Robust beam forming method and system based on sparse reconstruction under nonlinear array configuration

Abstract

The invention discloses a robust beam forming method and system based on sparse reconstruction under a nonlinear array configuration, and the method comprises the following steps: S1, determining the specific configuration of a pitching-dimension nonlinear array, and generating multi-channel echo data; s2, calculating the slope distance difference of the multi-channel echo signals based on a space vector model, and constructing a signal guide vector; s3, designing a guide vector constraint, ensuring that the calculated weight vector can apply distortionless response to all expected signals, and suppressing an interference component; s4, constructing a generalized LASSO regression model, and forming an optimal weight vector calculation architecture suitable for a nonlinear array configuration; and S5, constructing a pitching-dimension airspace snapshot signal, and weighting the pitching-dimension airspace snapshot signal by adopting the optimal weight vector in the step S4 to complete beam forming processing. The method can effectively solve the problem of accurate calculation of the guide vector under the nonlinear array and the problem of non-consistency of the guide vector introduced by azimuth pulse expansion under the SAR mode, and can be used for solving the problem of echo separation under the MIMO-SAR nonlinear array configuration.

Description

Technical Field

[0001] This invention relates to a robust beamforming method and system based on sparse reconstruction for nonlinear array configurations. The main idea of ​​this technology is to accurately calculate the guidance vector under the nonlinear array configuration using a spatial vector model, and to solve the inconsistency problem of the guidance vector under azimuth pulse spread through the sparse reconstruction principle, thereby effectively improving the DBF processing performance under nonlinear array configurations. Currently, this technology has been used to solve the echo separation problem in MIMO-SAR systems, belonging to the fields of MIMO-SAR technology and array signal processing technology. Background Technology

[0002] SAR, with its all-weather, 24 / 7 operational capabilities, has become an indispensable piece of equipment in global integrated environmental monitoring. However, with increasing application demands, current SAR systems need to possess capabilities such as high-resolution wide-strip imaging (HRWS), ground moving target indication (GMTI), simultaneous imaging from multiple angles / areas, and simultaneous imaging in multiple modes / resolutions. To achieve this, SAR systems require the use of multiple transmitters and receivers to implement transmit diversity and receive diversity. However, in practical applications, the number of channels in radar systems is limited due to constraints in size, weight, and power. These requirements necessitate the development of a new radar architecture, namely the MIMO-SAR system. By adopting MIMO technology, SAR can significantly improve the operational flexibility and imaging performance of the system, thus offering a possibility to alleviate or even resolve the previously conflicting imaging requirements.

[0003] As is well known, simultaneous transmission of multiple transmit waveforms in MIMO-SAR introduces severe waveform coupling. Therefore, waveform orthogonality is crucial for fully leveraging the advantages of MIMO-SAR. However, due to range ambiguity, frequency diversity effects, and limited spectrum resources, orthogonal transmit waveform sets obtained through time-division and frequency-division mechanisms are not suitable for SAR modes. In practical engineering applications, simultaneously transmitted waveforms at the same frequency and completely orthogonal do not exist. In this case, cross-correlation energy (CCE) caused by waveform coupling accumulates in distributed scenes, leading to a significant deterioration in imaging performance. Therefore, waveform separation research is essential for MIMO-SAR. To address the echo separation problem in MIMO-SAR, international researchers have proposed the Short Time Shift Orthogonality (STSO) scheme. Through partial orthogonality of the waveform and elevation-division multiplexing (DBF) processing, interference components from near and far ends can be suppressed respectively. Furthermore, to alleviate the constraints of STSO and increase the diversity of radar waveforms, domestic researchers have proposed the Segmented Phase Coding (SPC) scheme, which has been experimentally verified using an airborne DBF-SAR system.

