CN113163464B - Wireless sensor network clustering routing method and system based on maximum between-class variance - Google Patents

Wireless sensor network clustering routing method and system based on maximum between-class variance Download PDF

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CN113163464B
CN113163464B CN202110463299.4A CN202110463299A CN113163464B CN 113163464 B CN113163464 B CN 113163464B CN 202110463299 A CN202110463299 A CN 202110463299A CN 113163464 B CN113163464 B CN 113163464B
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CN113163464A (en
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赵小强
李雄
刘敏
文秦
高心岗
常虹
曾耀平
付银娟
翟永智
姚引娣
廖焕敏
高强
赵远洋
冯宁宁
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Xi'an Blue Sea Sky Electronic Information Technology Co ltd
Xian University of Posts and Telecommunications
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W40/00Communication routing or communication path finding
    • H04W40/02Communication route or path selection, e.g. power-based or shortest path routing
    • H04W40/04Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources
    • H04W40/10Communication route or path selection, e.g. power-based or shortest path routing based on wireless node resources based on available power or energy
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W84/00Network topologies
    • H04W84/18Self-organising networks, e.g. ad-hoc networks or sensor networks
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to a wireless sensor network clustering routing method and system based on maximum inter-class variance. The method comprises the following steps: calculating a node angle according to the coordinates of the base station and the coordinates of the node; determining the optimal cluster head position and the optimal cluster head number based on the wireless sensor network node energy consumption model; determining inter-cluster node angle variance according to node angles based on the optimal number of cluster heads; determining the number of nodes in each cluster according to the inter-cluster node angle variance; determining the number variance of the nodes among the clusters according to the optimal number of the cluster heads and the number of the nodes in each cluster; determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solving an optimal solution; dividing all the arranged nodes into a plurality of optimal clusters according to the optimal angle division threshold value; and determining an optimal cluster head position circle and node residual energy by taking the base station as a circle center and the optimal position of the cluster head as a radius, and selecting the optimal cluster head in each optimal cluster. The invention effectively reduces and balances the network energy consumption.

Description

Wireless sensor network clustering routing method and system based on maximum inter-class variance
Technical Field
The invention relates to the field of information communication, in particular to a wireless sensor network clustering routing method and system based on maximum inter-class variance.
Background
Wireless Sensor Networks (WSNs) are mobile ad hoc networks consisting of a large number of miniature, cheap and low-power-consumption sensor nodes, and the nodes cooperate with each other through Wireless communication multi-hop relay to complete application tasks and forward sensed data to a central acquisition aggregation node.
In the WSN clustering routing protocol, as shown in fig. 1, all nodes are partitioned by clusters according to some method, each cluster also being referred to as a cluster. And a certain node in the cluster is elected as a cluster head and is responsible for collecting and fusing data of other nodes in the cluster, and then the fused data is forwarded to the base station for processing. Because the cluster head undertakes the fusion and forwarding tasks of a large amount of data, the cluster head node tends to exhaust energy earlier than other nodes. Therefore, how to optimally select the cluster head so as to realize the minimum network energy consumption and prolong the service life of the network becomes an important challenge faced by the WSNs clustering routing protocol. The position, number and node clustering of the cluster head will affect the cluster head selection.
A journal article of a wireless sensor network clustering routing algorithm based on node angle clustering mentions a wireless sensor network clustering routing algorithm based on node angle clustering, and the algorithm principle in the article is as follows: improving an initial membership matrix of a fuzzy C-means clustering algorithm by using the angle information of the nodes to form an initial cluster; and then, selecting a cluster head by utilizing an improved grey wolf optimizer, node residual energy and the distance between the node residual energy and the base station, and adding all nodes into the cluster head nearby to form a final cluster. According to the journal thesis principle of the wireless sensor network clustering routing algorithm based on node angle clustering, the division of the initial clusters has great influence on cluster head selection, and the cluster head selection is an important factor influencing performance indexes such as network service life.
Therefore, the main disadvantages of the node clustering method of the wireless sensor network clustering routing algorithm based on node angle clustering are as follows:
firstly, based on the node angle clustering result of the fuzzy C mean value, only the nodes with similar angles can be divided into the same cluster, and the uniformity of the number of the nodes in each cluster can not be ensured; secondly, in the process of secondary clustering, the original result based on angle clustering is damaged, so that the cluster head distribution no longer has the advantage of uniformity.
Secondly, cluster head selection tends to take nodes with higher residual energy nodes and closer to the base station as cluster heads, and the optimal positions of the cluster heads are not considered, so that the reasonability of cluster head selection cannot be ensured, and the network energy consumption cannot be effectively reduced and equalized.
Disclosure of Invention
The invention aims to provide a wireless sensor network clustering routing method and system based on maximum between-class variance, and aims to solve the problems that the reasonability of cluster head selection is poor, and network energy consumption cannot be effectively reduced and equalized.
In order to achieve the purpose, the invention provides the following scheme:
a wireless sensor network clustering routing method based on maximum between-class variance comprises the following steps:
acquiring coordinates of a base station and node coordinates of all nodes in a wireless sensor network, and calculating a node angle of each node coordinate relative to the base station according to the coordinates of the base station and the node coordinates;
determining the optimal cluster head position and the optimal cluster head number of the cluster heads of the base station based on a wireless sensor network node energy consumption model;
determining inter-cluster node angle variance according to the node angles based on the optimal number of cluster heads;
clustering all nodes according to the inter-cluster node angle variance, and determining the number of nodes in each cluster;
determining the number variance of the nodes among the clusters according to the optimal number of the cluster heads and the number of the nodes in each cluster;
determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solving an optimal solution of the clustering multi-objective optimization function; the optimal solution is an optimal angle segmentation threshold;
arranging all the node angles in a descending order, and dividing all the arranged nodes into a plurality of optimal clusters according to the optimal angle division threshold value;
determining an optimal cluster head position circle and node residual energy, wherein the optimal cluster head position circle takes the base station as a circle center and the optimal cluster head position as a radius;
and selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy.
