A time-modulation-based single-channel orbital angular momentum mode spectrum estimation method

Abstract

The application discloses a kind of single-channel track angular momentum modal spectrum estimation methods based on time modulation, comprising the following steps;Step 1: establish the OAM modal spectrum estimation mathematical model based on time modulation array, obtain modulation function;Step 2: single-channel signal is carried out digital filtering, and harmonic signal is obtained;Step 3: it is reconstructed to equivalent multi-channel receiving signal by least square method;Step 4: based on multi-channel receiving signal, the signal covariance matrix is calculated;Step 5: the eigenvalue decomposition of matrix is carried out to signal covariance matrix, and signal subspace and noise subspace are orthogonal;Step 6: modal spectrum function is constructed and modal search is carried out, high-resolution estimation is realized;Step 7: the amplitude of each modal spectrum is calculated, and the final result is the energy distribution of the carrying modal spectrum of target signal.The application has the characteristics of high resolution, low hardware complexity, without array special structure, can simultaneously estimate any type of multi-modal OAM wave.

Description

Technical Field

[0001] This invention belongs to the field of single-channel orbital angular momentum mode spectrum estimation technology, specifically relating to a time-modulated single-channel orbital angular momentum mode spectrum estimation method. Background Technology

[0002] Electromagnetic waves carrying orbital angular momentum (OAM) are called vortex electromagnetic waves, and their different modes exhibit orthogonality. Orbital angular momentum modes constitute another independent dimension of electromagnetic waves besides frequency and polarization, thus showing significant application prospects in improving wireless communication capacity, enhancing anti-interference capabilities, realizing secure communication, and improving radar detection and imaging performance, and are increasingly becoming a research hotspot both domestically and internationally.

[0003] OAM mode spectrum estimation is a prerequisite for mode division multiplexing (MDM). Currently, methods for OAM mode spectrum estimation of vortex electromagnetic waves can be categorized into two types based on the sampling aperture size: full-aperture sampling and partial-aperture sampling. Full-aperture sampling ensures orthogonality between different OAM modes, and in this case, FFT-based OAM mode spectrum estimation performs well. Partial-aperture sampling, on the other hand, can reduce the number of sampling channels and, based on matrix equation solving or signal processing methods, can also achieve accurate OAM mode spectrum estimation.

[0004] A research team from the University of Glasgow in the UK mentioned in their paper "Angular diffraction" that there is a Fourier transform relationship between orbital angular momentum and modes. Therefore, the mode spectrum of OAM vortex waves can be estimated using Fourier transform under full aperture sampling.

[0005] In their paper "Enhanced Mode Measurement Method of Vortex Electromagnetic Wave with Partial Aperture Reception," Chen He et al. proposed a demodulation method for a novel mode measurement method with partial aperture reception, enabling the reception and demodulation of vortex electromagnetic waves with a smaller aperture. However, these OAM mode spectrum estimation methods all rely on multi-channel or multiple sampling sensors to sample the data.

[0006] Existing OAM mode estimation methods in the background art all rely on multiple channels or multiple sampling sensors to sample data, and there is no estimation method based on a single channel or a single sampling sensor. Summary of the Invention

[0007] To overcome the shortcomings of the existing technology, the present invention aims to provide a time-modulated single-channel orbital angular momentum mode spectrum estimation method. This method only requires one data sampling channel (sampling sensor) to accurately estimate the OAM mode spectrum carrying any number of modes. It has the characteristics of high resolution, low hardware complexity, no need for special array structure, and simultaneous estimation of any type of multimode OAM wave.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A time-modulated single-channel orbital angular momentum mode spectrum estimation method includes the following steps; Step 1: Establish a mathematical model for OAM mode spectrum estimation based on a 1-bit time modulation array, and obtain the periodic ON / OFF modulation function. The array manifold is obtained based on the spatiotemporal coding array form. This step forms the theoretical foundation of the entire method. It uses mathematical formulas to describe the radiation field of the time-modulated array, the timing switching functions of each element, and the mapping relationship between the received signal and the OAM mode. All subsequent steps rely on this model.

[0009] Step 2: Based on the modulation function Digital filtering is performed on single-channel signals carrying OAM. Since the signal generated by the time-modulated array contains multiple harmonic components in the spectrum, this step uses digital filters to separate the harmonics from the single-channel received signal. This step is crucial for achieving "obtaining multi-channel equivalent information using a single-channel RF link".

