CN113163422A - Random node joint probability distribution optimization method based on hexagonal cell - Google Patents

Random node joint probability distribution optimization method based on hexagonal cell Download PDF

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CN113163422A
CN113163422A CN202110367863.2A CN202110367863A CN113163422A CN 113163422 A CN113163422 A CN 113163422A CN 202110367863 A CN202110367863 A CN 202110367863A CN 113163422 A CN113163422 A CN 113163422A
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probability distribution
joint probability
distribution function
node
base station
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CN113163422B (en
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李正权
袁月
周燕萍
李树梅
顾斌
马可
陆波
丁文杰
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Ictehi Technology Development Jiangsu Co ltd
Jiangnan University
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Jiangnan University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • Y—GENERAL 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a random node joint probability distribution optimization method based on a hexagonal cell, and belongs to the technical field of wireless communication. The method is realized by researching an interference node O2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2And the interfering node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2To obtain an interference node O2To the central base station O1For interfering node O2To the central base station O1The distance of the hexagonal cell exceeds the critical value, the optimal approximate circle area of the hexagonal cell is obtained, and the complex joint probability distribution of the hexagon is converted into the solution of the random section in the circle areaThe joint probability distribution problem of points can reduce the calculation complexity by replacing the hexagon with the optimal circle when solving the actual communication problem.

Description

Random node joint probability distribution optimization method based on hexagonal cell
Technical Field
The invention relates to a random node joint probability distribution optimization method based on a hexagonal cell, and belongs to the technical field of wireless communication.
Background
Stochastic geometry has been widely used in modeling and analysis of wireless communication networks, and in research on system characteristics and performance indicators of wireless communication networks, reduction of computational complexity through modeling and analysis has become a research focus. The distance analysis is an important component for carrying out random geometric modeling on the wireless communication network by utilizing random geometry, and the structure of the wireless communication network can be accurately simulated. One of the bases of the distance analysis is the distance distribution between nodes, i.e. the probability density function or equivalent cumulative distribution function.
Existing studies on distance distribution in wireless communication network modeling are generally divided into two categories: 1) the distribution of distances between a given reference node (typically a base station) and random nodes (typically user terminals) within a communication cell; 2) the distances between two random nodes distributed in respective communication cells (the two communication cells may be disjoint, intersected or overlapped), which refer to the communication areas divided by the base station.
As is well known, in practical communication networks, a user terminal is usually connected to more than two nodes, and the nodes are divided into two categories: the first type is a node in a communication link, and the second type is a node in an interference link; for example, for a user terminal performing uplink communication, a local base station belongs to a first type node, i.e., a communication node; other user terminals belong to a second type of node, namely an interference node; i.e. the user terminal is also interfered by other user terminals during the actual communication with the local base station. For the local base station performing downlink communication, the user terminal as the receiver belongs to the first type communication node, and the base stations in the adjacent communication cells belong to the second type interference node; i.e. the local base station is also subject to interference from base stations in neighbouring communication cells during the actual communication with a certain user terminal.
The two existing researches on wireless communication network modeling distance distribution only concern probability distribution of one distance type, and the first research only concerns the distance between a user terminal and a communication node (namely a base station) in uplink communication; whereas the second category only concerns the distance between the user terminal and the interfering node (i.e. other user terminals) in downlink communication; this is not as consistent as practical. In uplink communication in practical applications, a user terminal is connected not only to a communication node (i.e., a base station) but also to an interfering node (i.e., other user terminals); in downlink communication in practical applications, the local base station is connected not only to the user terminal, but also to an interfering node (i.e., a base station in an adjacent communication cell). However, the above two types of studies on modeling distance distribution of a wireless communication network consider only the distance distribution between a user terminal and a communication node (referred to as distance distribution of a communication link), and consider only the distance distribution between the user terminal and an interference node (referred to as distance distribution of an interference link), and both types do not conform to the actual communication network. And simply multiplying the two distance distributions cannot accurately describe the actual communication network, because the communication link and the interference link do not exist independently, and a longer communication link necessarily means a shorter interference link, so that research on the joint probability distribution of the distances from the random node to two reference nodes in the cell is required, but no relevant literature is related to the part.
