Vortex electromagnetic wave transmitting method based on frequency-mode multiplexing and imaging method thereof

Abstract

This application relates to the field of electromagnetic wave imaging technology, specifically to a vortex electromagnetic wave transmission method and imaging method based on frequency-mode multiplexing, comprising the following steps: S1: generating multiple subcarrier signals and combining the subcarrier signals into an OFDM signal; S2: constructing a vortex electromagnetic wave transmission module at the origin, the vortex electromagnetic wave transmission module including several electromagnetic wave transmission units arranged in a circular array; S3: generating several distinct time delay constants, the number of time delay constants being equal to the number of electromagnetic wave transmission units; S4: using the time delay constants as the time delay of the OFDM signal to generate a delayed OFDM signal equal to the number of electromagnetic wave transmission units; This invention achieves simultaneous radiation of vortex electromagnetic waves containing multiple random composite OAM modes by generating random OFDM signals and applying distinct time delays that increase along the circumferential direction to each transmission unit of the circular array.

Description

Technical Field

[0001] This application relates to the field of electromagnetic wave imaging technology, and more specifically, to a vortex electromagnetic wave emission method and imaging method based on frequency-mode multiplexing. Background Technology

[0002] This section provides background information relevant to this application and may not constitute prior art. Vortex Electromagnetic Wave (VEMW) is a special type of electromagnetic beam carrying orbital angular momentum (OAM). Its wavefront exhibits a helical phase distribution in space, with a phase singularity at its center. Unlike traditional plane waves, vortex electromagnetic waves introduce degrees of freedom in the spatial domain. Their OAM modes are quantized using topological charge numbers (usually represented by the integer l), and beams of different modes possess natural orthogonality in the azimuth direction. Utilizing this characteristic, VEMW radar can directly analyze the azimuth scattering distribution of a target by transmitting and receiving signals of different modes, without relying on the relative motion between the radar and the target (such as synthetic aperture SAR / inverse synthetic aperture ISAR), thus demonstrating enormous application potential in the field of radar imaging.

[0003] In existing VEMW imaging technology systems, the signal transmitter typically uses a uniform circular array (UCA) as its hardware foundation, synthesizing vortex beams of specific modes by applying specific phase gradients to the array elements. However, limited by the beamforming mechanism of traditional phased arrays, current mainstream technologies generally employ an inter-pulse serial mode scanning mechanism. Under this mechanism, the radar system cannot radiate a composite beam containing multiple orthogonal modes simultaneously. Instead, it must employ a time division multiplexing (TDM) strategy, dynamically reconstructing the array's phase configuration between consecutive pulse transmission cycles (PRI) through electronic phase shifters or a feed network, ensuring that each independent transmission pulse can only carry a single specific OAM mode. For example, the system needs to transmit mode l=1 in the first time window, switch to and stabilize to mode l=2 in the second time window, and so on, gradually accumulating the modal domain data required for imaging through a time-for-space strategy.

[0004] The aforementioned imaging method based on inter-pulse serial switching suffers from significant technical bottlenecks. Since each transmitted pulse can only acquire observation information for a single OAM mode, to construct a target image with high azimuth resolution, the radar system must transmit at least N independent pulses to traverse N different OAM modes. This serial scanning method causes the acquisition period for all modes to increase linearly with the number of modes, greatly extending the beam's dwell time in the target area. This not only leads to low radar data acquisition efficiency, severely limiting the imaging frame rate, but also, when facing high-speed moving targets or rapidly changing dynamic scenes, the excessively long data acquisition time can cause time decorrelation effects caused by target motion between different mode echoes, resulting in imaging defocusing or reconstruction distortion. Summary of the Invention

[0005] The summary section of this application is intended to provide a brief overview of the concepts, which will be described in detail in the detailed description section below. This summary section is not intended to identify key or essential features of the claimed technical solutions, nor is it intended to limit the scope of the claimed technical solutions.

[0006] Some embodiments of this application propose a method to solve the technical problems mentioned in the background section above.

[0007] As a first aspect of this application, some embodiments of this application provide a vortex electromagnetic wave transmission method based on frequency-mode multiplexing, comprising the following steps: S1: Generate multiple subcarrier signals and combine them into an OFDM signal; S2: Construct a vortex electromagnetic wave transmitting module at the origin. The vortex electromagnetic wave transmitting module includes several electromagnetic wave transmitting units arranged in a circular array. S3: Generate several distinct time delay constants, the number of which is equal to the number of electromagnetic wave transmitting units; S4: Use the time delay constant as the time delay of the OFDM signal to generate a delayed OFDM signal with the same number of electromagnetic wave transmitting units; S5: SF modulate the delayed OFDM signal to generate an electromagnetic excitation signal equal to the number of electromagnetic wave transmitting units; S6: The electromagnetic wave excitation signals are loaded onto the electromagnetic wave emitting unit, and each electromagnetic wave emitting unit emits imaging electromagnetic waves to generate a radiation field at the far field point. Along the circumferential direction, the time delay of each electromagnetic wave emitting unit gradually increases.

