Three-dimensional radio map construction method for low-orbit satellite signals

Abstract

The invention discloses a three-dimensional radio map construction method for low-orbit satellite signals. The method comprises the following steps: S1, acquiring an incomplete input tensor # imgabs0 # including an observation measurement value; s2, representing a to-be-constructed three-dimensional radio map as a combination of a core tensor and a factor matrix; an objective function # imgabs1 # is constructed; s3, performing # imgabs2 round iteration, in each round iteration process, sequentially calculating gradients of a target function # imgabs3 # relative to each factor matrix and a core tensor # imgabs4 #, and updating the factor matrixes and the core tensor # imgabs5 # by using the gradients; and S4, according to the factor matrix after the secondary updating of the # imgabs6 # and the core tensor # imgabs7 #, calculating to obtain a complete tensor expression # imgabs8 # of the three-dimensional radio map. The method supports efficient spectrum monitoring of a wide-area LEO network, provides a dynamic view for spectrum sharing, interference management and resource allocation in a space-air-ground integrated network (SAGIN), and has the advantages of low cost, high expansibility and strong robustness.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and in particular, to a method for constructing a three-dimensional radio map for low-earth orbit satellite signals. Background Art

[0002] In recent years, with the deployment of large constellations in low earth orbit (LEO) such as Starlink and OneWeb, non-terrestrial networks (NTNs) have significantly expanded the communication coverage range and have obvious advantages compared with traditional terrestrial networks (TNs). However, with the rapid increase in the number of LEO constellations, the available spectrum resources are extremely limited, which poses a severe challenge to spectrum sharing in space-air-ground integrated networks (SAGIN).

[0003] To achieve efficient spectrum allocation and interference management, a new technology capable of constructing a three-dimensional radio map (3D RM) in LEO satellite networks is urgently needed. 3D RM provides a comprehensive view of spectrum usage for SAGIN by integrating three dimensions of 3D space (longitude, latitude, altitude). The steps of constructing 3D RM include deploying a large number of aerial and ground sensors within the area of interest to collect radio frequency signals at different locations. However, the coverage range of LEO satellites is extremely wide. For example, a very low earth orbit (VLEO) satellite at an altitude of 340 km can cover an area of 52 km² with a beam width of 1.5 degrees, and LEO satellites in the orbit of 500 km to 600 km have an even larger coverage range. To construct a wide-area 3D RM, a large number of sensors need to be deployed, resulting in a cost far exceeding that of small-scale monitoring in traditional TNs. Therefore, a technology capable of achieving high-precision 3D RM construction under sparse sensor deployment is urgently needed. Summary of the Invention

[0004] Aiming at the technical problems of high sensor deployment cost and insufficient data faced in the construction of wide-area 3D RM in LEO satellite networks, the present invention proposes a method for constructing a three-dimensional radio map for low-earth orbit satellite signals. Based on the neural tensor decomposition (Neural TD) technology of deep unsupervised learning, and using the non-linear fitting ability of neural networks (NNs), high-precision 3D RM construction is achieved under sparse sensor conditions.

[0005] To solve the above technical problems, the technical solution provided by the present invention is as follows: A method for constructing a three-dimensional radio map for low-earth orbit satellite signals, comprising the following steps: S1: Obtain an incomplete input tensor including observation measurements ; S2: Represent the three-dimensional radio map to be constructed as a combination of a core tensor and factor matrices, represent each factor matrix as a neural network function and input variables; and construct an objective function for representing the loss between the three-dimensional radio map under construction and the incomplete input tensor ; ; S3: Perform rounds of iteration. During each round of iteration: successively calculate the gradients of the objective function with respect to each factor matrix and the core tensor , and update the factor matrices and the core tensor using the gradients; S4: Calculate the complete tensor representation of the three-dimensional radio map according to the factor matrices and core tensor updated times .

[0006] A further improvement of the present invention is that the process of obtaining the incomplete input tensor includes: measuring the received signal strength of the downlink of the low-earth orbit satellite through ground or aerial sensors arranged at pre-planned spatial sampling positions; the form of the incomplete input tensor is set that the three-dimensional grid is divided into I , J , K nodes in the longitude, latitude, and altitude directions respectively, then ; where:

[0007] In the formula, represents the received power of the i, j, k-th node, and the set Ω represents the index set of the observation measurements; represents the orthogonal projection acting on the set Ω.