[0004] However, current waveform decoupling techniques based on orthogonal waveform beamforming cannot be directly applied to nonlinear array MIMO-SAR. In practice, MIMO-SAR may be subject to strict size, weight, and power constraints, making linear / standard array configurations unsuitable for conical or cylindrical fuselages. To maximize installation space utilization, subarrays typically employ nonlinear arrangements. Generally, nonlinear arrays significantly increase the difficulty of DBF processing, including accurate guidance vector calculation and optimal weight vector calculation. Due to the nonlinear arrangement, the guidance vector is related not only to the elevation angle but also to the azimuth angle. Considering that the radar signal in the same processing unit is formed by the accumulation of echoes from all scatterers within the azimuth pulse spread, the guidance vectors at different azimuth positions within the azimuth pulse spread are not the same. In other words, the guidance vector of a nonlinear array exhibits spatially varying characteristics within the same processing unit, which severely affects DBF processing performance and consequently deteriorates MIMO-SAR echo separation. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a robust beamforming method and system based on sparse reconstruction for nonlinear array configurations. This method can mitigate the impact of nonlinear array configurations and azimuth pulse spread on DBF processing performance, thereby improving the echo separation performance of MIMO-SAR.

[0006] This invention discloses a robust beamforming method based on sparse reconstruction in a nonlinear array configuration, comprising the following steps:

[0007] (1) Determine the elevation-dimensional nonlinear array configuration; use segmented phase coding (SPC) waveforms as M transmitted waveforms; acquire the mixed echo signal through the receiver; perform matched filtering on the mixed echo signal to generate multi-channel echo data;

[0008] (2) Based on the array configuration determined in step (1), define the target position space vector and the receiver position space vector; calculate the slant range difference between the receiving channels by using the spatial vector modulus operation and the inverse cosine function; construct the signal guidance vector related to the azimuth angle based on the slant range difference;

[0009] (3) Based on the signal guidance vector in step (2), design a distortion-free response constraint for the desired signal within the azimuth pulse extension range, so that the inner product of the weight vector and all desired signal guidance vectors is 1; design a suppression constraint for the interference component and set the interference suppression step interval.

[0010] (4) Construct the objective function of the generalized LASSO regression model using the distortion-free response constraint and interference suppression constraint from step (3); balance the weights of the desired signal and interference using the L2 norm term and the L1 norm penalty term; solve the convex optimization problem to obtain the optimal weight vector;

[0011] (5) Construct an elevation-dimensional spatial snapshot signal based on the multi-channel echo data from step (1); use the optimal weight vector from step (4) to weight the spatial snapshot signal; and output the desired signal after separation.

[0012] Preferably, in step (1), the SPC waveform consists of linearly shifted sub-pulses, which are phase-coded modulated, and the coding vector φ m satisfy:

[0013]

[0014] In the formula, (·) H For the conjugate transpose operation, the subscript m represents the encoding vector corresponding to the m-th transmitted waveform.

[0015] Preferably, the slant range difference between receiving channels n and n′ in step (2) is calculated as follows:

[0016]

[0017] In the formula, η, v a And ||·|| represent slow time, platform speed, and modulo operation, respectively, P i =[x i ,y i ,z i [] represents the spatial vector corresponding to the position coordinates of point target i. Let be the spatial vector corresponding to the position coordinates of receiver n, where the offset Δx in the X direction is... n Y-direction offset Δy n and Z-direction offset Δz n Depending on the specific array configuration, the incident angle θ n,n′ (η) is specifically represented as:

[0018]

[0019] In the formula, arccos{·}, (·) T and These are the spatial vectors corresponding to the inverse cosine operation, transpose operation, and array center position coordinates, respectively; the signal guidance vector constructed for the azimuth angle α is represented as:

[0020]

[0021] In the formula

[0022]

[0023] In the formula, R, λ, and H are the slant range, wavelength, and platform height, respectively, and α is... The angle between the trajectory and the platform.

[0024] Preferably, the azimuth range covered by the distortion-free response constraint in step (3) is:

[0025]

[0026] In the formula, α c and α W These are the beam center azimuth and beamwidth, respectively.

[0027] Preferably, the objective function of step (4) is:

[0028]

[0029] In the formula, I1=[1,1,…,1],||·||2,||·||1,μ and These are a vector with all elements equal to 1, the l2 norm, the l1 norm, the penalty coefficient, and the calculated optimal weight vector, respectively. and Ξ k The specific form of k 1k0 is:

[0030]

[0031] In the formula, c and T sub Δα represents the speed of light and the subpulse width, respectively. s and Δα i These are the step intervals set for the desired signal and the interference, respectively, where k and k0 are the subscripts corresponding to the desired signal and the interference components, respectively.

[0032] Preferably, step (5) is followed by echo separation post-processing:

[0033] Time-shift alignment is performed on the separated sub-pulse signals;

[0034] Sub-pulse signals are weighted and merged using an encoding matrix.