[0008] This invention generates random OFDM signals and applies distinct, circumferentially increasing time delays to each transmitting element of a circular array, enabling the simultaneous radiation of vortex electromagnetic waves containing multiple random composite OAM modes in a single SF subpulse. This fundamentally overcomes the core deficiency of traditional inter-pulse OAM mode switching techniques, which suffers from low efficiency. Therefore, the number of transmitting pulses required to acquire the same number (N) of different OAM mode information is significantly reduced, and the total data acquisition time is shortened exponentially, greatly improving the efficiency and speed of vortex electromagnetic wave radar imaging.

[0009] Furthermore, along the circumferential direction, the time delay constant of the OFDM signal corresponding to each electromagnetic wave transmitting unit gradually increases in integer multiples.

[0010] This scheme generates random OFDM signals and applies time delays that increase in integer multiples along the circumferential direction to each transmitting element of a circular array, enabling a single SF subpulse to simultaneously radiate vortex electromagnetic waves containing multiple specific, controllable composite OAM modes. This integer-multiple-increment time delay design precisely corresponds to the phase difference between adjacent electromagnetic wave transmitting elements required by different OAM modes, allowing each transmitted SF subpulse to efficiently and deterministically synthesize and radiate the target combination of OAM modes.

[0011] Furthermore, in S1, the subcarrier signal is subjected to a fast Fourier inverse operation to generate an OFDM signal. ; ; ; Where k represents the subcarrier signal index, j represents the imaginary unit, π represents pi, t represents the time index, and e represents the natural constant. The complex symbol representing the k-th subcarrier signal. This represents the frequency of the k-th subcarrier signal. This represents an intermediate parameter, where K represents the number of subcarrier signals; Indicates the integer symbol; ; , , ; in, This is the peak-to-average power ratio (PAPR) suppression factor, used to ensure unit energy and suppress PAPR caused by the superposition of multiple subcarrier signals. express Random values, The effective OFDM symbol duration that guarantees the orthogonality of the subcarrier signals is represented by N, where N represents the number of electromagnetic wave transmitting units.

[0012] Furthermore, the time delay constant in S3 is ; ; n represents the index of the electromagnetic wave emitting unit, This represents the fundamental mode factor, and N represents the total number of electromagnetic wave emitting units. The duration of the effective OFDM symbol representing carrier orthogonality.

[0013] Furthermore, in S5, the delayed OFDM signal is SF modulated to generate an electromagnetic excitation signal equal to the number of electromagnetic wave transmitting units. ; ; in, ( ) indicates the first The SF sub-pulse input The signal from each electromagnetic wave transmitting unit; Represents a rectangular pulse. Let m be the carrier frequency of the m-th SF sub-pulse. The initial frequency, For the frequency step between adjacent SF sub-pulses, The total number of SF sub-pulses, The pulse repetition interval, The duration of the SF sub-pulse. ;j represents the imaginary unit, represents pi, e represents the natural constant, and t represents the time index. This represents the nth delayed OFDM signal.

[0014] Furthermore, the radiation field in S6 is ; ; radiation field By performing a Fourier transform and extracting the complex field at the corresponding frequency in the frequency domain, the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse can be obtained. ; ; ; ; in, , Let these represent the first intermediate multiplier and the second intermediate multiplier, respectively. This represents the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse; (·) indicates the first type The first-order Bessel function, where a is the radius of the vortex electromagnetic wave transmitting module, r represents the vector from the origin to the far-field point, θ represents the target elevation angle, and a represents the arrangement radius of the electromagnetic transmitting unit. This indicates the azimuth angle of the electromagnetic wave transmitting module. This represents the wavenumber of the m-th SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic.

[0015] As a second aspect of this application, this application provides an imaging method for demodulating the echo signal returned at a far-field point by the frequency-mode multiplexing-based vortex electromagnetic wave transmission method, comprising the following steps: T1: Equipped with a multi-transmitter single-receiver electromagnetic wave receiver, used to receive electromagnetic waves reflected from far-field points and obtain the baseband echo of the m-th SF sub-pulse; T2: Calculate the complex coefficient weights of the corresponding harmonics under each SF sub-pulse based on the baseband echo; T3: Demodulate the distance-azimuth two-dimensional image of the far-field point by weighting the complex coefficients.

[0016] Baseband echo ; ; ; Complex coefficient weights ; ; ; ; in, A4 represents the third intermediate multiplier, and A4 represents the fourth intermediate multiplier. (·) indicates the first category Bessel function of order 1, Indicates intermediate parameters. This represents the baseband echo of the m-th SF sub-pulse. This represents the complex coefficient weight of the k-th harmonic of the m-th SF sub-pulse, where j represents the imaginary unit. represents pi, e represents the natural constant, and t represents the time index. This represents a rectangular pulse, where m represents the sub-pulse index, M represents the total number of sub-pulses, k represents the harmonic index, and K represents the total number of harmonics. The complex number symbol representing the k-th harmonic. The pulse repetition interval, The duration of the SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic. Let represent the frequency of the k-th harmonic, q represent the index of the ideal scatterer in the target scene corresponding to the far-field point, and Q represent the total number of ideal scatterers. Let represent the vectors, elevation angle, and azimuth angle of the q-th ideal scatterer relative to the origin, respectively, and let a be the radius of the vortex electromagnetic wave transmitting module. Complex symbol representing the k-th subcarrier signal Single-shot SF subpulse imaging includes the following steps: T31a: Weighting complex coefficients Rewrite as a K×1 dimensional matrix-vector C; C represents the harmonic vector extracted from the single-pulse echo. n represents the scattering system number vector, and n' represents the noise vector; T32a: Solve the equations using the SBL method based on the weights of the complex coefficients. The scattering coefficient will be reconstructed. Reshape it into a two-dimensional matrix to obtain radar imaging results.

