Frequency-invariant broadband shaping directional diagram synthesis method based on superposition principle
By combining the superposition principle and Taylor weighting method with FIR filters, a fully analytical expression is given to solve the FIR filter coefficients, which solves the problem of large computational load in existing technologies and realizes real-time synthesis of broadband radiation patterns.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-12
- Publication Date
- 2026-03-31
AI Technical Summary
Existing broadband beamforming pattern synthesis methods require multiple iterations to calculate FIR filter coefficients, resulting in high computational costs and making real-time synthesis impossible.
By employing the superposition principle and Taylor weighted pattern synthesis method, combined with the FIR filter, a fully analytical expression is given to solve for the FIR filter coefficients. The coefficients are calculated through discrete-time Fourier transform and least squares or least norm solutions.
It achieves real-time synthesis of broadband radiation patterns, reduces computational load, and has real-time synthesis capabilities for engineering applications.
Smart Images
Figure CN121765175A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing, specifically relating to a frequency-invariant broadband beamforming pattern synthesis method based on the superposition principle. Background Technology
[0002] Most array antenna pattern synthesis techniques are based on the assumption of narrowband signals. When an array generates a broadband pattern, the main lobe widths of the low-frequency and high-frequency components differ significantly, adding different amplitude and phase responses to different frequency components of the signal, affecting the system's transmit or receive performance. Therefore, in broadband pattern synthesis, researchers have proposed frequency-invariant pattern synthesis techniques, which ensure the invariance of the array pattern at different frequencies through frequency-domain or time-domain implementation methods. The time-domain implementation method is based on the time delay line structure, which involves adding a set of taps to each array element. This can be implemented by appending finite-length unit impulse response (FIR) filter coefficients to the array element. Currently, researchers have proposed broadband pattern synthesis methods based on simulated annealing, second-order cone programming, and convex optimization algorithms. These algorithms can achieve good patterning results, but they cannot provide analytical expressions for the FIR filter coefficients, usually requiring multiple iterations to obtain the optimal result, resulting in a large computational load. To reduce the computational complexity of pattern synthesis methods and effectively implement broadband pattern synthesis in engineering applications, it is necessary to research a broadband pattern synthesis method with real-time synthesis capabilities. Summary of the Invention
[0003] The purpose of this invention is to provide a frequency-invariant broadband pattern synthesis method based on the superposition principle. It presents a fully analytical expression for the coefficients of a finite-length unit impulse response (FIR) filter during broadband pattern synthesis, which solves the problem that existing methods require multiple iterations of optimization algorithms to calculate FIR coefficients, resulting in a large computational load. It has real-time synthesis capability and has engineering application significance.
[0004] This invention achieves pattern synthesis of a broadband array based on the superposition principle and an FIR filter. The proposed solution first uses the Taylor-weighted pattern synthesis method and the superposition principle to obtain the array excitation vector at each sampling frequency, given a desired pattern. 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. Details are as follows:
[0005] Step 1: Generate the array element excitation vectors at each frequency point based on the superposition principle.
[0006] 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...
[0007] (1)
[0008] Perform uniform sampling at P points within the operating frequency band, with the sampling frequency being... , The desired radiation pattern is sampled, assuming there are K sampling angles. , Let be the angle between the array beam pointing and the array. The element excitation vectors at each frequency are obtained using a pattern synthesis method based on the superposition principle.
[0009] 1) Using the Taylor weighted pattern synthesis method, the operating frequency is obtained as follows: The excitation current of each array element is
[0010] (2)
[0011] 2) According to phased array theory, the desired radiation pattern can be represented as a weighted superposition of K narrow beams. The excitation weight expression for the m-th element used to generate the narrow beam corresponding to the k-th sampling angle is:
[0012] (3)
[0013] 3) Operating frequency is Array element excitation vector at time The expression is:
[0014] (4)
[0015] in, This represents the gain of the desired radiation pattern at each sampling angle. For the operating frequency is The matrix is composed of array excitation vectors corresponding to each sampling angle.
[0016] (5)
[0017] Step 2: Solve for the FIR filter coefficients.