Disclosure of Invention
In order to more accurately research the communication performance between any user terminal and a base station in the actual communication process and reduce the related calculation complexity, the invention provides a random node joint probability distribution optimization method based on a hexagonal cell, which is convenient to describe and assumes that the side length is RhIn the hexagonal cell, the user terminal U1To the central base station O1Is R, the user terminal U1Out-of-hexagonal cell interference node O2Is r, interfering node O2To the central base station O1Is d; the method comprises the following steps:
s1 calculating interference node O2To the central base station O1Is a distance threshold d0；
S2 judging interference node O2To the central base station O1Whether the distance d satisfies d is larger than or equal to d0；
If S3 satisfies d ≧ d0Then the hexagonal cell is approximated to the optimal circular area; converting the joint probability distribution function of the hexagonal cell into a joint probability distribution function of a circular region to realize optimization;
the hexagonal cell is a communication area divided by the base stations.
Optionally, the S1 calculates an interfering node O2To the central base station O1Is a distance threshold d0The method comprises the following steps:
calculating to obtain an interference node O2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2Is called diagonal-joint probability distribution function;
calculating to obtain an interference node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2Is called bisector-joint probability distribution function;
dividing diagonal-joint probability distribution function and bisectorMaking difference value by using combined probability distribution function, utilizing MATLAB simulation to obtain difference value correspondent to different d values, obtaining minimum d value correspondent to the condition that the difference value of diagonal-combined probability distribution function and bisector-combined probability distribution function is minimum and tends to be stable, and recording it as critical value d0。
Optionally, the difference values corresponding to different d values are obtained by using MATLAB simulation, and the corresponding minimum d value when the difference value between the diagonal-joint probability distribution function and the bisector-joint probability distribution function is minimum and tends to be stable is obtained and is recorded as the critical value d0The method comprises the following steps:
fitting the average relative error change of the diagonal-joint probability distribution function and the bisector-joint probability distribution function by using MATLAB to obtain a critical value d of d0＝5.597Rh。
Optionally, the process of establishing the joint probability distribution function of the hexagonal cell in S3 includes:
carrying out random geometric modeling on the hexagonal cell, and constructing a user terminal U in the hexagonal cell according to the area of a target region1To the central base station O1And interfering node O2A joint probability distribution function of the distances between;
Figure BDA0003008006550000031
in the formula, As(r,R,Rh) Represents the area of a target region, which is a circular region (O)1R), circular area (O)2R) and hexagonal cell intersection, circular area (O)1R) denotes by O1A circular region with a center and a radius R, a circular region (O)2R) denotes by O2A circular area with the circle center and the radius r; a. theh(Rh) Indicating the area of the hexagon.
Optionally, if d ≧ d is satisfied at S30Then the hexagonal cell is approximated to the optimal circular area; transforming the joint probability distribution function of the hexagonal cell into a joint probability distribution function of a circular region to realize optimization, comprising:
obtaining the optimal approximate circle radius by utilizing the Manhattan distance and/or Euclidean distance between the circle pairs with different radii and the joint probability distribution of the hexagonal area, and approximating the hexagonal cell to be the circular area;
and converting the diagonal-joint probability distribution function of the hexagonal cell into a joint probability function of the circular area to realize optimization.