Optionally, the calculating a node angle of each node coordinate relative to the base station according to the base station coordinate and the node coordinate specifically includes:
using formulas
Figure GDA0003777116920000031
Calculating a node angle of each node coordinate relative to the base station; wherein, theta i A node angle of the ith node coordinate relative to the base station; x is a radical of a fluorine atom i Is the abscissa, y, of the ith node i Is the ordinate of the ith node; x is the number of 0 Is the abscissa, y, of the base station 0 Is the ordinate of the base station.
Optionally, the determining, based on the wireless sensor network node energy consumption model, an optimal cluster head position and an optimal cluster head number of the cluster heads at the base station specifically includes:
in a single complete communication process, determining an overall energy consumption objective function of the wireless sensor network based on a wireless sensor network node energy consumption model;
and solving the overall energy consumption objective function, and determining the cluster head optimal position and the cluster head optimal quantity of the cluster heads, wherein the cluster heads are positioned at the base station.
Optionally, the determining, based on the optimal number of cluster heads, the inter-cluster node angle variance according to the node angle specifically includes:
based on the optimal number of the cluster heads, determining probability values of node angles of all nodes, a mean value of the node angles in each cluster and accumulated probability of the node angles in each cluster according to the node angles;
based on a maximum between-cluster variance algorithm, obtaining the between-cluster node angle variance according to the probability value of node angles of all nodes, the mean value of the node angles in each cluster and the accumulated probability of the node angles in each cluster.
Optionally, the determining the inter-cluster node number variance according to the optimal number of cluster heads and the number of nodes in each cluster specifically includes:
acquiring the total number of all nodes;
determining the average number of nodes in each cluster according to the optimal number of the cluster heads and the total number of the nodes;
and determining the variance of the number of the nodes among the clusters according to the average number of the nodes and the number of the nodes in each cluster.
Optionally, the determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solving an optimal solution of the clustering multi-objective optimization function specifically includes:
using a formula
Figure GDA0003777116920000041
α∈[0,1]Determining a clustering multi-objective optimization function; wherein, F 1 A clustering multi-objective optimization function with independent variables as angle segmentation thresholds;
Figure GDA0003777116920000042
the inter-cluster node angle variance after normalization processing is carried out;
Figure GDA0003777116920000043
the variance of the number of the nodes between clusters after normalization processing; alpha is an angle clustering weight factor, and the value range is [0,1 ]];
And solving the clustering multi-objective optimization function by adopting a swarm intelligent optimization algorithm, and determining the optimal solution of the clustering multi-objective optimization function.
Optionally, the selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy specifically includes:
using formulas
Figure GDA0003777116920000044
Determining a node with the maximum fitness function value in each optimal cluster in the optimal cluster heads as an optimal cluster head; wherein, F 2 (s i ) For a plurality of ith nodes s in the best cluster head i A fitness function of; omega 1 Is a residual energy weight factor; e re (s i ) Is a node s i The residual energy of (d); e o (s i ) Is a node s i The initial energy of (a); omega 2 Is a location weight factor;
Figure GDA0003777116920000045
is a node s i Distance to the best cluster head position; d toCmax Maximum distance d from all nodes in the same cluster to the optimal cluster head position toCmin The minimum distance from all nodes in the same cluster to the optimal cluster head position.
Optionally, the selecting an optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy further includes:
and each node sends a data packet to the optimal cluster head in the time division multiple access frame time slot allocated to each node, and each optimal cluster head fuses data in the data packet in the cluster and sends the fused data to the base station.
A wireless sensor network clustering routing system based on maximum between-class variance comprises:
the node angle calculation module is used for acquiring a base station coordinate and node coordinates of all nodes in the wireless sensor network, and calculating a node angle of each node coordinate relative to the base station according to the base station coordinate and the node coordinates;
the cluster head optimal position and cluster head optimal quantity determining module is used for determining the cluster head optimal position and cluster head optimal quantity of the cluster head positioned in the base station based on a wireless sensor network node energy consumption model;
the inter-cluster node angle variance determining module is used for determining the inter-cluster node angle variance according to the node angles based on the optimal number of the cluster heads;
the node number determining module is used for clustering all the nodes according to the inter-cluster node angle variance and determining the number of the nodes in each cluster;
the cluster node number variance determining module is used for determining the cluster node number variance according to the optimal number of the cluster heads and the number of nodes in each cluster;
the clustering multi-objective optimization function solving module is used for determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance and solving an optimal solution of the clustering multi-objective optimization function; the optimal solution is an optimal angle segmentation threshold;
the optimal cluster dividing module is used for arranging all the node angles according to the sequence from small to large and dividing all the arranged nodes into a plurality of optimal clusters according to the optimal angle dividing threshold value;
the optimal cluster head position circle determining module is used for determining an optimal cluster head position circle and node residual energy, wherein the optimal cluster head position circle takes the base station as a circle center and the optimal cluster head position as a radius;
and the optimal cluster head selecting module is used for selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy.
