Phased array radar high-resolution imaging method based on truncated singular value decomposition

Abstract

The invention discloses a phased array radar high-resolution imaging method based on truncated singular value decomposition, which comprises the following steps: firstly, measuring the radiation intensity of each angle of an antenna, obtaining a directional diagram function, carrying out Toeplitz transformation, constructing a corresponding Toeplitz matrix, measuring the echo signal power and noise power of a system, and calculating the signal-to-noise ratio of the system; singular value decomposition is carried out on the Toeplitz matrix, singular values are arranged from large to small, and phased array radar high-resolution imaging is completed in combination with a singular value processing strategy. The method effectively solves the problems that an existing deconvolution imaging method is poor in robustness, high in parameter dependence, high in operation complexity and the like under the condition of the low signal-to-noise ratio, reduces the algorithm complexity, inhibits the noise influence, has very high robustness, has unique advantages in a foresight radar imaging scene, and has good application prospects. The method is not only suitable for a forward-looking imaging task of a phased array radar, but also can be popularized to other radar scenes with insufficient direction angle resolution or limited aperture synthesis.

Description

Technical Field

[0001] The present invention belongs to the technical field of phased array radar imaging, and in particular relates to a phased array radar high-resolution imaging method based on truncated singular value decomposition. Background Art

[0002] Phased array radar is a modern radar system that utilizes multiple radiating elements in an antenna array, adjusting the phase and amplitude of each element's transmitted signal to achieve fast and flexible beam scanning. Compared to existing mechanically scanned radars, phased array radars can rapidly scan a target area in two or even three dimensions without physically rotating the antenna. This significantly improves the system's response speed, reliability, and detection efficiency, and has important application value in forward-looking imaging scenarios.

[0003] Radar imaging has always been an important area of ​​radar signal processing. It uses the time delay and Doppler frequency deviation of the echo signal to determine the target's motion state and uses imaging algorithms to restore the data into an image containing the target's outline. In addition to phased array radars, current imaging radars are mainly divided into the following three types:

[0004] The first is MIMO radar imaging. In a 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" a greater number of virtual array elements than the actual number of antennas. This virtual array structure gives the radar stronger target direction estimation capabilities and enables high-precision imaging in multiple dimensions such as distance, speed, and angle. However, MIMO radar hardware systems are highly complex and require multiple independent RF links, which increases cost and design difficulty. Furthermore, the data volume is large, the signal processing burden is heavy, and it is susceptible to interference from the Doppler effect.

[0005] The second type is real aperture radar. This uses a fixed-directional antenna mounted on a radar platform to directly illuminate the target area. It uses the time delay of the echo signal to determine the target's distance and the directionality of the antenna beam to determine the target's orientation, thereby generating a two-dimensional image. Real aperture radar offers the advantages of a simple structure, intuitive imaging principles, and strong real-time system performance. However, its azimuth resolution is determined by the antenna aperture, significantly increasing the system size and weight in applications such as aviation and aerospace.

[0006] The third type is synthetic aperture radar (SAR). SAR uses a mobile platform to continuously collect target echo signals while in flight. It then coherently superimposes echo signals from the same target at different locations, creating a virtual aperture much larger than the actual antenna aperture, achieving high-resolution imaging. However, SAR systems have a complex structure, require extensive signal processing, and are not suitable for forward-looking imaging.

[0007] The imaging resolution of a phased array radar is determined by its beamwidth. Achieving high-resolution imaging often requires increasing the array size, which significantly increases system cost. Deconvolution-based radar imaging algorithms can overcome beamwidth limitations and achieve super-resolution imaging. However, current deconvolution-based radar imaging methods suffer from high algorithmic complexity, susceptibility to noise, difficulty in parameter setting, and poor robustness. Summary of the Invention

[0008] To solve the above technical problems, the present invention provides a phased array radar high-resolution imaging method based on truncated singular value decomposition, which solves the problems of high algorithm complexity, susceptibility to noise, and poor robustness of the current deconvolution imaging method, and increases the reliability of the imaging algorithm.

[0009] The technical solution adopted by the present invention is: a phased array radar high-resolution imaging method based on truncated singular value decomposition, the specific steps are as follows:

[0010] S1. Measure the radiation intensity of the antenna at each angle and obtain the pattern function;

[0011] In a microwave darkroom, the antenna is mounted on a turntable and scanned in directional angles using a vector network analyzer. The radiation intensity distribution at each angle is accurately measured, and the radiation intensity in each direction is recorded to obtain complete directional pattern data G = [G1 G2…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 scale of the pattern matrix.