[0017] For imaging of a small number of SF sub-pulses, the specific steps include the following: T31b: Construct the echo matrix based on the complex coefficient weights. ; T32b: Decoupling echo matrix The contributions of mid-range and orientation are used to generate a range-orientation 2D image.

[0018] The technical solution of this application embodiment has at least the following advantages and beneficial effects: This invention employs an OFDM waveform with a preset time delay as the array excitation signal. Leveraging the orthogonality of OFDM subcarrier signals in the time-frequency domain, a specific time delay linearly related to the azimuth angle is introduced between each element of a uniform circular array, thereby establishing a deterministic mapping relationship between the subcarrier signal spectral index and the OAM mode. Based on this mapping mechanism, this scheme can simultaneously excite multiple orthogonal beams carrying different frequencies and OAM modes within a single pulse duration. The orthogonality of the subcarrier signals ensures stable omnidirectional coverage of the accumulated field strength, transforming the serial mode scanning required by traditional phased array OAM radars into a parallel frequency-mode multiplexing process. This technique overcomes the time loss caused by sequential switching of single modes at the physical level, significantly improving the radar's efficiency in acquiring full-mode data and enabling rapid data acquisition of dynamic targets.

[0019] 2. This invention proposes a single-SF sub-pulse sparse Bayesian learning (M-SBL) imaging method for applications requiring extremely high data acquisition efficiency. Utilizing the joint frequency-mode diversity information provided by the DP-OFDM waveform in a single snapshot, and combining this with the spatially sparse prior characteristics of the target in the radar detection scenario, a probabilistic solution model for the underdetermined inverse problem is constructed. This method constrains the scattering coefficients through hierarchical Gaussian priors, enabling the direct calculation of high-resolution two-dimensional target images from echo data of a single transmission, even in the absence of multi-pulse accumulation. Its principle lies in fully utilizing the rich orthogonal modal information inherent in the waveform to compensate for the insufficient number of snapshots, thereby achieving super-resolution reconstruction without long dwell times, maximizing data acquisition efficiency, and making it particularly suitable for the instantaneous capture of sparsely distributed targets in high signal-to-noise ratio environments.

[0020] 3. This invention addresses the computational bottleneck of real-time radar imaging processing by proposing a frequency-mode decoupling-based few-SF sub-pulse Fast Fourier Transform (S-FFT) imaging method. This method constructs a dedicated decoupling matrix within the signal processing flow and eliminates the geometric distortion of the two-dimensional point spread function caused by the linear coupling of frequency and OAM modes in the DP-OFDM waveform by applying phase compensation to the echo data in the range-gated domain. This decoupling mechanism fundamentally restores the independence of the range and azimuth dimensions, allowing the system to directly employ a two-dimensional FFT algorithm with a computational complexity of only logarithmic linearity for precise focusing imaging without relying on iterative optimization algorithms with cubically increasing computational complexity. This improvement significantly reduces computation while ensuring distortion-free images, effectively resolving the contradiction between high-resolution imaging and real-time processing. Attached Figure Description

[0021] Figure 1 This represents the field amplitude distribution under different modes obtained after demodulation of the multiplexed OAM wave.

[0022] Figure 2 This represents the field phase distribution under different modes obtained after demodulation of the multiplexed OAM wave.

[0023] Figure 3 This is a flowchart of a vortex electromagnetic wave transmission method based on frequency-mode multiplexing.

[0024] Figure 4 This is a flowchart of the imaging method.

[0025] Figure 5 This is a schematic diagram of the overall vortex electromagnetic wave transmission and imaging method based on frequency-mode multiplexing.

[0026] Figure 6 This is the imaging result of a single SF subpulse imaging.

[0027] Figure 7 The imaging results are for a small number of SF subpulse imaging. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments. The same reference numerals in the accompanying drawings represent the same components. It should be noted that the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the described embodiments of this application without creative effort are within the scope of protection of this application.

[0029] Compared to the embodiments shown in the accompanying drawings, feasible embodiments within the scope of this application may have fewer components, other components not shown in the drawings, different components, differently arranged components, or components with different connections, etc. Furthermore, two or more components in the drawings may be implemented in a single component, or a single component shown in the drawings may be implemented as multiple separate components.

