Broadband spectrum reconstruction method and system for low earth orbit satellite signals

Abstract

The invention discloses a broadband spectrum reconstruction method and system for low-orbit satellite signals, and the method comprises the steps: S1, carrying out the sampling of the low-orbit satellite signals through multi-coset compression sampling, and obtaining the sampling data; s2, performing fast Fourier transform on the sampled data to obtain a measured value matrix; and S3, reconstructing the input signal # imgabs2 # according to the measured value matrix # imgabs0 # and the sensing matrix # imgabs1 # by adopting a neural compressed sensing method, and taking the reconstructed input signal # imgabs3 # as the broadband frequency spectrum of the low-orbit satellite signal. According to the method, more accurate spectrum reconstruction can be realized; and the method also has relatively high performance in a scene with limited samples. According to the method, multi-coset compression sampling is adopted, so that the cost of signal acquisition equipment can be reduced.

Description

Technical Field

[0001] The present invention relates to the field of satellite communication technologies, and particularly to a broadband spectrum reconstruction method and system 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, showing 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). The scarcity of spectrum resources makes efficient spectrum management an urgent need. However, in the spectrum allocation scenario of SAGIN, when NTNs are the primary users and preferentially use the spectrum, while TNs are the secondary users and are dynamically allocated, challenges will be faced: LEO networks usually use large-bandwidth spectra. For example, Starlink operates in the Ku band from 10.7 GHz to 12.7 GHz, which requires sensors to be equipped with high-speed analog-to-digital converters (ADCs) to sense broadband radio frequency (RF) signals. However, high-speed ADCs are not only costly but also significantly increase energy consumption and system complexity, restricting the popularization and large-scale deployment of the technology on resource-constrained satellite platforms. Especially in LEO satellite networks, due to the satellites moving at speeds of up to 7-8 km / s, the network topology changes dynamically, and the spectrum environment changes rapidly, posing extremely high requirements for the real-time and accuracy of spectrum sensing. Traditional spectrum sensing technologies often rely on high sampling rates when dealing with large-bandwidth signals, resulting in a sharp increase in data volume and a significant increase in computational complexity, making it difficult to be efficiently implemented on satellites with limited hardware resources. Therefore, the reconstruction of large broadband spectra has become a core problem, and its solution is crucial for achieving efficient spectrum sharing, interference management, and resource optimization.

[0003] Therefore, there is an urgent need for a technology that can achieve wideband spectrum sensing and reconstruction under low sampling rate conditions. This technology can not only significantly reduce the dependence on high-speed ADCs, thereby reducing hardware costs and energy consumption, but also lighten the data processing burden and improve the efficiency and real-time performance of spectrum monitoring. By accurately reconstructing a large wideband spectrum at a low sampling rate, it can provide reliable support for the dynamic spectrum allocation in SAGIN and facilitate the wide application and development of LEO networks in global communication. Summary of the Invention

[0004] In view of the technical problem of high hardware costs faced by large bandwidth spectrum monitoring in LEO satellite networks, the present invention proposes a wideband spectrum reconstruction method and system for LEO satellite signals. This method uses the Neural Compressive Sensing (NCS) technology based on deep unsupervised learning to transform the spectrum sensing problem into an optimization problem of deep neural networks (NNs). The present invention makes full use of the non-linear fitting ability and signal sparsity of NNs to achieve high-precision wideband spectrum reconstruction under low sampling rate conditions.

[0005] To achieve the above object, the present invention provides a wideband spectrum reconstruction method for LEO satellite signals, which includes: S1: Sampling the LEO satellite signal using multi-coset compressive sampling to obtain sampling data; S2: Performing a fast Fourier transform on the sampling data to obtain a measurement value matrix; S3: Using the neural compressive sensing method, according to the measurement value matrix and the sensing matrix to reconstruct the input signal and taking the reconstructed input signal as the wideband spectrum of the LEO satellite signal.

[0006] A further improvement of the present invention is that the sampling device used in the multi-coset compressive sampling process includes parallel branches; each parallel branch includes a delay unit and a low sampling rate analog-to-digital converter; the sampling frequencies of each parallel branch are the same, all being ; the delay time of the delay unit of each parallel branch increases by compared with the previous parallel branch.

