Geometric representation method of space terahertz communication network topology space

Abstract

This invention discloses a geometric representation method for the topology of a space-based terahertz communication network. A network element model is constructed, using GEO constellations, LEO platforms, near-space platform clusters, and ground stations as nodes, forming an initial topology based on terahertz communication links. A high-dimensional geometric space is defined, mapping the dynamic topological relationships of network elements to a measurable geometric space. Considering the characteristics of the terahertz frequency band, time-series data of nodes are collected, and the covariance matrix is ​​estimated using information geometry methods. The geodesic distance between nodes is calculated using Fisher information metrics, mapping the time-varying network state to feature points or vectors in the geometric space. A high-dimensional geometric network is constructed based on a geodesic distance threshold. By adjusting the threshold, network sparsity is controlled, obtaining topological representations of different granularities. This invention significantly improves the modeling accuracy and interpretability of complex topologies, providing a unified theoretical framework and technical support for network design and performance optimization.

Description

Technical Field

[0001] This invention relates to the field of satellite communication network technology, and in particular to a geometric representation method for the topology of a space terahertz communication network. Background Technology

[0002] With the rapid development of information technology, space-based terahertz communication networks have gradually become a research hotspot. However, current network topology representation methods have limitations when facing the complexity and dynamics of space-based terahertz communication networks. Most existing methods can only handle univariate time series (UTS) and cannot effectively cope with the rich information and complex interrelationships contained in multivariate time series (MTS). In space-based terahertz communication networks, the data generated by multiple sensors or nodes are often multidimensional and interconnected, thus requiring a method that can process MTS and accurately represent the network topology space.

[0003] Information geometry provides a powerful tool for studying such problems. It combines mathematics with probability theory, particularly applying methods from differential geometry to probability theory, enabling the definition and computation of geodesic distances between data points. This is crucial for understanding the intrinsic structure and similarities of data. However, applying information geometry to the geometric representation of the topological space of spatial terahertz communication networks remains a challenge, requiring the development of new methods to handle the complexity and dynamics of such networks.

[0004] Chinese invention CN117221912A proposes a method for 6G-based integrated space-ground transmission optimization and topology mapping, but does not consider THz characteristics. Summary of the Invention

[0005] This invention discloses a geometric representation method for the topology space of a spatial terahertz communication network, which mainly includes the following steps.

[0006] S1. Construct a network element model and define network elements, including GEO constellations, LEO constellations, near-space platform clusters, and ground stations. Each network element is treated as a node. Based on the communication links between nodes, construct the initial network topology.

[0007] S2 defines a high-dimensional geometric space to represent the topological relationships between network elements. The dimension of this geometric space depends on the number of network elements and the complexity of the communication links.

[0008] S3 utilizes information geometry methods to transform time-series data. For each network element, its time-series data, such as signal strength and communication rate, is collected. These time-series data are then converted into points or vectors in geometric space using information geometry methods. Specifically, the time-series data is represented by estimating the covariance matrix, and the geodesic distance between covariance matrices is calculated using Fisher's information metric, thereby obtaining points or vectors in geometric space.

[0009] The time series data of a node i in a space terahertz communication network is as follows: Its dimension can be univariate or multivariate. A covariance matrix C can be constructed. i : in, A vector representing the mean of a time series.

[0010] Calculate the geodesic distance between any two nodes i and j in the covariance matrix space using Fisher's information metric: Where C1 and C2 are two covariance matrices, It is the geodesic distance between them, and tr represents the trace of the matrix.

[0011] S4. Construct a geometric network. Based on the points or vectors obtained in the geometric space in the previous step, construct a geometric network. Nodes correspond to network elements, and edges correspond to pairs of points whose geodesic distance between nodes is less than a certain threshold. By adjusting the threshold, the sparsity of the network can be controlled.

[0012] In S2, the phase space reconstruction method is used to convert univariate time series data into high-dimensional state vectors and estimate the covariance matrix; given the univariate time series data of node i... Define the embedding dimension m and the time delay τ, and construct a high-dimensional state vector: Where Xi(t) is an m-dimensional state vector, reflecting the state of node i in space.

[0013] Using the high-dimensional state vector data described above, the covariance matrix C is calculated. i in, .

[0014] The present invention has the following advantages: 1. By introducing the concept of information geometry, this invention can define and calculate geodesic distances, thereby revealing the inherent structure and similarity between data.

[0015] 2. The geometric representation method of the present invention can more accurately reflect the topology of space terahertz communication networks, which is helpful for network analysis, optimization and fault diagnosis. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the dynamic modeling method for space terahertz communication networks in this invention; Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings.