Optionally, the node angle determining module specifically includes:
a node angle determination unit for using a formula
Figure GDA0003777116920000061
Calculating a node angle of each node coordinate relative to the base station; wherein, theta i A node angle of the ith node coordinate relative to the base station; x is the number of i Is the abscissa, y, of the ith node i Is the ordinate of the ith node; x is a radical of a fluorine atom 0 Is the abscissa, y, of the base station 0 Is the ordinate of the base station.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a wireless sensor network clustering routing method and system based on maximum inter-class variance, which are characterized in that firstly, from the angle of minimizing network energy consumption, based on a wireless sensor network node energy consumption model, the optimal position of a cluster head at a base station and the optimal number of the cluster heads are determined; secondly, the nodes with smaller angle difference can be divided into a cluster based on the clustering mode of the angular variance of the nodes among the clusters, and a cluster head is selected in each cluster based on the clustering result of the angular division, so that the cluster heads can be distributed in each angular direction, namely, the cluster heads are uniformly distributed in a monitoring area, and the number of the nodes in each cluster is basically equal based on the clustering mode of the number of the nodes among the clusters, namely, the number of the loads of each cluster head is basically equal, so that the energy consumption difference among the cluster heads is smaller, and the distribution uniformity of the cluster heads and the load balance of the cluster heads are improved in two aspects; and finally, taking the base station as a circle center, taking the optimal cluster head position circle of the cluster head as a radius and the node residual energy C, selecting each optimal cluster head in the optimal cluster according to the optimal cluster head position circle and the node residual energy, enabling the cluster head to be positioned near the optimal cluster head position distribution circle C, considering the node residual energy, improving the reasonability of cluster head selection, and greatly reducing and balancing the energy consumption of the network.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a diagram of a clustered routing architecture for a WSN provided by the present invention;
FIG. 2 is a flowchart of a wireless sensor network clustering routing protocol based on maximum between-class variance provided by the present invention;
FIG. 3 is a schematic view of a node coordinate diagram illustrating a first quadrant according to the present invention;
FIG. 4 is a schematic diagram of a cluster region provided by the present invention;
FIG. 5 is a schematic diagram of the clustering based on the angle segmentation threshold provided by the present invention
FIG. 6 is a schematic diagram of a circle C of the best cluster head position according to the present invention;
FIG. 7 is a comparison of cluster head distributions provided by the present invention; FIG. 7(a) is a cluster head profile for a particular time during which the similar scheme algorithm is running; FIG. 7(b) is a plot of a cluster head profile for a certain time during operation of the present invention;
FIG. 8 is a comparison of cluster head load balancing provided by the present invention;
FIG. 9 is a graph comparing network residual energy provided by the present invention;
FIG. 10 is a comparison graph of node residual energy standard deviations provided by the present invention;
FIG. 11 is a diagram of a wireless sensor network clustering routing system based on maximum between-class variance according to the present invention;
fig. 12 is a schematic diagram of a wireless communication energy consumption model provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a wireless sensor network clustering routing method and system based on maximum inter-class variance, which ensure the uniformity of cluster head distribution, improve the load balance of cluster heads, improve the rationality of cluster head selection, greatly reduce the energy consumption of a network and effectively reduce and balance the energy consumption of the network.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Fig. 2 is a flowchart of a wireless sensor network clustering routing method based on the maximum inter-class variance, as shown in fig. 2, a wireless sensor network clustering routing method based on the maximum inter-class variance includes:
step 201: the method comprises the steps of obtaining coordinates of a base station and node coordinates of all nodes in a wireless sensor network, and calculating a node angle of each node coordinate relative to the base station according to the coordinates of the base station and the node coordinates.
Initializing network parameters of the wireless sensor network: the monitoring area of the wireless sensor network is approximately a circle with the radius of R, and N sensor nodes (hereinafter, nodes) are randomly deployed in the circle and are divided into K different sub-clusters.
Taking the first quadrant as an example, as shown in FIG. 3, assume node s i 1,2, the coordinates of N are (x) i ,y i ) The coordinates of the base station are (x) 0 ,y 0 ). Angle of node relative to base station
Figure GDA0003777116920000081
Can be derived from a mathematical relationship (inverse trigonometric function). Therefore, the angles of all nodes with respect to the base station are as shown in equation 1.
Figure GDA0003777116920000082
Step 202: and determining the optimal cluster head position and the optimal cluster head number of the cluster heads of the base station based on the wireless sensor network node energy consumption model.
According to the energy consumption model of the wireless sensor network nodes, the energy consumption of each cluster area comprises the communication energy consumption between the cluster head and the base station and between the common nodes in the cluster and the cluster head. Energy consumption E of Cluster head CHtoBS As shown in formula 2, the method mainly includes the following three parts: the first part is that the cluster head receives the energy consumption of sensing data of N/K-1 common nodes in the cluster; the second part is energy consumption for fusing N/K group data in a cluster by a cluster head, E DA Energy consumption for fusing unit bit data; the third part is the energy consumption of the cluster head node for sending data to the base station, d CHtoBS Is the distance between the cluster head and the base station (assuming that the communication model between the cluster head and the base station is a free space communication model), l is the number of bits for data transmission, E elec Energy consumed to transmit or receive a unit bit of data, E fs Energy consumption coefficient for free space communication model.
Figure GDA0003777116920000091
The energy consumption of the common nodes in the cluster mainly comprises energy consumption E for sending sensing data to the cluster head node SNtoCH As shown in equation 3. The nodes in the cluster are assumed to be uniformly distributed (the distribution density function is rho (x, y) ═ K/(pi R) 2 ) The quadratic expectation value of the distance between the common node and the cluster head in the cluster is shown in formula 4 (see fig. 4 in detail, assuming that the cluster area is a sector and the cluster head is located on the angular bisector of the sector), d SNtoCH The distance from the member node in the cluster to the cluster head.
Figure GDA0003777116920000092
Figure GDA0003777116920000093
Energy consumption E of each cluster in a single complete communication process Cluster And the overall network energy consumption are shown in equation 5 and equation 6, respectively. Minimizing the overall energy consumption E of the network as shown in equation 6 Total
Figure GDA0003777116920000094
The optimal distance between the cluster head and the base station as shown in formula 7 is easily obtained
Figure GDA0003777116920000095
(optimal cluster head position) and the optimal number of cluster heads K as shown in equation 8 op t。
Figure GDA0003777116920000096
Figure GDA0003777116920000097
Figure GDA0003777116920000098
Figure GDA0003777116920000099
Step 203: and determining the inter-cluster node angle variance according to the node angle based on the optimal number of the cluster heads.
