A radar coded waveform sidelobe quick cancellation suppression method

Abstract

The application belongs to the technical field of radar signal processing, and relates to a radar coding waveform sidelobe fast cancellation suppression method. The method converts the Doppler sidelobe cancellation problem into a signal recovery optimization problem, constructs an optimization model based on the minimum energy criterion of the target signal after cancellation, and realizes joint optimization estimation of target multidimensional parameters (velocity, angle, amplitude and phase information) by using a gradient descent algorithm. Finally, high-precision target parameter estimation and robust Doppler sidelobe cancellation performance can be realized. Through the application, high-precision estimation of target multidimensional parameters can be effectively realized, Doppler high-sidelobe cancellation can be realized, the detection capability of weak targets can be improved, and the missed detection rate can be reduced.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology and relates to a method for fast sidelobe cancellation suppression of radar coded waveforms. Background Technology

[0002] Multiple Input Multiple Output (MIMO) technology is widely used because it can achieve higher angular resolution for a given radar size and number of antennas. The transmitted waveforms of MIMO radar need to be mutually orthogonal, and phase-coded waveforms are one of the important ways to achieve mutual orthogonality of radar transmitted waveforms.

[0003] Due to its low hardware complexity and high Doppler tolerance, slow-time phase-coded waveforms have become a research hotspot in phase-coded waveforms. The basic idea is as follows: At the transmitting end, the initial phase of the signal is modulated by a slow-time phase-coded sequence and transmitted simultaneously by all antennas. At the receiving end, since the receiving antenna simultaneously receives signal echoes from different transmitting antennas, echo signal coupling between transmitting antennas is inevitable. Therefore, the echo signals need to be decoded to achieve echo separation. However, residual orthogonal components from each transmitting antenna still exist after decoding. These components, after being weighted by the target amplitude, will cause an overall increase in the sidelobes on the Doppler spectrum, resulting in weak targets being submerged in the high sidelobes of strong targets, leading to missed detection. Therefore, how to suppress Doppler sidelobes is a key research focus in the application of slow-time phase-coded waveforms.

[0004] To address the high sidelobe problem in Doppler imaging, some studies have focused on designing the coding waveform to improve the orthogonality of slow-time phase coding sequences, thereby mitigating the influence of residual orthogonal components. However, this method has a theoretical lower limit; under ideal conditions, the Doppler sidelobe suppression effect will not exceed 10log. 10 (L)dB, where L is the length of the encoded sequence.

[0005] To address the high sidelobes issue in slow-time phase-coded waveforms, further research is needed on Doppler sidelobe cancellation methods to reduce the impact of residual orthogonal components. In this regard, the patent "Residue cancellation for automated vehicle MIMO radar" (US9952319) proposes using a windowed truncation method of the target spectrum to extract target information, recover and decode residual orthogonal components, thereby achieving residual orthogonal component cancellation. Furthermore, the patent "Multi-target detection in CDMA radar system" (US10795013B2) proposes canceling residual time-domain signals by reconstructing and decoding target detection information. However, these methods rely on coarse estimation of target information, failing to consider factors such as parameter estimation errors, easily inducing spurious peaks in the spectrum, and exhibiting poor robustness in sidelobe suppression. Summary of the Invention

[0006] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and propose a fast sidelobe cancellation suppression method for radar-coded waveforms. This method transforms the Doppler sidelobe cancellation problem into a signal restoration optimization problem, constructs an optimization model based on the criterion of minimizing the energy of the target signal after cancellation, and uses a gradient descent algorithm to achieve joint optimization estimation of multi-dimensional target parameters (velocity, angle, amplitude and phase information). Ultimately, it can achieve high-precision target parameter estimation and robust Doppler sidelobe cancellation performance. This invention can effectively achieve high-precision estimation of multi-dimensional target parameters and achieve high-sidelobe cancellation of Doppler, thereby improving the detection capability of weak targets and reducing the false detection rate.

[0007] A method for fast sidelobe cancellation suppression of radar-coded waveforms, comprising the following steps:

[0008] Step 1: Perform range-dimensional matched filtering on the radar echo to obtain the target range-dimensional focused echo signal, and construct a target range-dimensional focused echo signal model based on the obtained target range-dimensional focused echo signal;

[0009] Step 2: Based on the criterion of minimizing the energy of the canceled signal, construct an optimization model using the target range dimension focused echo signal model built in Step 1;

[0010] Step 3: Perform multi-dimensional matched filtering on the target range-focused echo signal obtained in Step 1 to obtain a coarse estimate of the target's multi-dimensional parameters (velocity, angle, amplitude, and phase).