Optionally, the obtaining an optimal approximate circle radius by using a manhattan distance and/or a euclidean distance between the circle pairs with different radii and the joint probability distribution of the hexagonal region includes:
obtaining an interference node O according to equation (1)2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2The diagonal-joint probability distribution function is as follows:
Figure BDA0003008006550000032
wherein the content of the first and second substances,
Figure BDA0003008006550000033
Figure BDA0003008006550000041
η＝(π-2ε-sin(2ε))R2，
Figure BDA0003008006550000042
the 5 critical values of the value range of r are respectively:
Figure BDA0003008006550000043
Figure BDA0003008006550000044
assuming that the optimal approximate circle radius is RxThen, after the hexagonal cell is processed into the approximate circle, the random user terminal should be in the approximate circle, that is, R is less than or equal to Rx、d-Rx≤r≤d+RxThen, the joint probability distribution function corresponding to the circle at this time is:
Figure BDA0003008006550000045
the Manhattan distance c between the circles with different radii and the joint probability distribution of the hexagonal area is calculated according to the following formula:
c＝∑|Fd(ri,Rj)-FO(ri,Rj)|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
Figure BDA0003008006550000046
wherein, Fd(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riFunction value of the time-corresponding diagonal-joint probability distribution, FO(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riA joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB toolxObtaining R corresponding to the minimum value of the Manhattan distance c and/or the Euclidean distance l according to the Manhattan distance c and/or the Euclidean distance l during changexI.e. the optimum approximate circle radius Rx≈0.9037Rh。
Optionally, the interfering node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2The joint probability distribution function of the distances between (a), i.e. the bisector-joint probability distribution function, is:
Figure BDA0003008006550000051
wherein the content of the first and second substances,
Figure BDA0003008006550000052
Figure BDA0003008006550000053
Figure BDA0003008006550000061
Figure BDA0003008006550000062
the six critical values of the value range of r are:
Figure BDA0003008006550000063
Figure BDA0003008006550000064
optionally, the method further includes verifying correctness of the diagonal-joint probability distribution function and the bisector-joint probability distribution function by using monte carlo simulation, and drawing an image of the diagonal-joint probability distribution function and the bisector-joint probability distribution function by using MATLAB simulation to verify function continuity.
The invention also provides a communication performance index calculation method of the wireless communication network, and the method adopts the optimization method based on the hexagonal cell random node joint probability distribution to obtain the optimized user terminal U1To the central base station O1And interfering node O2According to the optimized user terminal U1To the central base station O1And interfering node O2The joint probability distribution function of the distances between calculates the communication performance index of the wireless communication network.
Optionally, the communication performance indicators of the wireless communication network include path loss, carrier-to-interference ratio, and link reliability.
The invention has the beneficial effects that:
by studying interfering nodes O2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2And the interfering node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2To obtain an interference node O2To the central base station O1For interfering node O2To the central base station O1The distance of the communication cell exceeds the critical value, the optimal approximate circle area of the hexagonal cell is obtained, the complex joint probability distribution of the hexagon is converted into the problem of solving the joint probability distribution of random nodes in the circular area, the calculation complexity can be reduced by replacing the hexagon with the optimal circle when the actual communication problem is solved, and in order to analyze the performance of the reference node outside the communication cell, which is positioned at a common position, the position of the reference node outside the hexagon is generalized, so that the calculation complexity of performance analysis is reduced.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced 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 based on these drawings without creative efforts.
Fig. 1 shows the distance relationship between a random node and a cell center base station and an out-of-cell interference node after the hexagonal cell geometric modeling is performed in the present invention.
FIG. 2 is a joint probability distribution function of the distance between a random node and two reference nodes under the condition that the outer reference nodes of the hexagon are located on the diagonal line, the inner reference nodes of the hexagon are located at the center of the hexagon, and the random nodes are uniformly distributed in the hexagon.
Fig. 3 shows the variation of manhattan distance between the joint probability distribution corresponding to the hexagonal cell and the joint probability distribution corresponding to the approximate circle under the condition of continuously changing the radius of the hexagonal approximate circle in the present invention.
Fig. 4 is a euclidean distance variation between the joint probability distribution corresponding to the hexagonal cell and the joint probability distribution corresponding to the approximate circle under the condition that the radius of the hexagonal approximate circle is continuously changed.
Fig. 5 is a diagram showing the variation of the difference between the probability statistics corresponding to the positions of the external hexagonal interference nodes and the probability statistics of the interference nodes located on the diagonals of the hexagon according to the present invention.
