Cavity-free low-interference open space three-dimensional coverage method and system for polyhedron filling

Abstract

The invention discloses a void-free low-interference open space three-dimensional coverage method and system for polyhedron filling, and mainly solves the problems that a three-dimensional coverage structure based on a ground network is difficult to determine and the overall coverage performance of the air and the ground cannot be considered in the prior art. According to the scheme, the method comprises the steps of selecting triangular prism filling lattice point set base vectors and constructing and generating a matrix family; generating triangular prisms of different shapes meeting the requirement that a partitioned diagonal form generation matrix exists in the generation matrix family, and iteratively calculating the coverage rate of signals outside the triangular prisms to obtain a triangular prism shape with minimum signal out-of-column dispersion; selecting a base station from the base station set, and constructing a triangular prism network composed of dispersion triangular prisms outside minimum signal columns; the coverage rate and the overlapping coverage rate of signals in each triangular prism are optimized by adjusting the vertical wave width and the upper inclination angle of each base station coverage wave beam on the bottom surface of the triangular prism. According to the method, signal overlapping coverage can be minimized while no signal coverage hole exists in the air and the ground, the method can be used for rapidly determining a three-dimensional coverage polyhedral structure based on the ground network, and hole-free low-interference three-dimensional coverage of the air and the ground is achieved.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and specifically relates to a hole-free, low-interference, three-dimensional coverage method. It can be used to quickly determine an effective three-dimensional coverage polyhedral structure based on ground infrastructure, achieving hole-free, low-interference three-dimensional coverage that considers both aerial and ground-based needs. Background Technology

[0002] Existing terrestrial cellular networks, with their mature technology and well-developed infrastructure, are considered a key path to achieving wide-area, ubiquitous, and high-speed signal coverage in low-altitude three-dimensional space. However, as the signal coverage range expands from a two-dimensional plane to three-dimensional space, the cellular network structure is no longer suitable. Furthermore, simply tilting the beam upwards to extend low-altitude coverage significantly impairs ground coverage performance, making it difficult to simultaneously achieve optimal performance for both aerial and ground coverage. Therefore, the industry urgently needs a three-dimensional coverage structure and beam optimization method to achieve efficient coverage in low-altitude areas while ensuring communication performance for ground users.

[0003] A research team at Virginia Tech proposed a three-dimensional spatial signal filling method based on a truncated octahedral structure in their paper "Beyond 5G With UAVs: Foundations of a 3D Wireless Cellular Network". This method divides three-dimensional space into several truncated octahedral units and deploys a UAV base station at the center of each unit to achieve seamless three-dimensional coverage. However, the truncated octahedral structure in this method cannot achieve seamless half-space filling with a single layer of filling points. When ground base stations are built using a truncated octahedral structure for three-dimensional coverage, serious coverage holes exist. Furthermore, because this method is based on an ideal omnidirectional antenna and does not consider the radiation differences of the base station beam in the horizontal and vertical directions, it is difficult to achieve hole-free signal filling within the units during actual deployment.

[0004] Patent application CN202110893934.2 discloses a ground-to-air hole-free collaborative coverage method based on triangulation optimization. Its core idea is to divide a low-altitude three-dimensional area into multiple triangular prism coverage units through triangulation, with three base stations at the vertices of the base triangle of each unit collaboratively covering the three-dimensional area. However, this method directly adopts a triangular prism structure, failing to verify the feasibility of using a triangular prism structure to achieve ground-to-air coverage. Furthermore, because this method improves air coverage performance by adjusting the sector height of ground base stations, it reduces the number of ground-to-ground coverage beams, resulting in insufficient coverage performance for ground users.

[0005] A research team from New York University proposed a beam optimization method that balances air-to-ground coverage performance in their paper, "Merits of Serving UAVs via Terrestrial Networks: A Vertical Antenna Radiation Study." By analyzing the vertical radiation patterns of base station antennas, they found that adjusting the antenna downtilt angle and vertical beamwidth can simultaneously maximize the coverage probability for both ground users and UAVs. However, because the antenna beam is tilted downwards, the main lobe energy is concentrated towards the ground, resulting in insufficient actual coverage height. Furthermore, this method optimizes directly on traditional cellular networks, and its network structure is not adapted to the geometric characteristics of three-dimensional space, leading to insufficient three-dimensional coverage efficiency. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technology by proposing a multi-faceted, hole-free, low-interference air-to-ground three-dimensional coverage method. This method aims to quickly determine an effective multi-faceted three-dimensional coverage structure based on a terrestrial network, improve network efficiency and quality, achieve effective design of air-to-ground three-dimensional coverage beams, and balance coverage performance for both air and ground users.

[0007] To achieve the above objectives, the present invention aims to establish a rapid and effective feasibility criterion for a polyhedral three-dimensional coverage structure based on terrestrial networks, enabling the invention to determine the feasibility of achieving three-dimensional coverage over air using a triangular prism structure. The Monte Carlo method is used to calculate the overlap coverage rate to determine the triangular prism shape with minimal out-of-pillar signal dispersion. A genetic algorithm is used to select the optimal set of base stations and perform Delaunay triangulation, allowing the invention to construct a low-overlap network approximately composed of triangular prisms with minimal out-of-pillar signal dispersion. A hybrid particle swarm optimization algorithm is used to collaboratively optimize the uptilt angle and vertical beamwidth of each base station beam within the triangular prism, ensuring no coverage holes while minimizing beam overlap within the triangular prism, thus achieving hole-free, low-interference three-dimensional coverage over air.