As known from the principle of the maximum between-class variance algorithm, when the region is divided into K opt When clustering (from the optimal cluster head number, equation 8), K is required opt -1 angular clustering threshold (T) 1 ,T 2 ,...,T Kopt-1 ). Expression f for obtaining inter-cluster node angle variance 1 First, all nodes s are calculated separately i 1,2,3., N, the angle value θ of N i Probability of occurrence p i As shown in equation 9, the mean value of the node angles in each cluster is shown in equation 10, and the angle in each clusterThe cumulative probability calculation of (c) is shown in equation 11.
Figure GDA0003777116920000101
Figure GDA0003777116920000102
Figure GDA0003777116920000103
Wherein the content of the first and second substances,
Figure GDA0003777116920000104
representing an angle value theta i The number of times of occurrence of the event,
Figure GDA0003777116920000105
respectively representing the cumulative probability of the angle value probability of each node in each cluster, so that an angle-based inter-class variance expression can be obtained, as shown in formula 12:
f 1 (T 1 ,T 2 ,..,T Kopt-1 )=w 11 -u T ) 2 +w 22 -u T ) 2 +···+w KoptKopt -u T ) 2 equation 12
Wherein, mu T The angle mean of all nodes in the whole area is shown, and the calculation is shown in formula 13.
μ T =w 1 μ 1 +w 2 u 2 +....+w Kopt μ Kopt Equation 13
Step 204: and clustering all nodes according to the inter-cluster node angle variance, and determining the number of nodes in each cluster.
When all nodes are divided into K by the angle variance of the nodes between clusters opt After each cluster, the number of nodes in each cluster NC k ,k=1,2,,,K opt Will be determined and therefore an expression for the variance in the number of inter-cluster nodes can be calculated from equation 14. Wherein the content of the first and second substances,
Figure GDA0003777116920000106
represents an average of the number of nodes in each cluster, having a value of
Figure GDA0003777116920000107
Step 205: and determining the number variance of the nodes among the clusters according to the optimal number of the cluster heads and the number of the nodes in each cluster.
The inter-cluster node number variance is:
Figure GDA0003777116920000111
step 206: determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solving an optimal solution of the clustering multi-objective optimization function; the optimal solution is an optimal angle segmentation threshold.
By making a pair of f 1 And f 2 The normalization and linear weighting can be performed to obtain an objective function expression based on the inter-cluster node angle and the number variance as shown in equation 15,
Figure GDA0003777116920000112
and
Figure GDA0003777116920000113
representing the normalized function.
Figure GDA0003777116920000114
Step 207: and arranging all the node angles according to the sequence from small to large, and segmenting all the arranged nodes into a plurality of optimal clusters according to the optimal angle segmentation threshold value.
As shown in the formula 15, the objective function F1 is divided into points with respect to the independent variableCut threshold value (T) 1 ,T 2 ,..,T Kopt-1 ) The multi-objective optimization function of (1). With division of threshold number (T) 1 ,T 2 ,..,T Kopt-1 ) The time complexity of the algorithm solution increases with the increase of (independent variable dimension). The swarm intelligent optimization algorithm is used as an effective tool for solving the large-scale high-dimensional engineering problem, and the solution of the swarm intelligent optimization algorithm to the objective function can obtain the approximate optimal solution (a group of optimal segmentation threshold values) of the algorithm in an acceptable time
Figure GDA0003777116920000115
) When the optimal solution (angle division threshold) is obtained
Figure GDA0003777116920000116
) Then, the angles of all nodes are arranged according to the sizes of the nodes, and then the nodes are divided into K by using the optimal angle division threshold value opt A schematic of this process is shown in figure 5.
Step 208: and determining an optimal cluster head position circle and node residual energy by taking the base station as a circle center and the optimal cluster head position as a radius.
After the nodes are divided into Kopt clusters, a proper cluster head is selected for each cluster
Figure GDA0003777116920000117
(derived from the best cluster position equation 7) is referred to as the best cluster position circle C, as shown in fig. 6.
Step 209: and selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy.
Designing a cluster head selection evaluation function related to the C distance between the node and the optimal cluster head circle and the residual energy, as shown in formula 16, and then selecting the node s with the maximum fitness function value in each cluster in a greedy manner i Becomes the cluster head of the cluster.
Figure GDA0003777116920000121
Wherein, F 2 (s i ) For a plurality of ith nodes s in the optimal cluster head i A fitness function of; omega 1 Is a residual energy weight factor; e re (s i ) Is a node s i The residual energy of (d); e o (s i ) Is a node s i The initial energy of (a); omega 2 Is a location weight factor;
Figure GDA0003777116920000122
representing a node s i Distance to best cluster head position circle C, d toCmax 、d toCmin Respectively representing the maximum distance and the minimum distance from all nodes in the same cluster to the circle C of the optimal cluster head position.
And the nodes send the data packets to the cluster heads in the TDMA frame time slots distributed by the nodes, and the cluster heads fuse the data in the clusters and send the fused data to the base station to complete further processing. If the energy of all the nodes is exhausted, the algorithm is ended; otherwise, the procedure returns to step 209. The algorithm is executed in "rounds" until all nodes die (energy exhausted). The whole process of node clustering, cluster head selection and data transmission is called a turn.
In conclusion, the invention can divide the nodes with smaller angle difference into a cluster based on the clustering mode of the angular variance of the nodes among the clusters. Based on the cluster result of angle division, then a cluster head is selected in each cluster, so that the cluster heads can be distributed in each angle direction, namely the cluster heads are uniformly distributed in a monitoring area. The main reason why the cluster heads in the similar papers are poor in distribution uniformity is that secondary clustering destroys the advantages of original angle clustering, so that the cluster heads are not distributed uniformly any more. The above analysis can be characterized by fig. 7. Fig. 7 is a cluster head distribution diagram of two algorithms at a certain time during the algorithm operation. It can be seen that the cluster head distribution of the algorithm of the present invention is more uniform.