FIG. 6 is a combined probability distribution function of distances between random nodes and two reference nodes under the condition that the reference nodes outside the hexagon are located on the vertical bisector of the boundary, the reference nodes inside the hexagon are located at the center of the hexagon, and the random nodes are uniformly distributed in the hexagon.
FIG. 7 is a diagram showing the relative error of two corresponding joint probability distribution functions of the reference nodes outside the hexagon on the perpendicular bisector of the hexagon boundary and on the diagonal of the hexagon, and the derivative function distribution of the error function, under the condition of continuously changing the distance between the reference nodes inside and outside the hexagon.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The first embodiment is as follows:
this embodiment provides an optimization method based on hexagonal cell random node joint probability distribution, which assumes that the side length is R for convenient descriptionhIn the hexagonal cell, the user terminal U1To the central base station O1Is R, the user terminal U1Out-of-hexagonal cell interference node O2Is r, interfering node O2To the central base station O1Is d; the method comprises the following steps:
s1 calculating interference node O2To the central base station O1Is a distance threshold d0；
Specifically, the method comprises the following steps:
carrying out random geometric modeling on the hexagonal cell, and constructing a user terminal U in the hexagonal cell according to the area of a target region1To the central base station O1And interfering node O2A joint probability distribution function of the distances between;
Figure BDA0003008006550000081
in the formula, As(r,R,Rh) Represents the area of a target region, which is a circular region (O)1R), circular area (O)2R) and hexagonal cell intersection, circular area (O)1R) denotes by O1A circular region with a center and a radius R, a circular region (O)2R) denotes by O2A circular area with the circle center and the radius r; a. theh(Rh) Indicating the area of the hexagon.
Calculating to obtain an interference node O according to the formula (1)2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2Is called diagonal-joint probability distribution function;
Figure BDA0003008006550000082
wherein the content of the first and second substances,
Figure BDA0003008006550000083
Figure BDA0003008006550000084
η＝(π-2ε-sin(2ε))R2，
Figure BDA0003008006550000085
the 5 critical values of the value range of r are respectively:
Figure BDA0003008006550000086
Figure BDA0003008006550000087
calculating to obtain an interference node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2Is called bisector-joint probability distribution function;
Figure BDA0003008006550000091
wherein the content of the first and second substances,
Figure BDA0003008006550000092
Figure BDA0003008006550000093
Figure BDA0003008006550000101
Figure BDA0003008006550000102
the six critical values of the value range of r are:
Figure BDA0003008006550000103
Figure BDA0003008006550000104
making difference value between diagonal-joint probability distribution function and bisector-joint probability distribution function, utilizing MATLAB simulation to obtain difference value corresponding to different d values, obtaining minimum d value when the difference value of diagonal-joint probability distribution function and bisector-joint probability distribution function is minimum and tends to be stable, and recording as critical value d0. Generally, the rate of change of the difference is less than 0.0001, and the stability is considered to be stable.
S2 judging interference node O2To the central base station O1Whether the distance d satisfies d is not less than or equal tod0；
If S3 satisfies d ≧ d0Then the hexagonal cell is approximated to the optimal circular area; converting the joint probability distribution function of the hexagonal cell into a joint probability distribution function of a circular region to realize optimization;
the hexagonal cell is a communication area divided by the base stations.
Before approximating a hexagonal cell to an optimal circular area, first assume that the optimal approximate circle radius is RxThen, after the hexagonal cell is processed into the approximate circle, the random user terminal should be in the approximate circle, that is, R is less than or equal to Rx、d-Rx≤r≤d+RxThen, the joint probability distribution function corresponding to the circle at this time is:
Figure BDA0003008006550000105
the Manhattan distance c between the circles with different radii and the joint probability distribution of the hexagonal area is calculated according to the following formula:
c＝∑|Fd(ri,Rj)-FO(ri,Rj)|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
Figure BDA0003008006550000106
wherein, Fd(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riFunction value of the time-corresponding diagonal-joint probability distribution, FO(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riA joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB toolxObtaining R corresponding to the minimum value of the Manhattan distance c and/or the Euclidean distance l according to the Manhattan distance c and/or the Euclidean distance l during changexI.e. the optimum approximate circle radius Rx≈0.9037Rh。
Approximating a hexagonal cell as a radius Rx≈0.9037RhAt the radius Rx≈0.9037RhAs the interference node O, the optimal circular area of the interference node is corresponding to the joint probability distribution function2To the central base station O1Is greater than or equal to a critical value d0And (4) combining the probability distribution functions to realize the optimization of the combined probability distribution function of the hexagonal cells.