[0035] The present invention also provides a nonlinear array beamforming system, comprising:

[0036] Echo generation module: configured to execute step (1) of the method to generate multi-channel echo data;

[0037] Guiding vector calculation module: configured to perform step (2) of the method, outputting a signal guiding vector based on a spatial vector model;

[0038] Constraint design module: configured to perform step (3) of the method to generate distortion-free response constraints and disturbance suppression constraints;

[0039] Optimization and solution module: configured to execute step (4) of the method to solve the LASSO model and output the optimal weight vector;

[0040] Beamforming module: configured to perform step (5) of the method and output the desired separated signal.

[0041] Preferably, the optimization solution module integrates a convex optimization solver, which supports the calculation of L1 / L2 mixed norm penalty terms.

[0042] The present invention also provides a MIMO-SAR echo separation device, which, using the method, includes:

[0043] Pitch-dimensional nonlinear array antenna;

[0044] SPC waveform transmitter;

[0045] Multi-channel receiver;

[0046] The processor is configured to perform beamforming processing and output the desired separated signal.

[0047] Preferably, the nonlinear array antenna is mounted on the surface of a conical or cylindrical carrier, with the array normal parallel to the flight trajectory.

[0048] Compared with existing technologies, the beneficial effects of the invented robust beamforming method and system based on sparse reconstruction under nonlinear array configuration are: the method provides an accurate calculation method for the guidance vector based on the spatial vector model, and alleviates the influence of the inconsistency of the guidance vector in the azimuth pulse extension on DBF processing by designing guidance vector constraints, which can effectively improve the DBF processing performance under nonlinear array configuration.

[0049] Specifically, this invention has the following innovative features and beneficial effects:

[0050] 1. A method is proposed to accurately calculate the slant range difference of a nonlinear array based on spatial vector modulus operation and inverse cosine function, and to construct a signal guidance vector that is strongly correlated with the azimuth angle.

[0051] Beneficial effects: Solves the problem of the guidance vector varying with azimuth angle under nonlinear arrays, avoiding the geometric errors of traditional linear array models. Applicable to irregular array arrangements of any carrier (conical / cylindrical), improving engineering adaptability.

[0052] 2. Design distortion-free response constraints (inner product = 1) and interference suppression step constraints covering the azimuth pulse extension range.

[0053] Construct an objective function with a mixed L1 / L2 norm to balance the desired signal fidelity with interference sparsity.

[0054] Beneficial effects: Significantly alleviates the problem of inconsistent guidance vectors caused by azimuth pulse spread.

[0055] 3. A post-processing workflow of time-shift alignment and weighted merging of encoding matrices is proposed. Sub-pulse delay is unified through inverse Fourier transform to eliminate waveform aliasing.

[0056] Beneficial effects: It solves the time delay misalignment problem after the sub-pulse separation of SPC waveform and realizes high-fidelity reconstruction of MIMO-SAR echo.

[0057] 4. Develop a processing module integrating a convex optimization solver to support real-time calculation of L1 / L2 penalty terms. Design a forward-looking nonlinear array (parallel normal flight trajectory) adapted to conical / cylindrical carriers.

[0058] Beneficial effects: The hardware system can be deployed in confined spaces, meeting size / weight constraints. Attached Figure Description

[0059] Figure 1 The results obtained by least squares (LS) beamforming and the proposed technique are shown, where (a) is the range profile after echo separation using different DBF techniques; and (b) is... Figure 1 (a) Upsampling result at the left ellipse position; (c) is Figure 1 (a) Upsampling results at the middle ellipse position; (d) is Figure 1 (a) Upsampling results at the position of the ellipse on the right;

[0060] Figure 2 The images are the results of the echo signal from transmitter 1, where (a) is the point target imaging performance analysis without DBF processing; (b) is the point target imaging performance analysis after processing with LS beamforming technology; and (c) is the point target imaging performance analysis after processing with the proposed technology.

[0061] Figure 3 The images are the DBF processing performance of the proposed technique under a nonlinear array configuration verified by surface target simulation. (a) is the ground truth map corresponding to the MIMO-SAR imaging scene; (b) is the imaging result corresponding to the mixed echo of the two transmitted waveforms; (c) is the imaging result of waveform 1 after processing by LS beamforming technology; and (d) is the imaging result of waveform 1 after processing by the proposed technique.

