A low-complexity main-lobe interference suppression method based on frequency-constrained laguerre
By proposing a low-complexity main lobe interference suppression method based on frequency-constrained Laguerre structure, a low-dimensional constraint matrix is constructed using Laguerre structure and singular value decomposition. The weights are then optimized using the LCMV criterion, which solves the problems of main lobe interference suppression and computational complexity in broadband beamforming and achieves high stability and low complexity in main lobe interference suppression.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-01-20
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies struggle to simultaneously achieve effective suppression of main lobe interference, low computational complexity, and high stability in broadband beamforming. Traditional algorithms are prone to main lobe distortion and increased side lobe levels.
A low-complexity main lobe interference suppression method based on frequency-constrained Laguerre is adopted. A low-dimensional constraint matrix is constructed by Laguerre structure preprocessing, singular value decomposition and rank reduction processing, and the weights are optimized by combining the LCMV criterion to achieve effective suppression of main lobe interference and reduction of computational complexity.
It achieves high stability with low complexity and effective suppression of main lobe interference in main lobe interference scenarios, avoids main lobe deformation and side lobe level increase, and improves the anti-interference performance and signal-to-noise ratio of beamforming.
Smart Images
Figure CN122394579A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array interference suppression and relates to a low-complexity main lobe interference suppression method based on frequency-constrained Laguerre. Background Technology
[0002] Broadband beamforming is a core technology in radar, communications, and other fields, and its performance directly affects the anti-interference capability and signal-to-noise ratio of signal reception. However, when interference signals fall into the main lobe region, traditional adaptive beamforming algorithms are prone to main lobe deformation and increased side lobe levels, severely degrading output performance. Among existing solutions, Frost beamforming (FB) relies on a pre-bias delay structure, which is prone to delay errors in practical applications; Laguerre beamforming (LB) balances stability and broadband performance with its unipolar characteristics, but lacks a targeted suppression mechanism for main lobe interference. Constraint matrix reconstruction can suppress main lobe interference by strengthening interference constraints, but the high-dimensional matrix leads to a surge in computational complexity. Nonuniform decomposition (NUDM) can directly construct a low-dimensional constraint matrix, significantly reducing complexity, but it does not consider the adaptability to main lobe interference scenarios. In summary, existing technologies cannot simultaneously meet the requirements of "effective suppression of main lobe interference, low computational complexity, and high stability." Therefore, targeted interference suppression strategies and low-dimensional optimization methods are needed to propose novel broadband beamforming schemes. Summary of the Invention
[0003] Therefore, this invention provides a low-complexity main lobe interference suppression method based on frequency-constrained Laguerre law. In this method, under main lobe interference scenarios, low complexity and high stability are achieved, effectively suppressing main lobe interference.
[0004] To achieve the above objectives, the present invention provides the following technical solution:
[0005] A low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law, characterized by the following steps:
[0006] S1: Acquire the array received signal and perform time-domain preprocessing using a Laguerre structure;
[0007] S2: A low-dimensional constraint matrix and response vector are generated by dividing the frequency band based on relative bandwidth;
[0008] S3: Rank reduction processing based on Singular Value Decomposition (SVD);
[0009] S4: Construct the joint constraint matrix of the target signal and the main lobe interference;
[0010] S5: Solve for the optimal weights based on the LCMV criterion and the constraint matrix;
[0011] S6: Perform broadband beamforming using optimal weights and output the target signal.
[0012] Furthermore, in step S1, each sensor in the array is omnidirectional, and the number of array elements and the number of Laguerre structures in each array branch are respectively... and The spacing between adjacent array elements is The speed of radio waves is Assume the signal is incident on ULA from far-field space.
[0013] At any moment After the first The first of the array elements The output after processing by a Laguerre delay structure It can be represented as
[0014]
[0015] in, It is a single pole of the Laguerre structure.
