Complementary waveform design method for SAR (Synthetic Aperture Radar) distance sidelobe suppression

Abstract

The invention discloses a complementary waveform design method for SAR (Synthetic Aperture Radar) distance sidelobe suppression, which is applied to the technical field of radars, and introduces a concept of a complementary sequence in order to solve the adverse effect caused by waveform agility, explore the feasibility of waveform agility in improvement of SAR distance sidelobe suppression performance and maintain the distance resolution at the same time. The side lobes of the complementary sequences can offset each other in any non-zero phase lag theory. However, direct application of a complementary sequence to SAR may lead to decrease in SAR image quality. Therefore, the amplitude-phase modulation effect introduced by waveform agility is considered in a combined manner, and the low-sidelobe waveform design of SAR imaging under the condition that the main lobe is not expanded is realized.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to a complementary waveform design technology for suppressing mid-range side lobes in SAR imaging. Background Art

[0002] Synthetic aperture radar (SAR) is a radar system that can achieve high-resolution imaging in all weather conditions. SAR transmits a linear frequency modulation signal with a large time-width product and achieves pulse compression through matched filtering at the receiving end, thereby achieving high resolution in the distance direction. Using synthetic aperture technology, SAR can also achieve high resolution in azimuth, so it has a wide range of applications in disaster monitoring, resource exploration, geological mapping, military reconnaissance and other fields.

[0003] Range sidelobes are a common concern in SAR imaging. Sidelobes of strong scattering targets may mask weak targets, reduce SAR image quality, and increase the difficulty of image interpretation. Traditional single waveform design reduces range resolution while reducing sidelobes due to the limitation of energy conservation principle. Typical methods for suppressing range sidelobes can be summarized into two categories: receiving processing and waveform optimization. Among them, the space-varying apodization (SVA) method eliminates sidelobes through different weighting functions, but this nonlinear processing may reduce the signal-to-noise ratio (SNR) and cause loss of phase information. Nonlinear frequency modulation (NLFM) signals have attracted widespread attention due to their potential in reducing sidelobes, but their design is still limited by energy conservation.

[0004] In the paper “First demonstration of echo separation for orthogonal waveform encoding MIMO-SAR based on airborne experiments,” (IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–16, 2022.), it is proposed to use chaotic frequency modulation (CFM) signals to overcome this limitation, and to cancel the range sidelobes by transmitting different CFM signals between different pulses. However, waveforms transmitted in different azimuths also bring new challenges, such as energy spikes caused by Doppler spectrum aliasing and incoherent azimuth compression. The paper “New insights into SAR alternate transmitting mode based on waveform diversity,” (IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–9, 2022.) proposes an azimuth compensation algorithm to eliminate the azimuth ambiguity caused by waveform agility, but this processing will reduce the signal-to-noise ratio and compensate different waveforms to the same waveform. Summary of the invention

[0005] The range sidelobe problem in SAR imaging in the prior art can cause the sidelobes of strong scattering targets to cover weak targets, reduce the quality of SAR images, and increase the difficulty of image interpretation. In order to overcome the energy conservation limitation of traditional single waveform design, the present invention proposes a SAR range sidelobe suppression method based on complementary waveform design. This method fully utilizes the freedom of the transmitter, transmits multiple waveforms, and utilizes the information difference between different pulses, thereby reducing the sidelobe level while maintaining the range resolution unchanged.

[0006] The technical solution adopted by the present invention is: a complementary waveform design method for SAR range sidelobe suppression, comprising:

[0007] S1, transmit complementary waveforms between different pulses;

[0008] S2, based on the complementary waveform of step S1, with the goal of minimizing the weighted integrated sidelobe level of the point spread function, introducing spectrum constraints and normal mode constraints, and constructing a waveform optimization problem;

[0009] S3, introducing two auxiliary variables to replace the variables in the spectrum constraint and the normal mode constraint respectively; and using the auxiliary variables to reconstruct the waveform optimization problem in step S2;

[0010] S4. Minimize the augmented Lagrangian function by iteratively optimizing the waveform parameters to obtain the final transmission signal.