Example two:
the present embodiment provides an optimization method based on hexagonal random node distance joint distribution in a wireless communication system, and an applicable system model is joint probability distribution of distances from a random user end to a network center base station and an external interference node in a cellular network.
When the external interference node of the cellular network is located on the diagonal of the cell, referring to fig. 1, the side length of the hexagonal cell is RhRandom node (user terminal) U in a cell1To the central base station O1Is R, U1Interference node O on diagonal to outside of cell2R, an out-of-cell interference node O2The distance to the central base station is d. Random node U1The corresponding joint probability distribution function is the area of the target area (shaded in fig. 1) divided by the area of the hexagonal cell, and the random ue to the base station O can be calculated1And interfering node O2The joint probability distribution of the distances between is:
Figure BDA0003008006550000111
in the formula
Figure BDA0003008006550000112
Figure BDA0003008006550000121
η＝(π-2ε-sin(2ε))R2，
Figure BDA0003008006550000122
Several critical values for r are:
Figure BDA0003008006550000123
Figure BDA0003008006550000124
Figure BDA0003008006550000125
the joint probability distribution function was MATLAB mapped, see fig. 2.
After the hexagonal cell is processed by the round approximation, the round radius is set as RxAfter the hexagonal cell is processed into the approximate circle, the random user terminal should be in the approximate circle, that is, R is less than or equal to Rx、d-Rx≤r≤d+RxThen, the joint probability distribution function corresponding to the circle at this time is:
Figure BDA0003008006550000126
calculating the radius R of the circle by using MATLAB toolxWhen varied, F (R, R) and FoThe manhattan distance and the euclidean distance between (R, R) are such that the smaller the distance, the closer the two joint distribution functions are. The Manhattan distance and the Euclidean distance respectively have the following calculation formulas:
c＝∑|Fd(ri,Rj)-FO(ri,Rj)|
in the formula ri+1-ri＝0.05，Rj+1-Rj0.05, Manhattan distance with RxSee fig. 3.
Figure BDA0003008006550000127
In the formula ri+1-ri＝0.1，Rj+1-Rj0.1, Euclidean distance with RxSee fig. 4.
It should be noted that, when the manhattan distance and the euclidean distance are simulated, the smaller the distance difference between two adjacent position changes of the user terminal, the better.
Analyzing the data of the Manhattan distance calculation and the Euclidean distance calculation to obtain the optimal radius R of the approximate circlex≈0.9037Rh。
In wireless communication, an interfering node outside a cell may be located at an arbitrary position. Maintaining out-of-cell interference node O2And cell center base station O1Is constant, changes the position of the interfering node, i.e. O1O2The angle between the diagonal of the hexagon changes. The invention utilizes MATLAB numerical simulation to change the included angle value from 0 to be increased
Figure BDA0003008006550000131
Comparing the corresponding statistical probability of each included angle value with O2The sum of the statistical probabilities corresponds to the sum of the six-deformation diagonals, and this sum of differences varies with angle, see fig. 5. The abscissa value is 1, that is, when the interference node is located on the perpendicular bisector of one side of the hexagon, the difference is the largest, and then the joint probability distribution and O at that time are obtained2The joint probability distribution when located on the diagonal has the largest difference. Changing the size of d to obtain a critical value d0，d≥d0When is, O2When the corresponding joint probability distribution is positioned on a perpendicular bisector of one side of the hexagon, the joint probability distribution is very close to O2Joint probability distribution when located on diagonal, then O2At a general location, which can be approximated by a joint probability distribution on the diagonal of the hexagon. To O2And when the cell is positioned on a perpendicular bisector of one side of the hexagon, calculating a joint probability distribution function corresponding to the user terminal in the cell:
Figure BDA0003008006550000141
in the formula
Figure BDA0003008006550000142
Figure BDA0003008006550000143
Figure BDA0003008006550000151
Figure BDA0003008006550000152
Several critical values of the range of values of r are:
Figure BDA0003008006550000153
Figure BDA0003008006550000154
the joint probability distribution function was MATLAB mapped, see fig. 6.