[0013] S2, performing a Toeplitz transform on the directional pattern function obtained in step S1 to construct a corresponding Toeplitz matrix;

[0014] The obtained antenna direction function G is used to construct the corresponding Toeplitz matrix T according to the Toeplitz transformation rule. The expression is as follows:

[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. It then performs singular value decomposition on the Toeplitz matrix obtained in step S2 and arranges the singular values ​​from largest to smallest.

[0017] The signal received by the antenna is first input into a low-noise amplifier to increase the signal power and minimize the additional noise.

[0018] The amplified signal is then filtered by the RF filter. The filtered signal is then down-converted to an intermediate frequency (IF) using an image rejection mixer. After further IF filtering and amplification, it is converted to a digital signal by the ADC. The digital signal undergoes digital down-conversion to generate a 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 calculate the echo signal power P. s , measure the background noise signal power P when there is no echo n , and calculate the system signal-to-noise ratio, the expression is as follows:

[0020]

[0021] Then perform singular value decomposition on the Toeplitz matrix T, that is, T = UΛV H .

[0022] Among them, U∈C M×M and V∈C M×M is a unitary matrix, representing the orthogonal basis of the left and right singular vectors, V H represents the transpose of V, Λ=diag(σ1,σ2,...,σ M ) is a singular value matrix, and the diagonal elements σ are singular values.

[0023] Finally, the singular values ​​are arranged from large to small, that is, 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 so, proceed to step S6; otherwise, proceed to step S5;

[0025] S5, the radar system has a high signal-to-noise ratio, and a fixed energy method is used to calculate the singular value cutoff point of the Toeplitz matrix, and then proceeds to step S7;

[0026] The system has a high signal-to-noise ratio, then according to the relationship between the energy of the echo and the singular value The energy retention threshold is set to 99%, and the minimum singular value cutoff point k when the retained echo signal energy is less than 99% is calculated by gradually accumulating the squares of the singular values, that is,

[0027] S6: The radar system has a low signal-to-noise ratio, and the singular value cutoff point of the Toeplitz matrix is ​​calculated using the L-curve method, and then the process proceeds to step S7;

[0028] If the system has a low signal-to-noise ratio, the singular values ​​are processed logarithmically to amplify the differences between the singular values. Calculate the second-order difference κ of the singular value sequence after logarithmic processing i =ln(σ i+1 )-2ln(σi )+ln(σ i-1 ), traverse the singular value sequence, according to the |κ corresponding to each singular value i | the size of κ, find |κ i |The largest index position is taken as the singular value truncation point k, that is, |κ k |≥|κ i |,(1<i<M).

[0029] S7. According to the obtained truncation point, truncation singular value processing is performed on the Toeplitz matrix, and matrix reconstruction is performed to obtain a processed Toeplitz matrix;

[0030] Retain the largest first k 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 Toeplitz matrix T and obtain the processed Toeplitz matrix T1 = UΛ1V H .

[0031] S8. Based on the processing result obtained in step S7, perform matrix inversion deconvolution processing on the echo signal model to obtain an approximate target scattering distribution, thereby completing high-resolution imaging of the phased array radar;

[0032] Set the echo signal model as S rx =G*α+n, where S rx represents the echo signal, G represents the pattern function, α represents the target scattering distribution, and n represents the noise function.

[0033] According to the echo signal model S rx =G*α+n=Tα+n, and the echo signal S is processed using the Toeplitz matrix T1. rx Perform matrix inversion deconvolution processing to obtain the approximate target scattering distribution α', that is,

[0034] Among them, v i represents the i-th row vector of the unitary matrix V, u i represents the i-th column vector of the unitary matrix U, U H represents the transpose of U.

[0035] Beneficial effects of the present invention: The method of the present invention first measures the radiation intensity of the antenna at each angle, obtains the directional pattern function, performs a Toeplitz transform, constructs the corresponding Toeplitz matrix, measures the system echo signal power and noise power and calculates the system signal-to-noise ratio, then performs singular value decomposition on the Toeplitz matrix, arranges the singular values ​​from large to small, and combines the singular value processing strategy to complete the high-resolution imaging of the phased array radar. The method of the present invention effectively solves the problems of existing deconvolution imaging methods under low signal-to-noise ratio conditions, such as poor robustness, strong parameter dependence, and high computational complexity. It reduces algorithm complexity, suppresses the influence of noise, and has strong robustness. It has unique advantages in forward-looking radar imaging scenarios. It is not only suitable for forward-looking imaging tasks of phased array radars, but can also be extended to other radar scenarios with insufficient angular resolution or limited aperture synthesis. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention provides a flow chart of a phased array radar high-resolution imaging method based on truncated singular value decomposition.

