A method for fast generation of broadband null pattern
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- THE 54TH RESEARCH INSTITUTE OF CHINA ELECTRONICS TECHNOLOGY GROUP CORPORATION
- Filing Date
- 2026-02-10
- Publication Date
- 2026-06-02
Smart Images
Figure CN122137411A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing, specifically relating to a method for rapid generation of broadband null patterns. Background Technology
[0002] The increasingly complex electromagnetic environment places higher demands on the spatial anti-interference capabilities of array antennas. To avoid the system being affected by strong clutter or interference, forming nulls in the interference direction has become an important optimization objective in array antenna pattern synthesis. In broadband pattern synthesis of arrays, researchers have proposed various synthesis methods based on convex optimization and evolutionary algorithms. These algorithms can achieve good shaping effects and form nulls at specified locations. However, these algorithms usually require multiple iterations to obtain the optimal result, resulting in long computation times. To effectively implement broadband null pattern synthesis in engineering applications, it is necessary to study a fast broadband null pattern generation method with low computational cost and real-time synthesis capabilities. Summary of the Invention
[0003] In view of this, the present invention proposes a fast method for generating broadband null patterns. This method solves the problem that existing methods require multiple iterations of optimization algorithms to solve for array element excitations, resulting in large computational load and long operation time. It has real-time synthesis capability and has engineering application significance.
[0004] The technical solution adopted in this invention is as follows:
[0005] A fast broadband null pattern generation method is proposed, applied to a uniform linear array containing M elements with an element spacing of d and an operating frequency band of [missing information]. The method includes the following steps:
[0006] Step 1: Construct the objective function and constraints based on the orientation of the main lobe and null in the radiation pattern;
[0007] Step 2: Use the Lagrange multiplier method to obtain the array element excitation vectors at each sampling frequency point;
[0008] Step 3: Solve for the FIR filter coefficients based on the array element excitation vectors at each sampling frequency.
[0009] Step 4: Construct a filter based on the FIR filter coefficients, transmit or receive the broadband signal through the filter and array elements, form the main lobe and null at the specified position, and obtain the desired broadband null pattern synthesis result.
[0010] Furthermore, in step 1, the objective function and constraints are as follows:
[0011]
[0012] in, The pointing angle of the main lobe in the radiation pattern. For the null angle of the radiation pattern, For the operating frequency is The excitation vector of the array elements at time, with the superscript H indicating the conjugate transpose; For the operating frequency is The main lobe steering vector at time, the m-th element of which is ; For the operating frequency is The zero-trap position guide vector at time, the m-th element of which is c represents the speed of light, d represents the spacing between array elements, and the superscript T indicates transpose.
[0013] Furthermore, the specific method for step 2 is as follows:
[0014] Step 201: Perform uniform sampling at point P on the operating frequency band, with the sampling frequency being... , ;
[0015] Step 202, construct the Lagrange function:
[0016]
[0017] in, For Lagrange multipliers, For the activation vector, , ;
[0018] Step 203, differentiate the Lagrange function to obtain the following system of equations:
[0019]
[0020] Transform into matrix representation:
[0021]
[0022] Where I is the identity matrix;
[0023] Step 204, let , , The matrix representation is modified as follows:
[0024]
[0025] Step 205, calculate Least squares solution:
[0026]
[0027] The superscript + indicates that the pseudo-inverse matrix is being sought.
[0028] Step 206, take the vector The first M values are the operating frequency. When the Lagrange function L reaches its minimum value, the array element excitation vector is... .
[0029] Furthermore, the specific method for step 3 is as follows:
[0030] Step 301, for sampling frequency points The excitation vector w of the m-th element m Represented in matrix form:
[0031]
[0032] in,
[0033]
[0034]
[0035]
[0036] In the formula, Where is the signal sampling frequency, and K is the order of the FIR filter. This refers to the k-th coefficient of the FIR filter corresponding to the m-th channel;
[0037] Step 302: When K < P, substitute the array element excitation vectors obtained in Step 2 at each sampling frequency point to obtain the FIR filter coefficients corresponding to the m-th array element channel. The least squares solution is:
[0038]
[0039] When K ≥ P, we can obtain The least 2 norm solution is:
[0040] .
