A phased array radar high-resolution imaging method based on truncated singular value decomposition
By constructing the Toplitz matrix and determining the signal-to-noise ratio based on the truncated singular value decomposition method, the problems of high algorithm complexity and poor robustness in phased array radar imaging are solved, achieving high-resolution imaging that is applicable to various radar scenarios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2025-06-13
- Publication Date
- 2026-05-19
AI Technical Summary
Existing phased array radar imaging methods have high algorithm complexity, are susceptible to noise, and have poor robustness, making it difficult to achieve high-resolution imaging.
A method based on truncated singular value decomposition is adopted. The Toplitz matrix is constructed by measuring the antenna radiation intensity, and singular value decomposition and truncation are performed. Combined with the signal-to-noise ratio judgment, matrix reconstruction and matrix inversion deconvolution processing are performed to achieve high-resolution imaging.
It reduces algorithm complexity, improves imaging robustness, suppresses noise effects, and is suitable for forward-looking and other radar scenarios with insufficient resolution or limited aperture synthesis.
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Figure CN120630198B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of phased array radar imaging technology, specifically relating to a high-resolution imaging method for phased array radar based on truncated singular value decomposition. Background Technology
[0002] Phased array radar is a modern radar system that utilizes multiple radiating elements in an antenna array to achieve rapid and flexible beam pointing by adjusting the phase and amplitude of the signals emitted by each element. Compared with existing mechanically scanned radars, phased array radars can complete rapid two-dimensional or even three-dimensional scanning of target areas without physically rotating the antenna, significantly improving the system's response speed, reliability, and detection efficiency, and has important application value in forward-looking imaging scenarios.
[0003] Radar imaging has long been an important area of radar signal processing. It utilizes the time delay and Doppler frequency shift of echo signals to determine the target's motion state, and then uses imaging algorithms to reconstruct an image containing the target's outline. Besides phased array radar, imaging radars are currently mainly divided into the following three types:
[0004] The first type is MIMO radar imaging. In MIMO radar, each transmitting antenna emits a modulated signal with good orthogonality, and multiple receiving antennas simultaneously receive the echoes. By jointly processing these signals, the system can "synthesize" more virtual array elements than the actual number of antennas. This virtual array structure gives the radar a stronger target direction estimation capability, enabling high-precision imaging in multiple dimensions such as range, velocity, and angle. However, MIMO radar hardware systems are highly complex, requiring multiple independent radio frequency links, which increases cost and design difficulty. Furthermore, it generates a large amount of data, places a heavy burden on signal processing, and is susceptible to Doppler interference.
[0005] The second type is real aperture radar (PARa). PARa uses a fixed-directional antenna mounted on a radar platform to directly illuminate the target area. It determines the target distance by utilizing the time delay of the echo signal and the target's azimuth by using the directionality of the antenna beam, thus generating a two-dimensional image. PARa has the advantages of simple structure, intuitive imaging principle, and strong real-time performance. However, the azimuth resolution of PARa is determined by the antenna aperture, which significantly increases the system size and weight in applications such as aviation and aerospace.
[0006] The third type is synthetic aperture radar (SAR). SAR utilizes a mobile platform to continuously collect target echo signals during flight, coherently superimposing the echo signals of the same target at different locations to "synthesize" a virtual aperture much larger than the actual antenna aperture, thus achieving high-resolution imaging. However, SAR systems are complex in structure, computationally intensive in signal processing, and are not suitable for forward-looking imaging.
[0007] The imaging resolution of phased array radar is determined by its beamwidth. Achieving high-resolution imaging often requires increasing the array size, which undoubtedly increases the system cost significantly. Radar imaging algorithms based on deconvolution can overcome the beamwidth limitation and achieve super-resolution imaging. However, current deconvolution-based radar imaging methods suffer from high algorithm complexity, susceptibility to noise, difficulty in parameter setting, and poor robustness. Summary of the Invention
[0008] To address the aforementioned technical problems, this invention provides a high-resolution imaging method for phased array radar based on truncated singular value decomposition, which solves the problems of high algorithm complexity, susceptibility to noise, and poor robustness of current deconvolution imaging methods, thereby increasing the reliability of the imaging algorithm.