[0062] Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation

[0063] The present invention will be further explained and described below with reference to the accompanying drawings and embodiments.

[0064] Example 1

[0065] This embodiment provides a detailed description of the robust beamforming method and system based on sparse reconstruction in a nonlinear array configuration proposed in this invention. The main steps are as follows:

[0066] S1: Determine the specific configuration of the pitch-dimensional nonlinear array and generate multi-channel echo data based on it;

[0067] This invention selects the SPC waveform as the transmit waveform of the MIMO-SAR system. It can be regarded as consisting of linearly shifted sub-pulse signals, and phase coding is used to modulate the sub-pulse signals. Its specific form can be expressed as follows:

[0068]

[0069] In the formula

[0070]

[0071] In the formula, and These represent the modulation phase and linear frequency modulation (LFM) signals, respectively. and s m (t) have the same signal bandwidth B r ,but The pulse width is T sub s m The pulse width of (t) is MT sub Furthermore, to avoid signal-to-noise ratio (SNR) loss, the encoded vector φ m Must meet:

[0072]

[0073] To satisfy the above conditions, φ m The specific form can be expressed as:

[0074]

[0075] Let the transmitter m and receiver n be Txm, m = 1, 2, ..., M and Rxn, n = 1, 2, ..., N, respectively. Then the baseband echo signal received by Rxn after the transmitted waveform is backscattered by the point target and transmitted by Txm can be expressed as:

[0076]

[0077] Considering that in a MIMO-SAR system, the same receiver Rxn will receive echo signals from all transmitted waveforms, the mixed echo signal received by Rxn can be expressed as:

[0078]

[0079] In the formula

[0080]

[0081] In the formula, Represents the complex field.

[0082] Next, the mixed signal r needs to be processed. n The matched filter is designed to perform matched filtering on (t,η).

[0083]

[0084] In the formula, (·) * rect(·) and k r These represent the conjugate operation, the rectangular window function, and the frequency modulation slope, respectively. Based on the Resident Phase Perspective (POSP) principle, the corresponding matched filtering result can be expressed as:

[0085]

[0086] In the formula

[0087] ξ k =[Φ(k,1),Φ(k,2),…,Φ(k,M)] T

[0088]

[0089] In the formula, sinc(x) = sin(πx) / (πx), Let represent the pulse compression result of the i-th sub-pulse signal. Observing the above formula, we can see that the time delay interval between different sub-pulse signals is T. sub In distributed imaging scenarios, when the mapping swath is wide enough, the sub-pulse signals generated by point targets at different locations will be aliased. Therefore, in order to achieve echo separation, it is necessary to separate the aliased sub-pulse signals through DBF processing.

[0090] S2: Calculate the slant range difference of multi-channel echoes based on the spatial vector model, and construct the signal guidance vector accordingly;

[0091] Define the spatial vector corresponding to the point target's position coordinates as P. i =[x i ,y i ,z i The spatial vector corresponding to the position coordinates of receiver n is: Where Δx n Δy n and Δz n Depending on the array configuration determined in step S1, it can then be accessed via P. i and Calculate the slant range difference between receiving channels n and n′, i.e.:

[0092]

[0093] In the formula

[0094]

[0095] Based on the slope distance difference Δd nn′ The signal guidance vector in a nonlinear array configuration can be expressed as:

[0096]

[0097] In the above equation, the signal guidance vector is related to the slow time η, which can be further simplified to:

[0098]

[0099] In the formula

[0100]

[0101] It should be noted that the above method for calculating the guidance vector is applicable to any array configuration.