[0008] Based on the above ideas, the technical solution of the present invention includes:

[0009] 1. A method for three-dimensional ground cover with polyhedral filling, characterized by comprising:

[0010] (1) Select a set of lattice point set basis vectors of a set of triangular prisms to form a lattice point set generating matrix, and multiply it with any monomodular matrix to obtain a family of generating matrices of the lattice point set.

[0011] (2) Determine whether there exists a block diagonal matrix in the family of triangular prism generating matrices:

[0012] If it exists, execute (3);

[0013] Conversely, it is impossible to achieve three-dimensional air-ground coverage based on terrestrial networks;

[0014] (3) Under the condition that the generating matrix family has a block diagonal matrix, the shape of the triangular prism can be changed to obtain triangular prisms of different shapes;

[0015] (4) Iteratively calculate the signal coverage outside the prism of different shaped triangular prisms to obtain the triangular prism with the minimum signal diffusion outside the prism;

[0016] (5) Divide the base station set of the ground network into an internal base station set and an edge base station set. Select N base stations from the internal base station set and combine them with the edge base station set to form a three-dimensional coverage base station set. Construct a three-dimensional coverage triangular prism network through triangulation. Iteratively update the selected internal base stations so that the triangular prism network is approximately composed of several triangular prisms with the minimum signal dispersion.

[0017] (6) By adjusting the vertical beamwidth and uptilt angle of the coverage beam of each base station on the bottom surface of each triangular prism in the triangular prism network, the signal coverage and overlap coverage within each triangular prism are optimized, thereby achieving low-overlap, hole-free signal coverage in the air-ground three-dimensional area.

[0018] Furthermore, in (3), changing the shape of the triangular prism means changing the angle of the triangular prism and the size of the base triangle. Specifically, the angle of the triangular prism is changed by fixing the positions of the two vertices of the base of the triangular prism and changing the position of the third vertex. After determining the angle, the size of the triangular prism is changed by changing the perimeter of the base triangle. In (5), constructing a three-dimensional coverage triangular prism network by triangulation is to divide the polygonal area enclosed by the base station set into a triangular network based on the two-dimensional coordinates of each base station in the three-dimensional coverage base station set. Then, the triangular network is extended longitudinally along the direction perpendicular to the ground to obtain the triangular prism network.

[0019] Furthermore, the iterative calculation of the signal coverage outside the prisms of different shapes in (4) includes the following implementation:

[0020] 4a) Divide the triangular prism into layers and configure the beam parameters of each base station on the base of the prism:

[0021] 4b) Randomly deploy several reference points in the space where the triangular prism is located. Calculate the ratio of the number of covered reference points outside the triangular prism to the number of covered reference points inside the triangular prism based on the beam parameters of the three base stations at the base of the prism. This yields the signal coverage rate outside the prism. .

[0022] Furthermore, in step (5), the selected internal base stations are iteratively updated so that the triangular prism network is approximately composed of several triangular prisms with minimum signal dispersion outside the prisms. This is achieved by:

[0023] 5a) Initialize the triangular prism network to the historical best triangular prism network;

[0024] 5b) Calculate the fitness function value of the triangular prism network. ,

[0025] 5c) Determine whether the fitness function value of the triangular prism network is better than the historical best fitness function value. The historical best triangular prism network is approximately composed of several triangular prisms with minimum signal out-of-pipe dispersion.

[0026] Furthermore, step (6) involves adjusting the vertical beamwidth and uptilt angle of the coverage beam of each base station on the base of each triangular prism in the triangular prism network to optimize the signal coverage and overlap coverage within each triangular prism. This is achieved by:

[0027] 6a) Each base station on the base of each triangular prism determines the azimuth angle and horizontal beamwidth of its coverage beam according to the angle of each triangular prism.

[0028] 6b) Each base station on the base of each triangular prism is configured with a random uptilt angle and vertical beamwidth for its coverage beam, and these, together with the azimuth angle and horizontal beamwidth determined by each base station, are used as the initial beam parameters and historical best beam parameters for the coverage beam of each base station.

[0029] 6c) For each triangular prism, the signal coverage within the prism is calculated using the Monte Carlo algorithm based on the beam parameters of each base station on the base surface. and overlap coverage The fitness function values ​​for each triangular prism are then weighted and summed. :

[0030] 6d) For each prism, determine whether its fitness function value is better than the fitness function value when the base station beam configuration in the prism is the historical best beam parameter. The historical best beam parameter of the base station in each prism is the base station beam parameter to achieve low overlap and hole-free signal coverage in each prism.

[0031] 2. A multi-faceted, void-free, low-interference open-ground three-dimensional coverage system, characterized in that it comprises:

[0032] The matrix family construction module is used to construct a matrix family from all the generating matrices of the polyhedron filling lattice point set;

[0033] The block diagonal matrix query module is used to query whether there is a block diagonal matrix in the generated matrix family, so as to determine whether the polyhedral structure corresponding to the generated matrix family can achieve half-space three-dimensional filling with filling points deployed only on the ground layer.

