the other exists outside the sensing circle $S_{i}$ of node $s_{i}$ . Let $v_{ij}^{2}$ exist outside the sensing circle $S_{i}$ , and $v_{ij}^{1}$ exist inside the sensing circle $S_{i}$ , that is, $d (s_{i}, v_{ij}^{2}) > R$ , $d (s_{i}, v_{ij}^{1}) ⩽ R$ . In the above case, the sensing circle $S_{i}$ cannot completely cover $Δ s_{i} v_{ij}^{1} v_{ij}^{2}$ , so there is $Δ s_{i} v_{ij}^{1} v_{ij}^{2}$ in the coverage blind area. The angle $∠ s_{i} v_{ij}^{1} v_{ij}^{2}$ is calculated by cosine formula. $\begin{matrix} (21) & ∠ s_{i} v_{ij}^{1} v_{ij}^{2} = {cos}^{- 1} [\frac{d {(v_{ij}^{1}, s_{i})}^{2} + d {(v_{ij}^{1}, v_{ij}^{2})}^{2} - d {(v_{ij}^{2}, s_{i})}^{2}}{2 \times d (v_{ij}^{1}, s_{i}) \times d (v_{ij}^{1}, v_{ij}^{2})}] \end{matrix}$

The blind area of coverage in Voronoi triangle $T_{ij}$ is calculated by the following two cases:

When $∠ s_{i} v_{ij}^{1} v_{ij}^{2} ⩽ \frac{π}{2}$

In this case, the area value corresponding to $Δ s_{i} v_{ij}^{1} v_{ij}^{2}$ is calculated by the following formula: $\begin{matrix} (22) & area (Δ s_{i} v_{ij}^{1} v_{ij}^{2}) = \frac{1}{2} d (v_{ij}^{1}, v_{ij}^{2}) \times d (s_{i}, p) \end{matrix}$

On the basis of the above formula, the area of $Δ s_{i} v_{ij}^{1} q$ is obtained, and its calculation formula is as follows: $\begin{matrix} (23) & area (Δ s_{i} v_{ij}^{1} q) = \frac{1}{2} d (v_{ij}^{1}, q) \times d (s_{i}, p) \end{matrix}$

Supposing that $area (q s_{i} w)$ represents the area value corresponding to sector $q s_{i} w$ , and its calculation formula is as follows: $\begin{matrix} (24) & area (q s_{i} w) = \frac{∠ q s_{i} v_{ij}^{2}}{2 π} \times π R^{2} \end{matrix}$

Therefore, the area of the covering blind area in the triangle $Δ s_{i} v_{ij}^{1} v_{ij}^{2}$ is as follows: $\begin{matrix} (25) & area (b a_{ij}) = area (Δ s_{i} v_{ij}^{1} v_{ij}^{2}) - area (Δ s_{i} v_{ij}^{1} q) - area (q s_{i} w) \end{matrix}$

On the basis of formula (25), the area formula is introduced to get the following formula: $\begin{matrix} (26) & area (b a_{ij}) = \frac{1}{2} d (v_{ij}^{1}, v_{ij}^{2}) \times d (s_{i}, p) - \frac{1}{2} d (v_{ij}^{1}, q) \times d (s_{i}, p) - \frac{∠ q s_{i} v_{ij}^{2}}{2} R^{2} \end{matrix}$

Where, $d (s_{i}, p)$ describes the distance between the line segment $v_{ij}^{1} v_{ij}^{2}$ and the node $s_{i}$ , and its calculation formula is as follows: $\begin{array}{l} (27) & d (v_{ij}^{1}, q) = d (v_{ij}^{1}, q) + d (p, q) = \sqrt{d {(s_{i}, v_{ij}^{1})}^{2} - d {(s_{i}, p)}^{2}} + \sqrt{R^{2} - d {(s_{i}, p)}^{2}} \\ (28) & ∠ q s_{i} v_{ij}^{2} = {cos}^{- 1} (\frac{d (v_{ij}^{1}, s_{i}) + R^{2} - {[d (v_{ij}^{1}, v_{ij}^{2}) - d (v_{ij}^{1}, q)]}^{2}}{2 \times d (v_{ij}^{2}, s_{i})}) \end{array}$

