WSN coverage optimization problem in wireless sensor network

1. Relevant basis

1 Related concepts

1. wireless sensor network(Wireless Sensor Networks, WSNs) is a distributed sensor network. Smart devices embedded with sensors sense, communicate, process, and collect data, and then transmit the data to monitors through the Internet for further analysis. It is through wireless communication. A multi-hop self-organizing network is formed, which can be used for large-scale Internet of Things applications. Since its sensors communicate wirelessly, the location can be changed at any time, making it very flexible. The coverage optimization problem of WSN can be described as the node deployment problem under the condition of ensuring the connectivity of the sensor network in the specified monitoring area .

2. WSNs system consists of three parts:
   (1) The sensor node is essentially a small embedded system, which consists of four parts: sensor module, processor module, wireless communication module, and energy supply module. It can act as both a data sender and an intermediate router.
   Responsible for collecting local information and processing data ( storage , management, fusion), transmitting data to other sensor nodes, and cooperating with other sensor nodes to complete some tasks; The wireless communication is transmitted to the management node;
   (3) The management node is a terminal monitoring platform, and the user configures and manages WSNs through the management node, publishes monitoring tasks and collects monitoring data.
   The data monitored by the sensor nodes is transmitted to the aggregation node after multiple hops, and then reaches the management node through the Internet or satellites .
   WSN can be defined as a two-dimensional network with three layers in the following figure, the bottom layer is the sensor nodes distributed in the target area, there are several clusters, each cluster has a cluster head (convergence node), these cluster heads form the middle layer , each sensor node can directly communicate with their cluster head Communication, the cluster head can communicate with the top Sink node (management node).
   Each round of data transmission is divided into two phases: In the establishment phase of the cluster , the best deployment solution I is selected first in each round, and then the cluster head is elected (the cluster head in each round can be different), and then grouped (non-cluster head nodes are calculated with all cluster head nodes communication consumption, choose the lowest cluster head). In the phase of data transmission , the cluster head collects the data of the sensor nodes in the cluster, and then sends it to the sink node.
   

3. WSNs application: Military aviation, environmental monitoring, healthcare, industrial manufacturing, smart transportation, smart home, smart city, disaster relief, etc.

4. existing problems: Coverage blind area (not enough), node redundancy (too much, waste), processing capacity, storage capacity, and communication capacity are weak

2 related categories

2.1 Classification by Node Deployment Mode

1. Static WSN: The location of the node is determined before the network is running, and it will not be moved after deployment.
2. Dynamic WSN: All nodes (sensor nodes and aggregation nodes) can be moved and dynamically deployed according to the specific needs of the network (network expansion, fault repair, etc.).
3. Hybrid WSN: Most fixed nodes + a small number of mobile nodes, which mainly solves the problem of self-adjustment deployment of mobile nodes.

2.2 Classification by Coverage Target

1. dot coverage: Figure (a) is also called target coverage. Figure (a) dots are sensor nodes and squares are monitoring targets. Each target is required to be covered by at least one sensor node .
2. fence covering: As shown in (b), the sensor nodes are required to monitor the trajectory of the moving target . It is mainly used for the detection of illegal border crossers on national defense borders, the detection of enemy invasions in military battlefields, and the monitoring of species migration in environmental protection, etc.
3. area coverage: As shown in (c), it is required to cover the entire target area with as few sensor nodes as possible . It is mainly used in large-scale application environments such as forest fire early warning, lake water surface water quality monitoring, or safety monitoring applications in restricted areas such as coal mine roadways, factory workshops, and warehouses.

2.3 Classification by Sensor Type in the Network

1. Isomorphic WSNs: The sensor type is the same, and the network is homogeneous;
2. Heterogeneous WSNs: Sensor types and perception capabilities vary; in future smart cities, WSNs will be heterogeneous.

2.4 Sensor types

1. omnidirectional sensor: 2D is a disk, 3D is a ball, only covered and non-covered, non-0 or 1, generally based on a deterministic Boolean model, in practical applications, various capabilities will decrease with distance;
2. orientation sensor: Various abilities will decrease as the distance and angle increase.

2.5 Terrain classification

1. flat: two-dimensional;
2. saddle terrain: three-dimensional, as shown in figure a;
3. multi-peak terrain: Three-dimensional, as shown in Figure b, which is more complex than the first two.

In a three-dimensional environment, wireless signals are reflected, scattered, and diffracted along the transmission path.

3 Evaluation indicators

3.1 Coverage

The greater the network coverage, the better the deployment effect.

3.2 Uniformity

The uniformity index E of sensor nodes is the mean value of the sum of the distance standard deviations between all sensor nodes, calculated as follows:

3.3 Node moving distance

Each node must move from the initial position to the optimal position found by the algorithm. The smaller the moving distance, the smaller the energy consumption;

3.4 Connectivity

Nodes need to transmit information to each other, so the connectivity of the network should be guaranteed.
Establish a directed graph adjacency matrix $M_v$, if the distance between two sensor nodes i and j does not exceed the communication radius $R_i^c$, indicating that i can transmit information to j, corresponding to $M_v[i][j]=1$ . Finally, the matrix power algorithm is used for calculation. If there is 0 in the matrix, it means that the network is not connected.