[0011] Step 4: Based on the gradient descent algorithm, use the coarse estimation result obtained in Step 3 as the initial value to solve the optimization model constructed in Step 2, and obtain the fast cancellation suppression result of the radar coded waveform sidelobes.

[0012] In step one, the specific method for performing range-dimensional matched filtering on the radar echo is as follows:

[0013] The radar echo signal is processed by de-chirp, and the fast-time single frequency-modulated continuous wave signal is processed by data windowing and FFT to complete the target range dimension focusing and obtain the target range dimension focused echo signal.

[0014] In step one, the method for constructing the signal model is as follows:

[0015] Let M be the number of radar transmitting antennas, N be the number of receiving antennas, and L be the number of frequency modulation sequences. Then the received signal y of a range cell can be expressed as:

[0016] y = x + n

[0017] Where x represents the radar echo signals of K targets, and n represents Gaussian white noise;

[0018] Based on the slow-time (Doppler) coded modulation transmitted waveform, the echo signals x of K targets after range-dimensional focusing are represented as:

[0019] x=[ΦA Tx (θ)⊙A D (v)]αA Rx (θ)

[0020] Where ⊙ is the Hadamard product, and

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Where f0 is the radar carrier frequency; c represents the speed of light; α1, α2, α K These represent the magnitude information of the 1st, 2nd, and Kth targets, respectively. These represent the phase information of the 1st, 2nd, and Kth targets, respectively; v1, v2, v K These represent the velocity information of the 1st, 2nd, and Kth targets, respectively; θ1, θ2, θ K These represent the angle information of the 1st, 2nd, and Kth targets, respectively; T is the pulse repetition period; d Tx and d Rx These are the distances between the transmitting and receiving antennas, respectively.

[0027] In step two, the specific method for constructing the optimization model is as follows:

[0028] The optimization model is constructed by minimizing the energy of the target signal after cancellation, i.e., the sum of squared differences between the observed echo and the reconstructed echo matrices, as shown below:

[0029]

[0030] In step three, the specific method for multi-dimensional matching filtering is as follows:

[0031] In the range-slow time spectrum, along each range point, slow-time decoding is performed according to the preset phase encoding sequence Φ to separate the echo signal, resulting in the range-slow time spectrum of M*N virtual channels. Then, FFT processing is performed along the slow time dimension to achieve two-dimensional target focusing, resulting in the range-Doppler spectrum of M*N virtual channels. Target detection is performed on the range-Doppler spectrum to obtain K over-detected targets and extract their velocity information, yielding a coarse estimate of the target velocity. The M*N virtual channel data of the K over-detected targets are extracted, and FFT processing is performed along the channel dimension to obtain the target angle spectrum and extract its angle information, yielding a coarse estimate of the target angle. Finally, based on the extracted target velocity and angle information, the coarse estimate of the target amplitude and phase is obtained according to the following formula.

[0032] α k ={[ΦA Tx (θ)⊙A D (v)] -1 y[A Rx (θ)] -1} kk

[0033] In this context, the subscript kk represents the element in the k-th row and k-th column of the square matrix.

[0034] In step four, the method for solving the optimization model based on the gradient descent algorithm is as follows:

[0035] Referring to the focused echo model in step one, the reconstructed echo x is initialized using the coarse estimation results of the target multidimensional parameters obtained in step two;

[0036] The steps to obtain the optimal reconstructed echo by iterating through the multidimensional parameters of the target using the gradient descent algorithm in multiple rounds include the following four steps:

[0037] The first step is to calculate the gradient of the optimization model with respect to the target amplitude and phase parameters:

[0038]

[0039] The second step is to calculate the gradient of the optimization model with respect to the target velocity parameters:

[0040]

[0041] Where Im is the operation of extracting the imaginary part of a complex number, I L It is a diagonal matrix with elements from 0 to L-1;

[0042] The second step is to calculate the gradient of the optimization model with respect to the target angle parameters:

[0043]

[0044] in,

[0045] Tx(θ k )=Im{αA Rx (θ)Δy H [(Φ / M A Tx (θ)⊙A D (v))]} kk

[0046] Rx(θ k )=Im{A Rx (θ)I N Δy H [(ΦA Tx (θ)⊙A D (v))]α} kk

[0047] Among them, I M and I N It is a diagonal matrix with elements from 0 to M-1 and from 0 to N-1, respectively;

[0048] The fourth step involves iteratively applying the momentum method to obtain the optimal estimate of the target parameters and the optimal reconstructed echo, thus yielding the Doppler sidelobe cancellation result.