When $∠ s_{i} v_{ij}^{1} v_{ij}^{2} > \frac{π}{2}$

The corresponding area of blind area in Voronoi triangle $Δ s_{i} v_{ij}^{1} v_{ij}^{2}$ is basically the same as that in the case of $∠ s_{i} v_{ij}^{1} v_{ij}^{2} ⩽ \frac{π}{2}$ , and it only has a little difference. $\begin{matrix} (29) & \begin{matrix} area (b a_{ij}) & = area (Δ s_{i} v_{ij}^{1} v_{ij}^{2}) - area (Δ s_{i} v_{ij}^{1} q) - area (q s_{i} w) \\ = \frac{1}{2} d (v_{ij}^{1}, v_{ij}^{2}) \times d (s_{i}, p) - \frac{1}{2} d (v_{ij}^{1}, q) \times d (s_{i}, p) - \frac{∠ q s_{i} v_{ij}^{2}}{2} R^{2} \end{matrix} \end{matrix}$

Where $\begin{array}{l} (30) & d (v_{ij}^{1}, q) = d (p, q) - d (v_{ij}^{1}, q) = \sqrt{R^{2} - d {(s_{i}, p)}^{2}} - \sqrt{d {(s_{i}, v_{ij}^{1})}^{2} - d {(s_{i}, p)}^{2}} \\ (31) & ∠ q s_{i} v_{ij}^{2} = {cos}^{- 1} (\frac{d {(v_{ij}^{2}, s_{i})}^{2} + R^{2} - {[d (v_{ij}^{1}, v_{ij}^{2}) - d (v_{ij}^{1}, q)]}^{2}}{2 \times d (v_{ij}^{2}, s_{i}) \times R}) \end{array}$

Through the above process, the coverage area of the network node is the area not covered in the Voronoi triangle $T_{ij}$ . The area that cannot be covered in each Voronoi triangle is the area that cannot be covered by the node $s_{i}$ in the Voronoi region. $\begin{matrix} (32) & area (ba) = \sum_{j = 1}^{m_{i}} area (b a_{ij}) \end{matrix}$

The coverage area of the detection target area R in the whole wireless sensor network can be calculated by the sum of the areas that cannot be covered in the Voronoi area. $\begin{matrix} (33) & area (ba) = \sum_{j = 1}^{m_{i}} area (b a_{i}) \end{matrix}$

Through the above process, the location and area of the region which can not be covered by the nodes in the detection area are obtained to enhance the path coverage of wireless sensor network and improve the coverage performance of wireless sensor network.

4. Experimental verification

In order to verify the overall effectiveness of path coverage enhancement method based on CVT model in wireless sensor networks, a comparative experiment is needed. This test is implemented by $C + +$ programming, using 6 GB memory, 2.4 GHz main frequency and Intel dual core processor Windows 7 system. The overall scheme of the experiment is as: taking the detection probability, coverage uniformity and coverage rate as the comparative indicators, the method in this paper is compared with the methods in reference [4], reference [20] and reference [5] for verification.

Detection probability: detection probability refers to the effectiveness of different methods to detect target points. The higher the detection probability, the higher the detection performance of the method.

Coverage uniformity: coverage uniformity refers to the coverage uniformity of different methods. The higher the uniformity, the better the coverage performance of the method.

Coverage: coverage refers to the effective probability of path coverage of different methods in a certain range. Coverage indicates that the more effective the coverage method is.

4.1. Comparison of detection probability

The detection probability is used to reflect the detection probability of the target point. The detection probability comparison test results of the four methods are as follows:

Fig. 6.

Detection probability of four different methods.