[0007] A further improvement of the present invention is that in the neural compressive sensing method, the input signal is expressed as:

[0008] where: denotes a neural network; is a learnable input variable.

[0009] A further improvement of the present invention is that the neural network comprises 4 fully connected layers and two sin activation functions; where: starting from the input in sequence are the first fully connected layer, the first sin activation function, the second fully connected layer, the second sin activation function, the output of the second sin activation function is the input of the third fully connected layer and the fourth fully connected layer; the outputs of the third fully connected layer and the fourth fully connected layer are respectively used as the real part and the imaginary part of the input signal of.

[0010] A further improvement of the present invention is that the iterative optimization process includes times of joint optimization process and times of reconstruction optimization process; In the joint optimization process, jointly minimize the reconstruction and sparsity losses as the compressive sensing loss, and perform joint optimization on the neural network and the learnable input variable; In the reconstruction optimization process, minimize the reconstruction loss, and perform reconstruction optimization on the neural network and the learnable input variable.

[0011] A further improvement of the present invention is that each joint optimization process includes the following steps: S301: Calculate the predicted value of the input signal , and the expression is:

[0012] where the superscript represents the number of times of the joint optimization process; S302: Jointly minimize the reconstruction and sparsity losses as the joint loss , and its expression is:

[0013] where: λ is a regularization parameter; represents the number of non-zero rows in the matrix; is the Frobenius norm, representing the error between the measured value and the reconstructed value; S303: Calculate the gradients and , and update the neural network and the learnable input variable for

[0014]

[0015] Wherein: represents the learning rate, and is the gradient-based direction; represents the neural network .

[0016] A further improvement of the present invention lies in that each reconstruction optimization process includes the following steps: S311: Calculate the predicted value of the input signal , and the expression is:

[0017] Where the superscript represents the number of times of the reconstruction optimization process; S312: Calculate the reconstruction loss , and its expression is:

[0018] Wherein: is the Frobenius norm, representing the error between the measured value and the reconstructed value; S313: Calculate the gradients and , and update the neural network and the learnable input variables as follows:

[0019]

[0020] Wherein: represents the learning rate, and is the gradient-based direction; represents the neural network .

[0021] A broadband spectrum reconstruction system for low-earth orbit satellite signals, used to implement the above-mentioned broadband spectrum reconstruction method for low-earth orbit satellite signals, includes: A sampling device for performing multi-coset compressive sampling on low-earth orbit satellite signals to obtain sampling data; A signal processing unit that reconstructs the broadband spectrum of low-earth orbit satellite signals using the neural compressive sensing method.

[0022] The beneficial effects of the present invention include: This method can achieve more accurate spectrum reconstruction; it also has high performance in scenarios with limited samples. This method uses multi-coset compressive sampling, which can reduce the cost of signal acquisition equipment. Description of the Drawings

[0023] Figure 1 It is a schematic diagram of multi-coset compressive sampling; Figure 2 It is the neural network structure Figure 3 and Figure 4 They are respectively the performance displays of the neural compressive sensing bandwidth spectrum reconstruction in this embodiment. Specific Embodiments

[0024] The following uses specific specific examples to illustrate the implementation manners of the present invention. 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 implementation manners. The details in this specification can also be variously 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.

[0025] As Figure 1 shown, in this embodiment, multi-coset compressive sampling is used to sample the low-earth orbit satellite signal to obtain sampling data. The purpose of multi-coset compressive sampling (MCS) is: due to hardware limitations, sensors are limited by the sub-Nyquist sampling rate when sampling wideband signals. Multi-coset sampling (Multi-coset Sampling, MCS) is a sub-Nyquist sampling technique that uses multiple parallel branches, and each branch contains a delay unit and a low-sampling-rate analog-to-digital converter (ADC). This method achieves compressive sampling through different combinations of delays and reduced sampling rates. Due to its feasibility and easy-to-understand implementation method, MCS is widely selected for low-cost wideband signal sampling.