[0041] The beneficial effects of this invention are:
[0042] 1. This invention provides a fully analytical expression for generating broadband null pattern array element excitations, which solves the problem that existing methods require multiple iterations of optimization algorithms to solve for array element excitations, resulting in large computational loads and long computation times.
[0043] 2. This invention has real-time synthesis capability and has engineering application significance. Attached Figure Description
[0044] Figure 1This is a three-dimensional view of the array broadband null pattern synthesized in this invention.
[0045] Figure 2 This is a comparison between the null pattern synthesized in this invention and the null pattern synthesized using the convex optimization method. Detailed Implementation
[0046] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.
[0047] A fast method for generating broadband null patterns is proposed, based on the Lagrange multiplier method and FIR filters to generate broadband array patterns with nulls. The method first constructs an objective function and its constraints based on the pointing of the main lobe and nulls of the pattern, converts it into a Lagrange function, and solves for its extreme points to obtain the analytical expression of the array excitation vector at each sampling frequency. Next, the FIR filter coefficients are solved based on the element excitations corresponding to each frequency sampling point. Finally, a filter is constructed based on the FIR filter coefficients to obtain the desired broadband array pattern synthesis result.
[0048] Assume the array to be synthesized is a uniform linear array with M elements, an element spacing of d, and an operating frequency band of [missing information]. , This is the lower bound of the operating frequency band. This represents the upper bound of the operating frequency band. Its radiation pattern can be represented as:
[0049] (1)
[0050] in, This is the complex excitation of the m-th array element at the operating frequency f. The operating frequency band is uniformly sampled at P points, with the sampling frequency being... , The desired radiation pattern is sampled, assuming the main lobe of the radiation pattern points at an angle of... , directional pattern null angle .
[0051] The specific steps of this method are as follows:
[0052] Step 1: Construct the objective function based on the pointing of the main lobe and null of the given radiation pattern:
[0053] (2)
[0054] in, For the operating frequency is The excitation vector of the array element at that time. For the operating frequency is The main lobe steering vector at time, the m-th element of which is . For the operating frequency is The zero-trap position guide vector at time, the m-th element of which is .
[0055] Minimize the optimization objective This ensures that the normalized pattern gain is maximized. The two constraints guarantee that the gain is maximized at the main lobe and minimized at the null.
[0056] Step 2: Use the Lagrange multiplier method to quickly obtain the array element excitation vectors at each frequency point. The specific method is as follows:
[0057] Solving for extreme points using the Lagrange multiplier method:
[0058] Equation (2) can be used to construct the Lagrange function as follows:
[0059] (3)
[0060] in, For Lagrange multipliers, , .
[0061] Taking the derivative of the Lagrange function yields the excitation vector that minimizes the function L. We obtain the following system of equations:
[0062] (4)
[0063] The system of equations (4) can be transformed into a matrix expression.
[0064] (5)
[0065] make , , Equation (5) can be expressed as:
[0066] (6)
[0067] According to equation (6), we can obtain Least square solution
[0068] (7)
[0069] vector The first M values are the operating frequency. Optimal array element excitation vector at time .
[0070] Step 3: Solve for the FIR filter coefficients.
[0071] To achieve broadband beamforming, the signals from each element channel need to be processed by an FIR filter. (Pointing is...) The signal of the input filter for the m-th channel is The output signal after passing through the K-order FIR filter is
[0072] (8)
[0073] in, This represents the k-th coefficient of the FIR filter corresponding to the m-th channel.
[0074] Output signal The frequency domain representation can be obtained by performing a discrete-time Fourier transform on both sides of equation (8), or by using the array element excitation expressions corresponding to each frequency sampling point in equation (1). The array element excitation expressions can be obtained by comparison.
[0075] (9)
[0076] in, This refers to the signal sampling frequency. For the sampling frequency point... The excitation vector of the m-th element can be represented in matrix form:
[0077] (10)
[0078] in,
[0079] (11)
[0080] (12)
[0081] (13)
[0082] When K < P, substituting the array element excitation vectors obtained in step 1 for each sampling frequency point, the FIR filter coefficients corresponding to the m-th array element channel can be obtained. The least squares solution is:
[0083] (14)
[0084] When K ≥ P, it can be obtained The least 2 norm solution is:
[0085] (15)
[0086] Step 4: Construct a filter based on the FIR filter coefficients. Broadband signals are transmitted or received through the filter and array units, and the main lobe and null can be quickly formed at the specified location, thus completing the method for rapid generation of broadband null patterns.