Analysis of Fig. 6 shows that the detection probability of the path coverage enhancement method based on CVT model is higher than that of the methods in reference [4], reference [20] and reference [5] in multiple iterations. High detection probability indicates that the probability of target point detection is higher, because the path coverage enhancement method based on CVT model constructs a node model. Based on the node model, the coverage of wireless sensor network path is enhanced, and the detection probability of the path coverage enhancement method based on CVT model is improved.

4.2. Comparison of coverage uniformity

Coverage uniformity is a key problem in the research of path coverage enhancement in wireless sensor networks. It can be quantified by the standard deviation corresponding to the distance between nodes. The coverage uniformity changes with the increase of the standard deviation. The test results of coverage uniformity are as follows:

Fig. 7.

Coverage uniformity of four methods.

Analysis of Fig. 7 shows that the distance standard deviation of the path coverage enhancement method base on CVT model for wireless sensor network in multiple iterations is lower than that of the methods in reference [4], reference [20] and reference [5]. The lower the distance standard deviation is, the higher the coverage uniformity is. It is verified that the path coverage enhancement method base on CVT model for wireless sensor network has higher coverage uniformity because the path coverage enhancement method based on CVT model constructs a network coverage model, which enhances the path coverage of the network based on the network coverage model and improves the coverage uniformity of the method.

4.3. Comparison of coverage rate

In order to further verify the effectiveness of the path coverage enhancement method based on CVT model, the coverage rate is taken as the test indicator, and the test results are as follows:

Fig. 8.

Coverage rate of four methods.

It can be seen from Fig. 8 that the coverage rate of path coverage enhancement method based on CVT model in multiple iterations is higher than that of the methods in reference [4], reference [20] and reference [5], because the path coverage enhancement method based on wireless CVT model uses CVT model to enhance the path coverage of wireless sensor network, which improves the coverage rate of path coverage enhancement method based on CVT model.

5. Conclusions

With the development of sensor technology and computer communication technology, wireless sensor network has become a research hotspot. The traditional path coverage enhancement method of wireless sensor network can not meet the needs of the current development. Based on this, a path coverage enhancement method based on CVT model is proposed, which proves the following conclusions from both theoretical and experimental aspects. When enhancing the path coverage of wireless sensor networks, it has a high coverage uniformity and coverage rate. Specifically, compared with the methods based on mobile distance and repair radius, the coverage uniformity of the proposed method is greatly improved; compared with the methods based on connectivity, the coverage rate of the proposed method is significantly improved, up to 97%. Therefore, the proposed CVT model-based enhancement method can better meet the requirements of path coverage enhancement in wireless sensor network. In the future research process, we should further improve the coverage to improve the efficiency of computer communication.

Footnotes

Acknowledgement

2017 Henan Province Science and Technology Project “Research on the Construction of Virtual Experiment Platform in Cloud Environment” 172102210390.

References

Annamalai,

Bapat and

Das, Coverage enhancement for MTC devices using reduced search Viterbi decoder across RATs, IEEE Communications Letters20(9) (2016), 1892–1895. doi:10.1109/LCOMM.2016.2587862.

Annamalai,

Bapat and

Das, Constellation constraining-based coverage enhancement technique for MTC devices in LTE-A, IEEE Wireless Communications Letters5(6) (2016), 596–599. doi:10.1109/LWC.2016.2604244.

G.J.

Fan and

L.L.

Yang, Coverage holes discovery algorithm without location information in wireless sensor networks, Application Research of Computers32(6) (2018), 1826–1829.

X.G.

Fan,

J.J.

Yang and

Wang, Algorithm for enhancing probabilistic coverage in wireless sensor network, Journal of Software27(2) (2016), 418–431.

X.G.

Fan,

Z.C.

Zhang,

C.H.

Wang and

Tao, A probabilistic target coverage enhancing scheme in directional sensor network, Chinese Journal of Sensors and Actuators32(3) (2019), 108–113.

R.S.

Han and

Yang, A coverage-enhancing algorithm based on improved particle swarm optimization for WMSN of underground coal mine, Journal of China University of Mining & Technology45(1) (2017), 170–175.