[0049] The update results of the target's multidimensional parameters (amplitude, phase, velocity, angle) are expressed as follows:

[0050] α k (i+1)=α k (i)-εd α (i+1)

[0051] v k (i+1)=v k (i)-εd v (i+1)

[0052] θ k (i+1)=θ k (i)-εd θ (i+1)

[0053] Where i is the iteration number, ε is the learning rate, and dα d v d θ Represented as:

[0054]

[0055]

[0056]

[0057] Where γ is the momentum parameter.

[0058] In the above iterative process, after each round of iteration, the target signal energy E after cancellation in the current round is obtained. i If E in a series of iterations i If the change is less than the preset termination threshold, the iteration can be terminated early, and the target parameter estimation result and the Doppler sidelobe cancellation result y–x can be output. i If the termination condition is not met, the loop continues to iterate until the maximum number of iterations is reached.

[0059] The present invention has the following beneficial effects:

[0060] (1) It can achieve high-precision estimation of multidimensional parameters of the target.

[0061] This invention uses minimizing the energy of the canceled signal as the optimization model, and can simultaneously estimate the target velocity, angle and amplitude phase information, thereby achieving high-precision estimation of the target's multidimensional parameters.

[0062] (2) It has robust Doppler sidelobe cancellation performance.

[0063] Traditional methods suffer from poor robustness in sidelobe cancellation due to the limitations of parameter estimation accuracy. This invention transforms the sidelobe cancellation problem into an optimization problem and uses the gradient descent algorithm to solve it, which can effectively reduce the impact of errors and achieve robust Doppler sidelobe cancellation. Attached Figure Description

[0064] Figure 1 This is a flowchart of a method for fast sidelobe cancellation suppression of radar-coded waveforms.

[0065] Figure 2 The results show a comparison between the original Doppler spectrum and the Doppler spectrum after strong target sidelobe suppression.

[0066] Figure 3 The results show the Doppler spectrum comparison after sidelobe suppression of weak targets.

[0067] Figure 4 The results show the velocity and angle estimation of multiple targets. Detailed Implementation

[0068] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0069] This invention proposes a fast sidelobe cancellation suppression method for radar-coded waveforms. The overall processing flow of this method is as follows: Figure 1 As shown, the specific implementation method is as follows:

[0070] Step 1: Perform range-dimensional matched filtering on the radar echo to obtain the target range-dimensional focused echo signal, and construct a target range-dimensional focused echo signal model based on the obtained target range-dimensional focused echo signal. The specific method is as follows:

[0071] The radar echo signal is processed by de-chirp, and the fast-time single frequency-modulated continuous wave signal is processed by data windowing and FFT to complete the target range dimension focusing and obtain the target range dimension focused echo signal.

[0072] Let M be the number of radar transmitting antennas, N be the number of receiving antennas, and L be the number of frequency modulation sequences. Then the received signal y of a range cell can be expressed as:

[0073] y = x + n

[0074] Where x represents the radar echo signals of K targets, and n represents Gaussian white noise;

[0075] Based on the slow-time (Doppler) coded modulation transmitted waveform, the echo signals x of K targets after range-dimensional focusing are represented as:

[0076] x=[ΦA Tx (θ)⊙A D (v)]αA Rx (θ)

[0077] Where ⊙ is the Hadamard product, and

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] Where f0 is the radar carrier frequency; c represents the speed of light; α1, α2, α K These represent the magnitude information of the 1st, 2nd, and Kth targets, respectively. These represent the phase information of the 1st, 2nd, and Kth targets, respectively; v1, v2, v KThese represent the velocity information of the 1st, 2nd, and Kth targets, respectively; θ1, θ2, θ K These represent the angle information of the 1st, 2nd, and Kth targets, respectively; T is the pulse repetition period; d Tx and d Rx These are the distances between the transmitting and receiving antennas, respectively.

