CN113163422B - Random node joint probability distribution optimization method based on hexagonal cell - Google Patents
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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 O 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 And the interfering node O 2 When the user terminal U is positioned on the vertical bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 To obtain an interference node O 2 To the central base station O 1 For interfering node O 2 To the central base station O 1 The optimal approximate circle area of the hexagonal cell is obtained under the condition that the distance of the hexagonal cell exceeds the critical value, the problem of the joint probability distribution of random nodes in the circular area is solved by converting the complicated joint probability distribution of the hexagon, and the calculation complexity can be reduced by replacing the hexagon with the optimal circle when the problem of actual communication is solved.
Description
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 recipient 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 involved calculation complexity, the invention provides a combined probability distribution optimization method based on a hexagon cell random node, which is convenient to describe and assumes that the side length is R h In the hexagonal cell, the user terminal U 1 To the central base station O 1 Is R, the user terminal U 1 Out-of-hexagonal cell interference node O 2 Is r, interfering node O 2 To the central base station O 1 Is d; the method comprises the following steps:
s1 calculationInterference node O 2 To the central base station O 1 Is a distance threshold d 0 ；
S2 judging interference node O 2 To the central base station O 1 Whether the distance d satisfies d is larger than or equal to d 0 ；
If S3 satisfies d ≧ d 0 Then 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 O 2 To the central base station O 1 Is a distance threshold d 0 The method comprises the following steps:
calculating to obtain an interference node O 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 Is called diagonal-joint probability distribution function;
calculating to obtain an interference node O 2 When the user terminal U is positioned on the vertical bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 Is 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 corresponding to minimum difference value and stable difference value between diagonal-joint probability distribution function and bisector-joint probability distribution function, and recording as critical value d 0 。
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 d 0 The method comprises the following steps:
fitting the mean relative error of a diagonal-joint probability distribution function and a bisector-joint probability distribution function using MATLABChanging to obtain a critical value d of d 0 ＝5.597R h 。
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 region 1 To the central base station O 1 And interfering node O 2 A joint probability distribution function of the distances between;
in the formula, A s (r,R,R h ) Represents the area of a target region, which is a circular region (O) 1 R), circular area (O) 2 R) and hexagonal cell intersection, circular area (O) 1 R) denotes by O 1 A circular region with a center and a radius R, a circular region (O) 2 R) denotes by O 2 A circular area with the circle center and the radius r; a. the h (R h ) Indicating the area of the hexagon.
Optionally, if d ≧ d is satisfied at S3 0 Then 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) 2 On the diagonal outside the hexagonal cellTime, user terminal U 1 To the central base station O 1 And interfering node O 2 The diagonal-joint probability distribution function is as follows:
wherein,
η＝(π-2ε-sin(2ε))R 2 ，
the 5 critical values of the value range of r are respectively:
assuming that the optimal approximate circle radius is R x Then, 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 R x 、d-R x ≤r≤d+R x Then, the joint probability distribution function corresponding to the circle at this time is:
the Manhattan distance c between the joint probability distributions of the circles with different radii and the hexagonal region is calculated according to the following formula:
c＝∑|F d (r i ,R j )-F O (r i ,R j )|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
wherein, F d (r i ,R j ) For user terminal U 1 To the central base station O 1 A distance of R j To the hexagonal out-of-cell interference node O 2 Is a distance r i Function value of the time-corresponding diagonal-joint probability distribution, F O (r i ,R j ) For user terminal U 1 To the central base station O 1 A distance of R j To the hexagonal out-of-cell interference node O 2 A distance of r i A joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB tool x Obtaining 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 change x I.e. the optimum approximate circle radius R x ≈0.9037R h 。
Optionally, the interfering node O 2 When the user terminal U is positioned on the vertical bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 The joint probability distribution function of the distances between (a), i.e. the bisector-joint probability distribution function, is:
wherein,
the six critical values of the value range of r are:
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 U 1 To the central base station O 1 And interfering node O 2 According to the optimized user terminal U 1 To the central base station O 1 And interfering node O 2 Calculates a communication performance indicator 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 O 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 And the interfering node O 2 When the user terminal U is positioned on the vertical bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 To obtain an interference node O 2 To the central base station O 1 For interfering node O 2 To the central base station O 1 When the distance exceeds the critical value, the optimal hexagonal cell is obtainedIn order to analyze the performance of the reference nodes outside the communication cell at the general position, the invention provides that the position of the reference nodes outside the hexagon is generalized, and the computational 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 distances between a random node and two reference nodes under the condition that the reference nodes outside the hexagon are located on the diagonal lines, the reference nodes inside the hexagon are located at the center of the hexagon, and the random nodes are uniformly distributed in the hexagon according to the invention.