[0011] Beneficial effects of the present invention: The present invention proposes a complementary waveform design method for suppressing range sidelobes in SAR imaging. This method overcomes the limitations of traditional single waveform design by transmitting multiple complementary waveforms and utilizing the information differences between waveforms. The SAR waveform optimization problem is formulated as a non-convex optimization problem, and the inexact alternating direction penalty method (IADPM) framework is used to solve this problem. This method can effectively handle complex optimization problems and find approximate solutions. The augmented Lagrangian function is used to handle the constraints in the optimization problem, so that the algorithm can meet the spectrum constraints while keeping the waveform amplitude constant, thereby improving the practicality and flexibility of the algorithm. The iterative sequential quadratic optimization (ISQO) technique is used to solve the non-convex quartic optimization subproblem. This method effectively approximates the optimal solution by sequentially solving a series of approximate problems. Adaptive Lagrangian multipliers and penalty function parameter update rules are introduced into the algorithm, which dynamically adjust the parameters according to the changes in the residuals, thereby promoting the convergence of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a single waveform limit diagram.

[0013] Figure 2 It is a schematic diagram of waveform agility.

[0014] Figure 3 It is the flow chart of SAR-PSFS method.

[0015] Figure 4 Figure 2 is a comparison of the autocorrelation functions (ACF) of different waveform designs.

[0016] Figure 5 This is the compression result diagram of point target imaging distance under different waveforms;

[0017] Among them, (a) is the point target imaging distance compression result corresponding to LFM, (b) is the point target imaging distance compression result corresponding to NLFM, (c) is the point target imaging distance compression result corresponding to MM-WPSL, and (d) is the point target imaging distance compression result corresponding to SAR-PSFS.

[0018] Figure 6 It is the frequency-Doppler domain imaging result diagram under different waveforms;

[0019] Among them, (a) is the frequency-Doppler domain imaging result corresponding to LFM, (b) is the frequency-Doppler domain imaging result corresponding to NLFM, (c) is the frequency-Doppler domain imaging result corresponding to MM-WPSL, and (d) is the frequency-Doppler domain imaging result corresponding to SAR-PSFS.

[0020] Figure 7 This is the imaging result diagram of point target under different waveforms;

[0021] Among them, (a) is the point target imaging result corresponding to LFM, (b) is the point target imaging result corresponding to NLFM, (c) is the point target imaging result corresponding to MM-WPSL, and (d) is the point target imaging result corresponding to SAR-PSFS.

[0022] Figure 8 It is a comparison chart of distance profiles of different waveforms.

[0023] Fig. 9 is the distributed scene imaging result map;

[0024] Among them, (a) is the distributed scene imaging result corresponding to LFM, (b) is the distributed scene imaging result corresponding to NLFM, (c) is the distributed scene imaging result corresponding to MM-WPSL, and (d) is the distributed scene imaging result corresponding to SAR-PSFS. DETAILED DESCRIPTION

[0025] The present invention is mainly verified by simulation experiment method, and all steps and conclusions are verified by simulation in Matlab.

[0026] Step 1: Establish a signal model. According to the parameters of the SAR system, such as carrier frequency f0, pulse repetition frequency f a et al., established a SAR signal model that takes into account the target scattering characteristics and waveform transmission characteristics. Figure 1 As shown, the limitations of a single waveform design are demonstrated, and complementary waveform designs are therefore considered.

[0027] In the SAR signal model, it is considered that the target scattering does not change within a small change in the observation angle. In the side-looking spotlight mode, the expected echo of a point target can be expressed as:

[0028]

[0029] Where t and η represent fast and slow time variables, σ0 represents the radar cross-sectional area of ​​the point target, ω r (t) and ω a (η) represents the fast time envelope and the slow time envelope respectively, f0 is the carrier frequency, η c represents the zero Doppler moment, R(η) is the slant range between the radar and the target at the slow time η, c is the speed of light, and f a is the pulse repetition frequency (PRF), and δ is the Dirac function.

[0030] Consider ωr (t) is a rectangular window, then the echo signal s0(t,η) after range compression can be expressed as:

[0031]

[0032] in The transmitted signal x m (t) The distance compression result.