[0009] The technical solution adopted in this invention is: a high-resolution imaging method for phased array radar based on truncated singular value decomposition, the specific steps of which are as follows:
[0010] S1. Measure the radiation intensity of the antenna at various angles to obtain the radiation pattern function;
[0011] In a microwave anechoic chamber, the antenna is mounted on a turntable, and its directional angle is scanned using a vector network analyzer. The radiation intensity distribution at each angle is precisely measured, and the radiation intensity in each direction is recorded to obtain complete radiation pattern data G = [G1 G2…G ...…G……G……G……G……G……G……G……G……G……G……G……G……G……G……G……G………G………G………G…………G……………G…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… M ].
[0012] Among them, G i (1≤i≤M) represents the radiation intensity distribution corresponding to the i-th scanning angle, and M represents the size of the radiation pattern matrix.
[0013] S2. Perform a Toplitz transformation on the pattern function obtained in step S1 to construct the corresponding Toplitz matrix;
[0014] The obtained antenna direction function G is used to construct the corresponding Toplitz matrix T according to the Toplitz transformation rule, as shown in the following expression:
[0015]
[0016] S3. The radar system measures the system echo signal power and noise power based on the received echo signal and calculates the system signal-to-noise ratio. Then, it performs singular value decomposition on the Toplitz matrix obtained in step S2 and arranges the singular values from largest to smallest.
[0017] First, the signal received by the antenna is input into a low-noise amplifier to increase the signal power and minimize the added noise.
[0018] The amplified signal is then filtered by an RF filter. The filtered signal is down-converted to an intermediate frequency (IF) by a mirror-rejection mixer, then filtered and amplified by the IF filter before being converted into a digital signal by an ADC. The digital signal is then down-converted to obtain the baseband I / Q signal, which is then passed through a matched filter to maximize the signal-to-noise ratio.
[0019] The system uses constant false alarm rate (CFAR) to detect echoes and calculates the echo signal power P. s Measure the background noise signal power P when there is no echo n The system signal-to-noise ratio is calculated using the following expression:
[0020]
[0021] Then, singular value decomposition is performed on the Topulitz matrix T, i.e., T = UΛV H .
[0022] Where, U∈C M×M and V∈C M×M V is a unitary matrix, representing an orthogonal basis of the left and right singular vectors. H Denotes the transpose of V, Λ = diag(σ1,σ2,...,σ M ) is a singular value matrix, and the diagonal element σ is a singular value.
[0023] Finally, the singular values are arranged in descending order, i.e., σ1≥σ2≥…≥σ M .
[0024] S4. Based on step S3, determine whether the current radar system is in a low signal-to-noise ratio situation. If yes, proceed to step S6; otherwise, proceed to step S5.
[0025] S5. The radar system has a high signal-to-noise ratio. The singular value cutoff point of the Toplitz matrix is calculated using the fixed energy method, and then proceeds to step S7.
[0026] For a system with a high signal-to-noise ratio, the relationship between the echo energy and singular values should be considered. Setting the energy retention threshold to 99%, the minimum singular value cutoff point k when the retained echo signal energy is less than 99% is calculated by progressively accumulating the squares of the singular values.
[0027] S6. Since the radar system has a low signal-to-noise ratio, the singular value cutoff point of the Toplitz matrix is calculated using the L-curve method, and then proceed to step S7.
[0028] If the system has a low signal-to-noise ratio, logarithmic processing is applied to the singular values to amplify the differences between them. The second-order difference κ of the logarithmically transformed singular value sequence is then calculated. i =ln(σ i+1 )-2ln(σi )+ln(σ i-1 ), traverse the sequence of singular values, and determine the |κ| corresponding to each singular value. i The size of | is used to find |κ. i The position of the largest index is taken as the singular value cutoff point k, i.e., |κ| k |≥|κ i |,(1<i<M).