[0026] As Figure 1 shown, is an original signal band-limited within the frequency range , where represents the highest frequency of the band-limited signal. The Nyquist sampling interval is denoted as . In the MCS method, the signal is sampled in parallel by ADCs, and the sampling interval of each ADC is , where is a constant representing the ratio of the ADC sampling interval to the Nyquist sampling interval. Each ADC is configured with a unique delay time. Therefore, the The sampling sequence of each ADC is expressed as: (1) in Express satisfaction and A non-negative integer, Indicates the number of sampled data for each ADC. In this process, each parallel branch samples in turn, and the delay time of each parallel branch increases by 1% relative to the delay unit of the previous parallel branch. .

[0027] By applying a Fast Fourier Transform (FFT) to the sampled data, the MCS process follows a specific measurement procedure: (2) in, is the measurement value matrix, which is in the form of:

[0028] is the perception matrix, whose elements are defined as: (4) Corresponding to the signal The discrete version of the Discrete Fourier Transform (DFT) contains LN points, whose elements are: (5) Additive noise, caused by various factors such as channel noise and internal thermal noise of the receiver equipment. In a wideband spectrum, narrowband signals occupy only a limited number of subbands, so It has row sparsity, that is, only a small number of rows (corresponding to sub-band spectra) are non-zero. The goal of the neural compressed sensing method (CS) used in this embodiment is to solve the underdetermined equation To recover .

[0029] Since the perception matrix Satisfies the Restricted Isometric Property (RIP), and the broadband signal spectrum has block sparsity, It can be recovered by solving the following convex optimization problem: (6) in, Representation matrix The number of non-zero rows is used to enforce sparsity. is the Frobenius norm, representing the error between the measured value and the reconstructed value. represents the bound of the noise power. The unconstrained equivalent form of this constrained optimization problem is: (7) where is a regularization parameter used to balance the reconstruction error and sparsity.

[0030] In the specific implementation process, the broadband spectrum reconstruction method for low-earth orbit satellite signals of the present invention includes the following steps:

[0031] Compared with directly optimizing the variables in formula (7) , in this embodiment, the optimization variable is represented as , where represents a neural network. [[ID=Q27]]The input of is a learnable input variable , which is initialized as a random variable obeying the normal distribution The structure of Figure 2 is shown as follows, including 4 fully connected layers (FC) and two sin activation functions. Starting from the input, they are the first fully connected layer, the first sin activation function, the second fully connected layer, and the second sin activation function in sequence; the output of the second sin activation function is the input of the third fully connected layer and the fourth fully connected layer; the outputs of the third fully connected layer and the fourth fully connected layer are respectively used as the real part and the imaginary part of the input signal .

[0032] Specifically, the output of the th sin activation function is defined as: (8) where is a learnable weight matrix, is the initial input of the neural network, is the bias vector, is the non-linear activation function (in this embodiment, it is the sin activation function). Since the optimization variable is a complex matrix, the last layer of the neural network is designed to branch into the real part and the imaginary part, and generate the final complex output through the Complex (Real, Imag) operation. In this way, the CS optimization problem can be transformed into the optimization problem of the following loss function: (9) Among them, is a regularization parameter. By using iterative backpropagation of gradient descent, the optimal variable can be found in the non-linear space. We use the popular gradient evaluation tool autograd in Pytorch to calculate the gradient and . The parameters of and the input variable are updated in the t = 1, 2,... iterations, and the update rule is shown as follows: (10) (11) Among them, represents the learning rate, which is used to balance the convergence speed and stability. and are gradient-based directions, which are used to guide the parameter update and are calculated by the Adam optimizer according to and .

[0033] To accurately reconstruct the sparse signal , the model must adapt to the data structure while enforcing the sparsity constraint. To balance sparsity and reconstruction performance, we propose a two-stage optimization method, as detailed in Algorithm 1. In the first stage, we jointly minimize the reconstruction and sparsity losses to initialize the model and the input variable. In the second stage, we further optimize these parameters, focusing only on minimizing the reconstruction loss to improve the performance.