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 description h In the hexagonal cell, the user terminal U 1 To the central base station O 1 Is R, the user terminal U 1 Out-of-hexagonal cell interference node O 2 Is r, interfering node O 2 To the central base station O 1 Is d; the method comprises the following steps:
s1 calculating interference node O 2 To the central base station O 1 Is a distance threshold value d 0 ；
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 region 1 To the central base station O 1 And interfering node O 2 A joint probability distribution function of the distances between;
in the formula, A s (r,R,R h ) Represents the area of a target region, which is a circular region (O) 1 R), circular area (O) 2 R) and hexagonal cell, circular area (O) 1 R) denotes by O 1 A circular region with a circle center and a radius R, a circular region (O) 2 R) denotes by O 2 A circular area with the circle center and the radius r; a. the h (R h ) Indicating the area of the hexagon.
Calculating to obtain an interference node O according to the formula (1) 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 Is called diagonal-joint probability distribution function;
wherein,
η＝(π-2ε-sin(2ε))R 2 ，
the 5 critical values of the value range of r are respectively:
calculating to obtain an interference node O 2 When the user terminal U is positioned on the vertical bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 Is called bisector-joint probability distribution function;
wherein,
the six critical values of the value range of r are:
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 d 0 . 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 O 2 To the central base station O 1 Whether the distance d satisfies d is larger than or equal to d 0 ；
If S3 satisfies d ≧ d 0 Then 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 R x Then, 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 R x 、d-R x ≤r≤d+R x Then this is achievedThe joint probability distribution function corresponding to the time circle is:
the Manhattan distance c between the joint probability distributions of the circles with different radii and the hexagonal region is calculated according to the following formula:
c＝∑|F d (r i ,R j )-F O (r i ,R j )|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
wherein, F d (r i ,R j ) For user terminal U 1 To the central base station O 1 Is a distance R j To the out-of-hexagonal cell interference node O 2 A distance of r i Function value of the time-corresponding diagonal-joint probability distribution, F O (r i ,R j ) For a user terminal U 1 To the central base station O 1 Is a distance R j To the out-of-hexagonal cell interference node O 2 Is a distance r i A joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB tool x Obtaining 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 change x I.e. the optimum approximate circle radius R x ≈0.9037R h 。
Approximating a hexagonal cell as a radius R x ≈0.9037R h At the radius R x ≈0.9037R h As the interference node O, the optimal circular area of the interference node is corresponding to the joint probability distribution function 2 To the central base station O 1 Is greater than or equal to a critical value d 0 Time-joining probability distribution functions to realize pairsAnd optimizing a joint probability distribution function of the hexagonal cells.
Example two:
the 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 random user terminals to a network center base station and interference nodes outside a network 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 R h Random node (user terminal) U in a cell 1 To the central base station O 1 Is R, U 1 Interference node O on diagonal to outside of cell 2 R, an out-of-cell interference node O 2 The distance to the central base station is d. Random node U 1 The corresponding joint probability distribution function is the area of the target region (shaded in fig. 1) divided by the area of the hexagonal cell, and the random ue to the base station O can be calculated 1 And interfering node O 2 The joint probability distribution of the distances between is:
in the formula
η＝(π-2ε-sin(2ε))R 2 ，
Several critical values for r are:
MATLAB mapping was performed on this joint probability distribution function, see fig. 2.
After the hexagonal cell is processed by the round approximation, the round radius is set as R x After the hexagonal cell is processed into the approximate circle, the random user terminal should be in the approximate circle, that is, R is more than or equal to R x 、d-R x ≤r≤d+R x Then, the joint probability distribution function corresponding to the circle at this time is:
calculating the radius R of the circle by using MATLAB tool x When varied, F (R, R) and F o The 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＝∑|F d (r i ,R j )-F O (r i ,R j )|
in the formula r i+1 -r i ＝0.05，R j+1 -R j 0.05, Manhattan distance with R x See fig. 3 for variations of.
In the formula r i+1 -r i ＝0.1，R j+1 -R j 0.1, Euclidean distance with R x See fig. 4.
It should be noted that, when the manhattan distance and the euclidean distance are simulated here, the smaller the distance difference value corresponding to 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 circle x ≈0.9037R h 。
In radio communication, out-of-cellThe interfering node may be located anywhere. Maintaining out-of-cell interference node O 2 And cell center base station O 1 Is constant, changes the position of the interfering node, i.e. O 1 O 2 The 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
Comparing the corresponding statistical probability of each included angle value with O 2 The 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 value of the abscissa is 1, namely when the interference node is positioned on the perpendicular bisector of one side of the hexagon, the difference is maximum, and then the joint probability distribution and O at the moment 2 The joint probability distribution when located on the diagonal has the largest difference. Changing the size of d to obtain a critical value d 0 ，d≥d 0 When is, O 2 When 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 O 2 Joint probability distribution when located on diagonal, then O 2 At a general location, which can be approximated by a joint probability distribution on the diagonal of the hexagon. To O 2 And 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:
in the formula
r is a range of valuesSeveral thresholds are:
the joint probability distribution function was MATLAB mapped, see fig. 6.