[0037] Figure 2 FIG. 4 is a block diagram of a radar receiver in a radar system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The method of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0039] like Figure 1 As shown in FIG, a flow chart of a phased array radar high-resolution imaging method based on truncated singular value decomposition of the present invention is shown, and the specific steps are as follows:

[0040] S1. Measure the radiation intensity of the antenna at each angle and obtain the pattern function;

[0041] In a microwave darkroom, the antenna is mounted on a turntable and scanned in directional angles using a vector network analyzer. The radiation intensity distribution at each angle is accurately measured, and the radiation intensity in each direction is recorded to obtain complete directional pattern data G = [G1 G2…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 scale of the pattern matrix.

[0043] S2, performing a Toeplitz transform on the pattern function obtained in step S1, and constructing a corresponding Toeplitz matrix for subsequent array signal processing;

[0044] The obtained antenna direction function G is used to construct the corresponding Toeplitz matrix T according to the Toeplitz transformation rule. The expression is as follows:

[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. It then performs singular value decomposition on the Toeplitz 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 additional noise.

[0048] The amplified signal is then filtered by an RF filter to further suppress noise. The filtered signal is then down-converted to an intermediate frequency (IF) using an image-rejection mixer. After IF filtering and amplification, it is converted to a digital signal by an ADC. The digital signal undergoes digital down-conversion to generate a baseband I / Q signal, which is then passed through a matched filter to maximize the signal-to-noise ratio.

[0049] Among them, f LO Indicates the local oscillator frequency.

[0050] The system uses constant false alarm rate (CFAR) to detect echoes and calculate the echo signal power P. s , measure the background noise signal power P when there is no echo n , and calculate the system signal-to-noise ratio, the expression is as follows:

[0051]

[0052] Then perform singular value decomposition on the Toeplitz matrix T, that is, T = UΛV H .

[0053] Among them, U∈C M×M and V∈C M×M is a unitary matrix, representing the orthogonal basis of the left and right singular vectors, V H represents the transpose of V, Λ=diag(σ1,σ2,…,σ M ) is a singular value matrix, and the diagonal elements σ are singular values.

[0054] Finally, the singular values ​​are arranged from large to small, that is, 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 so, proceed to step S6; otherwise, proceed to step S5;

[0056] S5, the radar system has a high signal-to-noise ratio, and a fixed energy method is used to calculate the singular value cutoff point of the Toeplitz matrix, and then proceeds to step S7;

[0057] The system has a high signal-to-noise ratio, then according to the relationship between the energy of the echo and the singular value The energy retention threshold is set to 99%, and the minimum singular value cutoff point k when the retained echo signal energy is less than 99% is calculated by gradually accumulating the squares of the singular values, that is,

[0058] S6: The radar system has a low signal-to-noise ratio, and the singular value cutoff point of the Toeplitz matrix is ​​calculated using the L-curve method, and then the process proceeds to step S7;

[0059] If the system has a low signal-to-noise ratio, the singular values ​​are processed logarithmically to amplify the differences between the singular values. Calculate the second-order difference κ of the singular value sequence after logarithmic processing i =ln(σ i+1 )-2ln(σ i )+ln(σ i-1 ), traverse the singular value sequence, according to the |κ corresponding to each singular value i | the size of κ, find |κ i |The largest index position is taken as the singular value truncation point k, that is, |κ k |≥|κ i |,(1<i<M).

[0060] S7. According to the obtained truncation point, truncation singular value processing is performed on the Toeplitz matrix, and matrix reconstruction is performed to obtain a processed Toeplitz matrix;

[0061] Retain the largest first k 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 Toeplitz matrix T and obtain the processed Toeplitz matrix T1 = UΛ1V H .

[0062] S8. Based on the processing result obtained in step S7, perform matrix inversion deconvolution processing on the echo signal model to obtain an approximate target scattering distribution, thereby completing high-resolution imaging of the phased array radar;

[0063] Set the echo signal model as S rx =G*α+n, where S rx represents the echo signal, G represents the pattern function, α represents the target scattering distribution, and n represents the noise function.

[0064] According to the echo signal model S rx =G*α+n=Tα+n, and the processed Toeplitz matrix H1 is used to process the echo signal S rx Perform matrix inversion deconvolution processing to obtain the approximate target scattering distribution α', that is,

[0065]

[0066] Among them, v i represents the i-th row vector of the unitary matrix V, u i represents the i-th column vector of the unitary matrix U, U H represents the transpose of U.

