Radar sparse three-dimensional imaging and resource scheduling method based on circular ring array nesting

Abstract

The invention belongs to the technical field of radar imaging, and particularly relates to a radar sparse three-dimensional imaging and resource scheduling method based on ring array nesting, which comprises the following steps of: establishing a sparse imaging model under an OFDM (Orthogonal Frequency Division Multiplexing) framework; providing a sparse two-dimensional imaging method; proposing a pitch angle reconstruction method based on phase interference; calculating imaging parameters required by resource allocation in the multi-target imaging scene; and establishing an adaptive resource scheduling optimization model and providing a solving method. According to the radar sparse three-dimensional imaging method based on circular ring array nesting, three-dimensional high-resolution imaging is achieved under the condition that a small number of radar resources are consumed. And a self-adaptive resource scheduling algorithm is provided, so that a multi-target imaging self-adaptive resource scheduling model is established by taking time saving, improvement of array element and frequency band utilization rates and balance of radiation intensity of a mode selected by each target as optimization targets, and reasonable allocation of limited radar resources is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging, and particularly relates to a radar sparse three-dimensional imaging and resource scheduling method based on nested circular arrays. Background Art

[0002] Compared with range-azimuth two-dimensional imaging, radar three-dimensional imaging also has the resolution ability in the elevation angle direction, and can provide more target characteristic information. Since a radar based on a Uniform Circular Array (UCA) can transmit electromagnetic waves carrying different modes of Orbital Angular Momentum (OAM), the scattering points of stationary targets can be differentially measured in the azimuth direction, and related imaging technology research has become a hot spot in recent years.

[0003] In practice, under the conditions of multi-tasks and multi-targets in the battlefield, there are usually multiple targets in the radar observation area, such as formation cooperative operations, concentrated fire attacks, etc. At this time, how to effectively utilize limited radar resources and reasonably allocate them to each target is the key to optimizing the overall performance of the radar system. On the one hand, by using the sparsity of the echo signal caused by the sparse characteristics of the target scattering distribution, compressed sensing (CS) can be introduced into the circular array radar imaging under the framework of the signal sparse reconstruction theory, so as to save radar resources; on the other hand, designing a reasonable and effective adaptive scheduling algorithm is a necessary condition for the effective allocation of circular array radar resources under multi-target imaging conditions. However, although the existing technology 1 can achieve three-dimensional high-resolution imaging of targets, it needs to use all modes of OAM, has a large demand for radar resources, and has low flexibility in resource scheduling, making it difficult to meet the adaptive resource scheduling requirements under multi-target conditions; although the two-dimensional sparse imaging method proposed in the existing technology 2 can significantly save radar system resources, due to the limitations of the imaging model and signal form, it is difficult to extend it to three-dimensional imaging. In addition, the existing research on radar resource scheduling algorithms is basically based on traditional planar electromagnetic wave radars, most of which are oriented to multi-target search and tracking tasks, and a small number of studies are oriented to multi-target imaging tasks. However, due to the differences in radar systems and signal processing methods, these studies are not applicable to multi-target imaging based on circular arrays.

[0004] [1]S. Wang, Y. Qu, Y. Chen, J. Liang and Y. Luo, Three-Dimensional Interferometric Imaging with Vortex Electro-magnetic Wave Radar Based on Uniform Circular Array[J]. IEEE Sensors Journal, 2024, 24(20): 32858-32870. DOI: 10.1109 / JSEN.2024.3453869.

[0005] [2]S. Wang, Y. Chen, Y. Qu, H. Lou and Y. Luo, Vortex Electromagnetic Radar Imaging and Adaptive Resource Scheduling Based on Uniform Concentric Circular Arrays[J]. IEEE Sensors Journal, 2024, 24(14): 22658-22671. DOI: 10.1109 / JSEN.2024.3405969.

[0006] There are several key technical problems in the existing technologies, mainly including the following points:

[0007] First of all, the existing radar three-dimensional imaging technologies generally rely on full-modal OAM signals. This method has a large demand for radar resources, resulting in low system resource utilization rate and difficulty in meeting the requirements of multi-target imaging under limited resources.

[0008] Secondly, although traditional two-dimensional sparse imaging methods can effectively compress data and save resources, due to the limitations of the imaging model and signal form, it is difficult to directly extend to three-dimensional imaging, especially in achieving high-resolution imaging in the elevation angle direction, there are obvious deficiencies.

[0009] Thirdly, in the multi-target imaging scenario, there are multiple targets in the radar observation area. Most traditional resource scheduling algorithms are for target search and tracking tasks, lacking an adaptive resource allocation scheme for multi-target imaging tasks, resulting in difficulty in optimizing the overall system performance.

[0010] Finally, in the process of OAM mode selection in the existing technologies, the influence of the number of transmitting array elements on the mode amplitude is not considered. It is urgent to realize the reasonable selection and joint control of the mode, the number of array elements, and the carrier frequency band by optimizing the objective function and introducing the energy ratio evaluation index under the consideration of the periodic mode interference problem, so as to improve the overall imaging effect and the flexibility of resource scheduling. Summary of the Invention

[0011] Aiming at the problems existing in the prior art, the present invention provides a radar sparse three-dimensional imaging and resource scheduling method based on nested circular arrays. Specifically, in the case where there is no relative motion between the radar and the target, a Uniform Circular Array (UCA) radar observes the target in sparse OAM modes, and uses a Linear Frequency Modulation (LFM) signal modulated by Orthogonal Frequency Division Multiplexing (OFDM) technology to achieve three-dimensional high-resolution imaging of the target; on this basis, an adaptive resource scheduling algorithm is proposed, with the optimization objectives of saving time, improving the utilization rate of array elements and frequency bands, and balancing the radiation intensity of the selected modes of each target, to establish an adaptive resource scheduling model for multi-target imaging, thereby realizing the reasonable allocation of limited radar resources.

[0012] The present invention is realized as follows. A radar sparse three-dimensional imaging and resource scheduling method based on nested circular arrays includes:

[0013] S1: Establish a sparse imaging model under the OFDM framework;

[0014] S2: Propose a range-azimuth sparse two-dimensional imaging method;

[0015] S3: Propose a pitch angle reconstruction method based on phase interference;

[0016] S4: Calculate the imaging parameters required for resource allocation in the multi-target imaging scenario;

[0017] S5: Establish an adaptive resource scheduling optimization model and propose a solution method.

[0018] Furthermore, S1 specifically includes:

[0019] In the radar imaging model, the elements on the original UCA with a total number of array elements N are evenly arranged at equal intervals, and the azimuth angle φ of each element n =(2π(n - 1) / N)-π, n = 1, 2,..., N; assuming that there are I frequency bands available for transmitting OFDM-LFM signals, the starting carrier frequency of the signals in each frequency band is f 0i , i = 1, 2,…, I, the bandwidths are all B, and the chirp rates are all μ. Then, to make the OFDM-LFM signal in the i-th frequency band carry a vortex electromagnetic wave with an integer-order mode l q , the number of array elements required is NN(i, l q ), q = 1, 2,..., Q, where Q is the number of OAM modes.

[0020] The OFDM-LFM signal of the \(i\)-th frequency band carrying the \(q\)-th OAM mode at the scattering point can be expressed as

[0021]

[0022] where \(t\) is the fast time, \(rect(\cdot)\) is the rectangular window function, \(T\) p is the pulse duration, \(j\) is the imaginary unit, \(\varphi'\) n' \(=(2\pi(n' - 1) / NN(i, l q ))-\pi\) is the azimuth angle of the \(n'\)-th element in \(NN(i, l q )\), \(n' = 1, 2, \cdots, NN(i, l q )\), and \(\tau = r / c\) respectively represent the time delay from the \(n'\)-th element in \(NN(i, l q )\) and the array center to the scattering point \(P\), \(c\) is the speed of light, \(k\) i represents the wave number of the OFDM-LFM signal of the \(i\)-th frequency band, is the Bessel function of the first kind of order \(l\) q .

[0023] The echo of the signal of the \(i\)-th frequency band carrying the \(l\) mode received by the \(n_0\)-th element with azimuth angle q can be expressed as

[0024]

[0025] where represents the time delay from the scattering point \(P\) to the \(n_0\)-th element.