[0018] 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 Lth-order FIR filter is
[0019] (6)
[0020] in, These are the corresponding FIR filter coefficients. Taking a discrete-time Fourier transform of both sides of equation (3) yields...
[0021] (7)
[0022] in, and Time domain signals and Discrete-time Fourier transform, Here, n represents the signal sampling frequency, and n represents the nth data point of the received signal.
[0023] Consider equation (1), Alternatively, the excitation expression of the array element corresponding to each frequency sampling point can be used as follows:
[0024] (8)
[0025] in, This is the complex excitation of the m-th array element when the operating frequency is f.
[0026] Comparing formulas (7) and (8), we can obtain the excitation expression for the array elements.
[0027] (9)
[0028] For sampling frequency points The excitation vector of the m-th element can be represented in matrix form:
[0029] (10)
[0030] in,
[0031] (11)
[0032] (12)
[0033] (13)
[0034] When L < 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:
[0035] (14)
[0036] When L ≥ P, it can be obtained The least 2 norm solution is:
[0037] (15)
[0038] Step 3: Construct a filter based on the FIR filter coefficients. Broadband signals are transmitted or received through the filter and array units, and the desired broadband array pattern synthesis result can be obtained in the spatial domain, thus completing the frequency-invariant broadband pattern synthesis method based on the superposition principle.
[0039] The beneficial effects of this invention are:
[0040] This invention provides a fully analytical expression for the FIR filter coefficients in broadband pattern synthesis, which solves the problem that existing methods require multiple iterations of optimization algorithms to calculate FIR coefficients, resulting in a large computational load. It has real-time synthesis capability and has engineering application significance. Attached Figure Description
[0041] Figure 1 This is a three-dimensional view of the array broadband flat-top pattern synthesized in this invention.
[0042] Figure 2 This is a three-dimensional view of the array broadband cocut pattern synthesized in this invention. Detailed Implementation
[0043] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.
[0044] This invention presents a frequency-invariant broadband pattern synthesis method based on the superposition principle. The technical solution employed is as follows: First, based on the Taylor weighted pattern synthesis method and the superposition principle, the array excitation vector at each sampling frequency point is obtained, given the desired pattern. Next, the FIR filter coefficients are solved based on the array 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. Specifically, the method is as follows:
[0045] Step 1: Generate the array element excitation vectors at each frequency point based on the superposition principle.
[0046] 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...
[0047] (1)
[0048] Perform uniform sampling at P points within the operating frequency band, with the sampling frequency being... , The desired radiation pattern is sampled, assuming there are K sampling angles. , Let be the angle between the array beam pointing and the array. The element excitation vectors at each frequency are obtained using a pattern synthesis method based on the superposition principle.
[0049] 1) Using the Taylor weighted pattern synthesis method, the operating frequency is obtained as follows: The excitation current of each array element is
[0050] (2)
[0051] 2) According to phased array theory, the desired radiation pattern can be represented as a weighted superposition of K narrow beams. The excitation weight expression for the m-th element used to generate the narrow beam corresponding to the k-th sampling angle is:
[0052] (3)
[0053] 3) Operating frequency is Array element excitation vector at time The expression is:
[0054] (4)
[0055] in, This represents the gain of the desired radiation pattern at each sampling angle. For the operating frequency is The matrix is composed of array excitation vectors corresponding to each sampling angle.
[0056] (5)
[0057] Step 2: Solve for the FIR filter coefficients.
[0058] 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 Lth-order FIR filter is
[0059] (6)
[0060] in, These are the corresponding FIR filter coefficients. Taking a discrete-time Fourier transform of both sides of equation (3) yields...
[0061] (7)
[0062] in, and Time domain signals and Discrete-time Fourier transform, This is the signal sampling frequency.
[0063] Consider equation (1), Alternatively, the excitation expression of the array element corresponding to each frequency sampling point can be used as follows:
[0064] (8)
[0065] in, This is the complex excitation of the m-th array element when the operating frequency is f.
[0066] Comparing formulas (7) and (8), we can obtain the excitation expression for the array elements.