[0034] The triangular prism generation module is used to generate triangular prisms of different shapes that satisfy the condition that there are block diagonal matrices in the family of generating matrices.

[0035] The triangular prism shape determination module is used to calculate the signal coverage outside the prism for triangular prisms of different shapes and to determine the shape of the triangular prism with the minimum signal diffusion outside the prism.

[0036] The triangular prism network generation module is used to generate an approximate triangular prism network composed of triangular prisms with minimum signal dispersion outside the prism;

[0037] The beam generation module is used to generate a collaborative coverage beam for each base station on the base of each triangular prism, which can simultaneously take into account both air and ground coverage performance.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] Firstly, this invention abstracts all filling points of the polyhedron filling space into a grid set, and by verifying whether there is a block diagonal matrix in the family of generator matrices constructed from this grid set, it can quickly determine the effective three-dimensional coverage of polyhedron structures based on ground networks. Secondly, by forming a triangular prism network with triangular prisms that approximately have the minimum external signal dispersion under the condition that there is a block diagonal matrix in the family of generator matrices, the overlapping coverage of signals between triangular prisms can be effectively reduced.

[0040] Secondly, this invention divides the three-dimensional region at a set height into several triangular prisms. By adjusting the vertical beamwidth, uptilt angle, and power parameters of the base station coverage beams on the bottom surface of each triangular prism, it achieves efficient coordination among the base station coverage beams within each triangular prism.

[0041] Thirdly, this invention takes the overall coverage performance of the air and the ground as the optimization goal, achieving no coverage holes within the triangular prism and reducing signal overlap within the prism, while also taking into account the overall coverage performance of ground and low-altitude users. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the implementation of the polyhedral filling method for void-free, low-interference, three-dimensional ground coverage according to the present invention.

[0043] Figure 2 This is a schematic diagram of constructing a matrix by filling a lattice set of triangular prisms in the method of the present invention;

[0044] Figure 3 This is a block diagram of the polyhedral-filled, void-free, low-interference, open-ground three-dimensional coverage system of the present invention;

[0045] Figure 4 This is a comparison chart of the simulated performance of air-to-ground coverage after beam optimization of triangular prism networks and cellular networks using the beam optimization method of this invention.

[0046] Figure 5 This is a performance comparison diagram of the minimum signal column dispersion triangular prism network constructed in this invention and the existing triangular prism network constructed by randomly selecting base stations in air-to-ground signal coverage simulation.

[0047] Figure 6 This is a comparison chart showing the coverage performance of a base station at different heights of a triangular prism when the base station uses the beam optimization method of this invention to generate the beam and when it uses the existing scenario-based beam for signal coverage simulation. Detailed Implementation

[0048] To enable those skilled in the art to better understand the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative effort should all fall within the protection scope of the present invention.

[0049] Example 1: A method for three-dimensional ground cover without voids and with low interference by filling polyhedrons.

[0050] Reference Figure 1 The implementation steps of this example include the following:

[0051] Step 1: Construct a family of generating matrices for the triangular prism filling grid point set.

[0052] 1.1) Select an equilateral triangular prism as the polyhedron to fill the solid space, such as... Figure 2 As shown, using Let each set of basis vectors represent an equilateral triangular prism, and construct a generating matrix of the equilateral triangular prism under these basis vectors. ;

[0053] 1.2) Define the filling point as the geometric center of the triangular prism. Since the triangular prism fills space with rotation angles of 0 and 0 respectively... Two types of triangular prisms, using and These represent the starting grid point coordinates of the two types of triangular prism filling grid point sets, respectively. The resulting triangular prism filling grid point set is: ;

[0054] 1.3) Arbitrarily select the unitary matrix and Generate the matrix of the grid set of equilateral triangular prisms. With the unitary matrix Multiplication yields a new generating matrix of an equilateral triangular prism. By merging all the generating matrices of the equilateral triangular prism into a single set, we obtain the family of survival matrices of the equilateral triangular prism. .

[0055] Step 2: Determine whether there is a block diagonal matrix in the generated matrix family.

[0056] Fill the grid point set of the equilateral triangular prism Survival Matrix Family Determine if a block diagonal matrix exists within it:

[0057] If it exists, proceed to step 3;

[0058] Conversely, the polyhedron cannot achieve three-dimensional air-ground coverage based on ground infrastructure;

[0059] Step 3: Generate triangular prisms of different shapes, which have a block-diagonal generation matrix.

[0060] 3.1) Let the vertex of the base of the triangular prism be the first... The two-dimensional coordinates of each base station are ;

[0061] 3.2) Fix the position coordinates of the first and second base stations on the base of the triangular prism. , Change the location coordinates of the third base station This changes the angle of the triangular prism;

[0062] 3.3) Fix the angle of the triangular prism, and change the size of the triangular prism by changing the perimeter of the triangle on the base of the prism to obtain a new triangular prism;

[0063] 3.4) Establish a set of basis vectors for the new triangular prism. And construct the generator matrix under this basis vector. Determine whether there exists that can make A unitary matrix in block diagonal form :

[0064] If it exists, the new triangular prism is a triangular prism of different shapes with a block diagonal generating matrix;

[0065] Otherwise, return to step 3.2).