[0010] Step 3: Map the harmonic signal to a multi-channel signal carrying OAM corresponding to a 1-bit time modulation array; reconstruct the filtered harmonic components into an equivalent multi-channel signal using the least squares method. This step completes the transformation from the time dimension to the space dimension.

[0011] Step 4: Calculate the signal covariance matrix; This step transforms the original time / spatial sampling data into a compact statistical representation. The covariance matrix contains second-order statistical information about the signals, reflecting the correlation between different modes and the statistical characteristics of noise. This matrix is ​​the direct object of subsequent subspace decomposition. Without the covariance matrix, eigenvalue decomposition is impossible.

[0012] Step 5: Perform eigenvalue decomposition on the signal covariance matrix and construct orthogonal signal and noise subspaces to obtain orthogonal signal and noise subspaces; The core function of this step is to construct the signal subspace and the noise subspace, and to conclude that the signal subspace and the noise subspace are orthogonal, thus laying the foundation for subsequent high-resolution modal spectrum estimation.

[0013] Step 6: Based on the orthogonality of the signal subspace and the noise subspace, construct the modal spectrum function and perform mode search. Transform the orthogonality of the subspace into searchable spectral peaks. By performing MUSI spectral peak search on the range of OAM modes of interest, locate the peaks and obtain the estimated value of the incident OAM mode, thus achieving high-resolution estimation. The estimation result is the modal spectrum of the target signal. Step 7: Calculate the amplitude of each modal spectrum. The final result is the energy distribution of the OAM modal spectrum carried by the target signal. Step 7 is a quantitative supplement to the results of Step 6. Step 6 indicates "which modes exist" in the incoming signal, and Step 7 indicates "how strong the energy of each mode is." Only by combining the two can a complete modal spectrum estimation result be obtained.

[0014] Step 1 specifically involves: Suppose there is a 1-bit time modulation array, the 1-bit time modulation array consists of Array elements with arbitrary orientation are arranged in any form, and the coordinates of the array elements are... ( Each array element is followed by a 1-bit phase shifter, and the 1-bit time modulation array is combined to form an output signal; A transmitter with an aperture of The center coordinates are ; The transmitter has Same center frequency A narrowband spatial signal is incident orthogonally onto the receiver. Orthogonal incidence means that the propagation direction of the narrowband spatial signal is perpendicular to the plane where the receiving antenna array is located. Each signal carries an OAM mode. Let the th... The modes carried by each signal are ( If the noise is set to additive white Gaussian noise, then The mathematical model of the element time-modulated array is expressed as: in, for Array data vector, Let be the complex envelope vector of the signal. for Array noise vector.

[0015] The specific forms of the array data vector, the complex envelope vector of the signal, and the array noise vector are as follows: , , .

[0016] It is an array manifold, also known as an array steering matrix, which depends only on the shape of the array and the modes of the source signal; The specific form is Array guiding matrix (array manifold) any column vector It is an array that carries a signal source. The steering vector of a mode; for Column vectors, specifically in the form of: Among them, modality The magnitude of the guide vector for: Category 1 Bézier function of order, wavenumber , At the speed of light, Indicates transpose; for The modal vortex wave in the first The divergence angle at each array element.

[0017] and ; Modal Phase of the steering vector for: The modal vortex wave in the first The spatial azimuth angle at each array element is ;in, These are the coordinates of the nth element of a 1-bit time modulation array. These are the coordinates of the center of the transmitter.

[0018] For a 1-bit time modulation array, the received signal is then passed through a modulation function. Modulate and combine into a single-channel signal: in Modulation function The expression is: in, Indicates an amplitude of 1 and a phase of plural of. Modulation function The period number (or period count index). Represents the modulation period. This reflects the "on" time of phase 0.

[0019] Step 2 specifically involves: Due to the periodicity of the modulation function, It can be decomposed into Fourier series with different frequency components, and its expression is: Among them, the 1-bit phase shifter modulation frequency , Represents the Fourier expansion coefficients. For the first Second harmonic Indicates the receiving array number Each array element, Represents time, and the corresponding Fourier coefficients The expression is: Pick The modulation function vector is within the range of harmonics. Represented as: Where is the modulation function. The corresponding harmonic coefficient matrix Its expression is and The harmonic basis vectors within are ; Therefore, a single-channel signal is written as By filtering out each harmonic through a bandpass filter, each harmonic can be represented as: ; in Indicates harmonics, Indicates the first Second harmonics, of which .