[0067] (9)
[0068] For sampling frequency points The excitation vector of the m-th element can be represented in matrix form:
[0069] (10)
[0070] in,
[0071] (11)
[0072] (12)
[0073] (13)
[0074] When L < 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:
[0075] (14)
[0076] When L ≥ P, it can be obtained The least 2 norm solution is:
[0077] (15)
[0078] Step 3: Construct a filter based on the FIR filter coefficients. Broadband signals are transmitted or received through the filter and array units, and the desired broadband array pattern synthesis result can be obtained in the spatial domain, thus completing the frequency-invariant broadband pattern synthesis method based on the superposition principle.
[0079] The following is a more specific example:
[0080] The uniform linear array has 20 elements (M=20), an element spacing of half a wavelength, an operating frequency of 1 GHz, and an operating bandwidth of 300 MHz. The desired flat-top pattern has a main lobe width of 40°, a main lobe center pointing at 90°, and a sidelobe level of -20 dB. The desired cosecant pattern also has a main lobe width of 40°, a main lobe located between 40° and 80°, and a sidelobe level of -20 dB. The FIR filter order is L=32.
[0081] Based on the desired radiation pattern, the array element excitation vectors at each sampling frequency can be obtained using equations (2)-(5), and the optimal FIR filter coefficients can be obtained using equations (14) or (15), thereby calculating the broadband array radiation pattern. Figure 1 As shown, the method of the present invention can form the desired flat-top radiation pattern, with the main lobe width and side lobe level meeting the requirements, and the main lobe shape of the radiation pattern does not change significantly at each frequency. Figure 2 As shown, the method of the present invention can form the desired cocut pattern, with the main lobe width and side lobe level meeting the requirements, and ensures that the shape of the main lobe of the pattern does not change much at each frequency.
[0082] Based on the Taylor weighted pattern synthesis method and the superposition principle, this invention provides a fully analytical expression for the FIR filter coefficients in broadband pattern synthesis. It solves the problem that existing methods require multiple iterations of optimization algorithms to calculate FIR coefficients, resulting in a large computational load. It has real-time synthesis capability and has engineering application significance.
Claims
1. A frequency-invariant broadband beamforming pattern synthesis method based on the superposition principle, characterized in that, Specifically, the process includes the following: Step 1: Based on the Taylor weighted pattern synthesis method and the superposition principle, the array excitation vector at each sampling frequency point is obtained under the premise of a given desired pattern gain. Step 2: Solve for the FIR filter coefficients based on the array excitation vectors obtained at each sampling frequency point, and construct the filter based on the FIR filter coefficients; Step 3: Broadband signals are transmitted or received via filters and array units to obtain the desired broadband array pattern synthesis result in the spatial domain, thus completing frequency-invariant broadband pattern synthesis based on the superposition principle.
2. The frequency-invariant broadband beamforming pattern synthesis method based on the superposition principle according to claim 1, characterized in that, Step 1 in detail Includes the following processes: Step 101: Using the Taylor weighted pattern synthesis method, the operating frequency is obtained as follows: The excitation current of each array element is: ； Here, it is assumed that the array to be synthesized is a uniform linear array with M elements; the operating frequency band of the uniform linear array is... Perform uniform sampling at point P, with the sampling frequency being... , ; This is the lower bound of the operating frequency band. This is the upper limit of the operating frequency band; Step 102: According to phased array theory, the desired radiation pattern is represented as a weighted superposition of K narrow beams. The excitation weight expression for the m-th element of the narrow beam corresponding to the k-th sampling angle is as follows: ； Wherein, the element spacing is d. The angle between the array beam pointing and the array itself has K sampling angles. c represents the speed of light; Step 103, operating frequency is Array element excitation vector at time The expression is: ； For the operating frequency is The matrix composed of the array excitation vectors corresponding to each sampling angle: ； This represents the gain of the desired radiation pattern at each sampling angle.
3. The frequency-invariant broadband beamforming pattern synthesis method based on the superposition principle according to claim 2, characterized in that, Step 2 details Includes the following processes: For an L-order FIR filter with M array element channels: When L < P, the FIR filter coefficients corresponding to the m-th array element channel are obtained. for: ； When L ≥ P, the FIR filter coefficients corresponding to the m-th array element channel are obtained. for: ； in, ； ， ； This is the sampling frequency of the received signal.