[0102] S3: Design guiding vector constraints to ensure that the calculated weight vector can apply a distortion-free response to all desired signals and effectively suppress interference components;

[0103] For nonlinear array configurations, the slant range difference of each receiving channel is related to the incident angle θ. n,n′ (η) is related, as can be seen from step S2, θ n,n′ (η) can be further expressed as:

[0104]

[0105] Observing the above formula, we can see that θ n,n′ (η) is related to the azimuth angle α. Within the azimuth pulse spread, if the target's azimuth angle changes, the corresponding slant range difference and signal guidance vector will also change. In other words, azimuth pulse spread will result in the guidance vectors of the desired signal and interference within the same processing unit not having unique determinism, which will further increase the difficulty of DBF processing. To mitigate the impact of azimuth pulse spread on nonlinear array DBF processing, this section introduces guidance vector constraints. According to the guidance vector calculation method in step S2, the signal guidance vector corresponding to the sub-pulse k generated by the target located at slant range R and azimuth angle α can be expressed as:

[0106]

[0107] Furthermore, the set of signal guidance vectors corresponding to different azimuth positions within the azimuth pulse extension can be represented as:

[0108]

[0109] With the split sub-pulse signal For example, the guidance vector constraints designed for the desired signal and interference components can be expressed as follows:

[0110]

[0111] In the formula, k = 1, 2, ..., M, k ≠ k0.

[0112] S4: Construct a generalized LASSO regression model and use it to form an optimal weight vector calculation architecture suitable for nonlinear array configurations;

[0113] Generally, the generalized LASSO regression model is expressed as follows:

[0114]

[0115] In the formula, y, Let C and represent the array output signal, the measurement matrix, the unknown regression coefficients, and the penalty matrix, respectively. Inspired by the above equation, it can be used to construct a robust beamformer to mitigate the impact of nonlinear array configurations and azimuth pulse spread on DBF processing performance. Based on the above equation, the beamforming problem can be expressed as:

[0116]

[0117] It should be noted that, when the array has limited degrees of freedom, the beamformer constructed by the above equation cannot target Ξ. S All guidance vectors in the middle are subjected to a distortion-free response, while Ξ is sufficiently suppressed. I The corresponding interference components can only be as close as possible to this target.

[0118] S5: Construct a pitch-dimensional spatial snapshot signal and weight it using the optimal weight vector from S4 to complete beamforming processing.

[0119] Based on multi-channel echo signals The image of the vertical dimension of the airspace can be described as:

[0120]

[0121] Using the optimal weight vector right After weighting, the corresponding result can be expressed as:

[0122]

[0123] In the formula, This indicates the desired signal separated by DBF processing.

[0124] Based on the above processing, the sub-pulse signals can be separated sequentially. k = 1, 2, ..., M. Note that the separated sub-pulse signals have different time delay ranges. To achieve MIMO-SAR echo separation, the separated sub-pulse signals first need to undergo time-shifting processing, i.e.:

[0125]

[0126] In the formula

[0127]

[0128] In the formula, F t F t -1 ⊙ and ⊙ represent the Fast Time Fourier Transform, the Inverse Fast Time Fourier Transform, and the dot product operation, respectively. After processing by the above formula, all sub-pulse signals... k = 1, 2, ..., M will have the same time delay range. Furthermore, for sub-pulse signals... Weighted processing is performed for k = 1, 2, ..., M:

[0129]

[0130] In the formula

[0131]

[0132] In the formula, Φ, Ι m and(·) -1 These are the encoding matrix, the unit vector, and the inversion operation, respectively. After processing by the above formula, the transmitted waveform s can be separated. m The echo signal of (t).

[0133] Furthermore, simulation data was used to verify the robust beamforming method and system processing performance based on sparse reconstruction under a nonlinear array configuration proposed in this invention. The simulation parameters involved in the experiment are shown in Table 1. The MIMO-SAR system will simultaneously transmit two transmission waveforms, specifically as follows:

[0134]

[0135] Furthermore, the specific distribution of the transmitters and receivers is detailed in Table 2, where the coordinates of the transmitters can be represented as follows: It should be noted that this array configuration is a forward-looking array, and the array normal is parallel to the flight trajectory.