[0029] S7. Based on the obtained cutoff points, perform singular value truncation on the Toplitz matrix and reconstruct the matrix to obtain the processed Toplitz matrix.
[0030] Retain the top k largest singular values in Λ and set the remaining singular values to zero to obtain the truncated singular value matrix Λ1. Use the truncated singular value matrix and the original U and V to reconstruct the Topletz matrix T, obtaining the processed Topletz matrix T1 = UΛ1V. H .
[0031] S8. Based on the processing results obtained in step S7, matrix inversion and deconvolution processing is performed on the echo signal model to obtain an approximate target scattering distribution and complete the high-resolution imaging of the phased array radar.
[0032] The echo signal is modeled as S rx =G*α+n, where S rx Let G represent the echo signal, α represent the pattern function, α represent the target scattering distribution, and n represent the noise function.
[0033] Then according to the echo signal model S rx =G*α+n=Tα+n, using the processed Toplitz matrix T1 to analyze the echo signal S rx After performing matrix inversion and deconvolution, the approximate target scattering distribution α' is obtained, i.e.
[0034] Among them, v i Let u represent the i-th row vector of the unitary matrix V. i Let U represent the i-th column vector of the unitary matrix U. H This represents the transpose of U.
[0035] The beneficial effects of this invention are as follows: The method of this invention first measures the radiation intensity of the antenna at various angles to obtain the radiation pattern function, performs a Toplitz transformation, and constructs the corresponding Toplitz matrix. After measuring the system echo signal power and noise power and calculating the system signal-to-noise ratio (SNR), singular value decomposition is performed on the Toplitz matrix. The singular values are arranged from largest to smallest. Combined with a singular value processing strategy, high-resolution imaging of phased array radar is achieved. This invention effectively solves the problems of poor robustness, strong parameter dependence, and high computational complexity of existing deconvolution imaging methods under low SNR conditions. It reduces algorithm complexity, suppresses noise influence, and has strong robustness. It has unique advantages in forward-looking radar imaging scenarios and is not only suitable for forward-looking imaging tasks of phased array radar but can also be extended to other radar scenarios with insufficient angular resolution or limited aperture synthesis. Attached Figure Description
[0036] Figure 1 This is a flowchart of a phased array radar high-resolution imaging method based on truncated singular value decomposition according to the present invention.
[0037] Figure 2 This is a block diagram of the radar receiver in the radar system according to an embodiment of the present invention. Detailed Implementation
[0038] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0039] like Figure 1 The flowchart of a phased array radar high-resolution imaging method based on truncated singular value decomposition according to the present invention is shown below. The specific steps are as follows:
[0040] S1. Measure the radiation intensity of the antenna at various angles to obtain the radiation pattern function;
[0041] In a microwave anechoic chamber, the antenna is mounted on a turntable, and its directional angle is scanned using a vector network analyzer. The radiation intensity distribution at each angle is precisely measured, and the radiation intensity in each direction is recorded to obtain complete radiation pattern data G = [G1 G2…G ...…G……G……G……G……G……G……G……G……G……G……G……G……G……G……G……G………G………G………G…………G……………G…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… M ].
[0042] Among them, G i (1≤i≤M) represents the radiation intensity distribution corresponding to the i-th scanning angle, and M represents the size of the radiation pattern matrix.
[0043] S2. Perform a Toplitz transformation on the pattern function obtained in step S1 to construct the corresponding Toplitz matrix for subsequent array signal processing.
[0044] The obtained antenna direction function G is used to construct the corresponding Toplitz matrix T according to the Toplitz transformation rule, as shown in the following expression:
[0045]
[0046] S3. The radar system measures the system echo signal power and noise power based on the received echo signal and calculates the system signal-to-noise ratio. Then, it performs singular value decomposition on the Toplitz matrix obtained in step S2 and arranges the singular values from largest to smallest.
[0047] like Figure 2 As shown, the signal received by the antenna is first input into a low-noise amplifier to increase the signal power and minimize the added noise.