[0066] Step 4: Calculate the triangular prism shape with the minimum signal dispersion outside the column.

[0067] To reduce inter-column signal overlap, this step involves changing the angle and size of the triangular prism to obtain a triangular prism shape with minimal out-of-column signal dispersion. This is achieved through the following steps:

[0068] 4.1) Divide the triangular prism into three layers: high, medium, and low. The three base stations at the apex of the base of the triangular prism are configured with the uptilt angle and vertical beamwidth of the coverage beam according to the layer height, and the horizontal beamwidth and azimuth angle of the beam are configured according to the angle of the triangular prism.

[0069] 4.2) Using the free-space path loss model as the wireless channel propagation model in the air-to-ground coverage scenario:

[0070]

[0071] in, Path loss, unit is

[0072] The distance between the user and the base station, in units of ,

[0073] Signal frequency, unit is ;

[0074] 4.3) Obtain the position of the first vertex at the base of the triangular prism. The maximum distance between a base station and its coverage layer Communication signal frequency and user signal reception threshold Calculate base station Transmit power of the coverage beam :

[0075] ,

[0076] in, For base stations Coverage beam;

[0077] 4.4) Distribute several reference points evenly in the space where the triangular prism is located, and calculate the received signal power of each reference point based on the beam parameters of each base station. :

[0078] ,

[0079] in, For the first Each reference point receives data from the covering beam. signal power,

[0080] For the first The first reference point and the first The distance between base stations.

[0081] 4.5) Based on the received signal power at each reference point in space, the Monte Carlo method is used to calculate the signal coverage outside the triangular prism. :

[0082] ,

[0083] in, Reference point outside the triangular prism region Receive beam The received signal power,

[0084] Reference point within the triangular prism region Receive beam The received signal power,

[0085] For receiving signal threshold, This represents the total number of reference points outside the triangular prism. This represents the total number of reference points within the triangular prism.

[0086] 4.6) Using the method in step 3, new triangular prisms are continuously generated, and the signal coverage outside the prisms is calculated. The triangular prism shape with the smallest signal coverage outside the prism is taken as the triangular prism shape with the smallest signal diffusion outside the prism.

[0087] Step 5: Construct a triangular prism network with minimal signal dispersion outside the prism.

[0088] For a set of ground base stations, selecting base stations to construct a triangular prism network with minimum out-of-pillar signal dispersion is a single-objective combinatorial optimization problem with a globally optimal solution. This invention solves this problem using a genetic algorithm, the implementation of which includes:

[0089] 5.1) The latitude and longitude coordinates of the base station are converted into two-dimensional Cartesian coordinates using the Mercat projection;

[0090] 5.2) Based on the location of the base station in the two-dimensional Cartesian coordinate system, the ground base station set... Divided into internal base station sets and edge base station set ;

[0091] 5.3) From internal base station set Random selection One base station, and this The location information of each base station is used as the chromosome of an individual in the genetic algorithm. At this time, each gene on the chromosome corresponds to the location information of one base station.

[0092] 5.3) Repeatedly generate a certain number of individuals to form the first generation population;

[0093] 5.4) Calculate the fitness function value for each individual. That is, the average similarity between each triangular prism in the triangular prism network and the triangular prism with the minimum out-of-prism signal diffusion in step 4:

[0094] ,

[0095] in, Let the vector be the side length of the triangle at the base of the triangular prism with the minimum out-of-cylinder signal dispersion.

[0096] For the first triangular prism network The side length vectors of the base triangles of a triangular prism;

[0097] 5.5) Based on the fitness function value of each individual, sort the individuals in the population from largest to smallest, retain the first half of the individuals, and cull the second half of the individuals;

[0098] 5.6) Perform crossover and mutation operations using a genetic algorithm on the first half of the retained individuals to generate new individuals in a number equal to half the number of individuals in the initial population, so as to ensure that the population size remains unchanged during the iteration process;

[0099] 5.7) Merge the individuals retained in the original population with the newly generated individuals to form a new population;

[0100] 5.8) Determine if the maximum number of iterations has been reached:

[0101] If so, then the individual with the maximum fitness function value in the new population will be... Individual internal base stations and edge base station sets Merging is performed, and the merged base station set is triangulated to obtain a triangular network. Extending this triangular network vertically results in a triangular prism network with minimum signal out-of-pivot dispersion.

[0102] Otherwise, return to step (5.4).

[0103] Step 6: Optimize the beam parameters of each base station on the base of each triangular prism.