[0020] Step 3 specifically involves: Harmonic signals With tradition Received signals of array element system The relationship is: when When the column is full, can be Recovery, in the sense of least squares, is represented as: in This indicates the conjugate transpose, where... , That is, the multi-channel signal obtained in step 3.

[0021] Step 4 specifically involves: Traditional in the sense of least squares Estimated value of the received signal of the array element system From the previous step, we can conclude that under additive white Gaussian noise background, the received signal... The covariance matrix is The covariance matrix of an ideal signal It is impossible to obtain the exact value. Based on the stationarity of the array signal, a finite number of snapshots are used in practice to estimate the covariance matrix. For a finite number of snapshots, the estimated value of the signal covariance matrix is... for: in, for The estimated value of a finite number of quicksort iterations. k Indicates the first Secondary sampling or rapid sorting of samples. It represents the total number of snapshots or the number of samples.

[0022] Step 5 specifically involves: The signal covariance matrix obtained by a finite number of quicksort operations It is a positive definite Hermitian matrix, which is diagonalized using unitary transformation, and its eigenvalue decomposition is: in, It is a diagonal matrix composed of eigenvalues. The matrix formed by the eigenvectors corresponding to the eigenvalues. This represents the conjugate transpose operation; All eigenvalues ​​are arranged in descending order, i.e. , and These are the large eigenvalues ​​and their corresponding eigenvectors. Representing the eigenvector The conjugate transpose of; and These are the small eigenvalues ​​and their corresponding eigenvectors. Representing the eigenvector The conjugate transpose of ; the subspace spanned by the eigenvectors corresponding to the large eigenvalues ​​is called the signal subspace, denoted as . The subspace spanned by the eigenvectors corresponding to small eigenvalues ​​is called the noise subspace, denoted as . ; According to signal processing principles, the signal subspace is equal to the subspace spanned by the signal steering vector, i.e. The signal subspace and the noise subspace are orthogonal, that is... .

[0023] Step 6 specifically involves: There are many criteria for modal search. For MUSIC (Multiple Signal Classification) spectral peak search, since the signal subspace is equal to the subspace spanned by the signal steering vector, and the signal subspace is orthogonal to the noise subspace, meaning the subspace spanned by the signal steering vector is perpendicular to the noise subspace, that is: That is to say Due to the orthogonality between the noise eigenvector and the signal steering vector, the modal spectrum function of the array can be obtained, i.e.: For modal spectrum The largest The independent variable corresponding to each value This refers to the modal spectrum to be estimated.

[0024] Step 7 specifically involves: Let the estimated value of the modal spectrum be... Then the estimated value of the array manifold in step 1 is: The signal model now becomes: in Given the measured data, under the condition of the least squares solution, the signal vector The estimated value is Then the estimated value of the signal vector The covariance matrix is: Using the diagonal elements as power estimates, the modal... The power amplitude is: ; Indicates the first The modes carried by each signal power, Indicates the first A wave signal. P This indicates the number of incoming wave signals. Represents the first of the matrix Okay, number The elements of the column.

[0025] The corresponding field strength amplitude is: ; in, Indicates the first The modes carried by each signal The range, Indicates the first A wave signal. P This indicates the number of incoming wave signals.

[0026] The beneficial effects of this invention are: 1. This invention provides a time-modulation-based single-channel orbital angular momentum mode spectrum estimation method. The method uses a time-modulation array at the receiver to "modulate" multi-channel information from the spatial domain onto multiple harmonic components in the time domain, thus requiring only one RF link. The equivalent multi-channel signal is then recovered through digital filtering. Therefore, this method only requires one sampling channel to estimate the multi-mode OAM spectrum. Compared to existing methods, this invention significantly reduces the number of sampling channels.

[0027] 2. This invention reconstructs multi-channel data from sampled single-channel data using digital filtering, and decomposes it into signal and noise subspaces. Since this invention recovers multi-channel data mathematically equivalently through "time modulation + single-channel sampling + digital reconstruction," the subsequent subspace processing is mathematically consistent with traditional multi-channel subspace algorithms. Therefore, the resolution and estimation accuracy (mean square error) of this invention's algorithm are comparable to those of traditional multi-channel subspace-based algorithms. Attached Figure Description

[0028] Figure 1 This is a flowchart of the technical solution of the present invention.