[0048] The amplified signal is then filtered by an RF filter to further suppress noise. The filtered signal is down-converted to an intermediate frequency (IF) by a mirror-rejection mixer, then filtered and amplified by the IF filter before being converted to a digital signal by an ADC. The digital signal undergoes digital down-conversion to obtain the baseband I / Q signal, which is then passed through a matched filter to maximize the signal-to-noise ratio.
[0049] Wherein, f in the figure LO This indicates the local oscillator frequency.
[0050] The system uses constant false alarm rate (CFAR) to detect echoes and calculates the echo signal power P. s Measure the background noise signal power P when there is no echo n The system signal-to-noise ratio is calculated using the following expression:
[0051]
[0052] Then, singular value decomposition is performed on the Topulitz matrix T, i.e., T = UΛV H .
[0053] Where, U∈C M×M and V∈C M×M V is a unitary matrix, representing an orthogonal basis of the left and right singular vectors. H Denotes the transpose of V, Λ = diag(σ1,σ2,…,σ M ) is a singular value matrix, and the diagonal element σ is a singular value.
[0054] Finally, the singular values are arranged in descending order, i.e., σ1≥σ2≥…≥σ M .
[0055] S4. Based on step S3, determine whether the current radar system is in a low signal-to-noise ratio situation. If yes, proceed to step S6; otherwise, proceed to step S5.
[0056] S5. The radar system has a high signal-to-noise ratio. The singular value cutoff point of the Toplitz matrix is calculated using the fixed energy method, and then proceeds to step S7.
[0057] For a system with a high signal-to-noise ratio, the relationship between the echo energy and singular values should be considered. Setting the energy retention threshold to 99%, the minimum singular value cutoff point k when the retained echo signal energy is less than 99% is calculated by progressively accumulating the squares of the singular values.
[0058] S6. Since the radar system has a low signal-to-noise ratio, the singular value cutoff point of the Toplitz matrix is calculated using the L-curve method, and then proceed to step S7.
[0059] If the system has a low signal-to-noise ratio, logarithmic processing is applied to the singular values to amplify the differences between them. The second-order difference κ of the logarithmically transformed singular value sequence is then calculated. i =ln(σ i+1 )-2ln(σ i )+ln(σ i-1 ), traverse the sequence of singular values, and determine the |κ| corresponding to each singular value. i The size of | is used to find |κ. i The position of the largest index is taken as the singular value cutoff point k, i.e., |κ| k |≥|κ i |,(1<i<M).
[0060] S7. Based on the obtained cutoff points, perform singular value truncation on the Toplitz matrix and reconstruct the matrix to obtain the processed Toplitz matrix.
[0061] Retain the top k largest singular values in Λ and set the remaining singular values to zero to obtain the truncated singular value matrix Λ1. Use the truncated singular value matrix and the original U and V to reconstruct the Topletz matrix T, obtaining the processed Topletz matrix T1 = UΛ1V. H .
[0062] S8. Based on the processing results obtained in step S7, matrix inversion and deconvolution processing is performed on the echo signal model to obtain an approximate target scattering distribution and complete the high-resolution imaging of the phased array radar.
[0063] The echo signal is modeled as S rx =G*α+n, where S rx Let G represent the echo signal, α represent the pattern function, α represent the target scattering distribution, and n represent the noise function.
[0064] Then according to the echo signal model S rx =G*α+n=Tα+n, using the processed Toplitz matrix H1 to analyze the echo signal S rx After performing matrix inversion and deconvolution, the approximate target scattering distribution α' is obtained, i.e.
[0065]
[0066] Among them, v i Let u represent the i-th row vector of the unitary matrix V. i Let U represent the i-th column vector of the unitary matrix U. H This represents the transpose of U.
[0067] In summary, the method of this invention effectively solves the problems of poor robustness, strong parameter dependence, and high computational complexity of existing deconvolution imaging methods under low signal-to-noise ratio conditions. It reduces algorithm complexity, suppresses the influence of noise, and has strong robustness. It has unique advantages in forward-looking radar imaging scenarios and is not only suitable for forward-looking imaging tasks of phased array radar, but can also be extended to radar scenarios with insufficient angular resolution or limited aperture synthesis in other directions.