[0067] In summary, the method of the present invention effectively solves the problems of existing deconvolution imaging methods such as poor robustness, strong parameter dependence and high computational complexity under low signal-to-noise ratio conditions, reduces algorithm complexity, suppresses the influence of noise, has strong robustness, and has unique advantages in forward-looking radar imaging scenarios. It is not only suitable for forward-looking imaging tasks of phased array radars, but can also be extended to radar scenarios with insufficient angular resolution in other directions or limited aperture synthesis.

[0068] Those skilled in the art will appreciate that the embodiments described herein are intended to aid the reader in understanding the principles of the present invention, and it should be understood that the scope of the present invention is not limited to such specific descriptions and embodiments. Various modifications and variations are readily apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A phased array radar high-resolution imaging method based on truncated singular value decomposition, the specific steps are as follows: S1. Measure the radiation intensity of the antenna at each angle and obtain the pattern function; In a microwave darkroom, the antenna is mounted on a turntable and scanned in directional angles using a vector network analyzer. The radiation intensity distribution at each angle is accurately measured, and the radiation intensity in each direction is recorded to obtain complete directional pattern data G = [G1 G2…G M ]; in, G i (1≤i≤M) represents the radiation intensity distribution corresponding to the i-th scanning angle, and M represents the scale of the pattern matrix; S2, performing a Toeplitz transform on the directional pattern function obtained in step S1 to construct a corresponding Toeplitz matrix; The obtained antenna direction function G is used to construct the corresponding Toeplitz matrix T according to the Toeplitz transformation rule. 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. It then performs singular value decomposition on the Toeplitz 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 additional noise; The amplified signal is then filtered by the RF filter. The filtered signal is then down-converted to an intermediate frequency (IF) via an image rejection mixer. After IF filtering and amplification, it is converted to a digital signal by the ADC. The digital signal undergoes digital down-conversion to obtain a baseband I / Q signal, which is 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 P. s , measure the background noise signal power P when there is no echo n , and calculate the system signal-to-noise ratio, the expression is as follows: Then perform singular value decomposition on the Toeplitz matrix T, that is, T = UΛV H ; Among them, U∈C M×M and V∈C M×M is a unitary matrix, representing the orthogonal basis of the left and right singular vectors, V H represents the transpose of V, Λ=diag(σ1,σ2,…,σ M ) is a singular value matrix, and the diagonal elements σ are singular values; Finally, the singular values ​​are arranged from large to small, that is, σ1≥σ2≥…≥σ M ; S4. Based on step S3, determine whether the current radar system is in a low signal-to-noise ratio situation. If so, proceed to step S6; otherwise, proceed to step S5; S5, the radar system has a high signal-to-noise ratio, and a fixed energy method is used to calculate the singular value cutoff point of the Toeplitz matrix, and then proceeds to step S7; The system has a high signal-to-noise ratio, then according to the relationship between the energy of the echo and the singular value The energy retention threshold is set to 99%, and the minimum singular value cutoff point k when the retained echo signal energy is less than 99% is calculated by gradually accumulating the squares of the singular values, that is, S6: The radar system has a low signal-to-noise ratio, and the singular value cutoff point of the Toeplitz matrix is ​​calculated using the L-curve method, and then the process proceeds to step S7; If the system has a low signal-to-noise ratio, the singular values ​​are processed logarithmically to amplify the differences between the singular values; the second-order difference κ of the singular value sequence after logarithmic transformation is calculated. i =ln(σ i+1 )-2ln(σ i )+ln(σ i-1 ), traverse the singular value sequence, according to the |κ corresponding to each singular value i | the size of κ, find |κ i |The largest index position is taken as the singular value truncation point k, that is, |κ k |≥|κ i |,(1<i<M); S7. According to the obtained truncation point, truncation singular value processing is performed on the Toeplitz matrix, and matrix reconstruction is performed to obtain a processed Toeplitz matrix; Retain the largest first k 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 Toeplitz matrix T to obtain the processed Toeplitz matrix T1 = UΛ1V H ; S8. Based on the processing result obtained in step S7, perform matrix inversion deconvolution processing on the echo signal model to obtain an approximate target scattering distribution, thereby completing high-resolution imaging of the phased array radar; Set the echo signal model as S rx =G*α+n, where S rx represents the echo signal, G represents the pattern function, α represents the target scattering distribution, and n represents the noise function; According to the echo signal model S rx =G*α+n=Tα+n, and the echo signal S is processed using the Toeplitz matrix T1. rx Perform matrix inversion deconvolution processing to obtain the approximate target scattering distribution Right now Among them, v i represents the i-th row vector of the unitary matrix V, u i represents the i-th column vector of the unitary matrix U, U H represents the transpose of U.

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