The clustering mode based on the variance of the number degree of the nodes among the clusters can ensure that the number of the nodes in each cluster is basically equal, namely the number of loads of each cluster head is basically equal, so that the energy consumption difference among the cluster heads is smaller. Fig. 8 shows a comparison of cluster head energy consumption variances for the first 500 runs of the two algorithms. The cluster head energy consumption variance of the scheme is smaller, and the cluster head load balance of the algorithm is better.
The cluster head selection of the scheme of the invention is selected based on two factors, namely the optimal cluster head position (a conclusion obtained according to network energy consumption minimization) and node residual energy (balance network energy consumption). Particularly, when the cluster head is selected, the cluster head is located near the optimal cluster head position distribution circle as much as possible, and energy consumption of a network is reduced; meanwhile, the residual energy of the nodes is considered, the nodes with more residual energy are used as cluster heads, so that the energy consumption difference between nodes in each round is smaller, and the balance of network energy consumption is ensured. The algorithm in the similar paper tends to select nodes with high residual energy and close to the base station as cluster heads, and fails to consider the relation between the optimal cluster head position and the minimum network energy consumption; in addition, contradictory relations often exist between nodes meeting the requirements of high residual energy and nodes close to the base station, the nodes meeting the requirements of the high residual energy and the nodes meeting the requirements of the base station are few, and the cluster head finally selected by the algorithm in the similar paper is probably not optimal, so that the network energy consumption cannot be balanced. Simulation verification of specific conclusions can be seen from fig. 9 and 10. The remaining energy of the algorithm network of the scheme of the invention in fig. 9 is always higher than that of the algorithm of the similar scheme, which shows that the algorithm network of the scheme of the invention has smaller energy consumption; in fig. 10, the peak value of the standard deviation of the residual energy of the algorithm node in the scheme of the invention is lower than that of the algorithm in the similar scheme, which shows that the algorithm in the scheme of the invention has better network energy consumption balance.
The node clustering method using the inter-cluster node angle and the number variance can adopt other multi-threshold segmentation algorithms to complete node clustering, for example: maximum entropy theorem, which is the f-term in the foregoing if the number of nodes is not considered in clustering by adopting the maximum entropy theorem 2 The balance of the number of nodes between clusters cannot be guaranteed.
In practical application, a cluster head selection evaluation function can be designed by adopting factors such as the residual energy of the cluster head, the distance between the cluster head and a base station and the like to select the cluster head, the position of the selected cluster head is not the optimal cluster head position (which is a result obtained based on network energy consumption minimization) in the invention due to a cluster head selection mode based on the cluster head evaluation function, and meanwhile, due to the fact that multiple factors are considered for evaluation, various factors are usually considered in the selection mode, the obtained result is not the best, and the minimization and equalization of network energy consumption cannot be ensured.
Fig. 11 is a structural diagram of a wireless sensor network clustering routing system based on the maximum between-class variance, as shown in fig. 11, a wireless sensor network clustering routing system based on the maximum between-class variance includes:
the node angle calculation module 1101 is configured to obtain coordinates of a base station and node coordinates of all nodes in the wireless sensor network, and calculate a node angle of each node coordinate relative to the base station according to the coordinates of the base station and the node coordinates.
The node angle determining module 1101 specifically includes: a node angle determination unit for using a formula
Figure GDA0003777116920000141
Calculating a node angle of each node coordinate relative to the base station; wherein, theta i A node angle of the ith node coordinate relative to the base station; x is the number of i Is the abscissa, y, of the ith node i Is the ordinate of the ith node; x is the number of 0 Is the abscissa, y, of the base station 0 Is the ordinate of the base station.
A module 1102 for determining an optimal cluster head position and an optimal cluster head number, configured to determine, based on an energy consumption model of a wireless sensor network node, an optimal cluster head position and an optimal cluster head number of a cluster head located in the base station.
An inter-cluster node angle variance determining module 1103, configured to determine an inter-cluster node angle variance according to the node angles based on the optimal number of cluster heads.
And a node number determining module 1104, configured to cluster all nodes according to the inter-cluster node angle variance, and determine the number of nodes in each cluster.
A module 1105 for determining the variance of the number of nodes between clusters, configured to determine the variance of the number of nodes between clusters according to the optimal number of cluster heads and the number of nodes in each cluster.
A clustering multi-objective optimization function solving module 1106, configured to determine a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solve an optimal solution of the clustering multi-objective optimization function; the optimal solution is an optimal angle segmentation threshold.
An optimal cluster dividing module 1107, configured to arrange all the node angles in order from small to large, and divide all the arranged nodes into multiple optimal clusters according to the optimal angle division threshold.
A best cluster head position circle determining module 1108, configured to determine a best cluster head position circle and node remaining energy, where the best cluster head position circle is centered at the base station and the radius is the best cluster head position.
An optimal cluster head selecting module 1109, configured to select an optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node remaining energy.