[0016] Frequency-Constrained Laguerre Beamforming (FCLB) utilizes a frequency constraint matrix to eliminate pre-steering delay and guides the beam along the incident direction of a known SOI. The frequency passband is decomposed into... Each frequency point satisfies ,in and These represent the maximum and minimum endpoints of the signal bandwidth, respectively. The frequency constraint matrix of FCLB is:
[0017]
[0018] in, for A 3D column vector, expressed as:
[0019]
[0020] in
[0021]
[0022]
[0023] , The sampling period. Constraint matrix. response vector for 3D column vector, expressed as
[0024]
[0025] Furthermore, in step S2, the low-dimensional FCLB frequency constraint matrix is quickly obtained using NUDM based on the relative bandwidth method.
[0026] The relative bandwidth defined by the relative bandwidth method (RBM) is:
[0027]
[0028] From the formula It is known that the relative bandwidth of each frequency band in broadband beamforming is independent of its center frequency. Therefore, with the same relative bandwidth, the absolute bandwidth corresponding to the high-frequency band is greater than that of the low-frequency band.
[0029] Assuming the passband is decomposed into The non-uniform frequency band, the first The minimum and maximum frequencies of each frequency band are denoted as follows: and ,in , . No. The center frequency of each frequency band is:
[0030]
[0031] No. The relative bandwidth of each frequency band is expressed as:
[0032]
[0033] The formula The transformation yields:
[0034]
[0035] in, .make ,because Therefore This tense Can be rewritten as That is, the frequency band boundaries satisfy a geometric sequence relationship. Combined with... , No. The highest frequency of each frequency band is:
[0036]
[0037] From the formula and , No. The center frequency of each frequency band It can be represented as:
[0038]
[0039] From the formula It can be seen that, since the relative bandwidth of each frequency band is the same, their center frequencies perfectly satisfy a geometric sequence relationship. The low-dimensional FCLB frequency constraint matrix is constructed based on the NUDM using the relative bandwidth method. for:
[0040]
[0041] Define a new frequency constraint matrix of The dimensional response vector is:
[0042]
[0043] Furthermore, in step S3, since the frequency domain constraint matrix contains a large amount of redundant information, which is not necessary but occupies a large number of degrees of freedom, it is necessary to consider how to extract the main feature information while discarding useless information, so as to reduce the consumption of computing resources and make more resources available for the interference suppression part.
[0044] 2D frequency domain constraint matrix Through SVD decomposition, it is decomposed into a product of several matrices, as expressed below:
[0045]
[0046] In the formula, and They are respectively and unitary matrix, for A 3D diagonal matrix whose diagonal elements are constraint matrices. The singular values of are sorted in descending order, i.e.:
[0047]
[0048] in, express The singular values satisfy Diagonal matrix The former The first diagonal element is much larger than the others, therefore the first one can be selected. Construct a diagonal matrix using diagonal elements. , Must meet:
[0049]
[0050] in, The threshold represents right The degree of approximation. Assume Preset value, through formula The minimum rank can be calculated. .
[0051] and It can be broken down into two parts:
[0052]
[0053] in, express The former Column vector, corresponding to The front of the middle The largest singular value, It contains the remaining column vectors. The same applies.
[0054] Select matrix The former Columns form a matrix , Approximate or complete characterization In Constraint matrix response vector for:
[0055]
[0056] The reduced-rank matrix is:
[0057]
[0058] Then the reduced-rank covariance matrix It can be represented as:
[0059]
[0060] In the formula, Indicates that the received data has passed through The data matrix after step-tap recombination. .