[0136] First, the DBF processing performance of the proposed method is verified through point target simulation experiments. Figure 1 The processing results obtained by least squares (LS) beamforming and the proposed technique are shown. It can be seen that the time delay difference between the desired signal and the interference component is T. sub To clearly compare the suppression effect of interference components, upsampling was performed on the three regions marked by the ellipse, and the results are as follows. Figure 1 As shown in (b)-(c), observations reveal that after processing with the proposed technique, the suppression of interference components approaches -40 dB, and the normalized amplitude of residual interference from the proposed technique is consistently lower than that of the LS beamforming technique. For example, in the region marked by the red ellipse, the interference suppression capability of the proposed technique is approximately 20 dB higher than that of the LS beamforming technique. Calculations show that the residual interference energies of the LS beamforming technique and the proposed technique are -15.84 dB and -27.77 dB, respectively, indicating that the proposed technique has better echo separation performance. Furthermore, the polar coordinate format algorithm (PFA) is used for imaging processing of the echo-separated data. Figure 2 The imaging results of the echo signal from transmitter 1 show that, without DBF processing, the target response will be submerged in the residual interference energy introduced by waveform coupling. Figure 2 (b) shows the imaging result after LS processing, which still contains a lot of residual interference energy. Figure 2 Image (c) shows the imaging results after processing with the proposed technique. It can be seen that the interference energy has been greatly suppressed and the imaging effect is good, which also confirms the effectiveness of the proposed technique.

[0137] Furthermore, the proposed technique's DBF processing performance under a nonlinear array configuration was verified using area target simulation. The imaging results are as follows: Figure 3 As shown. Figure 3 Image (a) is the scene ground truth map, with an image size of 2km × 2km. Figure 3 Image (b) shows the imaging result of the mixed signal before echo separation. The cross-correlation energy of the waveforms will cause a serious deterioration in imaging quality. To improve the imaging performance of the MIMO-SAR system, LS technology and the proposed technique are also used to suppress the interference energy in the image, and the results are as follows. Figure 3 As shown in (c) and (d), it can be seen that, although Figure 3 Compared to (b), image quality in (c) is improved, but interference energy still exists in the imaging results. After using the proposed technique, Figure 3 Interference energy in (d) was significantly suppressed, and the obtained imaging performance was comparable to the ground truth map. The simulation results above all confirm that the proposed sparse reconstruction-based beamforming technique has superior processing performance in nonlinear array configurations.

[0138] Table 1 Simulation parameters of nonlinear array MIMO-SAR

[0139]

[0140] Table 2 Location information of transmitting and receiving antennas

[0141]

[0142] Example 2

[0143] This embodiment provides a nonlinear array beamforming system, including:

[0144] Echo generation module: configured to execute step S1 of embodiment 1 to generate multi-channel echo data;

[0145] Guidance vector calculation module: configured to execute step S2 of embodiment 1, output signal guidance vector based on spatial vector model;

[0146] Constraint design module: configured to execute step S3 of embodiment 1 to generate distortion-free response constraints and disturbance suppression constraints;

[0147] Optimization and solution module: configured to execute step S4 of Example 1, solve the LASSO model and output the optimal weight vector;

[0148] Beamforming module: configured to execute step S5 of embodiment 1 and output the desired separated signal.

[0149] Example 3

[0150] This embodiment provides a MIMO-SAR echo separation device, including:

[0151] Elevation-dimensional nonlinear array antenna: Composed of multiple non-uniformly arranged receiving antenna elements, whose spatial positions are determined by a three-dimensional offset (Δx). n Δy n Δz n Definition; the array configuration must satisfy: receiver unit position vector The nonlinear array antenna is rigidly mounted on the surface of a conical or cylindrical carrier to adapt to the aerodynamic shape of the aircraft. Array orientation constraint: the array normal direction is strictly parallel to the platform's flight trajectory to ensure that the azimuth beam direction is consistent with the direction of motion.

[0152] SPC waveform transmitter: Employs segmented phase-coded waveforms, the mathematical form of which is:

[0153] Multi-channel receiver: Each receiving channel n independently acquires the mixed echo signal. The echoes need to be matched and filtered to generate multi-channel data.

[0154] The processor is configured to perform beamforming processing and output the desired signal after separation, i.e., to execute the entire process of S1-S5 in Example 1; it includes a post-processing module: performing time-shift alignment and weighted merging of the separated sub-pulses.