In order to further understand the technical solution of the present invention, the algorithm mentioned in the present invention specifically refers to the following:
maximum between-class variance algorithm: the japanese scholars have proposed a classical maximum between-class variance (OTSU) algorithm based on the principle of least squares. The OTSU algorithm is widely applied to threshold image segmentation due to the advantages of simple calculation, strong algorithm stability and robustness and the like. The principle of the OTSU algorithm is as follows:
let the image have a gray scale from 0 to L-1 and a total number of pixels N, N i Indicating the number of gray values i. The calculation of the probability of occurrence of the gray value i is shown by equation 17:
p i =n i /N equation 17
Assuming that the image is segmented into m +1 classes, then m segmentation thresholds t are required i 1, 2. To obtain the inter-class variance expression of the gray values, the mean gray value of each class is first calculated, as shown in equation 18:
Figure GDA0003777116920000151
w 0 (t),w 1 (t),.....,w m (t) represents the cumulative probability of each class separately, calculated as shown in equation 19:
Figure GDA0003777116920000152
the expression for the between-class variance is therefore shown in equation 20:
f(t) max =w 00T ) 2 +w 11T ) 2 +···+w mmT ) 2
equation 20
Wherein, mu T Representing the mean of the gray values of the entire image. The calculation is shown in equation 21:
μ T =w 0 μ 0 +w 1 u 1 +....+w m μ m equation 21
The energy consumption model of the wireless sensor network node is as follows: data transmission between nodes is based on the wireless communication energy consumption model in fig. 3, and can be divided into two types of free space communication and multipath fading communication according to the communication distance, wherein a single complete communication process comprises data transmission and data reception. As shown in fig. 12, the data transmission module includes a signal transmission unit and a signal amplification unit, and is configured to transmit a signal to a data transmission line l Energy consumption E for data transmission d distance of bits T Can be calculated by equation 22. E elec Is the energy consumption per bit per distance of data transmission, E fs And E mp Is the energy consumption coefficient of the amplifying circuit (corresponding to the free space and multipath fading channel model respectively), E T (l, d) is the transmission power consumption of the transmitter, E R (l) For the receiver's reception power consumption, d is the communication distance between the transmitter and the receiver, which together affect the distance threshold d as shown in equation 23 th (ii) a Energy consumption E of data receiving module for receiving l bit data R Can pass throughEquation 24.
Figure GDA0003777116920000161
Figure GDA0003777116920000162
E R (l)=l×E elec Equation 24
Maximum entropy theorem: the maximum entropy threshold segmentation algorithm is also a commonly used threshold segmentation algorithm in image segmentation, and the basic principle is as follows:
assuming an image with a gray level L, the total number of pixels is N, N i Number of pixels, p, representing gray scale i i Probability of tabular gray scale being i, then
Figure GDA0003777116920000163
i-0, 1, L-1. Let m thresholds divide the image into m +1 parts: c 1 ,C 2 ,...,C m+1 The gray values are { 0.,. multidot.,. respectively 1 },{t 1 +1,...,t 2 },...,{t m + 1., L-1 }. Then, the gray level probabilities corresponding to the respective regions are: c 1 :p 1 /w 1 ,...,p t1 /w 1 ,C 2 :p t1 +1/w 2 ,...,p t2 /w 2 ,...,C m+1 :p tm +1/w m+1 ,...,p L-1 /w m+1 Wherein
Figure GDA0003777116920000164
k 1, 2.., m + 1. Then each class C k The entropy of (A) is:
Figure GDA0003777116920000165
thus, the discriminant function of entropy is:
Figure GDA0003777116920000166
by solving for optimal thresholds
Figure GDA0003777116920000167
The total entropy is maximized, and image segmentation is completed.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A wireless sensor network clustering routing method based on maximum between-class variance is characterized by comprising the following steps:
acquiring coordinates of a base station and node coordinates of all nodes in a wireless sensor network, and calculating a node angle of each node coordinate relative to the base station according to the coordinates of the base station and the node coordinates;
determining the optimal cluster head position and the optimal cluster head number of the cluster heads of the base station based on a wireless sensor network node energy consumption model; according to the energy consumption model of the wireless sensor network nodes, the energy consumption of each cluster area comprises the communication energy consumption between a cluster head and a base station and between a common node in the cluster and the cluster head; energy consumption of the cluster head E CHtoBS As shown in formula 2, the method mainly includes the following three parts: the first part is that the cluster head receives the energy consumption of sensing data of N/K-1 common nodes in a cluster, wherein N is the number of sensor nodes, and K is the number of sub-clusters; the second part is energy consumption for fusing N/K group data in the cluster by the cluster head,E DA Energy consumption for fusing unit bit data; the third part is the energy consumption of the cluster head node for sending data to the base station, d CHtoBS Is the distance between the cluster head and the base station, l is the number of bits for data transmission, E elec Energy consumed for transmitting or receiving unit bit data, E fs Energy consumption coefficient of free space communication model;
Figure FDA0003777116910000011
the energy consumption of the common nodes in the cluster mainly comprises energy consumption E for sending sensing data to the cluster head node SNtoCH If the nodes in the cluster are uniformly distributed, as shown in formula 3, the expected value of the distance between the common node in the cluster and the cluster head to the square is shown in formula 4, and d is SNtoCH The distance from the member node in the cluster to the cluster head;
Figure FDA0003777116910000012
Figure FDA0003777116910000013
wherein x is the abscissa of the node, y is the ordinate of the node, ρ (x, y) is a distribution density function, R is the radius of a circular monitoring area of the wireless sensor network, and the energy consumption E of each cluster is realized in a single complete communication process Cluster And the overall network energy consumption is respectively shown in formula 5 and formula 6; minimizing the overall energy consumption E of the network as shown in equation 6 Total The optimal distance between the cluster head and the base station as shown in equation 7 can be easily obtained
Figure FDA0003777116910000021
And the optimal number of clusterheads K as shown in equation 8 opt
Figure FDA0003777116910000022
Figure FDA0003777116910000023
Figure FDA0003777116910000024
Figure FDA0003777116910000025
Determining inter-cluster node angle variance according to the node angles based on the optimal number of cluster heads; as known from the principle of the maximum between-class variance algorithm, when the region is divided into K opt When clustered, requires K opt -1 angular clustering threshold
Figure FDA0003777116910000026
Expression f for obtaining inter-cluster node angle variance 1 First, all nodes s are calculated separately i 1,2,3, the angle value θ of N i Probability of occurrence p i As shown in equation 9, the mean value of the node angles in each cluster is shown in equation 10 and the cumulative probability calculation of the angles in each cluster is shown in equation 11;
Figure FDA0003777116910000027
Figure FDA0003777116910000028
Figure FDA0003777116910000029
wherein the content of the first and second substances,
Figure FDA00037771169100000210
representing an angle value theta i The number of times of occurrence of the event,
Figure FDA00037771169100000211
respectively representing the cumulative probability of the angle value probability of the nodes in each cluster,
Figure FDA00037771169100000212
is the average of the node angles within each cluster,
Figure FDA00037771169100000213
is the K th opt The mean value of the angles of the nodes within each cluster,
Figure FDA00037771169100000214
is the kth opt The cumulative probability of the angle value probability of each intra-cluster node, so that an angle-based inter-class variance expression can be obtained, as shown in formula 12:
Figure FDA00037771169100000215
wherein, mu T Representing the angle mean value of all nodes in the whole area, and calculating as shown in formula 13;
μ T =w 1 μ 1 +w 2 u 2 +....+w Kopt μ Kopt equation 13
Clustering all nodes according to the inter-cluster node angle variance, and determining the number of nodes in each cluster;
determining the number variance of the nodes among the clusters according to the optimal number of the cluster heads and the number of the nodes in each cluster;
determining a clustering multi-objective optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance, and solving an optimal solution of the clustering multi-objective optimization function; the optimal solution is an optimal angle segmentation threshold;
arranging all the node angles according to the sequence from small to large, and segmenting all the arranged nodes into a plurality of optimal clusters according to the optimal angle segmentation threshold value;
determining an optimal cluster head position circle and node residual energy, wherein the optimal cluster head position circle takes the base station as a circle center and the optimal cluster head position as a radius;
and selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy.