[0068] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.
Claims
1. A high-resolution imaging method for phased array radar based on truncated singular value decomposition, the specific steps of which are as follows: S1. Measure the radiation intensity of the antenna at various angles to obtain the radiation pattern function; In a microwave anechoic chamber, the antenna is mounted on a turntable, and its directional angle is scanned using a vector network analyzer to accurately measure the radiation intensity distribution at various angles. The radiation intensity in each direction is recorded to obtain complete radiation pattern data. ; in, This represents the radiation intensity distribution corresponding to the i-th scanning angle, and M represents the size of the radiation pattern matrix; S2. Perform a Toplitz transformation on the pattern function obtained in step S1 to construct the corresponding Toplitz matrix; The obtained antenna direction function Construct the corresponding Topletz matrix according to the Topletz transformation rules. The expression is as follows: ； S3. The radar system measures the system echo signal power and noise power based on the received echo signal and calculates the system signal-to-noise ratio. Then, it performs singular value decomposition on the Toplitz matrix obtained in step S2 and arranges the singular values from largest to smallest. First, the signal received by the antenna is input into a low-noise amplifier to increase the signal power and minimize the added noise. The amplified signal is then filtered by the RF filter. The filtered signal is down-converted to the intermediate frequency by the image rejection mixer, and then after intermediate frequency filtering and amplification, it is converted into a digital signal by the ADC. The digital signal is then down-converted to obtain the baseband I / Q signal, and then passed through a matched filter to maximize the signal-to-noise ratio. The system uses constant false alarm rate (CFAR) to detect echoes and calculate the echo signal power. Measure background noise signal power when there is no echo The system signal-to-noise ratio is calculated using the following expression: ； Then, regarding the Toplitz matrix... Perform singular value decomposition, i.e. ; in, and Let be a unitary matrix, representing an orthogonal basis for the left and right singular vectors. express transpose, For a singular value matrix, the diagonal elements It is a singular value; Finally, the singular values are sorted in descending order, i.e. ; S4. Based on step S3, determine whether the current radar system is in a low signal-to-noise ratio situation. If yes, proceed to step S6; otherwise, proceed to step S5. S5. The radar system has a high signal-to-noise ratio. The singular value cutoff point of the Toplitz matrix is calculated using the fixed energy method, and then proceeds to step S7. For a system with a high signal-to-noise ratio, the relationship between the echo energy and singular values should be considered. The energy retention threshold is set to 99%. By progressively accumulating the squares of the singular values, the minimum singular value cutoff point when the retained echo signal energy is less than 99% is calculated. ,Right now , ; S6. Since the radar system has a low signal-to-noise ratio, the singular value cutoff point of the Toplitz matrix is calculated using the L-curve method, and then proceed to step S7. If the system has a low signal-to-noise ratio, logarithmic processing is applied to the singular values to amplify the differences between them; the second difference of the logarithmically transformed singular value sequence is then calculated. Traverse the sequence of singular values, and based on the singular value corresponding to each singular value... Size, find The largest index position is used as the singular value cutoff point. ,Right now ; S7. Based on the obtained cutoff points, perform singular value truncation on the Toplitz matrix and reconstruct the matrix to obtain the processed Toplitz matrix. reserve The largest front Take one singular value and set the remaining singular values to zero to obtain the truncated singular value matrix. ; Use the truncated singular value matrix and the original and For Topletz matrix Matrix reconstruction is performed to obtain the processed Toplitz matrix. ; S8. Based on the processing results obtained in step S7, matrix inversion and deconvolution processing is performed on the echo signal model to obtain an approximate target scattering distribution and complete the high-resolution imaging of the phased array radar. Set the echo signal model as ,in, Indicates the echo signal. Represents the pattern function. Indicates the target scattering distribution. Represents the noise function; Based on the echo signal model Using the processed Toplitz matrix For echo signal Perform matrix inversion and deconvolution to obtain the approximate target scattering distribution. ,Right now ; in, Represents a unitary matrix The row vectors. Represents a unitary matrix The column vectors, express The transpose of .