[0104] To achieve comprehensive coverage performance across both the air and ground, it is necessary to optimize the vertical beamwidth and uptilt angle of each base station beam on the base of the triangular prism to achieve low-overlap, hole-free signal coverage across the entire triangular prism's three-dimensional region. Existing optimization methods include simulated annealing, genetic algorithms, ant colony optimization, and hybrid particle swarm optimization. This step employs, but is not limited to, a hybrid particle swarm optimization algorithm to optimize the vertical beamwidth and uptilt angle of the coverage beam for each base station on the base of the triangular prism. The implementation steps include:

[0105] 6.1) Each individual in the hybrid particle swarm algorithm possesses information on the tilt angle, vertical beamwidth, horizontal beamwidth, and azimuth angle of each base station on the base of the triangular prism;

[0106] 6.2) Each individual determines its horizontal wave width and azimuth information based on the angle of the triangular prism;

[0107] 6.3) The dip angle and vertical beamwidth information of each individual are determined by random selection;

[0108] 6.4) Repeatedly generate a certain number of individuals to form the first generation population;

[0109] 6.5) Divide the first generation population into two equal parts, and update the tilt angle and vertical beamwidth information of each individual in the first part, population 1, using the particle swarm optimization (PSO) algorithm, and update the tilt angle and vertical beamwidth information of each individual in the second part, population 2, using the artificial bee colony (ABC) algorithm.

[0110] 6.6) Based on the beam information of each individual in population 1 and population 2, namely tilt angle, vertical beamwidth, horizontal beamwidth, and azimuth angle, the Monte Carlo algorithm is used to calculate the signal coverage within the triangular prism under different individual beam information. and overlap coverage The fitness function value for each individual is obtained by weighting these values. :

[0111] ,

[0112] in, , The total number of reference points evenly distributed within the triangular prism. For reference point Received from beam The received signal power, The threshold for receiving signals;

[0113] The overlap coverage of the triangular prism;

[0114] For coverage weight, The weight is the overlap coverage rate.

[0115] 6.7) Determine whether the maximum fitness function value in population 1 is greater than the maximum fitness function value in population 2:

[0116] If so, individuals in population 2 update their tilt angle and vertical beamwidth based on the tilt angle and vertical beamwidth information of individuals in population 1, while individuals in population 1 update their tilt angle and vertical beamwidth based on the beamwidth information of their previous generation.

[0117] Conversely, individuals in population 1 update their tilt angle and vertical beamwidth based on the tilt angle and vertical beamwidth information of individuals in population 2, while individuals in population 2 still update their tilt angle and vertical beamwidth based on the beamwidth information of their previous generation.

[0118] 6.8) Determine if the maximum number of iterations has been reached:

[0119] If so, then the wavenumber parameter corresponding to the maximum fitness function value in the entire population is the optimal beam parameter for each base station on the base of the triangular prism, and step 6.9 is executed.

[0120] Conversely, return to step 6.6);

[0121] 6.9) Determine if all prisms in the triangular prism network have been traversed:

[0122] If so, the beam parameters of each base station on the base of each triangular prism are optimized.

[0123] Conversely, if the condition is not met, select a new triangular prism from a triangular prism network and return to 6.2).

[0124] It should be noted that the step numbers in the above methods and claims are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and their order is not limited.

[0125] Example 2: A three-dimensional ground cover system with polyhedral filling, free of voids and with low interference.

[0126] Reference Figure 3 This example includes: a matrix family construction module 1, a block diagonal matrix query module 2, a triangular prism generation module 3, a triangular prism shape determination module 4, a triangular prism network generation module 5, and a beam generation module 6. Specifically, the triangular prism network generation module 5 includes: a three-dimensional coverage base station set construction submodule 51, a three-dimensional spatial triangulation submodule 52, a similarity calculation submodule 53, an optimal triangular prism judgment submodule 54, and a network construction iteration count judgment submodule 55. The beam generation module 6 includes: a beam parameter generation submodule 61, an in-pillar signal coverage performance calculation submodule 62, an optimal coverage beam judgment submodule 63, and a beam optimization iteration count judgment submodule 64.

[0127] The working principle of the entire system is as follows:

[0128] The generating matrix family construction module 1 is used to construct the generating matrix family of triangular prisms and pass the generating matrix family to the block diagonal matrix query module 2;

[0129] The block diagonal matrix query module 2 is used to query whether there is a block diagonal matrix in the triangular prism generation matrix family. If it exists, the triangular prism is passed to the triangular prism generation module 3.

[0130] The triangular prism generation module 3 is used to generate a series of new triangular prisms with different shapes from the triangular prisms passed from the block diagonal matrix query module 2, and to pass the triangular prisms with block diagonal form generation matrices to the triangular prism shape determination module 4.

[0131] The triangular prism shape determination module 4 is used to calculate and determine the triangular prism with the minimum signal external dispersion in the triangular prism generation module 3, and then transmit the triangular prism to the triangular prism network generation module 5.

[0132] The triangular prism network generation module 5 is used to generate an approximate triangular prism network composed of triangular prisms with minimum signal dispersion. The three-dimensional coverage base station set construction submodule 51 is used to select ground base stations to construct a three-dimensional coverage base station set and transmit this set to the three-dimensional spatial triangulation submodule 52. The three-dimensional spatial triangulation submodule 52 is used to divide the three-dimensional region enclosed by the base stations in the three-dimensional coverage base station set into a triangular prism network and transmit this triangular prism network to the similarity calculation submodule 53. The similarity calculation submodule 53 is used to calculate the fitness function value of the triangular prism network, and... The fitness function value is passed to the optimal triangular prism judgment submodule 54. The triangular prism judgment submodule 54 is used to determine whether the fitness function value passed from the similarity calculation submodule 53 is better than the fitness function value of the historical best triangular prism network. If so, the historical best triangular prism network and the historical best fitness function value are updated. The network construction iteration count judgment submodule 55 is used to determine whether the number of times the triangular prism judgment submodule 54 runs is equal to the maximum number of iterations. If it is equal, the current historical best triangular prism network is passed to the beam generation module 6. Otherwise, the three-dimensional coverage base station set construction submodule 51 is run.