Claims

1. A robust beamforming method and system based on sparse reconstruction in a nonlinear array configuration, characterized in that, Includes the following steps: (1) Determine the pitch-dimensional nonlinear array configuration; use segmented phase coding (SPC) waveforms as M transmit waveforms; The mixed echo signal is acquired by the receiver; the mixed echo signal is then subjected to matched filtering to generate multi-channel echo data. (2) Based on the array configuration determined in step (1), define the target position space vector and the receiver position space vector; calculate the slant range difference between the receiving channels by using the spatial vector modulus operation and the inverse cosine function; construct the signal guidance vector related to the azimuth angle based on the slant range difference; (3) Based on the signal guidance vector in step (2), design a distortion-free response constraint for the desired signal within the azimuth pulse extension range, so that the inner product of the weight vector and all desired signal guidance vectors is 1; design a suppression constraint for the interference component and set the interference suppression step interval. (4) Construct the objective function of the generalized LASSO regression model using the distortion-free response constraint and interference suppression constraint from step (3); balance the weights of the desired signal and interference using the L2 norm term and the L1 norm penalty term; solve the convex optimization problem to obtain the optimal weight vector; (5) Construct an elevation-dimensional spatial snapshot signal based on the multi-channel echo data from step (1); use the optimal weight vector from step (4) to weight the spatial snapshot signal; and output the desired signal after separation.

2. The method according to claim 1, characterized in that, In step (1), the SPC waveform consists of linearly shifted sub-pulses, which are phase-coded modulated, and the coding vector φ m satisfy: In the formula, (·) H For the conjugate transpose operation, the subscript m represents the encoding vector corresponding to the m-th transmitted waveform.

3. The method according to claim 1, characterized in that, The slant range difference between receiving channels n and n′ in step (2) is calculated as follows: In the formula, η, v a And ||·|| represent slow time, platform speed, and modulo operation, respectively, P i =[x i ,y i ,z i [] represents the spatial vector corresponding to the position coordinates of point target i. Let be the spatial vector corresponding to the position coordinates of receiver n, where the offset Δx in the X direction is... n Y-direction offset Δy n and Z-direction offset Δz n Depending on the specific array configuration, the incident angle θ n,n′ (η) is specifically represented as: In the formula, arccos{·}, (·) T and These are the spatial vectors corresponding to the inverse cosine operation, transpose operation, and array center position coordinates, respectively; the signal guidance vector constructed for the azimuth angle α is represented as: In the formula In the formula, R, λ, and H are the slant range, wavelength, and platform height, respectively, and α is... The angle between the trajectory and the platform.

4. The method according to claim 1, characterized in that, The azimuth range covered by the distortion-free response constraint in step (3) is: In the formula, α c and α W These are the beam center azimuth and beamwidth, respectively.

5. The method according to claim 1, characterized in that, The objective function for step (4) is: where \(I_1 = [1, 1, \ldots, 1]\), \(\|\cdot\|_2\), \(\|\cdot\|_1\), \(\mu\) and are a vector with all elements being 1, the \(l_2\) norm, the \(l_1\) norm, the penalty coefficient, and the calculated optimal weight vector, respectively; and \(\Xi\) k , the specific form of \(k\neq k_0\) is: In the formula, c and T sub Δα represents the speed of light and the subpulse width, respectively. s and Δα i These are the step intervals set for the desired signal and the interference, respectively, where k and k0 are the subscripts corresponding to the desired signal and the interference components, respectively.

6. The method according to claim 1, characterized in that, Step (5) is followed by echo separation post-processing: Time-shift alignment is performed on the separated sub-pulse signals; Sub-pulse signals are weighted and merged using an encoding matrix.

7. A nonlinear array beamforming system, characterized in that, include: Echo generation module: configured to perform step (1) of claim 1 to generate multi-channel echo data; Guiding vector calculation module: configured to execute step (2) of claim 1, outputting a signal guiding vector based on a spatial vector model; Constraint design module: configured to execute step (3) of claim 1 to generate distortion-free response constraints and disturbance suppression constraints; Optimization and solution module: configured to execute step (4) of claim 1, solve the LASSO model and output the optimal weight vector; Beamforming module: configured to perform step (5) of claim 1 and output the desired separated signal.

8. The system according to claim 7, characterized in that: The optimization solution module integrates a convex optimization solver and supports the calculation of L1 / L2 mixed norm penalty terms.

9. A MIMO-SAR echo separation device, characterized in that... Applying the method of any one of claims 1-6, comprising: Pitch-dimensional nonlinear array antenna; SPC waveform transmitter; Multi-channel receiver; The processor is configured to perform beamforming processing and output the desired separated signal.

10. The apparatus according to claim 9, characterized in that: The nonlinear array antenna is mounted on the surface of a conical or cylindrical carrier, with the array normal parallel to the flight trajectory.

Images