The invention utilizes MATLAB simulation to obtain interference nodes O corresponding to different d values 2 When 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 5.597R h The corresponding fitting curve area is stable, and the derivative function curve tends to 0, so that the critical value d of d is obtained 0 ＝5.597R h 。
When communication performance indexes of a wireless communication network in an actual communication process are researched, for an interference node O 2 To the central base station O 1 Is greater than or equal to a critical value d 0 ＝5.597R h Then, the hexagonal cell is approximated to a radius R x ≈0.9037R h At the radius R x ≈0.9037R h The optimal circular area is taken as the user terminal U in the hexagonal cell 1 To the central base station O 1 And interfering node O 2 The 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 (4)
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 R h In the hexagonal cell, the user terminal U 1 To the central base station O 1 Is R, the user terminal U 1 Out-of-hexagonal cell interference node O 2 Is r, interfering node O 2 To the central base station O 1 Is d; the method comprises the following steps:
s1 calculating interference node O 2 To the central base station O 1 Is a distance threshold d 0 ；
S2 judging interference node O 2 To the central base station O 1 Whether the distance d satisfies d is larger than or equal to d 0 ；
If S3 satisfies d ≧ d 0 Then 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;
the S1 calculates an interference node O 2 To the central base station O 1 Is a distance threshold d 0 The method comprises the following steps:
calculating to obtain an interference node O 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 Is called diagonal-joint probability distribution function;
calculating to obtain an interference node O 2 When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 Is called bisector-joint probability distribution function;
making difference between the diagonal-joint probability distribution function and the bisector-joint probability distribution function, and obtaining the difference corresponding to different d values by using MATLAB simulation,the corresponding minimum d value when the difference value of the diagonal-joint probability distribution function and the bisector-joint probability distribution function is minimum and tends to be stable is solved and is marked as a critical value d 0 ；
Obtaining the corresponding difference values of different d values by using MATLAB simulation, solving the corresponding minimum d value when the difference value of the diagonal-joint probability distribution function and the bisector-joint probability distribution function is minimum and tends to be stable, and marking as a critical value d 0 The 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 d 0 ＝5.597R h ；
The process of establishing the joint probability distribution function of the hexagonal cells 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 region 1 To the central base station O 1 And interfering node O 2 A joint probability distribution function of the distances between;
in the formula, A s (r,R,R h ) Represents the area of a target region, which is a circular region (O) 1 R), circular area (O) 2 R) and hexagonal cell intersection, circular area (O) 1 R) denotes by O 1 A circular region with a center and a radius R, a circular region (O) 2 R) denotes by O 2 A circular area with a circle center and a radius of r; a. the h (R h ) Represents the area of a hexagon;
if the S3 satisfies d ≧ d 0 Then 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;
converting the diagonal-joint probability distribution function of the hexagonal cell into a joint probability function of a circular region to realize optimization;
the method for obtaining the optimal approximate circle radius by utilizing the Manhattan distance and/or the Euclidean distance between the circle pairs with different radii and the joint probability distribution of the hexagonal region comprises the following steps:
obtaining an interference node O according to equation (1) 2 When located on the outer diagonal of the hexagonal cell, the user terminal U 1 To the central base station O 1 And interfering node O 2 The diagonal-joint probability distribution function is as follows:
wherein,
η＝(π-2ε-sin(2ε))R 2 ，
the 5 critical values of the value range of r are respectively:
assuming that the optimal approximate circle radius is R x Then, 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 R x 、d-R x ≤r≤d+R x Then the joint probability distribution function corresponding to the circle at this time is：
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＝∑|F d (r i ,R j )-F O (r i ,R j )|
the euclidean distance l between the joint probability distributions of the circles of different radii and the hexagonal region is calculated as follows:
wherein, F d (r i ,R j ) For user terminal U 1 To the central base station O 1 Is a distance R j To the hexagonal out-of-cell interference node O 2 A distance of r i Function value of the time-corresponding diagonal-joint probability distribution, F O (r i ,R j ) For a user terminal U 1 To the central base station O 1 A distance of R j To the out-of-hexagonal cell interference node O 2 Is a distance r i A joint probability distribution function value corresponding to the time circle;
calculating the radius R of the circle by using MATLAB tool x Obtaining 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 change x I.e. the optimum approximate circle radius R x ≈0.9037R h ；
The interference node O 2 When the user terminal U is positioned on a perpendicular bisector of one side of the hexagon 1 To the central base station O 1 And interfering node O 2 The joint probability distribution function of the distances between (a), i.e. the bisector-joint probability distribution function, is:
wherein,
the six critical values of the value range of r are:
2. the method of claim 1, 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 an image of the diagonal-joint probability distribution function and the bisector-joint probability distribution function using a MATLAB simulation to verify function continuity.
3. A communication performance index calculation method of a wireless communication network is characterized in that the method adopts the optimization method based on hexagonal cell random node joint probability distribution in claim 1 or 2 to obtain an optimized user terminal U 1 To the central base station O 1 And interfering node O 2 According to the optimized user terminal U 1 To the central base station O 1 And interfering node O 2 To calculate a wireless communication networkThe communication performance index of (1).
4. The method of claim 3, wherein the communication performance indicators of the wireless communication network comprise path loss, carrier-to-interference ratio and link reliability.
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