[0033] make A deterministic signal (such as LFM) distance compression result, then It can be expressed as:

[0034]

[0035] where u m (t) is the value of Modulation; deterministic signals such as LFM (Linear Frequency Modulation, linear frequency modulation signal).

[0036] Therefore, the expression for the original pulse compression result can be reformulated as:

[0037]

[0038] make And split the above equation into the form of the sum of the main lobe area and the side lobe area:

[0039]

[0040] Where b0 is the maximum value of the matched filter, w(t) is a rectangular window with the main lobe area being 1 and the other areas being 0. is the complementary window function of w(t), satisfying

[0041] Due to the law of conservation of energy, the matched filter values ​​of different waveforms in the main lobe are the same, so d(t,η) in the expression can be simplified to b0. From s3(t,η), it can be seen that the imaging expression of the main lobe area is consistent with the traditional transmission mode, while the additional term d(t,η) introduced by the waveform agility in the side lobe area will increase the amplitude and phase modulation in the azimuth dimension, so the SAR image can be expressed as:

[0042]

[0043] in R0 represents the slant range at zero Doppler moment, p a (η) is the amplitude of the impulse response in the azimuth dimension, and h(t,η) is the compression result. Specifically, pa (η) is ω a (η-η c ) is a manifestation of the azimuth dimension. This relationship is reflected in p a (η) as The multiplier factor of the window function directly affects the signal amplitude in the main lobe area; h(t,η) is As a result of the orientation processing, this relationship is reflected in h(t,η) as The multiplier factor of the window function directly affects the signal amplitude and phase in the sidelobe area.

[0044] While maintaining the consistency of waveform energy, waveform agility does not affect the energy accumulation of SAR, but in the sidelobe area, waveform agility adds an azimuth modulation term. Therefore, by jointly optimizing all transmitted waveforms, it is theoretically possible to suppress both range sidelobes and amplitude and phase modulation.

[0045] Step 2: Complementary waveform design. The concept of complementary sequence is introduced to construct a waveform optimization problem. The goal is to minimize the point spread function weighted integrated sidelobe level (PSFWISL). The waveform agility method of range sidelobe suppression is achieved by transmitting different waveforms between different pulses, such as Figure 2 shown.

[0046] First, we introduce the concept of complementary sequence, assuming that the sequence set Represents the transmitted signal x m (t) is a discrete form, where represents a set of complex numbers, m=1,...,M represents the discrete phase coded signal transmitted at the mth pulse time, M is the total number of pulse times, and N is the number of coded sub-pulses. When the autocorrelation sum of is zero at any non-phase lag k, the sequence set is called a complementary sequence, that is:

[0047]

[0048] in represents the sequence x m The aperiodic autocorrelation function at lag k is, yes discrete form of .

[0049] Combining the concept of complementary sequence and the azimuth characteristics of SAR echo, a waveform optimization problem is constructed. The optimization goal is to minimize the point spread function weighted integrated sidelobe level (PSFWISL), which is defined as:

[0050]

[0051] where ω(k,a) is the weight of the SAR imaging result at lag k and a-th azimuth, h m (a) is the response at the ath azimuth.

[0052] Step 3: Construction of the optimization problem. The waveform optimization problem is formulated as a non-convex optimization problem with a quartic objective function.

[0053] In order to improve the adaptability of the designed phase-coded signal and prevent the interpolation operation from affecting the signal performance, the spectrum constraint is introduced:

[0054]

[0055] where f l is the discrete Fourier transform vector of the lth frequency point, represents f l The conjugate transpose of , q(l,m) is the value of the mth spectrum mask at the lth frequency point. Specifically, q(l,m) is a window in the frequency domain, which can be a rectangular window, Hanning window or other window functions.

[0056] To avoid degradation or distortion when generating waveforms in SAR systems, normal mode constraints are considered:

[0057]

[0058] Taking the above factors into consideration, the waveform optimization problem can be expressed as:

[0059]

[0060] Among them, J k Represents a matrix, J k (i,j)=1if ji=k,else J k (i, j) = 0, the optimization problem is a non-convex optimization problem with a quartic objective function.