The invention utilizes MATLAB simulation to obtain the interference nodes O corresponding to different d values2When the difference value of the two joint probability distribution functions is positioned on the diagonal line of the hexagon and the perpendicular bisector of one side of the hexagon, the average relative error can reflect the accuracy degree better, so the change of the average relative error of the two functions is fitted, referring to fig. 7, the upper curve in the figure is a fitting curve, the lower curve is a derivative function curve of the fitting curve, and the d is greater than or equal to 5.597R, so that the result that the d is greater than or equal to 5.597RhThe corresponding fitting curve area is stable, and the derivative function curve tends to 0, so that the critical value d of d is obtained0＝5.597Rh。
When communication performance indexes of a wireless communication network in an actual communication process are researched, for an interference node O2To the central base station O1Is greater than or equal to a critical value d0＝5.597RhThen, the hexagonal cell is approximated to a radius Rx≈0.9037RhAt the radius Rx≈0.9037RhOptimal circular area correspondence associationThe probability distribution function is used as the user terminal U in the hexagonal cell1To the central base station O1And interfering node O2The distance between the two adjacent hexagonal cells is used for optimizing the joint probability distribution function of the hexagonal cell, and the calculation amount involved in the calculation of the communication performance index is reduced.
Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. An optimization method based on hexagonal cell random node joint probability distribution is characterized in that: for convenience of description, assume that the side length is RhIn the hexagonal cell, the user terminal U1To the central base station O1Is R, the user terminal U1Out-of-hexagonal cell interference node O2Is r, interfering node O2To the central base station O1Is d; the method comprises the following steps:
s1 calculating interference node O2To the central base station O1Is a distance threshold d0；
S2 judging interference node O2To the central base station O1Whether the distance d satisfies d is larger than or equal to d0；
If S3 satisfies d ≧ d0Then the hexagonal cell is approximated to the optimal circular area; converting the joint probability distribution function of the hexagonal cell into a joint probability distribution function of a circular region to realize optimization;
the hexagonal cell is a communication area divided by the base stations.
2. The method of claim 1, wherein the S1 calculates an interfering node O2To the central base stationO1Is a distance threshold d0The method comprises the following steps:
calculating to obtain an interference node O2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2Is called diagonal-joint probability distribution function;
calculating to obtain an interference node O2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2Is called bisector-joint probability distribution function;
making difference value between diagonal-joint probability distribution function and bisector-joint probability distribution function, utilizing MATLAB simulation to obtain difference value corresponding to different d values, obtaining minimum d value when the difference value of diagonal-joint probability distribution function and bisector-joint probability distribution function is minimum and tends to be stable, and recording as critical value d0。
3. The method according to claim 2, wherein the difference values corresponding to different values of d are obtained by using MATLAB simulation, and the minimum value of d corresponding to the condition that the difference value between the diagonal-joint probability distribution function and the bisector-joint probability distribution function is minimum and tends to be stable is obtained and recorded as a critical value d0The method comprises the following steps:
fitting the average relative error change of the diagonal-joint probability distribution function and the bisector-joint probability distribution function by using MATLAB to obtain a critical value d of d0＝5.597Rh。
4. The method according to claim 3, wherein the establishing of the joint probability distribution function of the hexagonal cells in S3 comprises:
carrying out random geometric modeling on the hexagonal cell, and constructing a user terminal U in the hexagonal cell according to the area of a target region1To the central base station O1And interfering node O2A joint probability distribution function of the distances between;
Figure FDA0003008006540000011
in the formula, As(r,R,Rh) Represents the area of a target region, which is a circular region (O)1R), circular area (O)2R) and hexagonal cell intersection, circular area (O)1R) denotes by O1A circular region with a center and a radius R, a circular region (O)2R) denotes by O2A circular area with the circle center and the radius r; a. theh(Rh) Indicating the area of the hexagon.