[0026] Assume that the target contains \(M\) scattering points, \(\sigma\) m , \(r\) m , \(\theta\) m and respectively represent the scattering coefficient, distance, elevation angle and azimuth angle of the scattering point \(P\) m , \(m = 1, 2, \cdots, M\), then the echo of the signal of the \(i\)-th frequency band carrying the \(l\) q mode received by the \(n_0\)-th element can be expressed as

[0027]

[0028] where \(\tau\) m \(= r m / c\) represents the time delay from the scattering point \(P\) m to the array center.

[0029] At this time, through de-chirp sub-pulse compression and fast-time domain Fast Fourier Transform (FFT), the one-dimensional range profile of the target with a range resolution of ρ r = c / 2B can be obtained

[0030]

[0031] where sinc(·) is the sinc function, r Δm = r m - r ref is the relative range of the m-th scattering point, r ref represents the range of the reference signal, is the one-dimensional range profile of the echo signal of the i-th frequency band carrying the l q mode received by the n0-th array element, which is the result after removing the influence of the number of transmitting array elements.

[0032] To save radar resources, according to the compressive sensing theory, a sparse representation model can be established for the one-dimensional range profile of the echo signal received by the n0-th array element. Assuming that the number of sampling points in the fast-time domain is H, then for the h-th range cell in the imaging area, h = 1, 2, …, H, the OAM domain sparse representation model is

[0033]

[0034] where is the matrix of the observation signal received by the n0-th array element in the h-th range cell, represents the all-one vector, is the carrier frequency selection matrix for each selected OAM mode, ⊙ is the Hadamard product, is the matrix of the number of transmitting array elements associated with each selected OAM mode and carrier frequency, is the all-mode signal matrix of all frequency bands received by the n0-th array element in the h-th range cell on the basis of removing the influence of the number of transmitting array elements, is the observation matrix in the mode domain, Q' is the observation dimension in the OAM domain, ·T is the transpose symbol, is the noise matrix in the h-th range cell, represents the Fourier sparse transform matrix, represents the high-resolution azimuth image of the target in the h-th range cell.

[0035] Since the carrier frequency, the number of transmitting array elements, and the OAM mode carried in each range cell within the same echo are the same, the one-dimensional range profile of the echo signal received by the n0-th array element can be expressed as

[0036]

[0037] Thus, a sparse two-dimensional imaging model can be established for the n0-th receiving array element:

[0038]

[0039] where represents the high-resolution two-dimensional image of the target, represents the all-one vector, is an all-one matrix composed of H , is a carrier frequency selection matrix composed of H , is a transmitting array element number matrix composed of H , is the full-mode signal echo matrix received by the n0-th array element on the basis of removing the influence of the number of transmitting array elements, is the noise matrix.

[0040] Furthermore, S2 specifically includes:

[0041] First, design the OAM domain observation matrix Φ Q' . According to the compressive sensing theory, when the sparse observation matrix satisfies the RIP condition, the original signal can be reconstructed, and the equivalent condition of RIP is that the sparse observation matrix is uncorrelated with the sparse transformation matrix. Therefore, minimizing the correlation coefficient between the sparse observation matrix and the sparse transformation matrix is taken as one of the objectives for constructing Φ Q' . In addition, according to the different beam directions and radiation intensities of the vortex electromagnetic waves carrying each mode of OAM, taking the target centroid pitch angle θ T obtained from target search and tracking as prior information, calculate the beam radiation intensities of each mode of OAM under the condition of the same number of transmitting array elements, and taking maximizing the average radiation intensity of the selected OAM mode as another construction objective for Φ Q' . The calculation of each construction parameter of Φ Q' is as follows:

[0042] (1) Global correlation coefficient ρ avg :

[0043] The Pearson correlation coefficient between any two vectors in the observation matrix Φ Q' and the sparse transformation matrix Ψ Q is

[0044]

[0045] where is the row vector of , is the column vector of . Then the global correlation coefficient is

[0046]

[0047] (2) Maximum correlation coefficient ρ max :

[0048]

[0049] (3) Beam average radiation intensity Bessel avg :

[0050] When the number of transmitting array elements is the same, the difference in the radiation intensity of the beams carrying each OAM mode is mainly reflected in the Bessel function. Since different carrier frequencies will also modulate the Bessel function, for each OAM mode, based on the target centroid pitch angle θ T , the maximum value of the modulus of the Bessel function under each carrier frequency condition is taken as the radiation intensity of the beam, that is

[0051]

[0052] The average radiation intensity of the selected OAM beam can be defined as

[0053]

[0054] where L q represents the vector of the complete OAM mode.

[0055] According to the above parameters, taking the minimization of the global correlation coefficient and the maximum correlation coefficient between the sparse observation matrix and the sparse transformation matrix, and at the same time maximizing the beam average radiation intensity as the optimization objective, an OAM mode selection model is established. Since both the global correlation coefficient and the maximum correlation coefficient are between 0 and 1, the beam average radiation intensity is also dimensionless when establishing the optimization objective function.

[0056]

[0057] where q 01 , q 02 and q 03 are adjustment coefficients, represents the all-one vector; the constraint condition is to meet the azimuth angle observation dimension requirements of the target and ensure that the selected modes are not repeated.

[0058] Solving equation (13) gives the observation matrix Φ Q' in the OAM mode domain. Therefore, the selected OAM mode vector is On this basis, the carrier frequencies and the number of transmitting array elements of each selected OAM mode are jointly selected. From equation (5), the carrier frequency vector and the number of transmitting array elements vector of the selected mode are F0Φ I ' and 1 I (ΦI' ⊙NN Q' ), where F0 = [f 01 f 02 …f 0I is the complete carrier frequency vector. Therefore, it is necessary to calculate the carrier frequency selection matrix Φ I' and the number of transmitting array elements matrix NN Q' for each selected mode under each carrier frequency condition. Here, first calculate the number of transmitting array elements matrix NN Q' , and the specific steps are as follows:

[0059] (1) The principle of using UCA to generate vortex electromagnetic waves is to add a phase factor that increases sequentially to the signals emitted by each array element, so as to integrate the signals to synthesize vortex electromagnetic waves. At this time, it is not possible to ideally generate only the pure expected mode, but other modes that are continuously extended with the number of transmitting array elements as the period will be generated at the same time, which are called periodic modes. Obviously, when other conditions are fixed, the more the number of transmitting array elements, the farther the interval between the periodic mode and the expected mode, and the purer the expected mode. In order to determine the minimum required number of transmitting array elements on the basis of ensuring the purity of the expected mode, the Fundamental Mode Energy Ratio (FER) is introduced as a measure of the mode purity, and its calculation formula is

[0060]

[0061] where l q is the expected mode. Obviously, the closer FER is to 1, the higher the purity of the expected mode. Set the FER threshold to 0.9, and the minimum number of transmitting array elements NN FER (i, l q ) for each expected mode under each carrier frequency condition can be obtained.

[0062] (2) However, the positions of each array element on the original UCA are fixed, and the positions of each transmitting array element cannot be randomly selected, but need to be arranged at equal intervals. Therefore, the number of transmitting array elements can only be a factor of the total number of array elements N of the original UCA. In addition, based on the limitation of the number of array elements on the integration path on the transmitted OAM mode, the number of transmitting array elements needs to be greater than 2|l q |. Therefore, the actual minimum number of transmitting array elements for each mode under each carrier frequency condition is

[0063]

[0064] where, N factor is the vector composed of each factor of the total number of array elements N of the original UCA.

[0065] (3) According to the actual minimum number of transmitting array elements Calculate the radiation intensity of its OAM beam under each carrier frequency condition, and select the mode with the maximum radiation intensity from them.

[0066]

[0067] (4) To make the radiation intensity of each mode more balanced, taking the maximum radiation intensity as the reference, recalculate the number of transmitting array elements of each selected mode under each carrier frequency condition.