[0029] Figure 2 This invention provides a spatial distribution diagram of a rectangular aperture array.

[0030] Figure 3The time-modulated single-channel signal of this invention The amplitude, phase, and corresponding spectrum The amplitude and phase.

[0031] Figure 4 The simulation results are for the OAM modal spectrum estimation of this invention.

[0032] Figure 5 The mean square error (RMSE) of the modal amplitude under different signal-to-noise ratios (SNR) in this invention is given. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings.

[0034] Example: A time-modulated single-channel orbital angular momentum mode spectrum estimation method to achieve multi-mode demodulation of a rectangular aperture.

[0035] like Figure 1 As shown, the implementation steps of this example include the following: Step 1: Parameter Setting: Determine the operating frequency of the angular momentum mode conversion device for the incoming vortex wave trajectory in the simulation. The aperture of the transmission array With geometric center position Number of receiver arrays and the coordinates of the array elements are ( The number of OAM modes carried by the incoming wave. .

[0036] In this example, the total number of elements in the rectangular array ,in , These represent the number of array elements in the x and y directions, respectively. The position coordinates of the receiving array elements are determined by the following formula. in, λ is the wavelength.

[0037] Step 2: Generate the signal envelope: Assume the signal sampling rate is... The intermediate frequency is The number of samples in quicksort is ,but The intermediate frequency signal of each signal is In this example , .

[0038] Step 3: Set the signal-to-noise ratio and generate noise: The signal-to-noise ratio of each signal is If the noise is random Gaussian white noise, then... randn represents Gaussian white noise. The noise is standardized. std represents calculating the standard deviation.

[0039] Step 4: Set up the signal model: Assume the simulated true mode of the incoming wave is Then the modal guidance matrix The element in the nth row and pth column is in, , .

[0040] Step 5: Data Generation: Based on steps 2, 3, and 4, the final number of samples in the simulation is... Step 6: Time Encoding: The modulation frequency of the 1-bit phase shifter is... The corresponding modulation function The expression is in , .

[0041] Single-channel signal Step 7: Harmonic Digital Filtering: The expression for the low-pass filter is... in Round down to the nearest integer. The center frequency of the intermediate frequency is... Then the first one after the filter The expression for the subharmonic is: in This indicates that a Fourier transform is performed on the function. This indicates performing the inverse Fourier transform on the function. Here... The value is 20.

[0042] Step 8: Calculation matrix: The matrix elements in the matrix are The harmonic signal is recovered into a multi-channel signal corresponding to a 1-bit time modulation array: the estimated value of the multi-channel signal is... in This indicates the conjugate transpose. .

[0043] Step 10: Calculate the covariance matrix: The estimated value of the corresponding signal covariance matrix is... Step 11: Eigendecomposition: For positive definite Hermitian matrices Diagonalization is achieved using unitary transformation, and its eigenvalues ​​are decomposed into... in, It is a diagonal matrix composed of eigenvalues. This is a matrix consisting of the eigenvectors corresponding to the eigenvalues. All eigenvalues ​​are arranged in descending order. The subspace spanned by the eigenvectors corresponding to the smallest eigenvalues ​​is . .

[0044] Number of OAM modes in this example The number is 3. It is 36.

[0045] Step 12: Modal Search: For the obtained modal spectrum function of the array, i.e. Perform integer traversal; in this example, the traversal range is... Modal spectrum The three largest values ​​correspond to the independent variables This refers to the modal spectrum to be estimated.

[0046] Step 13: Calculate the amplitude of each modal spectrum: the estimated value of the modal spectrum is... ,according to The covariance matrix of the signal can be calculated. The subscript element is used as the amplitude estimate, i.e., the mode shape. The amplitude is The technical effects of the present invention will be further explained below in conjunction with simulation experiments and analysis of experimental results.

[0047] The embodiments were simulated using MATLAB software. For ease of explanation, the proposed algorithm is denoted as TMA (Time-Modulated Array TMA), and the algorithm using the multi-channel estimation method is denoted as MCA (Multi-Channel array MCA).