[0133] The beam generation module 6 is used to generate a cooperative coverage beam that takes into account both air and ground coverage performance for each triangular prism. The beam parameter generation submodule 61 is used to generate the beam parameters of each base station on the base of each triangular prism in the triangular prism network transmitted by the triangular prism network generation module 5, and transmit them to the in-prism signal coverage performance calculation submodule 62. The in-prism signal coverage performance calculation submodule 62 is used to calculate the coverage performance value of the signal in each triangular prism based on the beam parameters of each triangular prism in the triangular prism network, and transmit the coverage performance value to the optimal coverage beam judgment submodule 63.

[0134] The optimal coverage beam judgment submodule 63 is used to determine whether the coverage performance value transmitted from the in-pillar signal coverage performance calculation submodule 62 is better than the historical best coverage performance value, and to update the coverage performance value that is better than the historical best coverage performance value. The beam optimization iteration count judgment submodule 64 is used to determine whether the number of times the optimal coverage beam judgment submodule 63 has run has reached the maximum number of iterations. If it has, the beam parameters corresponding to the current historical best coverage performance value are the optimal beam parameters for each prism in the triangular prism network; otherwise, the beam parameter generation submodule 61 is run.

[0135] It should be noted that the above functional modules can be implemented, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, they can be implemented, in whole or in part, as program instruction products. A program instruction product includes one or a set of program instructions. When the program instructions are loaded and executed on a computer, the described process or function is generated, in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or transferred from one computer's readable and writable storage medium to another.

[0136] In this embodiment, the transmission relationships between the modules can be achieved through indirect coupling or communication connections via interfaces, devices, or modules. The functional modules and sub-modules in this embodiment can dynamically reside within a single processing unit, or each module can exist physically independently, or two or more modules can dynamically reside within a single processing unit. When these dynamic components are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. This storage medium can be a memory, disk, or optical disc, etc.

[0137] The effects of this invention can be further illustrated by the following simulation experiments.

[0138] I. Simulation Conditions

[0139] The simulation experiment application platform of this invention is: Intel i5-11400H CPU with a main frequency of 2.70GHz, NVIDIA GeForce RTX 3050 Ti Laptop GPU, and 16GB of memory.

[0140] The software platform for the simulation experiment of this invention is: Windows 10 operating system and Matlab R2023b.

[0141] The simulation experiment scenario and base station parameter configuration are as shown in Figure 1:

[0142] Table 1 Parameter Configuration for Scenarios and Base Stations

[0143]

[0144] The parameter configurations in the beam optimization algorithm are shown in Table 2:

[0145] Table 2 Parameter configuration of beam optimization algorithm

[0146]

[0147] II. Simulation Content

[0148] Simulation 1: Under the above simulation conditions, the method of this invention and the traditional method of direct 3D extension of cellular networks are used to provide signal coverage for 3D spaces at different heights, respectively, and the signal coverage and overlap coverage of the entire 3D space are obtained as follows: Figure 4 As shown, where Figure 4 (a) Simulation results of coverage and overlap coverage obtained by directly extending a traditional cellular network in three dimensions. Figure 4 (b) shows the simulation results of coverage and overlap coverage obtained by the method of the present invention.

[0149] from Figure 4 As can be seen, compared with the traditional method of directly extending cellular networks in three dimensions, the method of the present invention improves the signal coverage in three-dimensional space by more than 20%. When the transmission power of the base station in the cellular network is increased to make its signal coverage the same as that of the method of the present invention, the overlap coverage increases by more than 40% compared with the method of the present invention, which aggravates the interference experienced by users in three-dimensional space. This verifies that the method of the present invention can achieve high coverage and low overlap in three-dimensional areas.

[0150] Simulation 2: Under the above simulation conditions, beam optimization was performed on a triangular prism network with minimum inter-pillar signal dispersion and a triangular prism network constructed by randomly selected base stations using the method of this invention. Signal coverage was then provided for a three-dimensional space with a height of 1000 meters. The signal coverage rate and overlap coverage rate of the three-dimensional space were obtained as follows: Figure 5 As shown.

[0151] from Figure 5 As can be seen, the triangular prism network with minimum inter-pillar signal dispersion reduces the signal overlap coverage in the three-dimensional region by more than 20% compared with the triangular prism network constructed by randomly selecting base stations, verifying that the triangular prism with minimum inter-pillar signal dispersion constructed in this invention can effectively reduce signal overlap coverage in the three-dimensional region.

[0152] Simulation 3: Under the above simulation conditions, the coverage beam generated by the beam optimization method of this invention for a single triangular prism and the existing scene-based beam are compared to provide signal coverage for a three-dimensional space with a height of 1000 meters. The signal coverage and overlap coverage at different height levels in the three-dimensional region are as follows: Figure 6 As shown.