[0068]

[0069] (5) Similarly, since the number of transmitting array elements can only be a factor of the total number of elements N of the original UCA, the final number of transmitting array elements can be obtained as

[0070]

[0071] Therefore, the vector of the number of transmitting array elements of each selected OAM mode under the i-th carrier frequency condition can be obtained as And

[0072] On the basis that the number of transmitting array elements matrix is determined according to the above process, further give the specific solution method of the carrier frequency selection matrix Φ I' . Construct the Bessel function matrix of the selected modes

[0073]

[0074] According to the Bessel function, it can be known that the carrier frequency also has a modulation effect on the radiation intensity of the OAM beam. Therefore, taking the balance of the radiation intensity of the OAM beams of each selected mode as the optimization goal, establish a joint selection model of the carrier frequency and the number of transmitting array elements of each mode. Since the coefficient of variation reflects the degree of dispersion of the data and is a dimensionless quantity, in order to make the fluctuation of the radiation intensity of the OAM beams of each selected mode smaller, minimize the coefficient of variation of the vector formed by it as the optimization objective function

[0075]

[0076] Among them, the constraint condition is to ensure that the selected transmission frequency corresponds to each selected mode. By solving Equation (20), the carrier frequency selection matrix can be obtained as Φ I' , so as to obtain the carrier frequency vector F0Φ I ' and the number of transmitting array elements vector 1 I (Φ I' ⊙NN Q' ).

[0077] In addition, to accelerate the iteration speed of Equation (13), use the NN obtained based on FER and the total number of elements factor min(i, l q ) Set a threshold T for the maximum radiation intensity of each mode int , thereby narrowing the mode selection range. At this time, the OAM mode selection model in Equation (13) can be optimized to

[0078]

[0079] In summary, according to the designed Φ Q' , NN Q' and Φ I' , using the Smoothed l0 (SL0) algorithm to solve Equation (7) can achieve the reconstruction of the target range-azimuth two-dimensional image. It should be noted that before solving Equation (7), the echo needs to be compensated with the negative Bessel function using the prior pitch angle of the target centroid.

[0080] Furthermore, S3 specifically includes:

[0081] By solving Equation (7), the accurate range-azimuth two-dimensional information of each scattering point of the target can be obtained However, there are multiple carrier frequencies in the phase information of the two-dimensional image, which interfere with the extraction of the pitch angle information. Therefore, the present invention uses the phase information of the one-dimensional range image of a specific mode to reconstruct the pitch angle. Since the pitch angles of each scattering point of the target are different, the selection principle of this specific mode is to irradiate all scattering points as much as possible, that is, the difference between the beam pointing of this mode and the prior pitch angle of the target centroid is the smallest. First, calculate the beam pointing (maximum gain angle) of each selected mode

[0082]

[0083] Among them, is the carrier frequency serial number corresponding to the selected mode . Then the mode with the smallest deviation angle between the maximum gain angle and the prior pitch angle of the target centroid is

[0084]

[0085] Record the frequency band serial number corresponding to this mode as i'. According to Equation (4), the one-dimensional range image of the n1th receiving array element for this mode is

[0086]

[0087] With the same number of transmitting array elements Transmit another frequency band f 0i” LFM signal carrying this mode to the target. The frequency band selection principle is: on the basis of being adjacent to i', the deviation angle between the maximum gain angle and the prior pitch angle of the target centroid is the smallest

[0088]

[0089] For this signal echo, the one-dimensional range profile obtained by the n1-th receiving array element is

[0090]

[0091] According to the accurate range-azimuth information For the same array element n1, the phase interference result between the one-dimensional range profiles of different carrier frequencies (f and f 0i' and f 0i” ) carrying the same OAM mode can be expressed as

[0092]

[0093] where is the accurate relative distance of the m-th scattering point, and the integer is the ambiguity number in the phase unwrapping process. To avoid the estimation error of the ambiguity number, it needs to be eliminated, that is, the absolute value of the phase interference result should be less than π

[0094]

[0095] Obviously, it is difficult to satisfy this condition in Equation (28). Therefore, the phase interference result between the one-dimensional range profiles of different carrier frequencies (f and f 0i' and f 0i” ) carrying this OAM mode received by another array element n2 is introduced, that is

[0096]

[0097] where and are the one-dimensional range profile results of the carrier frequencies f 0i' and f 0i” carrying received by the n2-th array element respectively, and the integer is the ambiguity number in the phase unwrapping process. By performing a second interference on the two phase interference results, we can obtain

[0098]

[0099] where the integer is the ambiguity number in the phase unwrapping process. Obviously, in most cases, regardless of and take any values, the absolute value of the first term in Equation (30) is less than π, that is, the ambiguity number is 0. Thus, the accurate elevation angle information corresponding to is

[0100]

[0101] Define the reconstruction error of the pitch angle. The calculation formula for the reconstruction error of the pitch angle of the m-th scatterer is as follows

[0102]

[0103] where represents the quadratic phase interference result of the m-th scatterer, and represent the coherent phase error, range measurement error, and azimuth measurement error of the m-th scatterer respectively. The influence of each error factor on the pitch angle reconstruction error is as follows:

[0104] (1) Influence of the coherent phase error:

[0105] For the same scatterer, the difference in the reconstructed range information of each receiving array element is less than the range cell, so the image registration step can be ignored. According to the analysis of Equation (30), after the phase interference processing of adjacent carrier frequencies and different array elements, the ambiguity number is 0, and the phase unwrapping process can be omitted. Therefore, noise is the main factor causing the coherent phase error. The partial derivative of the coherent phase for the m-th scatterer can be expressed as

[0106]

[0107] (2) Influence of the range-azimuth measurement error:

[0108] For the m-th scatterer, the range measurement error and azimuth measurement error can be expressed as

[0109]

[0110] The influence of the range measurement error on the pitch angle reconstruction error is mainly reflected in the mispositioning of the coherent phase, and the partial derivative with respect to the azimuth can be expressed as

[0111]

[0112] The smaller the partial derivative, the smaller the influence of each error factor on the pitch angle reconstruction error. When the sin function approaches the maximum or minimum value, the tan function approaches infinity. Therefore, when the coherent phase error, range measurement error, and azimuth measurement error are fixed, the minimum pitch angle reconstruction error is equivalent to

[0113]

[0114] First, design the azimuth relationship between receiving array elements n1 and n2. When i.e., n2 = n1 + N / 2, Equation (36) is initially maximized and can be rewritten as

[0115]

[0116] At this time, by selecting the receiving array element n1 for phase interference for each scattering point at different azimuth positions, the elevation angle reconstruction error of each scattering point can be minimized as much as possible. The calculation formula for the receiving array element n1(m) of the m-th scattering point is

[0117]

[0118] where Round{·} represents rounding. Another receiving array element of the m-th scattering point can be expressed as n2(m) = n1(m) + N / 2.

[0119] Furthermore, S4 specifically includes:

[0120] Assume that the number of targets to be imaged is K. Generally, the distance r Tk 、elevation angle θ Tk and scattering intensity σ Tk of the center of the k-th target can be obtained through target search and tracking, k = 1, 2,..., K. On this basis, the azimuth sparsity of the k targets can be calculated Azimuth observation dimension Q' k 、reference mode In addition, during the resource scheduling process, the present invention hopes to improve the utilization rate of resources such as time, array elements, and frequency as much as possible while obtaining satisfactory imaging quality, which can essentially be reflected as minimizing the actual number of transmissions of the array to complete all imaging tasks. However, when calculating the actual number of transmissions of the array, it is necessary to consider whether the number of array elements of each nested array matches to meet the requirement of equally spaced arrangement of array elements in each nested array, but using it as an optimization objective function will make the optimization model too complex. Therefore, define the planned number of transmissions of the array A Times and the frequency band usage times vector F Times to measure the imaging time required and the utilization rates of frequency bands and array elements, and thus can indirectly reflect the actual number of transmissions of the array. At the same time, to ensure imaging quality, the resource scheduling optimization objective should also include balancing the radiation intensities of the modes selected for each target. Therefore, define the radiation intensity vector Int of the mode selected for the k-th target k for calculating the subsequent optimization objective function.