[0061] Step 4: Inexact Alternating Direction Penalty Method (IADPM) is used. Auxiliary variables are introduced to transform the original problem into a minimization problem of augmented Lagrangian function. The discretized set of transmitted signals is updated alternately and iteratively using the IADPM framework. Auxiliary variable Y (t) , Lagrange multipliers and penalty function parameters

[0062] In order to solve the above quartic non-convex optimization problem, and considering that it is very challenging to directly solve the original problem, the alternating direction penalty method (IADPM) framework is adopted to decompose the original problem into several sub-problems that are easier to solve, and the solution of the original problem is approximated through alternating iterations.

[0063] 41 Introduction of auxiliary variables

[0064] In order to simplify the problem, auxiliary variables y(l,m) and z are introduced and defined as follows:

[0065]

[0066] The spectrum constraint and the normal mode constraint y(l,m) can be decomposed into two sub-problems through the IADPM framework, and z converts the sequence set into a vector, thereby simplifying the original problem.

[0067] 42 Reconstruction of the optimization problem

[0068] Using auxiliary variables, problem (11) can be reconstructed as:

[0069]

[0070] Among them, B k,a =J k Diag(c a ), Diag(c a ) means c a The diagonal matrix of

[0071] Step 5: Iteratively solve the subproblems. Use the Iterative Sequential Quadratic Optimization (ISQO) technique to solve the non-convex quartic optimization subproblem. Approximate the optimal solution by sequentially solving the approximate problem. After each iteration, update the discretized set of the transmitted signal. and auxiliary variable Y (t) , and check the convergence conditions. If the preset exit conditions are met, the iteration is terminated. Output the discretized set of the final converged emission signal like Figure 3 As shown in Figure 2, the iterative solution process includes the following steps:

[0072] 51 Initialization parameters

[0073] Set the initial set of discretized emission signals

[0074] Initial auxiliary variable Y (0)

[0075] Initial Lagrange multiplier

[0076] Initial penalty function parameters

[0077] Weight coefficient ω(k,a), k=1,…,N-1

[0078] Convergence parameter δ 1,c ,δ 2,c ,v

[0079] Initial iteration counter t = 0

[0080] 52 Update waveform parameters

[0081] Use the current auxiliary variable Y (t) , Lagrange multipliers and penalty function parameters Update the waveform parameters by minimizing the augmented Lagrangian function As shown in formula (15).

[0082]

[0083] And ensure that the updated waveform parameters satisfy the normal mode constraint |x m (n)|=1.

[0084] The iterative sequential quadratic optimization (ISQO) technique is used to solve (15):

[0085] enter

[0086] ω(k), k=1,…,N-1, i=0,Y (t) ,

[0087] initialization

[0088]

[0089] repeat

[0090] 1: Calculate Υ(z) and λ

[0091] in λ=max{eig(Υ(z))}, where λ is the maximum eigenvalue of Υ(z).

[0092] 2: Update I N is the identity matrix

[0093] 3: Calculation in, is a vector defined at iteration t as: is a vector defined at iteration t as: and Used to handle spectral constraints in augmented Lagrangian functions; ⊙ represents the Hadamard product;

[0094] 4: According to the formula Update x m(i+1)

[0095] 5: Update z i+\

[0096] 6: Increase the iteration counter i = i + 1

[0097] Final Output

[0098] 53 Update auxiliary variables

[0099] Discretize the set according to the latest emission signal Update the auxiliary variable Y by minimizing the augmented Lagrangian function (t+1) , as shown in formula (16).

[0100]

[0101] Ensure that the updated auxiliary variables satisfy the spectral constraints Omit the objective function of problem (16) and y m Using the square completion method, problem (16) becomes

[0102]

[0103] in,

[0104] Therefore, the solution is

[0105]

[0106] 54 Update Lagrange multipliers and penalty function parameters

[0107] According to the latest auxiliary variable Y (t+1) , update the Lagrange multiplier using equations (19) and (20) and penalty function parameters

[0108]

[0109] in is the residual of the mth waveform at the tth iteration, δ 1,c and δ 2,c is the convergence parameter, 0<δ 1,c <1,δ 2,c >1 but close to 1.