[0087] Here is a more specific example:
[0088] The uniform linear array has 6 elements (M=6), an element spacing of 120mm, and an operating frequency of 960MHz~1215MHz. The desired pencil pattern has a main lobe pointing to 0°, a null position of 60°, and a scanning range of -120°~120°. The FIR filter order is K=32. The method of this invention and the optimization method using a convex optimization toolkit were run simultaneously, and the running time was recorded.
[0089] Based on the given pattern constraints, the array element excitation vector at each sampling frequency can be obtained by equation (7) or convex optimization method. The optimal FIR filter coefficients can be obtained by equation (14) or (15), and the broadband array null pattern can be calculated accordingly.
[0090] like Figure 1 As shown, the method of the present invention can form the desired null radiation pattern, with minimal change in the shape of the main lobe at each frequency. Figure 2 As shown, the radiation pattern generated by the method of the present invention has a lower sidelobe compared with the convex optimization method. The running time of the convex optimization method is 28.5722s, while the method of the present invention provides an analytical solution for calculation, and the excitation time of generating each frequency point matrix element is 0.0074s, which has real-time synthesis capability.
[0091] In summary, this invention provides a fully analytical expression for generating broadband null pattern array element excitations using the Lagrange multiplier method. This solves the problem of large computational load and long operation time caused by the need for multiple iterations of optimization algorithms to solve for array element excitations in existing methods. It has real-time synthesis capability and has engineering application significance.
Claims
1. A method for rapid generation of broadband null patterns, applied to a uniform linear array containing M elements with an element spacing of d and an operating frequency band of [missing information]. Its characteristics are, Includes the following steps: Step 1: Construct the objective function and constraints based on the orientation of the main lobe and null in the radiation pattern; Step 2: Use the Lagrange multiplier method to obtain the array element excitation vectors at each sampling frequency point; Step 3: Solve for the FIR filter coefficients based on the array element excitation vectors at each sampling frequency. Step 4: Construct a filter based on the FIR filter coefficients, transmit or receive the broadband signal through the filter and array elements, form the main lobe and null at the specified position, and obtain the desired broadband null pattern synthesis result.
2. The method for rapid generation of broadband array null patterns according to claim 1, characterized in that, In step 1, the objective function and constraints are as follows: in, The pointing angle of the main lobe in the radiation pattern. For the null angle of the radiation pattern, For the operating frequency is The excitation vector of the array elements at time, with the superscript H indicating the conjugate transpose; For the operating frequency is The main lobe steering vector at time, the m-th element of which is ; For the operating frequency is The zero-trap position guide vector at time, the m-th element of which is c represents the speed of light, d represents the spacing between array elements, and the superscript T indicates transpose.
3. The method for rapid generation of broadband array null patterns according to claim 2, characterized in that, The specific method for step 2 is as follows: Step 201: Perform uniform sampling at point P on the operating frequency band, with the sampling frequency being... , ; Step 202, construct the Lagrange function: in, For Lagrange multipliers, For the activation vector, , ; Step 203, differentiate the Lagrange function to obtain the following system of equations: Transform into matrix representation: Where I is the identity matrix; Step 204, let , , The matrix representation is modified as follows: Step 205, calculate Least squares solution: The superscript + indicates that the pseudo-inverse matrix is being sought. Step 206, take the vector The first M values are the operating frequency. When the Lagrange function L reaches its minimum value, the array element excitation vector is... .
4. The method for rapid generation of broadband array null patterns according to claim 3, characterized in that, The specific method for step 3 is as follows: Step 301, for sampling frequency points The excitation vector w of the m-th array element m Represented in matrix form: in, In the formula, Where is the signal sampling frequency, and K is the order of the FIR filter. This refers to the k-th coefficient of the FIR filter corresponding to the m-th channel; Step 302: When K < P, substitute the array element excitation vectors obtained in Step 2 at each sampling frequency point to obtain the FIR filter coefficients corresponding to the m-th array element channel. The least squares solution is: When K ≥ P, we can obtain The least 2 norm solution is: 。