[0121] (1) Azimuth sparsity

[0122] For targets located at different elevation angles, the number of OAM modes that can be effectively irradiated is different, so the corresponding actual azimuth resolution is also different. Define the best azimuth resolution obtained by the two-dimensional FFT method in OFDM-LFM as a function of the target elevation angle According to the azimuth angle of the k-th target to the maximum estimated size and the best azimuth resolution the azimuth sparsity of the target can be calculated

[0123] (2) Azimuth observation dimension Q' k

[0124] The total azimuth observation dimension of the k-th target needs to satisfy

[0125]

[0126] where c1 is a constant related to the recovery accuracy

[0127] (3) Reference mode

[0128] When constructing the transmitting array element matrix NN in S2 Q' as shown in Equation (16), in the case of single-target imaging, the mode with the largest radiation intensity in the selected modes is used as the reference mode. Under the condition of multi-target imaging, considering the different requirements for the radar signal amplitude due to the scattering characteristic differences of different targets, for the target with large scattering intensity, the overall radiation intensity of the transmitted beam can be adjusted smaller. That is, among the radiation intensities calculated based on the actual minimum number of transmitting array elements of each selected mode, the mode with relatively small radiation intensity is selected as the reference mode, and based on the radiation intensity of this reference mode, the transmitted carrier frequency and the number of transmitting array elements of each selected mode are jointly selected. At this time, the number of transmitting array elements of each selected mode is relatively small, thus saving radar resources. Therefore, the selection calculation of the reference mode for the k-th target is as follows

[0129]

[0130] where is the selected OAM mode vector of the k-th target, p 01 and p 02 are adjustment coefficients. Subsequently, the number of transmitting array elements of each selected mode for the k-th target under each carrier frequency condition is calculated based on the radiation intensity of the reference mode to obtain the transmitting array element matrix

[0131] (4) Array planned transmission times A Times

[0132] On the basis of ignoring the requirement of equally spaced arrangement of array elements in each nested array, the pseudo-transmission times of the array are defined. Under this definition, when the sum of the number of array elements in multiple nested arrays is equal to the number of array elements in the original array, these nested arrays are considered to be fully matched and recognized as one pseudo-transmission of the array. Therefore, for K observation targets, the pseudo-transmission times of the array are

[0133]

[0134] where is the frequency selection matrix for the k-th target, represents the all-one vector.

[0135] (5) Band usage times vector F Times

[0136] When the number of transmitting array elements is equal to the total number of array elements in the original array, only a single-band signal carrying a single mode can be transmitted. Therefore, when calculating the number of idle bands, the number of bands used in this case is ignored. On this basis, the band usage times vector can be obtained as

[0137]

[0138] (6) Radiation intensity vector Int k

[0139] The mode selected for the k-th target of the Bessel function matrix is

[0140]

[0141] Thus, the radiation intensity vector of the mode selected for the k-th target can be obtained as

[0142]

[0143] Furthermore, S5 specifically includes:

[0144] Based on the distance r in the above analysis imaging parameters Tk , elevation angle θ Tk , azimuth sparsity and azimuth observation dimension Q' k , first, taking the minimization of the global correlation coefficient and the maximum correlation coefficient between the OAM mode domain observation matrix and the sparse transformation matrix, and simultaneously maximizing the beam average radiation intensity as the optimization objective, an OAM mode selection model for each target is established. The mode optimization selection model for the k-th target is:

[0145]

[0146] Among them, is the row vector of; Constraint conditions ① and ② are to meet the azimuth observation dimension requirements of the target and ensure that the selected modes are not repeated; Constraint condition ③ is to use the threshold T int to narrow the mode selection range. By solving equation (45) using the GA algorithm, the observation matrix of the OAM mode domain of the k-th target can be obtained and the selected OAM mode vector thereof is obtained as

[0147] On this basis, in order to make full use of the time, array elements, and frequency resources of the radar system, while obtaining satisfactory imaging performance and minimizing the actual number of transmissions of the array to complete all imaging tasks, the present invention takes saving time resources, improving the utilization rate of array elements and frequency bands, and balancing the radiation intensity of the selected modes of each target as the optimization objectives (i.e., minimizing the array proposed transmission times A Times the coefficient of variation of the frequency band usage times vector F Times and the coefficient of variation of the radiation intensity vector Int k of each target), takes the signal frequency band and the number of transmitting array elements of the selected modes of each target as the optimization variables, and establishes an adaptive resource scheduling model

[0148]

[0149] where q1, q2, and q3 are adjustment coefficients; the constraint conditions are to ensure that for the k-th target, the selected transmission frequency corresponds to each selected mode. By solving equation (46) using the GA algorithm, the carrier frequency selection matrix of each target can be obtained k = 1, 2,..., K, so as to obtain the carrier frequency vector corresponding to its selected mode vector and the number of transmitting array elements vector

[0150] Combined with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by the present invention are as follows:

[0151] In terms of signal transceiver design, the present invention constructs a mathematical model suitable for radar sparse three-dimensional imaging: 1) establishes a radar observation model based on the nested circular array, providing a basis for simultaneous multi-mode transmission while avoiding complex array forms; 2) based on the orthogonal frequency division multiplexing (OFDM) technology, uses linear frequency modulation signals with different carrier frequencies to carry different orbital angular momentum (OAM) modes, and specifically realizes simultaneous multi-mode transmission.

[0152] In terms of range-azimuth two-dimensional imaging, the present invention provides a method for sparse two-dimensional imaging using a small number of OAM modes in a short time: 1) Establish a modal-domain sparse observation matrix according to the correlation between the sparse observation matrix and the sparse transformation matrix and the radiation intensity of the beam in the direction of the target's prior elevation angle; 2) Based on considering the modal purity, jointly select the transmission carrier frequency and the number of transmitting array elements for each mode on the principle of balancing the radiation intensity of each selected mode.

[0153] In terms of elevation angle information reconstruction, a method for elevation angle reconstruction based on phase interference is proposed according to the signal characteristics of the imaging model, and the receiving array elements for phase interference processing are selected according to the analysis of elevation angle reconstruction error factors.

[0154] In terms of radar resource scheduling, aiming at the multi-target imaging situation, with the optimization goals of saving time, improving the utilization rate of array elements and frequency bands, and balancing the radiation intensity of the modes selected for each target, an adaptive resource scheduling algorithm is proposed to effectively allocate OAM modes, frequency bands and the number of transmitting array elements among multiple targets, significantly improving the resource utilization rate.

[0155] The technical solution of the present invention fills the technical gap at home and abroad in the industry: for the multi-target imaging scenario, most scholars have studied the resource scheduling algorithm based on the traditional plane-wave radar framework. However, due to the differences in radar systems, signal forms and radar tasks, it is not applicable to the radar imaging based on circular arrays; and the only relevant research is also for two-dimensional imaging. Due to the differences in array forms, signal processing methods and required resources, it is difficult to extend it to three-dimensional imaging. The adaptive resource scheduling algorithm proposed by the present invention fills the gap in the resource scheduling for multi-target three-dimensional imaging based on circular array radar.

[0156] When the prior art realizes high-resolution three-dimensional imaging, it needs to use all modes of OAM, which not only requires a large amount of radar resources, but also makes the resource scheduling flexibility relatively low. By introducing the compressed sensing theory, the present invention realizes the sparse reconstruction of the target echo signal under the framework of the sparse imaging model, effectively reducing the dependence on radar resources, thereby saving system resources and improving the imaging efficiency.

[0157] Although the traditional two-dimensional imaging method can achieve sparse reconstruction, due to the limitations of the imaging model and signal form, it is difficult to be directly applied to three-dimensional imaging. Based on two-dimensional sparse imaging, the present invention proposes a method for elevation angle reconstruction based on phase interference, effectively expanding the imaging model to the three-dimensional field, realizing high-precision reconstruction of the target in the elevation angle direction, and solving the problem that the two-dimensional method cannot meet the requirements of three-dimensional imaging.

[0158] Under the conditions of battlefield multi - tasks and multi - targets, there are multiple targets in the radar observation area. Most traditional resource scheduling algorithms are oriented towards target search and tracking and cannot meet the complex requirements of multi - target imaging tasks. The present invention establishes an adaptive resource scheduling optimization model. By calculating the imaging parameters required in the multi - target imaging scenario, an efficient resource allocation scheme is proposed to meet the reasonable allocation requirements of radar resources under multi - target three - dimensional imaging conditions and improve the overall performance of the system.