2. The method for cluster routing in a wireless sensor network based on the maximum between-cluster variance according to claim 1, wherein the calculating a node angle of each node coordinate relative to a base station according to the base station coordinate and the node coordinate specifically comprises:
using formulas
Figure FDA0003777116910000031
Calculating a node angle of each node coordinate relative to the base station; wherein, theta i A node angle of the ith node coordinate relative to the base station; x is the number of i Is the abscissa, y, of the ith node i Is the ordinate of the ith node; x is the number of 0 Is the abscissa, y, of the base station 0 Is the ordinate of the base station.
3. The method for cluster routing in the wireless sensor network based on the maximum between-cluster variance as claimed in claim 1, wherein the determining the optimal cluster head position and the optimal cluster head number of the cluster head at the base station based on the wireless sensor network node energy consumption model specifically comprises:
in a single complete communication process, determining an overall energy consumption objective function of the wireless sensor network based on a wireless sensor network node energy consumption model;
and solving the overall energy consumption objective function, and determining the cluster head optimal position and the cluster head optimal quantity of the cluster heads, wherein the cluster heads are positioned at the base station.
4. The method for routing in a cluster in a wireless sensor network based on the maximum between-cluster variance according to claim 1, wherein the determining the inter-cluster node angle variance according to the node angle based on the optimal number of cluster heads specifically comprises:
based on the optimal number of the cluster heads, determining probability values of node angles of all nodes, a mean value of the node angles in each cluster and accumulated probability of the node angles in each cluster according to the node angles;
based on a maximum between-cluster variance algorithm, obtaining the between-cluster node angle variance according to the probability value of node angles of all nodes, the mean value of the node angles in each cluster and the accumulated probability of the node angles in each cluster.
5. The method for cluster routing of the wireless sensor network based on the maximum between-cluster variance as claimed in claim 1, wherein the determining the cluster node number variance according to the optimal number of cluster heads and the number of nodes in each cluster specifically comprises:
acquiring the total number of all nodes;
determining the average number of nodes in each cluster according to the optimal number of the cluster heads and the total number of the nodes;
and determining the variance of the number of the nodes among the clusters according to the average number of the nodes and the number of the nodes in each cluster.
6. The method for cluster routing of the wireless sensor network based on the maximum between-cluster variance as claimed in claim 1, wherein the determining a cluster multi-objective optimization function according to the between-cluster node angle variance and the between-cluster node number variance and solving an optimal solution of the cluster multi-objective optimization function specifically comprises:
using formulas
Figure FDA0003777116910000041
Determining how many clusters areAn objective optimization function; wherein, F 1 A clustering multi-objective optimization function with independent variables as angle segmentation thresholds;
Figure FDA0003777116910000051
the inter-cluster node angle variance after normalization processing is carried out;
Figure FDA0003777116910000052
the variance of the number of the nodes between clusters after normalization processing; alpha is an angle clustering weight factor, and the value range is [0,1 ]];
And solving the clustering multi-objective optimization function by adopting a swarm intelligent optimization algorithm, and determining the optimal solution of the clustering multi-objective optimization function.
7. The wireless sensor network clustering routing method based on the maximum between-cluster variance as claimed in claim 1, wherein the selecting the best cluster head in each best cluster according to the best cluster head position circle and the node residual energy specifically comprises:
using formulas
Figure FDA0003777116910000053
Determining a node with the maximum fitness function value in each optimal cluster in the optimal cluster heads as the optimal cluster head; wherein, F 2 (s i ) For a plurality of ith nodes s in the optimal cluster head i A fitness function of; omega 1 Is a residual energy weight factor; e re (s i ) Is a node s i The residual energy of (d); e o (s i ) Is a node s i The initial energy of (a); omega 2 Is a location weight factor; d sitoC Is a node s i Distance to the best cluster head position; d toCmax Maximum distance d from all nodes in the same cluster to the optimal cluster head position toCmin The minimum distance from all nodes in the same cluster to the optimal cluster head position.