Z.J.

Hao,

N.J.

Qu and

X.C.

Dang, A three-dimensional coverage algorithm for WSN with multiple mobile nodes in complex environment, Computer Engineering45(2) (2019), 120–127, 134.

P.Y.

He, Delay optimization of SFN based on genetic algorithm, Science of Surveying and Mapping44(6) (2019), 341–346.

Huang, An improved multi-objective genetic algorithm for heterogeneous coverage RFID network planning, International Journal of Production Research54(8) (2016), 1–14.

10.

Kantaros and

M.M.

Zavlanos, Distributed communication-aware coverage control by mobile sensor networks, Automatica63(25) (2016), 209–220. doi:10.1016/j.automatica.2015.10.035.

11.

J.F.

Lan,

C.L.

Niu and

G.H.

Yu, Offshore coverage optimization and application of TD-LTE networks, Telecommunications Science34(6) (2018), 42–48.

12.

Li and

N.A.

Liu, Method of geometric connected disk cover problem for wireless mesh networks deployment, Computer Science44(6) (2017), 75–79.

13.

Lu,

Zhou and

L.C.

Wan, Improved method for 2D target coverage in wireless sensor networks, Journal of Xidian University(Natural Science)46(2) (2019), 107–112.

14.

Mahboubi,

Moezzi,

A.G.

Aghdam and

Sayrafian-Pour, Distributed sensor coordination algorithms for efficient coverage in a network of heterogeneous mobile sensors, IEEE Transactions on Automatic Control62(11) (2017), 5954–5961. doi:10.1109/TAC.2017.2714102.

15.

Ran and

A.T.

Murray, A parallel algorithm for coverage optimization on multi-core architectures, International Journal of Geographical Information Science30(12) (2016), 432–450.

16.

Sun,

Zhang,

Nie,

Wei,

Lloret and

Song, CASMOC: A novel complex alliance strategy with multi-objective optimization of coverage in wireless sensor networks, Wireless Networks23(4) (2017), 1201–1222. doi:10.1007/s11276-016-1213-3.

17.

Z.Y.

Sun,

C.F.

Li,

C.F.

Xing and

A.J.

Cao, An optimal coverage control algorithm with joint sensing for wireless sensor networks, Journal of Xi’an Jiaotong University50(10) (2016), 86–92.

18.

Tang,

Chen and

J.P.

Coon, Joint coverage enhancement by power allocation in Poisson clustered out-of-band D2D networks, IEEE Transactions on Vehicular Technology21(5) (2018), 18–23.

19.

Tang and

X.Q.

Lu, Research on optimization of optical interconnection network, Laser Journal38(1) (2017), 92–95.

20.

Z.M.

Xu,

Tan,

C.Y.

Yang and

X.J.

Tang, Node coverage optimization algorithm in directional heterogeneous wireless sensor network, Journal of Computer Applications37(7) (2017), 1849–1854.

21.

H.X.

Zhang, Wireless sensor network coverage optimization based on particle swarm optimization algorithm, Modern Electronics Technique40(9) (2017), 50–53.

22.

J.N.

Zhang,

X.F.

Zhang,

Jian,

S.Z.

Hu and

L.Z.

Wu, Crop covering algorithm using convolution neural network based on prior threshold optimization, Journal of Signal Processing33(9) (2017), 82–90.

23.

J.W.

Zhang,

Wang and

Yang, Path coverage scheme based on fuzzy particle swarm optimization algorithm for directional sensor networks, Pattern Recognition and Artificial Intelligence30(2) (2017), 183–192.

24.

Zhang,

Zhou,

Zhang,

Lee and

Li, Problem specific MOEA/D for barrier coverage with wireless sensors, IEEE Transactions on Cybernetics47(11) (2016), 3854–3865.

25.

S.R.

Zhao and

X.Z.

Meng, Simulation of optimization control of high speed interconnection network coverage in heterogeneous environment, Computer Simulation36(2) (2019), 289–292.