[0030] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” and similar terms used in this specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not necessarily indicate a quantity limitation. Terms such as “upper” and “lower” are used only to indicate relative positional relationships, and these relative positional relationships may change accordingly when the absolute position of the described object changes.

[0031] Existing vortex electromagnetic wave imaging technology utilizes the unique spiral phase wavefront structure of electromagnetic waves carrying orbital angular momentum (OAM) to directly acquire high-resolution azimuth information of targets without relying on the relative motion between the radar and the target by transmitting and receiving multimode vortex beams with natural orthogonality. However, in current mainstream transmission methods based on uniform circular arrays (UCA), the system can typically only excite a single-mode OAM beam by applying a fixed phase gradient at a single moment. To acquire the complete set of modes required for high-resolution imaging, a time-division multiplexing approach must be used to sequentially switch the transmission modes one by one. This serial scanning mechanism has significant technical limitations. Specifically, to switch between different OAM modes, existing systems need to repeatedly reconstruct the array element excitation phase or feed structure. This not only increases the hardware control burden of the system but also significantly extends the dwell time of full-mode data, greatly reducing data acquisition efficiency and making it difficult to meet the requirements for real-time imaging of high-speed moving targets or dynamically changing scenes. Although existing technologies attempt to achieve multimode generation using time-modulated arrays or frequency diversity arrays, these methods often suffer from rapid attenuation of harmonic energy due to square wave modulation or time-varying and distance-dependent unstable beam characteristics. As a result, they cannot simultaneously achieve high energy efficiency and robust detection under a single aperture, and thus cannot fundamentally solve the problem of low imaging efficiency.

[0032] Based on this, this embodiment provides a vortex electromagnetic wave transmission method based on frequency-mode multiplexing. This transmission method can superimpose multi-mode orbital angular momentum waves on the target scene within each SF subpulse cycle, thereby quickly achieving high-resolution radar imaging.

[0033] The technical approach of the frequency-mode multiplexing-based vortex electromagnetic wave transmission method provided in this solution is as follows: The subcarrier signal is converted into an OFDM signal using inverse fast Fourier transform (IFFT). Then, different time delays are applied to the OFDM signal, followed by SF modulation. These signals with different time delays are then transmitted to electromagnetic wave transmitting units. Each transmitting unit sends a signal with a different time delay to the target scene, thus generating a multimode orbital angular momentum (OAM) wave in the target scene. OFDM signal is short for Orthogonal Frequency Division Multiplexing signal, and SF modulation is short for Stepped Frequency Modulation.

[0034] The specific implementation method of this solution is described below: refer to Figure 1 , Figure 2 , Figure 3 as well as Figure 5 As shown in Example 1: A vortex electromagnetic wave transmission method based on frequency-mode multiplexing, comprising the following steps: S1: Generate multiple subcarrier signals and combine them into an OFDM signal.

[0035] The subcarrier signal is generated by dividing the pre-generated original signal (binary data stream) into K groups, and then mapping it into a complex symbol through signal modulation (QPSK). In this scheme, there are K subcarrier signals. After obtaining the K subcarrier signals, the K subcarrier signals are input into the IFFT processor to generate the OFDM signal.

[0036] In S1, the subcarrier signal is subjected to a fast Fourier inverse operation to generate an OFDM signal. ; ; ; Where k represents the subcarrier signal index, j represents the imaginary unit, π represents pi, t represents the time index, and e represents the natural constant. The complex symbol representing the k-th subcarrier signal. This represents the frequency of the k-th subcarrier signal. This represents an intermediate parameter, where K represents the number of subcarrier signals; Indicates the integer symbol; ; , , ; in, This is the random phase factor corresponding to the k-th subcarrier signal symbol, used to ensure unit energy and suppress the peak-to-average power ratio caused by the superposition of multiple subcarrier signals. express The value of is randomly selected, and N represents the number of electromagnetic wave emitting units.

[0037] The total number of subcarrier signals is limited by the number of electromagnetic wave transmitting units.

[0038] S2: Construct a vortex electromagnetic wave transmitting module at the origin. The vortex electromagnetic wave transmitting module includes several electromagnetic wave transmitting units arranged in a circular array.

[0039] The origin is the location of the vortex electromagnetic wave emitting module. To simplify the model, the center of the vortex electromagnetic wave emitting module's location is taken as the origin, and the center of the target scene is simplified to the far-field point. The vortex electromagnetic wave emitting module is used to emit imaging electromagnetic waves towards the far-field point to generate a radiation field there.

[0040] The vortex electromagnetic wave transmitting module includes N electromagnetic wave transmitting units arranged in a circular array. The electromagnetic wave transmitting units form a ring structure with a radius of a, and the spacing between each electromagnetic wave transmitting unit is the same.

[0041] When the vortex electromagnetic wave transmitting module emits imaging electromagnetic waves towards the far-field point, the origin is O, the far-field point is P, the vector from the origin O to the far-field point P is r, the overall target elevation angle of the vortex electromagnetic wave transmitting module is θ, and the azimuth angle of the vortex electromagnetic wave transmitting module is... The vortex electromagnetic wave transmitting module has multiple electromagnetic wave transmitting units, and each electromagnetic wave transmitting unit has an azimuth angle. azimuth This corresponds to the azimuth angle of the electromagnetic wave emitting unit, where n represents the index of the electromagnetic wave emitting unit.