[0159] Aiming at the periodic modal interference problem existing in the generation of each OAM mode in a circular - array radar, by introducing the fundamental modal energy ratio (FER) as an evaluation index of modal purity and designing an optimization objective function to minimize the correlation coefficient between the sparse observation matrix and the sparse transformation matrix, while maximizing the beam average radiation intensity, the reasonable selection and joint control of OAM modes are realized. This method not only improves the accuracy of target imaging but also enhances the adaptive scheduling ability of the system in complex environments, effectively solving the problem that it is difficult to balance multi - target imaging and resource scheduling in the prior art. Brief Description of the Drawings

[0160] Figure 1 is a flowchart of a method for radar sparse three - dimensional imaging and resource scheduling based on circular - array nesting provided by an embodiment of the present invention;

[0161] Figure 2 is a schematic diagram of a radar observation model provided by an embodiment of the present invention;

[0162] Figure 3 is the variation of azimuth resolution obtained by the two - dimensional FFT method with the target elevation angle provided by an embodiment of the present invention; where (a) different carrier - frequency cases (b) optimal resolution case;

[0163] Figure 4 is a schematic diagram of the multi - target two - dimensional imaging result provided by an embodiment of the present invention;

[0164] Figure 5 is a schematic diagram of the multi - target three - dimensional imaging result provided by an embodiment of the present invention; Detailed Embodiment

[0165] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0166] Application Embodiment: Military Radar System

[0167] In modern military, high-precision target detection and recognition are of great significance for battlefield situation awareness and decision-making. When traditional radar systems perform target imaging in complex environments, the imaging effect is not ideal.

[0168] The application of the present invention in military radar systems has greatly improved the accuracy and efficiency of target detection and recognition, provided strong technical support for battlefield situation awareness, and enhanced the scientificity and timeliness of combat command and decision-making.

[0169] As Figure 1 shown, the radar sparse three-dimensional imaging and resource scheduling based on nested circular arrays provided by the embodiments of the present invention include:

[0170] S1: Establish a sparse imaging model under the OFDM framework;

[0171] S2: Propose a range-azimuth sparse two-dimensional imaging method;

[0172] S3: Propose a pitch angle reconstruction method based on phase interference;

[0173] S4: Calculate the imaging parameters required for resource allocation in a multi-target imaging scenario;

[0174] S5: Establish an adaptive resource scheduling optimization model and propose a solution method.

[0175] The present invention first constructs a mathematical model suitable for radar sparse three-dimensional imaging based on orthogonal frequency division multiplexing (OFDM) technology. Specifically, an array nested structure is established. By superimposing multiple subcarriers with different frequencies in the transmitted signal and utilizing the orthogonal characteristics in the time domain, frequency domain, and spatial domain, the echo information of different target scattering points is effectively separated and collected. On this basis, the sparse representation of target scattering points in three-dimensional space is defined, forming a sparse observation matrix and a transmitted resource vector that can be used for subsequent reconstruction algorithms, thus laying a theoretical foundation for subsequent range-azimuth two-dimensional imaging and pitch angle reconstruction.

[0176] After establishing the sparse imaging model, combined with the characteristics of the circular array, the main factors affecting the beam radiation intensity are deeply analyzed, including the number of transmitting array elements, orbital angular momentum (OAM) modes, signal carrier frequency, array circular radius size, etc. Through sparse reconstruction algorithms (such as orthogonal matching pursuit and smoothed l0 norm methods), while keeping the target information complete, the sampling amount required for observation is greatly reduced, and then a sparse two-dimensional imaging scheme is proposed. This scheme can obtain high-resolution imaging results of the target in the azimuth and range directions under limited transmitted resources, while reducing the observation time and modal resources of the system.

[0177] In order to achieve more precise target positioning in three-dimensional space, based on two-dimensional imaging, the present invention introduces the principle of phase interference measurement, and proposes to use the phase difference of the received echoes between different array elements to achieve the accurate reconstruction of the elevation angle. The specific method is to use two-step phase interference processing. On the basis of eliminating the reconstruction errors brought by the interference term and the phase unwrapping step, the elevation angle information is extracted, and array element selection is used to minimize the error influence brought by other factors. Compared with traditional multi-baseline interference or monopulse direction finding, this method is more suitable for three-dimensional imaging in sparse observation scenarios, which can not only ensure the measurement accuracy, but also significantly reduce the occupation of observation resources.

[0178] After determining the key imaging parameters such as the prior position of the target, sparsity, and the number of planned transmissions of the array, the present invention further develops an adaptive resource scheduling optimization model. This model comprehensively considers factors such as the spatial resolution, observation time, transmission power, and number of sub-carrier frequencies required in the multi-target imaging scenario, and establishes a multi-constrained optimization problem with the goal of minimizing the observation time and resource usage. Through iterative solution algorithms (such as genetic algorithms, particle swarm algorithms, or adaptive iterative threshold algorithms), the OAM modes, corresponding carrier frequencies, and the number of transmitting array elements can be adaptively allocated, so as to achieve the optimal scheduling of radar resources on the premise of ensuring the imaging quality. The entire process coordinates the sparse imaging theory and phase interference measurement, which not only improves the three-dimensional imaging resolution, but also effectively reduces the comprehensive cost of system observation and calculation.

[0179] Step 1: Establish a sparse imaging model under the OFDM framework;

[0180] In the radar imaging model, the elements on the original UCA with a total number of array elements N are equally spaced and uniformly arranged, and the azimuth angle φ of each element n =(2π(n - 1) / N)-π, n = 1, 2,..., N; assume that there are I frequency bands available for transmitting OFDM-LFM signals, and the starting carrier frequencies of the signals in each frequency band are f 0i , i = 1, 2,…, I, the bandwidths are all B, and the chirp rates are all μ. Then, in order to make the OFDM-LFM signal in the i-th frequency band carry the vortex electromagnetic wave with the integer-order mode l q , the number of array elements required is NN(i, l q ), q = 1, 2,..., Q, where Q is the number of OAM modes. For the sake of understanding, take Figure 2 as an example to illustrate the vortex electromagnetic wave radar imaging model based on array nesting, where the total number of array elements N = 16, and the OFDM-LFM signals with carrier frequencies f 01 , f 02 , f 03 are used to simultaneously transmit the modes of The OAM beams have 4, 8, and 4 transmitting array elements respectively. At this time, the original UCA can be regarded as the result of nesting three UCAs.

[0181] The OFDM-LFM signal of the \(i\)-th frequency band carrying the \(q\)-th OAM mode at the scattering point can be expressed as

[0182]

[0183] where \(t\) is the fast time, \(rect(\cdot)\) is the rectangular window function, \(T\) p is the pulse duration, \(j\) is the imaginary unit, \(\varphi'\) n' \(=(2\pi(n'-1) / NN(i, l\) q ))-\pi\) is the azimuth angle of the \(n'\)-th element in \(NN(i, l\) q ), \(n' = 1, 2, \cdots, NN(i, l\) q ), and \(\tau = r / c\) respectively represent the time delays from the \(n'\)-th element in \(NN(i, l\) q ) and the array center to the scattering point \(P\). \(c\) is the speed of light, \(k\) i represents the wave number of the OFDM-LFM signal of the \(i\)-th frequency band, and \(J\) lq (\cdot)\) is the Bessel function of the first kind of order \(l\) q .

[0184] The echo of the signal of the \(i\)-th frequency band carrying the \(l\) mode received by the \(n_0\)-th element with azimuth angle q can be expressed as

[0185]

[0186] where represents the time delay from the scattering point \(P\) to the \(n_0\)-th element.

[0187] Assume that the target contains \(M\) scattering points. \(\sigma\) m , \(r\) m , \(\theta\) m and respectively represent the scattering coefficient, distance, elevation angle, and azimuth angle of the scattering point \(P\) m . \(m = 1, 2, \cdots, M\). Then the echo of the signal of the \(i\)-th frequency band carrying the \(l\) q mode received by the \(n_0\)-th element can be expressed as

[0188]

[0189] where \(\tau\) m \(=r\) m / c represents the time delay from the scattering point \(P\) m to the array center.