[0048] The sampling aperture of the array in the embodiment is as follows: Figure 2As shown, the black dots represent sampling sensors. In this embodiment, the 36 sampling sensors form a 6×6 square array, and their spatial distribution coordinates are as follows: Figure 2 As shown. The single-channel signal after time modulation. The amplitude, phase, and corresponding spectrum amplitude, phase, such as Figure 3 As shown. Regarding the spectrum. After filtering, the equivalent multi-channel data can be reconstructed using least squares. Simulation results for multimodal estimation are as follows: Figure 4 As shown, the search is performed within the modal range of -20 to +20. The three modes with the highest spectral energy are the estimated modes.

[0049] The actual OAM modes in the incoming signal are +1, +2, and +4. The TMA algorithm estimates the number of modes as +1, +2, and +4, while the MCA algorithm also estimates the number of modes as +1, +2, and +4. This demonstrates that the single-channel OAM mode spectrum estimation algorithm based on the time modulation array can achieve the same estimation results as the traditional multi-channel algorithm.

[0050] Furthermore, the mean square error of the amplitude of OAM estimation is calculated under different signal-to-noise ratios (SNR). The mean square error (RMSE) is defined as follows: Among them, the number of OAM incoming wave sources The number of Monte Carlo experiments was 100. , Indicates the first In this experiment The magnitude estimate. The corresponding results are as follows: Figure 5 As shown, it can be seen that the single-channel algorithm based on TMA and the MCA algorithm based on multi-channel have the same accuracy error.

[0051] The simulation results show that the single-channel algorithm based on TMA performs roughly the same as the multi-channel MCA algorithm in terms of OAM mode spectrum estimation performance. Therefore, the algorithm of this invention only requires one channel to estimate the orbital angular momentum mode spectrum of vortex waves.

Claims

1. A method for estimating the single-channel orbital angular momentum modal spectrum based on time modulation, characterized in that, Includes the following steps; Step 1: Establish a mathematical model for OAM mode spectrum estimation based on a 1-bit time modulation array, and obtain the periodic ON / OFF modulation function. ; Step 2: Based on the modulation function Digital filtering is performed on the single-channel signal carrying OAM to obtain the harmonic signal; Step 3: Map the harmonic signal to the multi-channel signal carrying OAM corresponding to the 1-bit time modulation array; reconstruct the filtered harmonic components into equivalent multi-channel signals using the least squares method. Step 4: Calculate the signal covariance matrix based on the multi-channel received signal; Step 5: Perform eigenvalue decomposition on the signal covariance matrix and construct orthogonal signal and noise subspaces; Step 6: Based on the orthogonality of the signal subspace and the noise subspace, construct the modal spectrum function and perform mode search. Transform the orthogonality of the subspace into searchable spectral peaks. By performing MUSI spectral peak search on the range of OAM modes of interest, locate the peaks and obtain the estimated value of the incident OAM mode, thus achieving high-resolution estimation. The estimation result is the modal spectrum of the target signal. Step 7: Calculate the amplitude of each modal spectrum. The final result is the energy distribution of the OAM modal spectrum carried by the target signal.

2. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 1, characterized in that, The mathematical model for OAM modal spectrum estimation in step 1 includes: A 1-bit time modulation array, the 1-bit time modulation array consists of Array elements with arbitrary orientation are arranged in any form, and the coordinates of the array elements are... ( Each array element is followed by a 1-bit phase shifter, and the 1-bit time modulation array is combined to form an output signal; A transmitter with an aperture of The center coordinates are ; The transmitter has Same center frequency A narrowband spatial signal is incident orthogonally onto the receiver. Orthogonal incidence means that the propagation direction of the narrowband spatial signal is perpendicular to the plane where the receiving antenna array is located. Each signal carries an OAM mode. Let the th... The modes carried by each signal are ( If the noise is set to additive white Gaussian noise, then The mathematical model of the element time-modulated array is expressed as: in, for Array data vector, Let be the complex envelope vector of the signal. for Array noise vector, It is an array manifold.

3. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 2, characterized in that, The specific forms of the array data vector, the complex envelope vector of the signal, and the array noise vector are as follows: ， ， ； The specific form is any one of the column vectors It is an array that carries a signal source. The steering vector of a mode; for Column vectors, specifically in the form of: Among them, modality The magnitude of the guide vector for: Category 1 Bézier function of order, wavenumber , At the speed of light, Indicates transpose; for The modal vortex wave in the first The divergence angle at each array element; and ; Modal Phase of the steering vector for: The modal vortex wave in the first The spatial azimuth angle at each array element is ;in, These are the coordinates of the nth element of a 1-bit time modulation array.

4. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 3, characterized in that, For a 1-bit time modulation array, the received signal is then passed through a modulation function. Modulate and combine into a single-channel signal: in Modulation function The expression is: in, Indicates an amplitude of 1 and a phase of plural, Modulation function The period number, Represents the modulation period. Reflects the "on" time of phase 0.

5. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 4, characterized in that, Step 2 specifically involves: Due to the periodicity of the modulation function, It can be decomposed into Fourier series with different frequency components, and its expression is: Among them, the 1-bit phase shifter modulation frequency , Represents the Fourier expansion coefficients. For the first Second harmonic Indicates the receiving array number Each array element, Represents time, and the corresponding Fourier coefficients The expression is: Pick The modulation function vector is within the range of harmonics. Represented as: Where is the modulation function. The corresponding harmonic coefficient matrix Its expression is: and The harmonic basis vectors within are ; Therefore, a single-channel signal is written as: By filtering out each harmonic through bandpass filtering, the harmonic vectors can be expressed as follows: ； in Indicates harmonics, Indicates the first Second harmonics, of which .

6. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 5, characterized in that, Step 3 specifically involves: Harmonic signals With tradition Received signals of array element system The relationship is: when When the column is full, can be Recovery, in the sense of least squares, of the estimated value of the received signal. Represented as: in This indicates the conjugate transpose, where... , That is, the multi-channel signal obtained in step 3.

7. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 6, characterized in that, Step 4 specifically involves: Traditional in the sense of least squares Estimated value of the received signal of the array element system From the previous step, we can derive the estimated value of the received signal against the background of additive white Gaussian noise. The covariance matrix is Based on the stationarity of the array signal, a finite number of snapshots are used in practice to estimate the covariance matrix. For a finite number of snapshots, the estimated value of the signal covariance matrix is... for: in, for The estimated value of a finite number of quicksort iterations. k Indicates the first Secondary sampling or rapid sorting of samples It represents the total number of snapshots or the number of samples.

8. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 7, characterized in that, Step 5 specifically involves: The signal covariance matrix obtained by a finite number of quicksort operations Diagonalization is achieved using unitary transformation, and its eigenvalue decomposition is as follows: in, It is a diagonal matrix composed of eigenvalues. The matrix formed by the eigenvectors corresponding to the eigenvalues. This represents the conjugate transpose operation; All eigenvalues ​​are arranged in descending order, i.e. , and These are the large eigenvalues ​​and their corresponding eigenvectors. Representing the eigenvector The conjugate transpose of; and These are the small eigenvalues ​​and their corresponding eigenvectors. Representing the eigenvector The conjugate transpose of ; the subspace spanned by the eigenvectors corresponding to the large eigenvalues ​​is called the signal subspace, denoted as . The subspace spanned by the eigenvectors corresponding to small eigenvalues ​​is called the noise subspace, denoted as . ; According to signal processing knowledge, the signal subspace is equal to the subspace spanned by the signal steering vector, that is: The signal subspace and the noise subspace are orthogonal, that is: 。 9. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 8, characterized in that, Step 6 specifically involves: For MUSIC spectrum peak search, the subspace spanned by the signal steering vector is perpendicular to the noise subspace, i.e.: That is: Due to the orthogonality between the noise eigenvector and the signal steering vector, the modal spectrum function of the array can be obtained, i.e.: For modal spectrum The largest The independent variable corresponding to each value This refers to the modal spectrum to be estimated.

10. The method for estimating the single-channel orbital angular momentum mode spectrum based on time modulation according to claim 9, characterized in that, Step 7 specifically involves: Let the estimated value of the modal spectrum be... Then the corresponding array manifold in step 1 The estimated value is Specifically: The signal model now becomes: in Given the measured data, under the condition of the least squares solution, the signal vector The estimated value is: Then the estimated value of the signal vector The covariance matrix is: Using the diagonal elements as power estimates, the modal... The power amplitude is: ； Indicates the first The modes carried by each signal power, Indicates the first A wave signal. P This indicates the number of incoming wave signals. Represents the first of the matrix Okay, number Column elements; The corresponding field strength amplitude is: ； in, Indicates the first The modes carried by each signal The range, Indicates the first A wave signal. P This indicates the number of incoming wave signals.

Images