[0042] Thus, the far-field point P is (r, θ, ... ).

[0043] S3: Generate several distinct time delay constants, the number of which is equal to the number of electromagnetic wave transmitting units.

[0044] One OFDM signal was generated in S1. The vortex electromagnetic wave transmitting module has multiple electromagnetic wave transmitting units, and if each electromagnetic wave transmitting unit uses OFDM signals... As a source signal, it will generate the same imaging electromagnetic waves. Therefore, it is necessary to modify the OFDM signal. Pre-modulation, that is, making the OFDM signal The modulation is divided into N, which exactly matches the number of electromagnetic wave transmitting units.

[0045] Based on this, S3 needs to generate N time delay constants. Along the circumferential direction, the time delay of each electromagnetic wave emitting unit gradually increases.

[0046] Furthermore, along the circumferential direction, the time delay constant of the OFDM signal corresponding to each electromagnetic wave transmitting unit gradually increases in integer multiples.

[0047] Specifically, ; n represents the index of the electromagnetic wave emitting unit, This represents the fundamental mode factor, and N represents the total number of electromagnetic wave emitting units. This indicates the duration of the effective OFDM symbol that guarantees the orthogonality of the subcarrier signals.

[0048] Time delay constant The number of [elements] is equal to the number of electromagnetic wave transmitting units, and they are matched. Therefore, this time delay constant [is used]. It shares a time index with the electromagnetic wave emitting unit.

[0049] S4: Use the time delay constant as the time delay of the OFDM signal to generate a delayed OFDM signal with the same number of electromagnetic wave transmitting units.

[0050] The OFDM signal subsequently requires SF modulation. SF modulation essentially refers to changing the carrier frequency in specific steps between SF sub-pulse sequences, thereby forming a frequency scan in the time domain to synthesize a large bandwidth. In this process, applying different array element delays to the OFDM baseband signal does not change the SF modulation itself, but rather utilizes the coupling effect between the OFDM subcarrier signal frequency and delay to construct a phase gradient in space that corresponds one-to-one with the frequency index, thereby exciting a specific OAM mode sequence.

[0051] Based on this, this application generates a delayed OFDM signal for each electromagnetic wave transmitting unit. Delayed OFDM signal That is, in the original OFDM signal Based on this, different time delay constants are applied to the time domain. .

[0052] Therefore, delay the OFDM signal. Can write The delayed OFDM signal, electromagnetic wave transmitting unit, and time delay constant share a common time index n.

[0053] S5: SF modulate the delayed OFDM signal to generate an electromagnetic excitation signal equal to the number of electromagnetic wave transmitting units. .

[0054] SF modulation converts information bits into spatial phase distribution commands, dynamically configures the array to generate symbol-switching OAM modes, and the result of SF modulation is the electromagnetic wave excitation signal. .

[0055] ; in, ( ) indicates the first The SF sub-pulse input The signal from each electromagnetic wave transmitting unit; Represents a rectangular pulse. , Let m be the carrier frequency of the m-th SF sub-pulse. The initial frequency, For the frequency step between adjacent SF sub-pulses, The total number of SF sub-pulses, The pulse repetition interval, The duration of the SF sub-pulse. ;j represents the imaginary unit, represents pi, e represents the natural constant, and t represents the time index. This represents the nth delayed OFDM signal, where m represents the sub-pulse index and M represents the total number of sub-pulses.

[0056] S6: The electromagnetic wave excitation signals are loaded onto the electromagnetic wave emitting unit, and each electromagnetic wave emitting unit emits imaging electromagnetic waves to generate a radiation field at the far field point. Radiation field generated at the far-field point of S6 for: ; radiation field By performing a Fourier transform and extracting the complex field at the corresponding frequency in the frequency domain, the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse can be obtained. ; ; ; ; in, , Let these represent the first intermediate multiplier and the second intermediate multiplier, respectively. This represents the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse; (·) indicates the first category The order Bessel function, r represents the vector from the origin to the far-field point, θ represents the target elevation angle, and a represents the radius of the electromagnetic launch unit. This indicates the azimuth angle of the electromagnetic wave transmitting module. This represents the wavenumber of the m-th SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic.

[0057] In the DP-OFDM excitation architecture of this invention, there is an essential physical equivalent correspondence between the subcarrier signals and harmonics of the OFDM waveform. This is because the subcarrier signal frequency spacing of the OFDM baseband signal... Total duration of symbols Strictly satisfying the reciprocal relation (i.e., the orthogonality condition) These subcarrier signals naturally form a set of equally spaced discrete harmonics in the frequency domain, which is mathematically equivalent to the Fourier series expansion of a periodic signal. Therefore, the k-th subcarrier signal directly serves as the k-th harmonic component of the signal. This one-to-one correspondence between the subcarrier signal index and the harmonic order forms the basis for establishing the spectrum index-OAM mode deterministic mapping in this invention, enabling the system to accurately excite the corresponding harmonic component by controlling the frequency offset of the k-th harmonic (subcarrier signal). OAM mode.