[0190] At this time, through de-chirp sub-pulse compression and fast-time domain FFT, the one-dimensional range image of the target with a range resolution of ρ r = c / 2B can be obtained

[0191]

[0192] where sinc(·) is the sinc function, r Δm = r m - r ref is the relative range of the m-th scattering point, r ref represents the range of the reference signal is the one-dimensional range image of the echo signal of the i-th frequency band carrying the l q mode received by the n0-th array element after removing the influence of the number of transmitting array elements

[0193] To save radar resources, according to the compressive sensing theory, a sparse representation model can be established for the one-dimensional range image of the echo signal received by the n0-th array element. Assuming that the number of sampling points in the fast-time domain is H, for the h-th range cell in the imaging region, h = 1, 2, …, H, the sparse representation model in the OAM domain is

[0194]

[0195] where is the matrix of the observation signal received by the n0-th array element in the h-th range cell, represents the all-one vector, is the carrier frequency selection matrix for each selected OAM mode, ⊙ is the Hadamard product, is the matrix of the number of transmitting array elements associated with each selected OAM mode and carrier frequency, is the all-mode signal matrix of all frequency bands received by the n0-th array element in the h-th range cell after removing the influence of the number of transmitting array elements, is the observation matrix in the mode domain, Q' is the observation dimension in the OAM domain, · T is the transpose symbol, is the noise matrix in the h-th range cell, represents the Fourier sparse transform matrix, represents the high-resolution azimuth image of the target in the h-th range cell

[0196] Since the carrier frequency, the number of transmitting array elements, and the carried OAM mode are the same for each range cell in the same echo, the one-dimensional range image of the echo signal received by the n0-th array element can be expressed as

[0197]

[0198] Thus, a sparse two-dimensional imaging model can be established for the n0th receiving array element:

[0199]

[0200] where represents the high-resolution two-dimensional image of the target, represents the all-one vector, is an all-one matrix composed of H , is a carrier frequency selection matrix composed of H , is a transmitting array element number matrix composed of H , is the full-modal signal echo matrix received by the n0th element on the basis of removing the influence of the number of transmitting array elements, is the noise matrix.

[0201] Step 2: Propose a range-azimuth sparse two-dimensional imaging method;

[0202] First, design the OAM domain observation matrix Φ Q' . According to the theory of compressive sensing, when the sparse observation matrix satisfies the RIP condition, the original signal can be reconstructed, and the equivalent condition of RIP is that the sparse observation matrix is uncorrelated with the sparse transformation matrix. Therefore, minimizing the correlation coefficient between the sparse observation matrix and the sparse transformation matrix is taken as one of the objectives for constructing Φ Q' . In addition, according to the different beam directions and radiation intensities of the vortex electromagnetic waves carrying each mode of OAM, the target centroid elevation angle θ T obtained from target search and tracking is used as prior information. Under the condition of the same number of transmitting array elements, the beam radiation intensities of each mode of OAM are calculated, and maximizing the average radiation intensity of the selected OAM mode is taken as another construction objective of Φ Q' . The calculation of each construction parameter of Φ Q' is as follows:

[0203] (1) Global correlation coefficient ρ avg :

[0204] The Pearson correlation coefficient between any two vectors in the observation matrix Φ Q' and the sparse transformation matrix Ψ Q is

[0205]

[0206] where is the row vector of , is the row vector of The column vectors of. Then the global correlation coefficient is

[0207]

[0208] (2) The maximum correlation coefficient ρ max :

[0209]

[0210] (3) The beam average radiation intensity Bessel avg :

[0211] When the number of transmitting array elements is the same, the difference in the radiation intensity of the beams carrying each OAM mode is mainly reflected in the Bessel function. Since different carrier frequencies will also modulate the Bessel function, for each OAM mode, based on the target centroid pitch angle θ T , take the maximum value of the modulus of the Bessel function under each carrier frequency condition as the radiation intensity of the beam, that is

[0212]

[0213] The average radiation intensity of the selected OAM beam can be defined as

[0214]

[0215] where L q represents the vector of the complete OAM mode.

[0216] Based on the above parameters, with the goal of minimizing the global correlation coefficient and the maximum correlation coefficient between the sparse observation matrix and the sparse transformation matrix, and simultaneously maximizing the beam average radiation intensity, an OAM mode selection model is established. Since both the global correlation coefficient and the maximum correlation coefficient are between 0 and 1, the beam average radiation intensity is also dimensionless when establishing the optimization objective function.

[0217]

[0218] where q 01 , q 02 and q 03 are adjustment coefficients, represents the all-one vector; the constraint condition is to meet the azimuth angle observation dimension requirements of the target and ensure that the selected modes are not repeated.

[0219] Solving equation (13) gives the observation matrix Φ Q' in the OAM mode domain. Therefore, the selected OAM mode vector is On this basis, the carrier frequencies and the number of transmitting array elements of each selected OAM mode are jointly selected. From equation (5), the carrier frequency vector and the number of transmitting array elements vector of the selected modes are F0ΦI ' and 1 I (Φ I' ⊙NN Q' ), where F0 = [f 01 f 02 …f 0I is the complete carrier frequency vector. Therefore, it is necessary to calculate the carrier frequency selection matrix Φ I' and the number of transmitting array elements matrix NN Q' for each selected mode under each carrier frequency condition. Here, first calculate the number of transmitting array elements matrix NN Q' , and the specific steps are as follows:

[0220] (1) The principle of generating vortex electromagnetic waves using UCA is to attach a sequentially increasing phase factor to the signals emitted by each array element, and then integrate the signals to synthesize vortex electromagnetic waves. At this time, it is not possible to ideally generate only the pure expected mode, but other modes that are continuously extended with the number of transmitting array elements as the period will also be generated, which are called periodic modes. Obviously, when other conditions are fixed, the more transmitting array elements, the farther the interval between the periodic mode and the expected mode, and the purer the expected mode. In order to determine the minimum required number of transmitting array elements while ensuring the purity of the expected mode, the Fundamental Mode Energy Ratio (FER) is introduced as a measure of the mode purity, and its calculation formula is

[0221]

[0222] where l q is the expected mode. Obviously, the closer FER is to 1, the higher the purity of the expected mode. Set the FER threshold to 0.9, and the minimum number of transmitting array elements NN FER (i, l q ) for each expected mode under each carrier frequency condition can be obtained.

[0223] (2) However, the positions of each array element on the original UCA are fixed, and the positions of each transmitting array element cannot be randomly selected, but need to be arranged at equal intervals. Therefore, the number of transmitting array elements can only be a factor of the total number of array elements N of the original UCA. In addition, based on the limitation of the number of array elements on the integration path on the transmitted OAM mode, the number of transmitting array elements needs to be greater than 2|l q |. Therefore, the actual minimum number of transmitting array elements for each mode under each carrier frequency condition is

[0224]

[0225] where, N factor is the vector composed of each factor of the total number of array elements N of the original UCA.

[0226] (3) According to the actual minimum number of transmitting array elements for each selected mode Calculate the radiation intensity of its OAM beam under each carrier frequency condition, and select the mode with the maximum radiation intensity from them

[0227]

[0228] (4) To make the radiation intensity of each mode more balanced, taking the maximum radiation intensity as a reference, recalculate the number of transmitting array elements for each selected mode under each carrier frequency condition

[0229]

[0230] (5) Similarly, since the number of transmitting array elements can only be a factor of the total number of array elements N of the original UCA, the final number of transmitting array elements can be obtained as

[0231]

[0232] Therefore, the vector of the number of transmitting array elements for each selected OAM mode under the i-th carrier frequency condition can be obtained as And

[0233] On the basis that the transmitting array element number matrix is determined according to the above process, further give the specific solution method of the carrier frequency selection matrix Φ I' Construct the Bessel function matrix of the selected modes

[0234]

[0235] According to the Bessel function, it can be known that the carrier frequency also has a modulation effect on the radiation intensity of the OAM beam. Therefore, taking the balance of the radiation intensity of the OAM beams of each selected mode as the optimization goal, establish a joint selection model of the carrier frequency and the number of transmitting array elements for each mode. Since the coefficient of variation reflects the degree of dispersion of the data and is a dimensionless quantity, in order to make the fluctuation of the radiation intensity of the OAM beams of each selected mode smaller, minimize the coefficient of variation of the vector formed by it as the optimization objective function

[0236]

[0237] Among them, the constraint condition is to ensure that the selected transmission frequency corresponds to each selected mode. By solving Equation (20), the carrier frequency selection matrix can be obtained as Φ I' , so as to obtain the carrier frequency vector F0Φ I ' and the number of transmitting array elements vector 1 I (Φ I' ⊙NN Q' ).