[0061] Reduced-rank frequency domain constraint matrix Represented as:
[0062]
[0063] Furthermore, in step S4, when the interference is located within the main lobe, the desired pointing is no longer accurate, severely affecting beamforming performance. To suppress main lobe interference, the constraint matrix is reconstructed as follows:
[0064]
[0065] in, Let be the frequency domain constraint matrix for constraining interference. The expression is:
[0066]
[0067] and , The angle of interference to the main lobe. for A 3D column vector, expressed as:
[0068]
[0069] Furthermore, in step S5, using the LCMV criterion, the optimization problem of the weight vector can be expressed as:
[0070]
[0071] Using the Lagrange multiplier method and the cost function, the analytical form of the optimal adaptive weight vector can be obtained as follows:
[0072]
[0073] Furthermore, in step S6, let the data received by the array antenna be... Its expression is:
[0074]
[0075] Accordingly, the weight vector of each array element It can be represented as:
[0076]
[0077] The output is:
[0078]
[0079] The effectiveness of this invention lies in addressing the problems of main lobe distortion and side lobe level elevation caused by main lobe interference, as well as the shortcomings of traditional algorithms such as complex high-dimensional matrix calculations and insufficient stability. This invention strengthens the directional constraint of main lobe interference through constraint matrix reconstruction, directly constructs a low-dimensional matrix using NUDM to reduce costs and increase efficiency, and relies on the Laguerre architecture to ensure stability. It achieves effective suppression of main lobe interference without main lobe distortion, significantly reduces computational complexity, and improves stability. Attached Figure Description
[0080] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:
[0081] Figure 1 This is a flowchart of low-complexity main lobe interference suppression based on Laguerre's algorithm, as described in an embodiment of the present invention.
[0082] Figure 2 This is a diagram of a universal Laguerre beamforming method without pre-steering delay according to an embodiment of the present invention. Detailed Implementation
[0083] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0084] To address the issues of main lobe deformation and side lobe level elevation caused by main lobe interference, and the problems of complex high-dimensional constraint matrix calculation and poor stability in traditional algorithms, a low-complexity method based on Laguerre architecture, constraint matrix reconstruction, and NUDM is proposed. By directionally constraining main lobe interference and directly constructing a low-dimensional matrix, the anti-interference performance of beamforming and the output SINR are improved.
[0085] Furthermore, in step S1, each sensor in the array is omnidirectional, and the number of array elements and the number of Laguerre structures in each array branch are respectively... and The spacing between adjacent array elements is The speed of radio waves is Assume the signal is incident on ULA from far-field space.
[0086] At any moment After the first The first of the array elements The output after processing by a Laguerre delay structure It can be represented as
[0087]
[0088] in, It is a single pole of the Laguerre structure.
[0089] Frequency-Constrained Laguerre Beamforming (FCLB) utilizes a frequency constraint matrix to eliminate pre-steering delay and guides the beam along the incident direction of a known SOI. The frequency passband is decomposed into... Each frequency point satisfies ,in and These represent the maximum and minimum endpoints of the signal bandwidth, respectively. The frequency constraint matrix of FCLB is:
[0090]
[0091] in, for A 3D column vector, expressed as:
[0092]
[0093] in
[0094]
[0095]
[0096] , The sampling period. Constraint matrix. response vector for 3D column vector, expressed as
[0097]
[0098] Furthermore, in step S2, the low-dimensional FCLB frequency constraint matrix is quickly obtained using NUDM based on the relative bandwidth method.
[0099] The relative bandwidth defined by the relative bandwidth method (RBM) is:
[0100]
[0101] From the formula It is known that the relative bandwidth of each frequency band in broadband beamforming is independent of its center frequency. Therefore, with the same relative bandwidth, the absolute bandwidth corresponding to the high-frequency band is greater than that of the low-frequency band.