[0110]

[0111] in is the intermediate update value of the penalty function parameter,

[0112] is the intermediate update value The maximum absolute value of .

[0113] 55 iteration counter update

[0114] Update iteration counter t=t+1.

[0115] 56 Exit iterative condition check

[0116] Check whether the preset exit condition is met, that is, the bi-norm of the difference between the two iteration results is less than a threshold or the maximum number of iterations is reached. If so, stop the iteration and output the converged discrete set of the transmitted signal

[0117] Step 6: Performance evaluation. By simulating point targets and distributed scenarios, the application effect of the proposed waveform design method in SAR imaging is evaluated. Figure 4 As shown, the autocorrelation functions (ACF, Autocorrelation Function) of different waveforms are displayed, and the linear frequency modulation (LFM), non-linear frequency modulation (NLFM, Non-Linear Frequency Modulated), minimum and maximum weighted peak sidelobe level (MM-WPSL, Min-Max Weighted Peak Sidelobe Level) and the complementary waveform design method proposed in the present invention are compared. Figure 6 The frequency-Doppler domain performance of different waveforms is shown. Figure 6 (a) shows that the Doppler bandwidth of the LFM signal is about 500 Hz, and the energy is mainly concentrated in the main lobe area. Figure 6 (b) shows that compared with the LFM signal, in order to suppress the peak sidelobe level (PSL), the spectrum of the NLFM signal is no longer rectangular. Figure 6 (c) shows that aliasing occurs in the Doppler domain of the MM-WPSL waveform, the energy spreads outside the Doppler bandwidth, and the signal within the Doppler bandwidth is severely modulated along the azimuth dimension. Figure 6(d) in the middle shows that the proposed SAR-PSFS (pointspread function shaping) waveform significantly reduces the aliasing phenomenon within the Doppler bandwidth, and the energy is mainly concentrated in the main lobe area, which indicates that the proposed waveform optimization method can effectively reduce Doppler aliasing, emphasizing that the sidelobe suppression effect of the method proposed in the present invention is better. Figure 7 (a) shows the imaging result of the LFM signal, where the sidelobe level is relatively high, resulting in more stray energy around the target and poor imaging quality. Figure 7 (b) shows that the imaging result of NLFM signal is improved compared with LFM, and the sidelobe level is reduced, but due to the limitation of its single waveform design, there is still a certain sidelobe level. Figure 7 The imaging result of the MM-WPSL waveform in (c) shows the effect of waveform agility, but due to the lack of joint optimization, energy peaks appear outside the main energy region, resulting in poor imaging quality. Figure 7 The imaging result of the SAR-PSFS waveform proposed in (d) reduces the sidelobe level while effectively suppressing the energy peak, improving the imaging quality and making the target clearer. Figure 8 The range profiles of different waveforms are shown. It can be seen that the range profile of the LFM signal shows a higher sidelobe level, resulting in stronger energy outside the main lobe area, which affects the clarity of the target; the range profile of the NLFM signal shows a lower sidelobe level than the LFM signal, indicating that the NLFM signal has a certain effect in sidelobe suppression, but the effect is not significant. The profile results of the MM-WPSL waveform show that the sidelobe level has been reduced, but there is still a certain amount of sidelobe energy, especially in the area far from the main lobe; the results of the Hanning window provide a better sidelobe suppression effect, but may lead to an increase in the mainlobe width; the SAR-PSFS waveform shows the lowest sidelobe level in the range profile, showing a significant sidelobe suppression effect, while maintaining the same mainlobe width as the Hanning window. This shows that the proposed method suppresses the sidelobes without sacrificing range resolution. Fig. 9 The imaging results of distributed scenes are demonstrated, verifying the application effect of the proposed waveform design method in actual scenes.

[0118] Through these steps, the present invention provides an effective SAR waveform optimization method, which can significantly suppress the range sidelobe while maintaining high resolution and improve the quality of SAR imaging. The flexibility and adaptability of this method make it applicable to different application scenarios and SAR system configurations. The present invention verifies the performance of the proposed waveform through simulation experiments. The experiment includes two cases: point target and distributed scenario. The simulation results show that compared with the traditional linear frequency modulation (LFM) signal, NLFM signal and minimum maximum weighted peak sidelobe level (MM-WPSL), the waveform designed by the present invention achieves a lower sidelobe level while maintaining the same main lobe width, and can effectively reduce the energy spike caused by waveform agility.