[0153] from Figure 6 As can be seen, when using the beam optimization method of this invention to provide signal coverage for a three-dimensional space at a height of 1000 meters, the signal coverage rate at different height levels is consistently greater than 90%. However, without beam optimization, directly using scenario-based beams to provide signal coverage for a three-dimensional space at a height of 1000 meters, although the signal coverage rate in the ground area reaches over 90%, it gradually decreases to 0 with increasing altitude. This verifies that the beam optimization method of this invention can simultaneously consider coverage performance in both the air and on the ground, achieving hole-free signal coverage in air-ground three-dimensional areas.

Claims

1. A polyhedral filled, void-free, low-interference, empty-ground three-dimensional coverage method, characterized by, Comprise (1) select a set of triangular column filling lattice set base vector generated matrix, and multiply it with any unit modulus matrix, get the generating matrix family of filling lattice set; (2) determine whether there is a block diagonal form matrix in the triangular column generating matrix family: If there is, execute (3); Otherwise, the ground network based air-ground three-dimensional coverage cannot be realized; (3) under the condition of meeting the existence of block diagonal form matrix in the generating matrix family, change the shape of triangular column to get triangular column with different shapes; (4) iterative calculation of the signal coverage rate of triangular column with different shapes, get the triangular column with the minimum signal column outside dispersion; (5) the base station set of ground network is divided into internal base station set and edge base station set, N base stations are selected from the internal base station set to form a three-dimensional coverage base station set with the edge base station set, and a three-dimensional coverage triangular column network is constructed by triangulation, and the selected internal base station is iteratively updated, so that the triangular column network is approximately composed of several triangular columns with minimum signal column outside dispersion; (6) by adjusting the vertical wave width and tilt angle of each base station coverage beam in the triangular column network, the signal coverage rate and overlapping coverage rate in each triangular column are optimized, and low overlap and no hole signal coverage of air-ground three-dimensional area is realized.

2. The method of claim 1, wherein, The filling lattice set selected in the (1) is represented as follows: ， wherein denotes the set of filled-in lattice points, is the initial triangular prism coordinate, is the generating matrix of the set of filled-in lattice points, is the unimodular matrix, is the family of generating matrices.

3. The method of claim 1, wherein, The block diagonal form matrix in the (2) is represented as follows: ， wherein, denotes a block diagonal matrix, denotes a generator matrix of a filled lattice set of two-dimensional sublattices in denotes a generator matrix of a filled lattice set of one-dimensional sublattices in .​ 4. The method of claim 1, wherein, In the (3), changing the shape of the triangular column refers to changing the angle of the triangular column and the size of the triangular column bottom, specifically by fixing the positions of two vertices of the triangular column bottom, changing the position of the third vertex to change the angle of the triangular column; after determining the angle, the size of the triangular column is changed by changing the perimeter of the triangular column bottom triangle; In the (5), the three-dimensional coverage triangular column network is constructed by triangulation, which is based on the two-dimensional coordinates of each base station in the three-dimensional coverage base station set, and the polygon area surrounded by the base station set is divided into a triangular network; then the triangular network is extended longitudinally along the direction perpendicular to the ground to obtain a triangular column network.

5. The method of claim 1, wherein, The implementation of the iterative calculation of the signal coverage rate of the triangular column with different shapes in the (4) includes: 4a) hierarchical division of the triangular column, configuration of the beam parameters of each base station on the bottom of the triangular column: 4a1) the triangular column is divided into high, medium and low three layers, and the three base stations at the vertices of the bottom of the triangular column are respectively configured with the tilt angle and vertical wave width of the base station coverage beam according to the layer height; 4a2) the three base stations are respectively configured with the horizontal wave width and azimuth angle of the base station coverage beam according to the angle of the triangular column; 4a3) each base station calculates and configures the transmission power of the base station beam according to the maximum distance between the layer to be covered and the base station position by using the free space path loss model, The implementation of the iterative updating of the selected internal base station in the (5) so that the triangular column network is approximately composed of several triangular columns with minimum signal column outside dispersion includes: 4b) Randomly deploy several reference points in the space where the triangular prism is located, and calculate the ratio of the number of covered reference points outside the triangular prism to the number of covered reference points inside the triangular prism according to the beam parameters of the three base stations on the bottom surface of the triangular prism, to obtain the signal coverage rate outside the prism : ， wherein, reference point for non-triangular prism region receiving a signal power of a beam from a base station ​ reference point within the triangular prism region receiving a signal power of a beam from the base station from the base station for a received signal threshold, for a number of out-of-column reference points, for a number of in-column reference points.

6. The method of claim 1, wherein, 5a) initialize the triangular column network to the historical best triangular column network; 5c) determine whether the fitness function value of the triangular column network is better than the historical optimal fitness function value: 5b) calculating the fitness function value of the triangular prism network i.e. the average similarity of the triangular prisms within the triangular prism network to the triangular prism with the smallest dispersion of the extracellular signal: , wherein is the edge length vector of the triangle of the base of the triangular prism with the smallest out-of-column signal dispersion, is the edge vector of the triangle at the bottom of the i-th pyramid in the triangular pyramid network; and is the edge vector of the triangle at the bottom of the i-th pyramid in the triangular pyramid network; and ​ If yes, the triangular prism network is regarded as the historical optimal triangular prism network and the historical optimal fitness function value is updated, a new set of three-dimensional coverage base stations is selected by using the genetic algorithm, the new set of three-dimensional coverage base stations is divided into a new triangular prism network, and the process returns to 5b); If no, a new set of three-dimensional coverage base stations is selected by using the genetic algorithm, the new set of three-dimensional coverage base stations is divided into a new triangular prism network, and the process returns to 5b); 5d) Repeat 5c) until a maximum number of iterations is reached, and the historical optimal triangular prism network at this time is a triangular prism network approximately composed of triangular prisms with minimum signal dispersion outside the prisms.