8. The method for cluster routing in a wireless sensor network based on maximum between-cluster variance as claimed in claim 1, wherein said selecting the best cluster head in each of the best clusters according to the best cluster head position circle and the node residual energy further comprises:
and each node sends a data packet to the optimal cluster head in the time division multiple access frame time slot allocated to each node, and each optimal cluster head fuses data in the data packet in the cluster and sends the fused data to the base station.
9. A wireless sensor network clustering routing system based on maximum between-class variance is characterized by comprising:
the node angle calculation module is used for acquiring a base station coordinate and node coordinates of all nodes in the wireless sensor network, and calculating a node angle of each node coordinate relative to the base station according to the base station coordinate and the node coordinates;
the cluster head optimal position and cluster head optimal quantity determining module is used for determining the cluster head optimal position and cluster head optimal quantity of the cluster head positioned in the base station based on a wireless sensor network node energy consumption model; according to the energy consumption model of the wireless sensor network nodes, the energy consumption of each cluster area comprises the communication energy consumption between a cluster head and a base station and between a common node in the cluster and the cluster head; energy consumption of the cluster head E CHtoBS As shown in formula 2, the method mainly includes the following three parts: the first part is that the cluster head receives the energy consumption of sensing data of N/K-1 common nodes in a cluster, wherein N is the number of sensor nodes, and K is the number of sub-clusters; the second part is energy consumption of the cluster head for fusing the N/K group data in the cluster, E DA Energy consumption for fusing unit bit data; the third part is the energy consumption of the cluster head node for sending data to the base station, d CHtoBS Is the distance between the cluster head and the base station, l is the number of bits for data transmission, E elec Energy consumed to transmit or receive a unit bit of data, E fs Energy consumption coefficient of free space communication model;
Figure FDA0003777116910000061
the energy consumption of the common nodes in the cluster mainly comprises energy consumption E for sending sensing data to the cluster head node SNtoCH If the nodes in the cluster are uniformly distributed, as shown in formula 3, the expected value of the distance between the common node in the cluster and the cluster head to the square is shown in formula 4, and d is SNtoCH The distance from the member node in the cluster to the cluster head;
Figure FDA0003777116910000062
Figure FDA0003777116910000063
wherein x is the abscissa of the node, y is the ordinate of the node, ρ (x, y) is the distribution density function, R is the radius of the circular monitoring area of the wireless sensor network, and the energy consumption E of each cluster is realized in the single complete communication process Cluster And the overall network energy consumption is respectively shown in formula 5 and formula 6; minimizing the overall energy consumption E of the network as shown in equation 6 Total The optimal distance between the cluster head and the base station as shown in equation 7 can be easily obtained
Figure FDA0003777116910000064
And the optimal number of cluster heads K as shown in equation 8 opt
Figure FDA0003777116910000065
Figure FDA0003777116910000071
Figure FDA0003777116910000072
Figure FDA0003777116910000073
The inter-cluster node angle variance determining module is used for determining the inter-cluster node angle variance according to the node angles based on the optimal number of the cluster heads; according to the principle of maximum between-class variance algorithm, when the region is divided into K opt When clustered, requires K opt -1 angular clustering threshold
Figure FDA00037771169100000713
Expression f for obtaining inter-cluster node angle variance 1 First, all nodes s are calculated separately i 1,2,3., N, the angle value θ of N i Probability of occurrence of p i As shown in equation 9, the mean value of the node angles in each cluster is as shown in equation 10, and the cumulative probability calculation of the angles in each cluster is as shown in equation 11;
Figure FDA0003777116910000074
Figure FDA0003777116910000075
Figure FDA0003777116910000076
wherein the content of the first and second substances,
Figure FDA0003777116910000077
representing an angle value theta i The number of times of occurrence of the event,
Figure FDA0003777116910000078
respectively representing the cumulative probability of the angle value probability of the nodes in each cluster,
Figure FDA0003777116910000079
is the average of the node angles within each cluster,
Figure FDA00037771169100000710
is the kth opt The mean value of the angles of the nodes within each cluster,
Figure FDA00037771169100000711
is the K th opt The cumulative probability of the angle value probability of each intra-cluster node, so that an angle-based inter-class variance expression can be obtained, as shown in formula 12:
Figure FDA00037771169100000712
wherein, mu T Representing the angle mean value of all nodes in the whole area, and calculating as shown in formula 13;
μ T =w 1 μ 1 +w 2 u 2 +....+w Kopt μ Kopt equation 13
The node number determining module is used for clustering all the nodes according to the inter-cluster node angle variance and determining the number of the nodes in each cluster;
the cluster node number variance determining module is used for determining the cluster node number variance according to the optimal number of the cluster heads and the number of nodes in each cluster;
the clustering multi-target optimization function solving module is used for determining a clustering multi-target optimization function according to the inter-cluster node angle variance and the inter-cluster node number variance and solving the optimal solution of the clustering multi-target optimization function; the optimal solution is an optimal angle segmentation threshold;
the optimal cluster dividing module is used for arranging all the node angles in a descending order and dividing all the arranged nodes into a plurality of optimal clusters according to the optimal angle dividing threshold value;
the optimal cluster head position circle determining module is used for determining an optimal cluster head position circle and node residual energy, wherein the optimal cluster head position circle takes the base station as a circle center and the optimal cluster head position as a radius;
and the optimal cluster head selecting module is used for selecting the optimal cluster head in each optimal cluster according to the optimal cluster head position circle and the node residual energy.
10. The wireless sensor network clustering routing system based on the maximum between-cluster variance according to claim 9, wherein the node angle determining module specifically comprises:
a node angle determination unit for using a formula
Figure FDA0003777116910000081
Calculating a node angle of each node coordinate relative to the base station; wherein, theta i A node angle of the ith node coordinate relative to the base station; x is the number of i Is the abscissa, y, of the ith node i Is the ordinate of the ith node; x is the number of 0 Is the abscissa, y, of the base station 0 Is the ordinate of the base station.
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