[0084] Step 2: Based on the criterion of minimizing the energy of the canceled signal, construct an optimization model using the target range dimension focused echo signal model built in Step 1. The specific method is as follows:

[0085] The optimization model is constructed by minimizing the energy of the target signal after cancellation, i.e., the sum of squared differences between the observed echo and the reconstructed echo matrices, as shown below:

[0086]

[0087] Step 3: Perform multi-dimensional matched filtering on the target range-focused echo signal obtained in Step 1 to obtain a coarse estimate of the target's multi-dimensional parameters (velocity, angle, amplitude, and phase). The specific method is as follows:

[0088] In the range-slow time spectrum, along each range point, slow-time decoding is performed according to the preset phase encoding sequence Φ to separate the echo signal, resulting in the range-slow time spectrum of M*N virtual channels. Then, FFT processing is performed along the slow time dimension to achieve two-dimensional target focusing, resulting in the range-Doppler spectrum of M*N virtual channels. Target detection is performed on the range-Doppler spectrum to obtain K over-detected targets and extract their velocity information, yielding a coarse estimate of the target velocity. The M*N virtual channel data of the K over-detected targets are extracted, and FFT processing is performed along the channel dimension to obtain the target angle spectrum and extract its angle information, yielding a coarse estimate of the target angle. Finally, based on the extracted target velocity and angle information, the coarse estimate of the target amplitude and phase is obtained according to the following formula.

[0089] α k ={[ΦA Tx (θ)⊙A D (v)] -1 y[A Rx (θ)] -1} kk

[0090] In this context, the subscript kk represents the element in the k-th row and k-th column of the square matrix.

[0091] Step 4: Based on the gradient descent algorithm, use the coarse estimation result obtained in Step 3 as the initial value to solve the optimization model constructed in Step 2, and obtain the fast sidelobe cancellation suppression result of the radar coded waveform. The specific method is as follows:

[0092] Referring to the focused echo model in Step 1, the reconstructed echo x is initialized using the coarse estimation results of the target multidimensional parameters obtained in Step 2; the steps to obtain the optimal reconstructed echo by iterating the target multidimensional parameters multiple times using the gradient descent algorithm include the following four steps:

[0093] The first step is to calculate the gradient of the optimization model with respect to the target amplitude and phase parameters:

[0094]

[0095] The second step is to calculate the gradient of the optimization model with respect to the target velocity parameters:

[0096]

[0097] Where Im is the operation of extracting the imaginary part of a complex number, I L It is a diagonal matrix with elements from 0 to L-1;

[0098] The second step is to calculate the gradient of the optimization model with respect to the target angle parameters:

[0099]

[0100] in,

[0101] Tx(θ k )=Im{αA Rx (θ)Δy H [(ΦI M A Tx (θ)⊙A D (v))]} kk

[0102] Rx(θ k )=Im{A Rx (θ)I N Δy H [(ΦA Tx (θ)⊙A D (v))]α} kk

[0103] Among them, I M and I N It is a diagonal matrix with elements from 0 to M-1 and from 0 to N-1, respectively;

[0104] The fourth step involves iteratively applying the momentum method to obtain the optimal estimate of the target parameters and the optimal reconstructed echo, thus yielding the Doppler sidelobe cancellation result.

[0105] The update results of the target's multidimensional parameters (amplitude, phase, velocity, angle) are expressed as follows:

[0106] α k (i+1)=αk (i)-εd α (i+1)

[0107] v k (i+1)=v k (i)-εd v (i+1)

[0108] θ k (i+1)=θ k (i)-εd θ (i+1)

[0109] Where i is the iteration number, ε is the learning rate, and d α d v d θ Represented as:

[0110]

[0111]

[0112]

[0113] Where γ is the momentum parameter.

[0114] In the above iterative process, after each round of iteration, the target signal energy E after cancellation in the current round is obtained. i If E in a series of iterations i If the change is less than the preset termination threshold, the iteration can be terminated early, and the target parameter estimation result and the Doppler sidelobe cancellation result yx will be output. i If the termination condition is not met, the loop continues to iterate until the maximum number of iterations is reached.

[0115] Example

[0116] The effectiveness of this invention can be demonstrated through the following simulation data experiments.

[0117] The system parameters are set as follows in this example:

[0118] Number of transmitting antennas M = 3;

[0119] Number of receiving antennas N = 4;

[0120] Number of frequency modulation sequences L = 256;

[0121] Encoding method: Pseudo-random four-phase encoding;

[0122] Learning rate ε = 10 -5 ;

[0123] Momentum parameter γ = 10 -2 .