[0008] A further improvement of the present invention is that the expression of the objective function is:

[0009] Where: is the Frobenius norm; is the neural network fitting function; is an input variable to be optimized; represents the mode product between a tensor and a matrix.

[0010] A further improvement of the present invention is that the factor matrix is , , and the neural network fitting function includes two fully connected layers and an activation function ; the activation function is a sine activation function.

[0011] A further improvement of the present invention is that during the update process of the input components and the core tensor using the gradient, the Adam optimizer is used for the update, and regularization is achieved by means of weight decay.

[0012] A further improvement of the present invention is that in step S4, the expression for calculating the complete tensor representation of the three-dimensional radio map is:

[0013] Where: is the factor matrix after T updates, , is the core tensor after T updates.

[0014] The technical solution provided by the present invention has the following technical effects: This method supports the efficient spectrum monitoring of a wide-area LEO network, provides a dynamic view for spectrum sharing, interference management, and resource allocation in the space-air-ground integrated network (SAGIN), and has the advantages of low cost, high scalability, and strong robustness.

[0015] The concept, specific structure, and technical effects of the present invention will be further described below in conjunction with the drawings to fully understand the purpose, features, and effects of the present invention. Description of the Drawings

[0016] Figure 1 is a schematic diagram of Tucker decomposition; Figure 2 is the neural network structure; Figure 3 , Figure 4 respectively show the 3D RM reconstruction performance of Neural TD. Detailed Embodiments

[0017] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand the other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0018] The reconstruction of a three-dimensional radio map (3D RM) can be regarded as a tensor completion problem, where effective techniques such as Canonical Polyadic (CP) decomposition, Tucker decomposition, and Block Term Decomposition (BTD) can be applied. Tucker decomposition Figure 1 As shown, due to its flexibility, a tensor is approximated by a core tensor and factor matrices, allowing different ranks in different modes. This enables effective capture of multi-dimensional correlations, making Tucker decomposition particularly suitable for accurately reconstructing 3D RM.

[0019] For a 3D RM tensor (third-order tensor) , assuming the rank of Tucker decomposition is , then can be decomposed into a core tensor, denoted as , and three factor matrices, denoted as , and . Its expression is as follows: (1) where, represents the mode product between a tensor and a matrix. The expression of Tucker decomposition can also be written in matrix form: (2) (3) (4) where, , and are the matrices obtained by unfolding the tensor along the first, second, and third dimensions respectively, with their sizes being , and . is the matrix obtained by unfolding the core tensor along the first, second, and third dimensions, with its size being , and symbols represent the Kronecker product tensors.

[0020] The tensor only contains sparse measurement values. The set represents the index set of the observed measurement values. represents the orthogonal projection acting on the set and is defined as follows: (5) Here, the reconstruction of the 3D RM can be achieved by solving an optimization problem to learn the factor matrices and the core tensor from the tensor and thus reconstruct the complete 3D RM. The optimization problem is formulated as follows: (6) where represents the regularization parameter. This optimization problem can be solved by applying alternating optimization to each factor in the tensor decomposition, usually implemented by Alternating Least Squares (ALS). The ALS method usually updates by alternately optimizing each factor matrix and the core tensor, and this method is fixed to the linear model. When dealing with sparse data with complex patterns, the ALS method may not be able to effectively capture the non-linear relationships in the data, resulting in a reduction in reconstruction accuracy. In this application, the factor matrix is not directly solved, but the problem is transformed into solving the neural network parameters and the input variable . The structure of the neural network fitting function is as shown in Figure 2 and includes two FC layers and an activation function . The optimization problem in equation (6) can be rewritten as a loss function optimization problem: (7) where does not include the regularization term because the regularization is achieved through weight decay in Pytorch. By calculating the gradients of the neural network parameters and the output variable using autograd in Pytorch, the loss function can be minimized to obtain the optimized factor matrix and the core tensor .