[0018] As shown in the figure, this invention discloses a geometric representation method for the topology space of a spatial terahertz communication network, such as... Figure 1 As shown, the method mainly includes the following steps.

[0019] S1. Construct a network element model and define network elements, including GEO constellations, LEO constellations, near-space platform clusters, and ground stations. Each network element is treated as a node. Based on the communication links between nodes, construct the initial network topology.

[0020] S2 defines a high-dimensional geometric space to represent the topological relationships between network elements. The dimension of this geometric space depends on the number of network elements and the complexity of the communication links.

[0021] S3 utilizes information geometry methods to transform time-series data. For each network element, its time-series data, such as signal strength and communication rate, is collected. These time-series data are then converted into points or vectors in geometric space using information geometry methods. Specifically, the time-series data is represented by estimating the covariance matrix, and the geodesic distance between covariance matrices is calculated using Fisher's information metric, thereby obtaining points or vectors in geometric space.

[0022] The time series data of a node i in a space terahertz communication network is as follows: Its dimension can be univariate or multivariate. A covariance matrix C can be constructed. i : in, A vector representing the mean of a time series.

[0023] Calculate the geodesic distance between any two nodes i and j in the covariance matrix space using Fisher's information metric: Where C1 and C2 are two covariance matrices, It is the geodesic distance between them, and tr represents the trace of the matrix.

[0024] S4. Construct a geometric network. Based on the points or vectors obtained in the geometric space in the previous step, construct a geometric network. Nodes correspond to network elements, and edges correspond to pairs of points whose geodesic distance between nodes is less than a certain threshold. By adjusting the threshold, the sparsity of the network can be controlled.

[0025] In S2, the phase space reconstruction method is used to convert univariate time series data into high-dimensional state vectors and estimate the covariance matrix; given the univariate time series data of node i... Define the embedding dimension m and the time delay τ, and construct a high-dimensional state vector: Where Xi(t) is an m-dimensional state vector, reflecting the state of node i in space.

[0026] Using the high-dimensional state vector data described above, the covariance matrix C is calculated. i in, .

[0027] The present invention has been described in detail above with reference to the accompanying drawings. However, those skilled in the art should understand that the specification is for interpreting the claims, and the scope of protection of the present invention is determined by the claims. Any modifications, equivalent substitutions, and improvements made based on the present invention should be within the scope of protection claimed.

Claims

1. A geometric representation method for the topology space of a spatial terahertz communication network, characterized in that, include: S1. Construct a network element model and define network elements, including GEO constellations, LEO constellations, near-space platform clusters, and ground stations. Each network element is treated as a node. Based on the communication links between nodes, construct the initial network topology. S2 defines a high-dimensional geometric space that maps the dynamic topological relationships of network elements to a measurable geometric space. The dimension of this geometric space depends on the number of network elements and the complexity of communication links. Information geometry methods are used to transform time-series data. For each network element, its time-series data, such as signal strength and communication rate, are collected. Information geometry methods are used to transform time series data into points or vectors in geometric space. Specifically, this includes: representing time series data by estimating the covariance matrix and using Fisher information metric to calculate the geodesic distance between covariance matrices, thereby obtaining points or vectors in geometric space. To address the time-varying topology characteristics of space-based terahertz communication networks and the intermittent connectivity issues caused by beam pointing and obstruction in terahertz links, dynamic parameters such as node location changes and link lifetime are considered in the time-series data of nodes. The time-series data of a node i in the space-based terahertz communication network is as follows: Its dimension can be univariate or multivariate; construct the covariance matrix C. i : in, A vector representing the mean of a time series; Calculate the geodesic distance between any two nodes i and j in the covariance matrix space using Fisher's information metric: Where C1 and C2 are two covariance matrices, It is the geodesic distance between them, and tr represents the trace of the matrix; S3. Construct a high-dimensional geometric network. Based on the points or vectors in the obtained geometric space, construct a geometric network. Nodes correspond to network elements, and edges correspond to pairs of points whose geodesic distance between nodes is less than a certain threshold. The sparsity of the network is controlled by adjusting the threshold.

2. The method according to claim 1, characterized in that, In S2, the phase space reconstruction method is used to convert univariate time series data into high-dimensional state vectors and estimate the covariance matrix. Given univariate time series data of node i Define the embedding dimension m and the time delay τ, and construct a high-dimensional state vector: Where Xi(t) is an m-dimensional state vector, reflecting the state of node i in space; Calculate the covariance matrix C using high-dimensional state vector data. i : in, .

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