[0058] The above is the vortex electromagnetic wave transmission method based on frequency-mode multiplexing provided in this application. Using this transmission method, multiple orbital angular momentum mode vortex electromagnetic wave signals can be transmitted to the far field point (target area) within one SF subpulse cycle. After receiving the vortex electromagnetic wave signals, the far field point will reflect these electromagnetic wave signals. Therefore, by analyzing these signals, imaging can be completed. Based on this, this application provides Embodiment 2.

[0059] Example 2: An imaging method for demodulating the electromagnetic wave signal reflected on the target scene in Example 1; The imaging method includes the following steps: T1: Equipped with a multi-transmitter single-receiver electromagnetic wave receiver, used to receive electromagnetic waves reflected from far-field points and obtain the baseband echo of the m-th SF sub-pulse; In Example 1, when transmitting electromagnetic waves, the target scene is considered as the far field point to configure the electromagnetic wave signal. When receiving the echo signal, only one receiving antenna (multi-transmit single-receive electromagnetic wave receiving device) is configured at the location where the electromagnetic wave is transmitted to receive the echo signal reflected back by the target scene.

[0060] When processing echo signals, the target scene cannot be treated as a single point. Therefore, the target scene is considered as a region composed of Q ideal scatterers. The position of each ideal scatterer q is represented as... Each ideal scatterer q has Radar cross-section; Let represent the vector, elevation angle, and azimuth angle of the q-th ideal scatterer relative to the origin, respectively.

[0061] Baseband echo ; ; This represents the baseband echo of the m-th SF sub-pulse. The complex coefficient weights represent the weights of the kth harmonic of the m-th SF sub-pulse.

[0062] T2: Calculate the complex coefficient weights of the corresponding harmonics under each SF sub-pulse based on the baseband echo.

[0063] After obtaining the baseband echo After mathematical derivation, the complex coefficient weights can be obtained. ; ; ; ; in, A4 represents the third intermediate multiplier, and A4 represents the fourth intermediate multiplier. (·) indicates the first category Bessel function of order 1, Indicates intermediate parameters. This represents the baseband echo of the m-th SF sub-pulse. This represents the complex coefficient weight of the k-th harmonic of the m-th SF sub-pulse, where j represents the imaginary unit. represents pi, e represents the natural constant, and t represents the time index. This represents a rectangular pulse, where m represents the sub-pulse index, M represents the total number of sub-pulses, k represents the harmonic index, and K represents the total number of harmonics. The complex number symbol representing the k-th harmonic. The pulse repetition interval, The duration of the SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic. Let represent the frequency of the k-th harmonic, q represent the index of the ideal scatterer in the target scene corresponding to the far-field point, and Q represent the total number of ideal scatterers. Let represent the vectors, elevation angle, and azimuth angle of the q-th ideal scatterer relative to the origin, respectively, and let a be the radius of the vortex electromagnetic wave transmitting module. The complex symbol representing the k-th subcarrier signal; T3: Demodulate the distance-azimuth two-dimensional image of the far-field point by weighting the complex coefficients.

[0064] Once the echo signal (baseband echo) of the target scene is obtained, a two-dimensional range-azimuth image of the far-field point can be obtained through demodulation. In this scheme, two implementation methods are provided for T3: Implementation method 1 selects to perform single SF subpulse imaging, and Implementation method 2 is used for a small number of SF subpulse imaging.

[0065] For single SF subpulse imaging, the following steps are included: T31a: Weighting complex coefficients Rewrite as a K×1 dimensional matrix-vector C; ; ; ; ; ; ; in, This represents a fixed elevation angle of the target scene relative to the electromagnetic wave emitting element array plane. In the imaging model of this invention, the preset region of interest (ROI) is located in this specific elevation angle direction, that is, it is assumed that all scattering points within the target scene are distributed in an elevation angle relative to the origin of the radar coordinate system. On the spatial cone surface, the target scene is discretized as A conical grid of points, represents the number of grid points in the radial and azimuth directions, respectively, and C represents the harmonic vector extracted from the single-pulse echo. represents the scattering system number vector, n' represents the noise vector, and d represents the index of the conical grid point. Represents the observation matrix. This represents the observation element in the k-th row and k-th column of the observation matrix. Let represent the vector between the q-th conical grid point and the origin, and the azimuth angle, respectively. This indicates the carrier wavenumber of the first SF subpulse. This represents the Kth element in the noise vector. This represents the D-th element in the scattering system number vector. The complex symbol represents the k-th subcarrier signal.

[0066] T32a: Solve the equations using the SBL method based on the weights of the complex coefficients. The reconstructed scattering coefficients of the scene are obtained. The scattering coefficient will be reconstructed. Reshape it into a two-dimensional matrix to obtain radar imaging results.

[0067] How to solve the equations using the SBL algorithm, and how to determine the reconstructed scattering coefficients? Reshaping into a two-dimensional matrix to obtain radar imaging results are all existing technologies, and the specific processing steps will not be elaborated here.