[0021] During the specific implementation process, the three-dimensional radio map construction method (Neural TD) for low-earth orbit satellite signals in this embodiment is as follows:

[0022] Incomplete input tensor is obtained by measuring the received signal strength of the low-earth orbit satellite downlink through ground (fixed stations) or airborne (airborne / UAV) sensors deployed at pre-planned space sampling positions; its form is that the three-dimensional grid is divided into I , J , K nodes in the longitude, latitude, and altitude directions respectively, then .

[0023]

[0024] Among them, represents the received power (unit: dBm) of the i, j, k-th node, and the set represents the index set of the observed measurement values; For nodes outside, sensors have not been deployed, and their signal values are recorded as missing in the incomplete tensor and need to be estimated through subsequent completion / reconstruction algorithms. represents the orthogonal projection acting on the set .

[0025] Figure 3 , Figure 4 The performance of Neural TD in reconstructing 3D RM is demonstrated by visualizing the reconstruction results of different two-dimensional sections. Compared with the advanced tensor completion baseline, Neural TD can still construct a more realistic and reliable radio map even in the case of sparse sensor deployment (missing rate of 0.98) and even when the signal is affected by strong shadows. Baseline algorithms such as Kriging almost lose all Received Signal Strength (RSS) information. Although KBR-TC and Tmac can recover some covered areas, their distributions are inaccurate and the noise is obvious. In contrast, Neural TD performs excellently, accurately reconstructing the fine-grained RSS distribution, high-intensity information, and covered areas, which highly match the true values, proving its efficiency and robustness in sparse data and complex environments.

[0026] The above embodiments are only illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A method for constructing a three-dimensional radio map for low-earth orbit satellite signals, characterized in that, Including the following steps: S1: Obtain an incomplete input tensor including observed measurement values ; S2: Represent the 3D radio map to be constructed as a combination of a core tensor and factor matrices, represent each factor matrix as a neural network function and input variables; and construct an objective function for representing the loss between the 3D radio map under construction and the incomplete input tensor between ; S3: Perform rounds of iteration, and in each round of iteration: successively calculate the objective function with respect to each factor matrix and the core tensor gradients, and use the gradients to update the factor matrix and the core tensor ; S4: According to the factor matrix and the core tensor after the next update, calculate the complete tensor representation of the three-dimensional radio map .

2. A method for constructing a three-dimensional radio map for low-earth orbit satellite signals according to claim 1, characterized in that, Obtaining an incomplete input tensor The process includes: measuring the received signal strength of the downlink of a low-earth orbit satellite through ground or aerial sensors deployed at pre-planned spatial sampling positions; the incomplete input tensor is in the form that a three-dimensional grid is divided into I , J , K nodes in the longitude, latitude, and altitude directions respectively, then ; where: ； wherein represents the received power of the i, j, k-th node, and the set Ω represents the index set of the observed measurement values; represents the orthogonal projection onto the set Ω.

3. A three-dimensional radio map construction method for low-earth orbit satellite signals according to claim 2, characterized in that Objective function The expression of which is as follows: ； Wherein: is the Frobenius norm; is a neural network fitting function; is an input variable to be optimized; represents the modal product between tensors and matrices.

4. A method for constructing a three-dimensional radio map for low-earth orbit satellite signals according to claim 3, wherein The factor matrix is , , and the neural network fitting function includes two fully connected layers and an activation function ; the activation function is a sine activation function.

5. A method for constructing a three-dimensional radio map for low-earth orbit satellite signals according to claim 4, characterized in that, During the update process of the input components and the core tensor using the gradient, the Adam optimizer is used for the update, and regularization is achieved by means of weight decay. During the update process of the input components and the core tensor using the gradient, the Adam optimizer is used for the update, and regularization is achieved by means of weight decay.

6. A method for constructing a three-dimensional radio map for low-earth orbit satellite signals according to claim 4, characterized in that, In step S4, calculate the complete tensor representation of the three-dimensional radio map The expression for this is: ； Wherein: is the factor matrix after T updates, , is the core tensor after T updates.

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