[0124] This example sets up three targets, with the specific parameter settings as follows:

[0125] Target 1: Velocity v1 = 4.0 m / s; Angle θ1 = 15°; Signal-to-noise ratio (SNR) = 20 dB;

[0126] Target 2: Velocity v2 = 4.8 m / s; Angle θ2 = 5°; Signal-to-noise ratio (SNR) = 18 dB;

[0127] Target 3: Speed ​​v3 = 5.5 m / s; Angle θ3 = -10°; Signal-to-noise ratio (SNR) = 12 dB.

[0128] In this implementation case, due to the superposition of orthogonal residual components of multiple targets, the decoded Doppler image exhibits significantly high sidelobes, such as... Figure 2 As shown, the weak target is now submerged, making effective detection impossible. After eliminating the strong target sidelobes using this method, the Doppler sidelobes are effectively suppressed, and the weak target becomes visible. Furthermore, statistics show that the average signal power after sidelobe cancellation using different methods is illustrated in Table 1. It can be seen that the average signal power after sidelobe cancellation using this method is basically consistent with the theoretical result (ideal cancellation signal power), and compared to traditional methods, it can improve the strong target sidelobe cancellation performance by approximately 4.4 dB in this implementation case.

[0129] Table 1 Comparison of average signal power after strong target sidelobe cancellation.

[0130]

[0131] Further analysis of the Doppler spectrum of the signal after weakening the target sidelobes, such as... Figure 3 As shown, the signal after cancellation using this method is basically consistent with the theoretical result (ideal signal power after cancellation). Table 2 shows the average signal power after weak target sidelobe cancellation achieved using different methods. It can be seen that compared to traditional methods, this method can improve the overall sidelobe cancellation performance by approximately 8.4 dB in this implementation case.

[0132] Table 2 Comparison of average signal power after sidelobe cancellation of weak targets.

[0133] Time domain CLEAN method IFFT processing method The method of the present invention Theoretical results Signal average power 35.79 dB 36.10 dB 27.40 dB 27.34 dB

[0134] The multi-target velocity and angle estimation results in this implementation case are as follows: Figure 4 As shown, traditional methods exhibit significant errors in velocity and angle estimation, while this method effectively improves the accuracy of multidimensional target parameter estimation, thus possessing robust sidelobe cancellation performance.

[0135] This invention proposes a fast sidelobe cancellation suppression method for radar-coded waveforms. By transforming the Doppler sidelobe cancellation problem into a signal restoration optimization problem, an optimization model is constructed based on the criterion of minimizing the energy of the target signal after cancellation. The gradient descent algorithm is used to achieve joint optimization estimation of multi-dimensional target parameters (velocity, angle, amplitude and phase information), which can ultimately achieve high-precision target parameter estimation and robust Doppler sidelobe cancellation performance.

[0136] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for fast sidelobe cancellation suppression of radar-coded waveforms, characterized in that... The steps of this method include: Step 1: Perform range-dimensional matched filtering on the radar echo to obtain the target range-dimensional focused echo signal, and construct a target range-dimensional focused echo signal model based on the obtained target range-dimensional focused echo signal; Step 2: Based on the criterion of minimizing the energy of the canceled signal, construct an optimization model using the target range dimension focused echo signal model built in Step 1; Step 3: Perform multi-dimensional matched filtering on the target range dimension echo signal obtained in Step 1 to obtain a coarse estimate of the target's multi-dimensional parameters. Step 4: Based on the gradient descent algorithm, use the coarse estimation result obtained in Step 3 as the initial value to solve the optimization model constructed in Step 2, and obtain the fast cancellation suppression result of the radar coded waveform sidelobes.

2. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 1, characterized in that: In step one, the specific method for performing range-dimensional matched filtering on the radar echo is as follows: The radar echo signal is processed by de-chirp, and the fast-time single frequency-modulated continuous wave signal is processed by data windowing and FFT to complete the target range dimension focusing, and the target range dimension focused echo signal is obtained.

3. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 2, characterized in that: In step one, the method for constructing the signal model is as follows: Let M be the number of radar transmitting antennas, N be the number of receiving antennas, and L be the number of frequency modulation sequences. Then the received signal y of a range cell can be expressed as: y = x + n Where x represents the radar echo signals of K targets, and n represents Gaussian white noise; Based on the slow-time Doppler-coded modulated transmission waveform, the echo signal x of K targets after range-dimensional focusing is represented as: x=[ΦA Tx (θ)⊙A D (v)]αA Rx (i) Where ⊙ is the Hadamard product, and Where f0 is the radar carrier frequency; c represents the speed of light; α1, α2, α K These represent the magnitude information of the 1st, 2nd, and Kth targets, respectively. These represent the phase information of the 1st, 2nd, and Kth targets, respectively; v1, v2, v K These represent the velocity information of the 1st, 2nd, and Kth targets, respectively; θ1, θ2, θ K These represent the angle information of the 1st, 2nd, and Kth targets, respectively; T is the pulse repetition period; d Tx and d Rx These represent the distance between the transmitting and receiving antennas, respectively.

4. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 3, characterized in that: In step two, the specific method for constructing the optimization model is as follows: The optimization model is constructed by minimizing the energy of the target signal after cancellation, i.e., the sum of squared differences between the observed echo and the reconstructed echo matrices, as shown below:

5. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 4, characterized in that: In step three, the target's multidimensional parameters include velocity, angle, and amplitude.

6. A method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 4 or 5, characterized in that: In step three, the specific method for multi-dimensional matching filtering is as follows: In the range-slow time spectrum, along each range point, slow-time decoding is performed according to the preset phase encoding sequence Φ to separate the echo signal, resulting in the range-slow time spectrum of M*N virtual channels. Then, FFT processing is performed along the slow time dimension to achieve two-dimensional target focusing, resulting in the range-Doppler spectrum of M*N virtual channels. Target detection is performed on the range-Doppler spectrum to obtain K over-detected targets and extract their velocity information, yielding a coarse estimate of the target velocity. The M*N virtual channel data of the K over-detected targets are extracted, and FFT processing is performed along the channel dimension to obtain the target angle spectrum and extract its angle information, yielding a coarse estimate of the target angle. Finally, based on the extracted target velocity and angle information, the coarse estimate of the target amplitude and phase is obtained according to the following formula. a k ={[ΦA Tx (θ)⊙A D (v)] -1 y[A Rx (i)] -1 } kk In this context, the subscript kk represents the element in the k-th row and k-th column of the square matrix.

7. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 6, characterized in that: In step four, the method for solving the optimization model based on the gradient descent algorithm is as follows: Referring to the focused echo model in step one, the reconstructed echo x is initialized using the coarse estimation results of the target multidimensional parameters obtained in step two.

8. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 7, characterized in that: The steps to obtain the optimal reconstructed echo by iterating through the multidimensional parameters of the target using the gradient descent algorithm in multiple rounds include the following four steps: The first step is to calculate the gradient of the optimization model with respect to the target amplitude and phase parameters: The second step is to calculate the gradient of the optimization model with respect to the target velocity parameters: Where Im is the operation of taking the imaginary part of a complex number, I L It is a diagonal matrix with elements from 0 to L-1; The second step is to calculate the gradient of the optimization model with respect to the target angle parameters: in, Tx(θ k )=Im{αA Rx (i)Δy H [(ΦI M A Tx (θ)⊙A D (v))]} kk Rx(θ k )=Im{A Rx (i)I N Δy H [(F A Tx (θ)⊙A D (v))]a} kk Among them, I M and I N It is a diagonal matrix with elements from 0 to M-1 and from 0 to N-1, respectively; The fourth step involves iteratively applying the momentum method to obtain the optimal estimate of the target parameters and the optimal reconstructed echo, thus yielding the Doppler sidelobe cancellation result. The result of the target multidimensional parameter update is represented as follows: a k (i+1)=a k (i)-ed α (i+1) v k (i+1)=v k (i)-εd v (i+1) θ k (i+1)=θ k (i)-εd θ (i+1) Where i is the iteration number, ε is the learning rate, and d α d v d θ Represented as: Where γ is the momentum parameter.

9. The method for fast sidelobe cancellation suppression of radar-coded waveforms according to claim 8, characterized in that: In the above iterative process, after each round of iteration, the target signal energy E after cancellation in the current round is obtained. i If E in the continuous iteration process i If the change is less than the preset termination threshold, the iteration can be terminated early, and the target parameter estimation result and the Doppler sidelobe cancellation result yx will be output. i If the termination condition is not met, the loop continues to iterate until the maximum number of iterations is reached.

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