[0068] However, when performing the SBL algorithm to solve the equations, it is necessary to assume that the scattering coefficient vector is set. Following the Gaussian prior distribution, the noise vector is modeled as a Gaussian distribution, as follows: ; in, Represents a hyperparameter vector. , used to control the sparsity of the scattering coefficient; , Indicates the accuracy of observation noise. , Let T denote the noise variance, T denote the matrix transpose, and I denote the identity matrix; Thus, the final result obtained by executing the SBL algorithm The expression is: ; ; in, The calculated covariance matrix, hyperparameter vector The corresponding diagonal matrix, H, represents the conjugate transpose, and the imaging result is as follows: Figure 7 As shown.

[0069] like Figure 4 , Figure 5 As shown, imaging of a small number of SF subpulses specifically includes the following steps: T31b: Construct the echo matrix based on the complex coefficient weights. ; T32b: Decoupling echo matrix The contributions of mid-range and orientation are used to generate a range-orientation 2D image.

[0070] In T31b: ; ; ; when hour, ; when hour, ; ; in, The Bessel function term represents the k-th harmonic of the m-th SF sub-pulse. This represents the compensation coefficient for the m-th sub-pulse of the Bessel function term. Represents the echo matrix The element in the k-th row and m-th column; (·) indicates the first category The Bessel function of order j, where j represents the imaginary unit. Let represent pi, e represent the natural constant, t represent the time index, m represent the sub-pulse index, M represent the total number of sub-pulses, k represent the harmonic index, and K represent the total number of harmonics. This represents the wave number of the k-th harmonic. This represents the carrier wavenumber of the m-th SF subpulse. This represents the fixed elevation angle of the target scene relative to the plane of the electromagnetic wave emitting unit array; Let represent the vectors, elevation angle, and azimuth angle of the q-th ideal scatterer relative to the origin, respectively, and let a be the radius of the vortex electromagnetic wave transmitting module. Let represent the radar cross-section of the ideal scatterer q; a is the radius of the vortex electromagnetic wave transmitting module. The complex symbol representing the k-th subcarrier signal. The pulse repetition interval, This represents the frequency of the k-th harmonic; The T32b includes the following steps: T32b1: Echo Matrix Fill the length N with zeros. FFT Fourier matrix And perform a Fourier transform to obtain the range-gated echo matrix. ; ; This represents the filled Fourier matrix. This represents the conjugate transpose of an N-dimensional Fourier transform matrix; T32b2: Uses a weight matrix D to supplement the range-gated echo matrix. To the range-gated echo matrix Frequency-mode decoupling is performed to obtain the frequency-mode decoupling echo matrix; ; ; The dot product symbol is used to represent the product of two products. The value of the element in the k-th row and k-th column of the weight matrix D; T32b3: Zero-padding is performed on the distance interval column vector of the frequency-mode decoupling echo matrix to ensure that its length is not less than K, and Fourier transform is performed to obtain the range-azimuth two-dimensional image I. .

[0071] Indicates Fourier transform, This represents the frequency-mode decoupling echo matrix after filling. The imaging results are as follows: Figure 7 As shown.

[0072] The above are merely preferred embodiments of this application and are not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for transmitting vortex electromagnetic waves based on frequency-mode multiplexing, characterized in that, include: S1: Generate multiple subcarrier signals and combine them into an OFDM signal; S2: Construct a vortex electromagnetic wave transmitting module at the origin. The vortex electromagnetic wave transmitting module includes several electromagnetic wave transmitting units arranged in a circular array. S3: Generate several distinct time delay constants, the number of which is equal to the number of electromagnetic wave transmitting units; S4: Use the time delay constant as the time delay of the OFDM signal to generate a delayed OFDM signal with the same number of electromagnetic wave transmitting units; S5: SF modulate the delayed OFDM signal to generate an electromagnetic excitation signal equal to the number of electromagnetic wave transmitting units; S6: The electromagnetic wave excitation signals are loaded onto the electromagnetic wave emitting unit, and each electromagnetic wave emitting unit emits imaging electromagnetic waves to generate a radiation field at the far field point. Along the circumferential direction, the time delay of each electromagnetic wave emitting unit gradually increases.

2. The vortex electromagnetic wave transmission method based on frequency-mode multiplexing according to claim 1, characterized in that, Along the circumferential direction, the time delay constant of the OFDM signal corresponding to each electromagnetic wave transmitting unit gradually increases in integer multiples.

3. The vortex electromagnetic wave transmission method based on frequency-mode multiplexing according to claim 2, characterized in that, In S1, the subcarrier signal is subjected to a fast Fourier inverse operation to generate an OFDM signal. ; ； ； Where k represents the subcarrier signal index, j represents the imaginary unit, π represents pi, t represents the time index, and e represents the natural constant. The complex symbol representing the k-th subcarrier signal. This represents the frequency of the k-th subcarrier signal. This represents an intermediate parameter, where K represents the number of subcarrier signals; Indicates the floor function; ； ， ， ； in, This is the random phase factor corresponding to the k-th subcarrier signal symbol, used to ensure unit energy and suppress the peak-to-average power ratio caused by the superposition of multiple subcarrier signals. express Random values, The effective OFDM symbol duration that guarantees the orthogonality of the subcarrier signals is represented by N, where N represents the number of electromagnetic wave transmitting units.