3.5 Energy Consumption and Lifespan

The battery of the sensor node is not rechargeable, so the energy loss should be reduced as much as possible to increase the network life under the premise of ensuring the maximum coverage.
What kind of energy consumption model to use is determined by the routing protocol used by the network . For example, in the LEACH protocol, the energy consumption of scheme I is $E\left(I\right)$ includes information communication consumption (data transmission and reception), data aggregation consumption and activation of nodes in deployment scheme I, calculated as follows:

while energy consumption is also related to the selected data transmission model, the commonly used data transmission model has free space model, multipath fading model, both of which depend on the distance between the sending node and the receiving node. In general, compare the transmission distance d with the threshold. When d is less than the threshold, the free space model is used, otherwise the multipath fading model is used. The energy consumption of transmitting l bit data is calculated as follows:

3.6 Number of information transfers

Under the premise of ensuring the maximum coverage, the more data the sensor node transmits to the cluster head, the more it can truly reflect the situation of the monitoring area, so as much data as possible should be transmitted;

3.7 Algorithm Complexity

The lower the better.

2. Related models

1 Sensor node perception model

1.1 Boolean perception model (Figure a)

Also known as the binary perception model, it is an ideal perception model. When a node transmits a signal, its ability will not decrease as the distance increases. It is suitable for nodes with a small monitoring radius and ignores the attenuation of the signal during transmission. It is often used in the derivation of basic theory, and less used in real life.

Perception probability calculation of a sensor node for a pixel: As shown in (a), dot $s_i$is the sensor node, square $m_j$is the monitoring target, $r^p$ is$s_i$The perceived radius of this disk is the node $s_i$area of ​​perception. If the monitoring target $m_j$At node $s_i$In the perception area, it is considered that $m_j$si $s_i$cover. (The communication radius $r^c$ is generally greater than or equal to$2r^p$ ).
Obviously, we have to calculate$m_j$give $s_i$the distance between. There are many kinds of distances between two points. If it is Euclidean distance and it is on a two-dimensional plane, then the distance between two points $d(s_i,m_j)=\sqrt{(x_i-x_j{)}^2+(y_i-y_j{)}^2}$, if it is a three-dimensional space, just add a coordinate z.
Then get $m_j$si $s_i$The perceived probability is:

this probability of either 1 or 0 is really "Boolean".

Calculation of the joint perception probability of all sensor nodes for a pixel: Monitoring node $m_j$The joint perception probability $C_p(s_{all},m_j)$ is calculated as follows:
$$C_p(s_{all},m_j)=1-\prod _{i=1}^N(1-p_{co}(s_i,m_j))$$
As long as there is a$s_i$can perceive $m_j$, $p_{co}(s_i,m_j)is1$ , then the subsequent multiplication is 0, and the final joint perception probability is 1.

2D Plane Coverage Calculation: Let N homogeneous sensor node sets S = { s 1 , s 2 , . . . , s N } S=\{s_1,s_2,...,s_N\}S={ s1​,s2​,...,sN​} , K monitoring node setM = { m 1 , m 2 , . . . , m K } M=\{m_1,m_2,...,m_K\}M={ m1​,m2​,...,mK​} , the area of ​​the rectangular monitoring area is$L\times W{m}^{2.}$ Divide the monitoring area into$L\times W$ grids, each grid area is$1m^{2.}$ If the monitoring node is located at the center of the grid, the coverage area = the sum of the joint sensing probabilities of all monitoring points, and the coverage rate is coverage area / monitoring area.
Coverage$C_r$The calculation is as follows:
$$C_r=\frac{{\sum }_{j=1}^K{C}_p(s_{all},m_j)}{L\times W}$$

1.2 Probabilistic perception model (Figure b)

When a node transmits a signal, its ability will decrease as the distance increases, which can more objectively reflect the network deployment environment in real life.

Perception probability calculation of a sensor node for a pixel: As shown in (b), it has an additional radius r 1 r_1 on the basis of (a)$r_1$, we first calculate $m_j$give $s_i$The distance between, and then get $m_j$si $s_i$Perceived probability:

This is well understood, if the distance between two points is less than $r_1$, means $m_j$Definitely can be $s_i$Perception; if the distance between two points is $r_1$with $r^{Between\; p}$ , means$m_j$It is possible to be $s_i$Perception, how likely is this? Calculated from the second sub-formula. The parameter ρ \rho in this subformula$\rho$和$\theta$ is determined by the sensor properties and monitoring environment.

2 Cluster head selection model

2.1 Jiangxi University of Technology

The probability of each sensor node being selected as a cluster head is p
c, if the sensor node randomly generates a value smaller than the cluster head selection threshold $H(i)\in [0,1]$ , the node is selected as the cluster head of the current round. $H\left(i\right)$ is calculated as follows:

3 Virtual force algorithm

4 Three-dimensional correlation algorithm

1. Calculation of surface area:
   For 3D space, the monitoring area is a curved surface. A simple method to calculate the surface area of ​​a surface is: first map the surface to a two-dimensional plane, then divide the plane into many small grids with the same area, and then use the surface integral formula to calculate the surface area of ​​the small surface corresponding to each small grid surface area, and finally add up to get the surface area of ​​the entire surface.
2. 3D perception blind zone:
   In the three-dimensional space, due to the occlusion of obstacles, although some targets are within the sensing range of the sensor node, they cannot be sensed, such as point C in the figure below.
   To judge whether there is occlusion between two points, there is a simple method to connect SC to get the surface equation within this range, and then calculate the zero point. If there is zero point, it means that there is occlusion. For example, point A is a zero point.