[0102] Assuming the passband is decomposed into The non-uniform frequency band, the first The minimum and maximum frequencies of each frequency band are denoted as follows: and ,in , . No. The center frequency of each frequency band is:
[0103]
[0104] No. The relative bandwidth of each frequency band is expressed as:
[0105]
[0106] The formula The transformation yields:
[0107]
[0108] in, .make ,because Therefore This tense Can be rewritten as That is, the frequency band boundaries satisfy a geometric sequence relationship. Combined with... , No. The highest frequency of each frequency band is:
[0109]
[0110] From the formula and , No. The center frequency of each frequency band It can be represented as:
[0111]
[0112] From the formula It can be seen that, since the relative bandwidth of each frequency band is the same, their center frequencies perfectly satisfy a geometric sequence relationship. The low-dimensional FCLB frequency constraint matrix is constructed based on the NUDM using the relative bandwidth method. for:
[0113]
[0114] Define a new frequency constraint matrix of The dimensional response vector is:
[0115]
[0116] Furthermore, in step S3, since the frequency domain constraint matrix contains a large amount of redundant information, which is not necessary but occupies a large number of degrees of freedom, it is necessary to consider how to extract the main feature information while discarding useless information, so as to reduce the consumption of computing resources and make more resources available for the interference suppression part.
[0117] 2D frequency domain constraint matrix Through SVD decomposition, it is decomposed into a product of several matrices, as expressed below:
[0118]
[0119] In the formula, and They are respectively and unitary matrix, for A 3D diagonal matrix whose diagonal elements are constraint matrices. The singular values of are sorted in descending order, i.e.:
[0120]
[0121] in, express The singular values satisfy Diagonal matrix The former The first diagonal element is much larger than the others, therefore the first one can be selected. Construct a diagonal matrix using diagonal elements. , Must meet:
[0122]
[0123] in, The threshold represents right The degree of approximation. Assume Preset value, through formula The minimum rank can be calculated. .
[0124] and It can be broken down into two parts:
[0125]
[0126] in, express The former Column vector, corresponding to The front of the middle The largest singular value, It contains the remaining column vectors. The same applies.
[0127] Select matrix The former Columns form a matrix , Approximate or complete characterization In Constraint matrix response vector for:
[0128]
[0129] The reduced-rank matrix is:
[0130]
[0131] Then the reduced-rank covariance matrix It can be represented as:
[0132]
[0133] In the formula, Indicates that the received data has passed through The data matrix after step-tap recombination. .
[0134] Reduced-rank frequency domain constraint matrix Represented as:
[0135]
[0136] Furthermore, in step S4, when the interference is located within the main lobe, the desired pointing is no longer accurate, severely affecting beamforming performance. To suppress main lobe interference, the constraint matrix is reconstructed as follows:
[0137]
[0138] in, Let be the frequency domain constraint matrix for constraining interference. The expression is:
[0139]
[0140] and , The angle of interference to the main lobe. for A 3D column vector, expressed as:
[0141]
[0142] Furthermore, in step S5, using the LCMV criterion, the optimization problem of the weight vector can be expressed as:
[0143]
[0144] Using the Lagrange multiplier method and the cost function, the analytical form of the optimal adaptive weight vector can be obtained as follows:
[0145]
[0146] Furthermore, in step S6, let the data received by the array antenna be... Its expression is:
[0147]
[0148] Accordingly, the weight vector of each array element It can be represented as:
[0149]
[0150] The output is:
[0151]
[0152] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.
Claims
1. A low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law, characterized in that: The method includes the following steps: S1: Acquire the array received signal and perform time-domain preprocessing using a Laguerre structure; S2: A low-dimensional constraint matrix and response vector are generated by dividing the frequency band based on relative bandwidth; S3: Rank reduction processing based on Singular Value Decomposition (SVD); S4: Construct the joint constraint matrix of the target signal and the main lobe interference; S5: Solve for the optimal weights based on the Linearly Constrained Minimum Variance (LCMV) criterion and the constraint matrix; S6: Perform broadband beamforming using optimal weights and output the target signal.
2. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: In step S1, each sensor in the array is omnidirectional, and the number of array elements and the number of Laguerre structures in each array branch are respectively... and The spacing between adjacent array elements is The speed of radio waves is Assume the signal is incident on ULA from far-field space; at time... After the first The first of the array elements The output after processing by a Laguerre delay structure It can be represented as ； in, It is a single pole of the Laguerre structure; Frequency-Constrained Laguerre Beamforming (FCLB) utilizes a frequency constraint matrix to eliminate pre-steering delay and guides the beam along the incident direction of a known SOI; it decomposes the frequency passband into... Each frequency point satisfies ,in and These represent the maximum and minimum endpoints of the signal bandwidth, respectively; the frequency constraint matrix of the FCLB is: ； in, for A 3D column vector, expressed as: ； in ； ； , Sampling period; constraint matrix response vector for A 3D column vector, expressed as: 。 3. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: In step S2, the low-dimensional FCLB frequency constraint matrix is quickly obtained using the NUDM based on the relative bandwidth method; the relative bandwidth defined by the relative bandwidth method (RBM) is: ； From the formula It can be seen that the relative bandwidth of each frequency band in broadband beamforming is independent of its center frequency; therefore, when the relative bandwidth is the same, the absolute bandwidth of the high frequency band is greater than that of the low frequency band. Assuming the passband is decomposed into The non-uniform frequency band, the first The minimum and maximum frequencies of each frequency band are denoted as follows: and ,in , , No. The center frequency of each frequency band is: ； No. The relative bandwidth of each frequency band is expressed as: ； The formula The transformation yields: ； in, ;make ,because Therefore ; at this time Can be rewritten as That is, the frequency band boundaries satisfy a geometric sequence relationship; combined with , No. The highest frequency of each frequency band is: ； From the formula and , No. The center frequency of each frequency band It can be represented as: ； From the formula It can be seen that, since the relative bandwidth of each frequency band is the same, their center frequencies completely satisfy the geometric sequence relationship. Therefore, the low-dimensional FCLB frequency constraint matrix constructed based on the relative bandwidth method of NUDM is... for: ； Define a new frequency constraint matrix of The dimensional response vector is: 。 4. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: In step S3, the main feature information is extracted while useless information is discarded to reduce the consumption of computing resources, allowing more resources to be used for the interference suppression part. 2D frequency domain constraint matrix Through SVD decomposition, it is decomposed into a product of several matrices, as expressed below: ； In the formula, and They are respectively and unitary matrix, for A 3D diagonal matrix whose diagonal elements are constraint matrices. The singular values are sorted in descending order, i.e.: ； in, express The singular values satisfy diagonal matrix The former The first diagonal element is much larger than the others, therefore the first one can be selected. Construct a diagonal matrix using diagonal elements. , Must meet: ； in, The threshold represents right The degree of approximation; assumption Preset value, through formula The minimum rank can be calculated. ; and Decomposed into two parts: ； in, express The former Column vector, corresponding to The front of the middle The largest singular value, It contains the remaining column vectors. The same applies; Select matrix The former Columns form a matrix , Approximate or complete characterization In Constraint matrix response vector for: ； The reduced-rank matrix is: ； Then the reduced-rank covariance matrix It can be represented as: ； In the formula, Indicates that the received data has passed through The data matrix after step-tap recombination. , Reduced-rank frequency domain constraint matrix Represented as: 。 5. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: In step S4, to suppress main lobe interference, the constraint matrix is reconstructed as follows: ； in, Let be the frequency domain constraint matrix for constraining interference. The expression is: ； and , The angle of interference on the main lobe. for A 3D column vector, expressed as: 。 6. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: Using the LCMV criterion, the optimization problem of the weight vector can be expressed as: ； Using the Lagrange multiplier method and the cost function, the analytical form of the optimal adaptive weight vector can be obtained as follows: 。 7. The low-complexity main lobe interference suppression method based on frequency-constrained Laguerre's law as described in claim 1, characterized in that: In step S6, assume the array antenna receives the following data: Its expression is: ； Accordingly, the weight vector of each array element It can be represented as: ； The output is: 。