[0238] In addition, to accelerate the iteration speed of Equation (13), an NN obtained based on the FER and the total number of array elements factor is used min (i, l q ) is used to set a threshold T for the maximum radiation intensity of each mode int , thereby narrowing the mode selection range. At this time, the OAM mode selection model of Equation (13) can be optimized to

[0239]

[0240] As shown above, according to the designed Φ Q' , NN Q' and Φ I' , the target range-azimuth two-dimensional image reconstruction can be achieved by using the Smoothed l0 (SL0) algorithm to solve Equation (7). It should be noted that before solving Equation (7), the echo needs to be compensated with the negative Bessel function using the prior pitch angle of the target centroid

[0241] Step 3: Propose a pitch angle reconstruction method based on phase interference;

[0242] The accurate range-azimuth two-dimensional information of each scattering point of the target can be obtained by solving Equation (7) However, there are multiple carrier frequencies in the phase information of the two-dimensional image, which interfere with the extraction of the pitch angle information. Therefore, the present invention uses the phase information of the one-dimensional range image of a specific mode to reconstruct the pitch angle. Since the pitch angles of each scattering point of the target are different, the selection principle of this specific mode is to irradiate all scattering points as much as possible, that is, the difference between the beam direction of this mode and the prior pitch angle of the target centroid is the smallest. First, calculate the beam direction (maximum gain angle) of each selected mode

[0243]

[0244] where is the carrier frequency serial number corresponding to the selected mode . Then, the mode with the smallest deviation angle between the maximum gain angle and the prior pitch angle of the target centroid is

[0245]

[0246] Record the frequency band serial number corresponding to this mode as i'. According to Equation (4), the one-dimensional range image of the n1th receiving array element for this mode is

[0247]

[0248] With the same number of transmitting array elements transmit another frequency band f carrying this mode to the target 0i”For the LFM signal, the principle for selecting the frequency band is: on the basis of being adjacent to i', the deviation angle between the maximum gain angle and the prior pitch angle of the target centroid is the smallest.

[0249]

[0250] For the echo of this signal, the one-dimensional range profile obtained by the n1-th receiving array element is

[0251]

[0252] According to the accurate range-azimuth information The phase interference result between the one-dimensional range profiles of different carrier frequencies (f and f 0i' and f 0i” ) carried by the same OAM mode received by the same array element n1 can be expressed as

[0253]

[0254] where is the accurate relative range of the m-th scattering point, and the integer is the ambiguity number in the phase unwrapping process. To avoid the estimation error of the ambiguity number, it needs to be eliminated, that is, the absolute value of the phase interference result should be less than π

[0255]

[0256] Obviously, it is difficult to meet this condition in Equation (28). Therefore, the phase interference result between the one-dimensional range profiles of different carrier frequencies (f and f 0i' and f 0i” ) carried by the same OAM mode received by another array element n2 is introduced, that is

[0257]

[0258] where and are the one-dimensional range profile results of the carrier frequencies f 0i' and f 0i” carried by the OAM mode received by the n2-th array element respectively, and the integer is the ambiguity number in the phase unwrapping process. By performing a second interference on the two phase interference results, we can obtain

[0259]

[0260] where the integer is the ambiguity number in the phase unwrapping process. Obviously, in most cases, regardless of and For any value, the absolute value of the first term in Equation (30) is less than π, that is, the fuzzy number is 0. Thus, the precise pitch angle information corresponding to is

[0261]

[0262] Define the pitch angle reconstruction error. The calculation formula for the pitch angle reconstruction error of the m-th scatterer is as follows

[0263]

[0264] where represents the quadratic phase interference result of the m-th scatterer, and represent the coherent phase error, range measurement error, and azimuth measurement error of the m-th scatterer, respectively. The influence of each error factor on the pitch angle reconstruction error is as follows:

[0265] (1) Influence of coherent phase error:

[0266] For the same scatterer, the difference in the range information reconstructed by each receiving array element is less than the range cell, so the image registration step can be ignored. According to the analysis of Equation (30), after the phase interference processing of adjacent carrier frequencies and different array elements, the fuzzy number is 0, and the phase unwrapping process can be omitted. Therefore, noise is the main factor causing the coherent phase error. The partial derivative of the coherent phase for the m-th scatterer can be expressed as

[0267]

[0268] (2) Influence of range-azimuth measurement error:

[0269] For the m-th scatterer, the range measurement error and azimuth measurement error can be expressed as

[0270]

[0271] The influence of the range measurement error on the pitch angle reconstruction error is mainly reflected in the mispositioning of the coherent phase, and the partial derivative with respect to the azimuth can be expressed as

[0272]

[0273] The smaller the partial derivative, the smaller the influence of each error factor on the pitch angle reconstruction error. When the sin function approaches the maximum or minimum value, the tan function approaches infinity. Therefore, when the coherent phase error, range measurement error, and azimuth measurement error are fixed, the minimum pitch angle reconstruction error is equivalent to

[0274]

[0275] First, design the azimuth relationship between receiving array elements n1 and n2. When , that is, n2 = n1 + N / 2, equation (36) achieves preliminary maximization and can be rewritten as

[0276]

[0277] At this time, by selecting the receiving array element n1 for phase interference for each scatterer at different azimuth positions, the reconstruction error of the elevation angle of each scatterer can be minimized as much as possible. The calculation formula for the receiving array element n1(m) of the m-th scatterer is

[0278]

[0279] where Round{·} represents rounding. The other receiving array element of the m-th scatterer can be expressed as n2(m) = n1(m) + N / 2.

[0280] Step 4: Calculate the imaging parameters required for resource allocation in the multi-target imaging scenario;

[0281] Assume that the number of targets to be imaged is K. Usually, the distance r Tk , elevation angle θ Tk and scattering intensity σ Tk of the k-th target center can be obtained through target search and tracking, k = 1, 2,..., K. On this basis, the azimuth sparsity of the k targets in the azimuth direction, the observation dimension Q' k in the azimuth direction, and the reference mode can be calculated. In addition, during the resource scheduling process, the present invention hopes to improve the utilization rate of resources such as time, array elements, and frequency as much as possible while obtaining satisfactory imaging quality. Essentially, it can be reflected as minimizing the actual number of transmissions of the array to complete all imaging tasks. However, when calculating the actual number of transmissions of the array, it is necessary to consider whether the number of array elements of each nested array matches to meet the requirement of equally spaced arrangement of array elements in each nested array. However, using this as the optimization objective function will make the optimization model too complex. Therefore, define the planned number of transmissions A Times of the array and the vector F Times of the number of times of using frequency bands to measure the time, frequency band, and array element utilization rates required for imaging, and then indirectly reflect the actual number of transmissions of the array. At the same time, to ensure imaging quality, the resource scheduling optimization objective should also include balancing the radiation intensities of the modes selected by each target. Therefore, define the radiation intensity vector Int k of the mode selected by the k-th target to calculate the subsequent optimization objective function.

[0282] (1) Azimuth sparsity

[0283] For targets located at different elevation angles, the number of OAM modes that can be effectively irradiated is different, so the corresponding actual azimuth resolution is also different. Since the radiation intensity of each mode of OAM is affected by the signal carrier frequency, array radius, and the number of transmitting array elements, when the given array radius, number of transmitting array elements, and OAM mode range are the same, the variation of the azimuth resolution obtained by the two-dimensional FFT method with different frequency bands with respect to the target elevation angle is as Figure 3 (a) shown; as Figure 3 (b) shown, the best azimuth resolution obtained by the two-dimensional FFT method in OFDM-LFM is defined as a function of the target elevation angle

[0284] The best azimuth resolution obtained by the two-dimensional FFT method in OFDM-LFM is defined as a function of the target elevation angle According to the azimuth angle of the k-th target to the maximum estimated size and the best azimuth resolution the azimuth sparsity of the target can be calculated

[0285] (2) Azimuth observation dimension Q' k

[0286] The total azimuth observation dimension of the k-th target needs to satisfy

[0287]

[0288] where c1 is a constant related to the recovery accuracy.