5. The method according to claim 4, wherein S3 is satisfied if d ≧ d0Then the hexagonal cell is approximated to the optimal circular area; transforming the joint probability distribution function of the hexagonal cell into a joint probability distribution function of a circular region to realize optimization, comprising:
obtaining the optimal approximate circle radius by utilizing the Manhattan distance and/or Euclidean distance between the circle pairs with different radii and the joint probability distribution of the hexagonal area, and approximating the hexagonal cell to be the circular area;
and converting the diagonal-joint probability distribution function of the hexagonal cell into a joint probability function of the circular area to realize optimization.
6. The method of claim 5, wherein the using the Manhattan distance and/or the Euclidean distance between the circle pairs with different radii and the joint probability distribution of the hexagonal region to obtain the optimal approximate circle radius comprises:
obtaining an interference node O according to equation (1)2When located on the outer diagonal of the hexagonal cell, the user terminal U1To the central base station O1And interfering node O2The diagonal-joint probability distribution function is as follows:
Figure FDA0003008006540000021
wherein the content of the first and second substances,
Figure FDA0003008006540000022
Figure FDA0003008006540000031
Figure FDA0003008006540000032
the 5 critical values of the value range of r are respectively:
Figure FDA0003008006540000033
Figure FDA0003008006540000034
assuming that the optimal approximate circle radius is RxThen, after the hexagonal cell is processed into the approximate circle, the random user terminal should be in the approximate circle, that is, R is less than or equal to Rx、d-Rx≤r≤d+RxThen, the joint probability distribution function corresponding to the circle at this time is:
Figure FDA0003008006540000035
the Manhattan distance c between the circles with different radii and the joint probability distribution of the hexagonal area is calculated according to the following formula:
c＝∑|Fd(ri,Rj)-FO(ri,Rj)|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
Figure FDA0003008006540000036
wherein，Fd(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riFunction value of the time-corresponding diagonal-joint probability distribution, FO(ri,Rj) For user terminal U1To the central base station O1A distance of RjTo the hexagonal out-of-cell interference node O2A distance of riA joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB toolxObtaining R corresponding to the minimum value of the Manhattan distance c and/or the Euclidean distance l according to the Manhattan distance c and/or the Euclidean distance l during changexI.e. the optimum approximate circle radius Rx≈0.9037Rh。
7. The method of claim 6, wherein the interfering node O is a base station2When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon1To the central base station O1And interfering node O2The joint probability distribution function of the distances between (a), i.e. the bisector-joint probability distribution function, is:
Figure FDA0003008006540000041
wherein the content of the first and second substances,
Figure FDA0003008006540000042
Figure FDA0003008006540000043
Figure FDA0003008006540000051
Figure FDA0003008006540000052
six criticalities of r value rangeThe values are:
Figure FDA0003008006540000053
Figure FDA0003008006540000054
8. the method of claim 7, further comprising verifying the correctness of the diagonal-joint probability distribution function and the bisector-joint probability distribution function using a Monte Carlo simulation, and plotting the images of the diagonal-joint probability distribution function and the bisector-joint probability distribution function using a MATLAB simulation to verify the function continuity.
9. A communication performance index calculation method of a wireless communication network, characterized in that the method adopts the optimization method based on hexagonal cell random node joint probability distribution according to any one of claims 1 to 8 to obtain an optimized user terminal U1To the central base station O1And interfering node O2According to the optimized user terminal U1To the central base station O1And interfering node O2The joint probability distribution function of the distances between calculates the communication performance index of the wireless communication network.
10. The method of claim 9, wherein the communication performance indicators of the wireless communication network comprise path loss, carrier-to-interference ratio and link reliability.
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