[0119] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A complementary waveform design method for SAR range sidelobe suppression, characterized in that: include: S1, transmit complementary waveforms between different pulses; S2, based on the complementary waveform of step S1, with the goal of minimizing the weighted integrated sidelobe level of the point spread function, introducing spectrum constraints and normal mode constraints, and constructing a waveform optimization problem; S3, introducing two auxiliary variables to replace the variables in the spectrum constraint and the normal mode constraint respectively; and using the auxiliary variables to reconstruct the waveform optimization problem in step S2; S4. Minimize the augmented Lagrangian function by iteratively optimizing the waveform parameters to obtain the final transmission signal.

2. The complementary waveform design method for SAR range sidelobe suppression according to claim 1, characterized in that: In step S1, if and only if When the autocorrelation sum of is zero at any non-zero phase lag k, it is said that is a complementary sequence, that is: Where M is the total number of pulse times, represents a sequence set, including all x from m=1 to M m , represents a complex number set, N is the number of coded sub-pulses, x m represents the mth transmitted signal x m (t) in discrete form; Represents the sequence x m Aperiodic autocorrelation function at lag k.

3. The complementary waveform design method for SAR range sidelobe suppression according to claim 2, characterized in that: The waveform optimization problem is expressed as: Among them, J k Represents a matrix, J k (i,j) is J k When ji=k, J k (i,j)=1, otherwise J k (i,j)=0; ω(k,a) is the weight of the SAR imaging result at the ath azimuth at the lag k time; h m (a) is the response at the ath azimuth; f l is the discrete Fourier transform vector of the lth frequency point, represents f l The conjugate transpose of , q(l,m) is the value of the mth spectrum mask at the lth frequency point, x m (n) is the value of the mth waveform at the nth sampling point. This condition means that at all sampling points n, the amplitude of the mth waveform |x m (n)|Must always be equal to 1.

4. The complementary waveform design method for SAR range sidelobe suppression according to claim 3, characterized in that: Introduce auxiliary variables y(l,m) to replace the variables in the spectrum constraint, that is: Introduce auxiliary variables z to replace the variables in the norm constraint, that is: The superscript T represents transposition, which converts the sequence set into a vector and simplifies the original problem; Reframe the optimization problem as: Among them, B k,a =J k Diag(c a ), Diag(c a ) means c a The diagonal matrix of 5. The complementary waveform design method for SAR range sidelobe suppression according to claim 4, characterized in that: The implementation process of step S4 includes: S41. Setting the initial set of discrete transmission signals Initial auxiliary variable Y (0) , initial Lagrange multiplier Initial penalty function parameters Weight coefficient ω(k,a), k=1,…,N-1, convergence parameter δ 1,c ,δ 2,c ,v, initial iteration counter t=0; S42, use the current auxiliary variable Y (t) , Lagrange multipliers and penalty function parameters Use iterative sequential quadratic optimization technology to solve the following equation to update the discretized set of transmitted signals 6. The complementary waveform design method for SAR range sidelobe suppression according to claim 5, characterized in that: During the iteration process, according to the latest waveform parameters Update the auxiliary variable Y by minimizing the augmented Lagrangian function (t+1) , Y is the matrix of y(l,m) combined together, as follows:

7. The complementary waveform design method for SAR range sidelobe suppression according to claim 6, characterized in that: During the iteration process, according to the latest auxiliary variable Y (t+1) , update the Lagrange multiplier in is x m The residual at the tth iteration, δ 1,c and δ 2,c is the convergence parameter, 0<δ 1,c <1,δ 2,c >1.

8. The complementary waveform design method for SAR range sidelobe suppression according to claim 6, characterized in that: During the iteration process, according to the latest auxiliary variable Y (t+1) , update the penalty function parameters in is the intermediate update value of the penalty function parameter, is the intermediate update value The maximum absolute value of .

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