[0289] (3) Reference mode

[0290] When constructing the transmitting array element matrix NN in S2 Q' as shown in Equation (16), in the case of single-target imaging, the mode with the largest radiation intensity in the selected modes is used as the reference mode. Under multi-target imaging conditions, considering the different requirements for the radar signal amplitude due to the differences in the scattering characteristics of different targets, for targets with large scattering intensity, the overall radiation intensity of the transmitted beam can be adjusted downwards. That is, among the radiation intensities calculated based on the actual minimum number of transmitting array elements of each selected mode, a mode with relatively small radiation intensity is selected as the reference mode, and based on the radiation intensity of this reference mode, the transmission carrier frequency and the number of transmitting array elements of each selected mode are jointly selected. At this time, the number of transmitting array elements of each selected mode is relatively small, thus saving radar resources. Therefore, the selection calculation of the reference mode for the k-th target is as follows

[0291]

[0292] where is the selected OAM modal vector of the k-th target, and p 01 and p 02 are adjustment coefficients. Subsequently, the number of transmitting array elements for each selected mode of the k-th target under each carrier frequency condition is calculated based on the radiation intensity of the reference mode to obtain the transmitting array element matrix

[0293] (4) Array intended transmission times A Times

[0294] On the basis of ignoring the requirement for equally spaced arrangement of array elements in each nested array, the array intended transmission times are defined. Under this definition, when the total number of array elements of multiple nested arrays is equal to the number of array elements of the original array, it is considered that these nested arrays can be fully matched and recognized as one array intended transmission. Therefore, for K observed targets, the array intended transmission times are

[0295]

[0296] where is the frequency selection matrix for the k-th target, represents the all-one vector.

[0297] (5) Band usage times vector F Times

[0298] When the number of transmitting array elements is equal to the total number of array elements of the original array, only a single-band signal carrying a single mode can be transmitted. Therefore, when calculating the number of idle bands, the number of bands used in this case is ignored. On this basis, the band usage times vector can be obtained

[0299]

[0300] (6) Radiation intensity vector Int k

[0301] The Bessel function matrix of the selected mode of the k-th target is For

[0302]

[0303] Thus, the radiation intensity vector of the selected mode of the k-th target can be obtained

[0304]

[0305] Step 5: Establish an adaptive resource scheduling optimization model and propose a solution method.

[0306] Based on the distance r in the above analysis imaging parameters Tk , elevation angle θ Tk , azimuth sparsity and azimuth observation dimension Q' k , first, taking the minimization of the global correlation coefficient and the maximum correlation coefficient between the OAM mode domain observation matrix and the sparse transformation matrix, and simultaneously maximizing the beam average radiation intensity as the optimization objective, an OAM mode selection model for each objective is established. The mode optimization selection model for the k-th objective is as follows:

[0307]

[0308] Among them, is the row vector of; Constraint conditions ① and ② are to meet the azimuth observation dimension requirements of the objective and ensure that the selected modes are not repeated; Constraint condition ③ is to use the threshold T int to narrow the mode selection range. By solving equation (45) through the GA algorithm, the observation matrix of the OAM mode domain of the k-th objective can be obtained and the selected OAM mode vector is obtained therefrom as

[0309] On this basis, in order to make full use of the time, array elements and frequency resources of the radar system, while obtaining satisfactory imaging performance, the actual number of transmissions of the array for completing all imaging tasks is minimized. The present invention takes saving time resources, improving the utilization rate of array elements and frequency bands, and balancing the radiation intensity of the modes selected for each objective as the optimization objective (that is, minimizing the array planned transmission number A Times , the coefficient of variation of the frequency band usage number vector F Times , and the coefficient of variation of the radiation intensity vector Int of the modes transmitted for each objective k ), taking the signal frequency band and the number of transmitting array elements of the modes selected for each objective as the optimization variables, an adaptive resource scheduling optimization model is established

[0310]

[0311] where q1, q2 and q3 are adjustment coefficients; the constraint condition is to ensure that for the k-th objective, the selected transmission frequency corresponds to each selected mode. By solving equation (46) through the GA algorithm, the carrier frequency selection matrix of each objective can be obtained k = 1, 2,..., K, so as to obtain the carrier frequency vector corresponding to its selected mode vector and the number of transmitting array elements vector

[0312] ​Suppose there are 4 targets to be imaged within the radar observation area. Based on the resource scheduling of the method of the present invention, Figure 4 is the two-dimensional imaging result diagram of range-azimuth angle of the method of the present invention, Figure 5 is the three-dimensional reconstruction result diagram of the method of the present invention.

[0313] As mentioned above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modification, equivalent replacement, and improvement made within the technical scope disclosed by the present invention by those skilled in the art within the spirit and principle of the present invention shall be covered by the protection scope of the present invention.

Claims

1. A radar sparse three-dimensional imaging and resource scheduling method based on the nesting of circular arrays, characterized in that The method includes: Establishing a target observation model with nested arrays under the framework of orthogonal frequency division multiplexing signals, transmitting sparse observation signals carrying orbital angular momentum modes, establishing an observation matrix, and forming a sparse representation; Modulating the radiation intensity of each mode beam based on the number of array elements and the signal carrier frequency, and constructing a multi-mode signal transmission model; Processing the echo signal using a sparse recovery algorithm to obtain the two-dimensional imaging results of the target scattering points in the range and azimuth directions; Performing phase interference on the echoes of the selected orbital angular momentum modes, and based on the obtained two-dimensional information, obtaining the three-dimensional position information of the target scattering points in the elevation angle direction; Calculating the imaging parameters in a multi-target imaging scenario and establishing an adaptive resource scheduling optimization model to schedule the transmission modes, the number of array elements, and the carrier frequency band.

2. The radar sparse three-dimensional imaging and resource scheduling method based on circular array nesting according to claim 1, characterized in that The step of establishing the observation matrix of the orbital angular momentum modes includes selecting the orbital angular momentum modes to be transmitted with the optimization goal of minimizing the correlation coefficient between the observation matrix in the orbital angular momentum mode domain and the sparse representation basis, and at the same time maximizing the radiation intensity of the selected modes at the prior elevation angle of the target centroid under the condition of the same number of array elements.

3. The radar sparse three-dimensional imaging and resource scheduling method based on circular array nesting according to claim 1, characterized in that The step of constructing the multi-mode signal transmission model includes, under the number of array elements and the carrier frequency of the orthogonal frequency division multiplexing-linear frequency modulation signal, using the beam radiation intensity modulation effect to constrain the echo amplitude equalization degree of each orbital angular momentum mode, and at the same time introducing the mode purity as a limiting condition to determine the number of array elements for transmitting each mode and the signal carrier frequency allocation.

4. The radar sparse three-dimensional imaging and resource scheduling method based on nested circular array according to claim 1, characterized in that The step of obtaining the elevation angle direction information includes selecting the mode with the smallest deviation from the target prior elevation angle in the selected orbital angular momentum modes, transmitting through the linear frequency modulation signals of adjacent frequency bands, and performing two-step phase interference on the one-dimensional range image of the echo signal of this mode to obtain the elevation angle information of the target scattering points.

5. The radar sparse three-dimensional imaging and resource scheduling method based on circular array nesting according to claim 1, characterized in that The step of calculating the imaging parameters in a multi-target imaging scenario includes determining the azimuth sparsity, the azimuth observation dimension, the reference orbital angular momentum mode, the array planned transmission times, the number of available frequency bands, and the radiation intensity vectors of the selected modes of each target.

6. The radar sparse three-dimensional imaging and resource scheduling method based on the nested circular array according to claim 1, wherein The step of establishing the adaptive resource scheduling optimization model includes setting goals such as the observation time, the utilization rate of array elements and frequency bands, and the balance of the radiation intensity of the selected modes for a multi-target imaging scenario, and using an adaptive iterative algorithm to solve the allocation of the orbital angular momentum modes, the transmission frequency band, and the number of array elements, so as to obtain a resource scheduling scheme that meets the above goals.

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