7. The method of claim 1, wherein, The (6) adjusting the vertical wave width and the tilt angle of each base station coverage beam in each triangular prism bottom surface of the triangular prism network, and optimizing the signal coverage and overlapping coverage in each triangular prism, comprises: 6a) Each base station in each triangular prism bottom surface determines the azimuth angle and the horizontal wave width of its coverage beam according to the angle of each triangular prism; 6b) Each base station in each triangular prism bottom surface configures a random tilt angle and a vertical wave width for its coverage beam, and takes the azimuth angle and the horizontal wave width determined by each base station and the random tilt angle and the vertical wave width as the initial beam parameters and the historical optimal beam parameters of each base station coverage beam; 6c) Each triangular prism calculates the coverage of the signal in the prism using the Monte Carlo method according to the beam parameters of the base stations on the base and the overlapping coverage and weights them to obtain the fitness function value of each triangular prism : ， wherein, is a coverage weight, is an overlap coverage weight; 6d) For each triangular prism, it is determined whether the fitness function value is better than the fitness function value when the base station beam configuration in the triangular prism is the historical optimal beam parameter: If yes, the beam parameters of each base station in the triangular prism at this time are taken as the historical optimal beam parameters of each base station, the hybrid particle swarm optimization algorithm is used to update the beam tilt angle and the vertical wave width, and the process returns to 6c); If no, the hybrid particle swarm optimization algorithm is used to update the beam tilt angle and the vertical wave width, and the process returns to 6c); 6e) Repeat 6d) until a maximum number of iterations is reached, and the historical optimal beam parameters of each base station in each triangular prism are the base station beam parameters for realizing low-overlapping and non-hollow signal coverage in each triangular prism.

8. A polyhedral filled, low-interference, void-free, air-ground stereocoverage system, characterized in that, Comprise: A matrix family construction module is configured to construct all generating matrices of the polyhedral filling lattice point set into a matrix family; A block diagonal matrix query module is configured to query whether a matrix in block diagonal form exists in the generating matrix family to determine whether the polyhedral structure corresponding to the generating matrix family can realize half-space three-dimensional filling with filling points only deployed on the ground; A triangular prism generation module is configured to generate triangular prisms with different shapes under the condition that a matrix in block diagonal form exists in the generating matrix family; A triangular prism shape determination module is configured to calculate the signal coverage rate outside the triangular prisms with different shapes and determine the shape of the triangular prism with the minimum signal dispersion outside the prism; A triangular prism network composed of triangular prisms with the minimum signal dispersion outside the prism; A beam generation module is configured to generate collaborative coverage beams for each base station in the bottom surface of each triangular prism, which can simultaneously consider the coverage performance in the air and on the ground.

9. The system of claim 8, wherein, The triangular prism network generation module comprises: A three-dimensional coverage base station set construction submodule is configured to select base stations from the ground base station set to construct a three-dimensional coverage base station set; A three-dimensional space triangular partitioning submodule is configured to partition a three-dimensional region surrounded by the base stations in the three-dimensional coverage base station set into a triangular prism network. The similarity calculation submodule is configured to calculate the fitness function value of the triangular prism network, i.e. the average similarity of each triangular prism in the triangular prism network to the triangular prism with the minimum signal column outer dispersion; The optimal triangular prism judgment submodule is configured to judge whether the fitness function value of the current triangular prism network is better than the fitness function value of the historical optimal triangular prism, and take the current triangular prism network with the better fitness function value as the historical optimal triangular prism network; The network construction iteration number judgment submodule is configured to judge whether the running number of the triangular prism judgment submodule is equal to the maximum iteration number, and if so, transmit the current historical optimal triangular prism network to the beam generation module; otherwise, run the three-dimensional coverage base station set construction submodule.

10. The system of claim 8, wherein, The beam generation module comprises: The beam parameter generation submodule is configured to generate the beam parameter of each base station on the bottom surface of each triangular prism; The in-column signal coverage performance calculation submodule is configured to calculate the coverage performance of each triangular prism, i.e. the weighted sum of the signal coverage rate and the overlapping coverage rate, according to the beam parameter of each base station on the bottom surface of each triangular prism; The optimal coverage beam judgment submodule is configured to judge whether the coverage performance of each triangular prism under the current beam parameter is better than the coverage performance under the historical optimal beam parameter, and take the current beam parameter with the better coverage performance as the historical optimal beam parameter of the base station; The beam optimization iteration number judgment submodule is configured to judge whether the running number of the optimal coverage beam judgment submodule reaches the maximum iteration number, and if so, take the beam parameter corresponding to the current historical optimal coverage performance value as the optimal beam parameter of each triangular prism in the triangular prism network; otherwise, run the beam parameter generation submodule.

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