4. The vortex electromagnetic wave transmission method based on frequency-mode multiplexing according to claim 3, characterized in that, The time delay constant in S3 is: ; ; n represents the index of the electromagnetic wave emitting unit, This represents the fundamental mode factor, and N represents the total number of electromagnetic wave emitting units. The duration of the effective OFDM symbol representing carrier orthogonality.

5. The vortex electromagnetic wave transmission method based on frequency-mode multiplexing according to claim 4, characterized in that, In S5, the delayed OFDM signal is SF modulated to generate an electromagnetic excitation signal equal to the number of electromagnetic wave transmitting units. ; ； in, ( ) indicates the first The SF sub-pulse input The signal from each electromagnetic wave transmitting unit; Represents a rectangular pulse. , Let m be the carrier frequency of the m-th SF sub-pulse. The initial frequency, For the frequency step between adjacent SF sub-pulses, The total number of SF sub-pulses, The pulse repetition interval, The duration of the SF sub-pulse. ;j represents the imaginary unit, represents pi, e represents the natural constant, and t represents the time index. This represents the nth delayed OFDM signal, where m represents the sub-pulse index and M represents the total number of sub-pulses.

6. The vortex electromagnetic wave transmission method based on frequency-mode multiplexing according to claim 5, characterized in that, The radiation field in S6 is ; ； radiation field By performing a Fourier transform and extracting the complex field at the corresponding frequency in the frequency domain, the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse can be obtained. ; ; ; ; in, , Let these represent the first intermediate multiplier and the second intermediate multiplier, respectively. This represents the spatial field distribution of the k-th harmonic under the m-th SF sub-pulse; (·) indicates the first category The first-order Bessel function, where a is the radius of the vortex electromagnetic wave transmitting module, r represents the vector from the origin to the far-field point, and θ represents the target elevation angle. This indicates the azimuth angle of the electromagnetic wave transmitting module. This represents the wavenumber of the m-th SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic.

7. An imaging method, characterized in that, The method for demodulating the echo signal returned at the far-field point by the vortex electromagnetic wave transmission method based on frequency-mode multiplexing as described in any one of claims 1 to 6 includes the following steps: T1: Equipped with a multi-transmitter single-receiver electromagnetic wave receiver, used to receive electromagnetic waves reflected from far-field points and obtain the baseband echo of the m-th SF sub-pulse; T2: Calculate the complex coefficient weights of the corresponding harmonics under each SF sub-pulse based on the baseband echo; T3: Demodulate the distance-azimuth two-dimensional image of the far-field point by weighting the complex coefficients.

8. The imaging method according to claim 7, characterized in that, Baseband echo ; ; ； Complex coefficient weights ; ; ； ; in, A4 represents the third intermediate multiplier, and A4 represents the fourth intermediate multiplier. (·) indicates the first category Bessel function of order 1, Indicates intermediate parameters. This represents the baseband echo of the m-th SF sub-pulse. This represents the complex coefficient weight of the k-th harmonic of the m-th SF sub-pulse, where j represents the imaginary unit. represents pi, e represents the natural constant, and t represents the time index. This represents a rectangular pulse, where m represents the sub-pulse index, M represents the total number of sub-pulses, k represents the harmonic index, and K represents the total number of harmonics. The complex number symbol representing the k-th harmonic. The pulse repetition interval, The duration of the SF sub-pulse. Let represent the orbital angular momentum mode carried by the k-th harmonic. Let represent the frequency of the k-th harmonic, q represent the index of the ideal scatterer in the target scene corresponding to the far-field point, and Q represent the total number of ideal scatterers. Let represent the vectors, elevation angle, and azimuth angle of the q-th ideal scatterer relative to the origin, respectively, and let a be the radius of the vortex electromagnetic wave transmitting module. The complex symbol represents the k-th subcarrier signal.

9. The imaging method according to claim 8, characterized in that, Single SF subpulse imaging includes the following steps: T31a: Weighting complex coefficients Rewrite as a K×1 dimensional matrix-vector C; C represents the harmonic vector extracted from the single-pulse echo. Represents the imaging dictionary matrix. n represents the scattering system number vector, and n' represents the noise vector; T32a: Solve the equations using the SBL method based on the weights of the complex coefficients. The reconstructed scattering coefficients of the scene are obtained. The scattering coefficient will be reconstructed. Reshape it into a two-dimensional matrix to obtain radar imaging results.

10. The imaging method according to claim 8, characterized in that, For imaging of a small number of SF sub-pulses, the specific steps include the following: T31b: Construct the echo matrix based on the complex coefficient weights. ; T32b: Decoupling echo matrix The contributions of mid-range and orientation are used to generate a range-orientation 2D image.

Images