[0034] Figure 3 and Figure 4 respectively show the performance of NCS in solving the compressive sensing problem when the number of sampling channels P is 14 and 10. From the visualization of the spectrum reconstruction results, it can be seen that even at 7 / 20 of the Nyquist rate (P = 14), NCS can achieve more accurate spectrum reconstruction compared with the PCSBL algorithm based on Bayesian learning and the SOMP algorithm based on greedy pursuit. In addition, when the sampling rate is 1 / 4 of the Nyquist rate (P = 10), NCS is significantly better than other baseline algorithms, further demonstrating its competitiveness in scenarios with limited samples.

[0035] The above embodiments only illustratively explain the principles and effects of the present invention, rather than limiting 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 completed by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A broadband spectrum reconstruction method for low-earth orbit satellite signals, characterized in that, Including: S1: Sampling the LEO satellite signal using multi-coset compressive sampling to obtain sampling data; S2: Performing a fast Fourier transform on the sampling data to obtain a measurement value matrix; S3: Apply the neural compressive sensing method to reconstruct the input signal based on the measurement matrix and the sensing matrix and use the reconstructed input signal as the broadband spectrum of the low-earth orbit satellite signal. ​ 2. The broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 1, wherein The sampling device used in the multi-coset compressive sampling process includes parallel branches; each parallel branch includes a delay unit and a low-sampling-rate analog-to-digital converter; The sampling frequencies of all parallel branches are the same, both being ; the delay time of the delay unit of each parallel branch increases with respect to the previous parallel branch by .

3. A broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 1, characterized in that In the neural compressive sensing method, the input signal is expressed as: ； Wherein: represents a neural network; is a learnable input variable.

4. A broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 3, characterized in that, The neural network comprises four fully connected layers and two sine activation functions; wherein: starting from the input, they are in sequence the first fully connected layer, the first sine activation function, the second fully connected layer, the second sine activation function, the output of the second sine activation function is the input of the third fully connected layer and the fourth fully connected layer; the outputs of the third fully connected layer and the fourth fully connected layer are respectively used as the real part and the imaginary part of the input signal.

5. A broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 3, characterized in that, The iterative optimization process includes times of joint optimization processes and times of reconstruction optimization processes; During the joint optimization process, jointly minimize the reconstruction and sparsity losses as the compressive sensing loss for the neural network and the learnable input variables for joint optimization; The reconstruction optimization process minimizes the reconstruction loss for the neural network and the learnable input variables to perform reconstruction optimization.

6. A broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 5, characterized in that, Each joint optimization process includes the following steps: S301: Calculate the predicted value of the input signal using the following expression: ； where the superscript represents the number of times of the joint optimization process; S302: Minimize the reconstruction and sparsity losses jointly as the joint loss , and its expression is: ； where: λ is a regularization parameter; represents the number of non-zero rows in the matrix; is the Frobenius norm, representing the error between the measured value and the reconstructed value; S303: Calculate the gradient and , and update the neural network and the learnable input variables for updating ； ； Wherein: represents the learning rate, and is the direction based on the gradient.

7. A broadband spectrum reconstruction method for low-earth orbit satellite signals according to claim 5, characterized in that Each reconstruction optimization process includes the following steps: S311: Calculate the predicted value of the input signal with the following expression: ； where the superscript indicates the number of reconstruction optimization processes; S312: Calculate the reconstruction loss , and its expression is: ； Wherein: is the Frobenius norm, representing the error between the measured value and the reconstructed value; S313: Calculate the gradient and , and update the neural network and the learnable input variables as follows: ； ； Wherein: represents the learning rate, and is the direction based on the gradient.

8. A broadband spectrum reconstruction system for low-earth orbit satellite signals, which is used to implement the broadband spectrum reconstruction method for low-earth orbit satellite signals according to any one of claims 1 to 7, characterized in that Including: A sampling device for performing multi-coset compressive sampling on the LEO satellite signal to obtain sampling data; A signal processing unit that reconstructs the broadband spectrum of the LEO satellite signal using the neural compressive sensing method.

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