Wideband linear array multi-beam forming method and amplitude comparison angle finding method

Abstract

The application discloses a broadband linear array multi-beam forming method and amplitude comparison angle measurement method, the multi-beam forming method comprising: establishing a one-dimensional normalized space frequency model and a DFT-based beam forming model; beam forming coefficient design; real-time beam forming calculation and detection processing.The amplitude comparison angle measurement method comprises: establishing an amplitude ratio table; normalized space frequency estimation; real azimuth solution.The application avoids the approximate processing error of beam forming and amplitude comparison angle measurement, simplifies the design and storage of beam forming coefficient and amplitude comparison curve, and reduces the complexity of receiver design through one-dimensional space DFT beam forming technology.

Description

Technical Field

[0001] This invention belongs to the field of passive radar direction finding technology, and particularly relates to a broadband linear array multi-beamforming method and an amplitude-to-angle measurement method. Background Technology

[0002] Passive radar does not emit electromagnetic signals itself, but detects and discovers targets by intercepting radar signals from the target's radiation source.

[0003] Compared to active detection radars, which generally employ narrowband processing, passive radars often require wider frequency coverage and broader instantaneous spatial coverage. Therefore, they necessitate a large number of simultaneous multi-beam processing operations across different frequencies and azimuth directions. Since beam patterns are functions of azimuth and frequency, designing each beam independently results in different beamforming factors and amplitude ratio curves between adjacent beams. This necessitates the receiver simultaneously maintaining numerous beamforming factors and amplitude ratio curves, significantly increasing the receiver's design complexity.

[0004] Beamforming of uniform linear arrays can be directly achieved through FFT (see the literature "Analysis and Design of Modern Radar Systems", edited by Chen Boxiao et al., Xi'an University of Electronic Science and Technology Press, 2012), which can save the design of beamforming coefficients with a large amount of data. For non-uniform linear arrays, the literature "A New Algorithm for Fourier Transform and Spectrum Estimation and Its Application in Electromagnetic Engineering" (Doctoral Dissertation of University of Electronic Science and Technology of China, 2009) introduces a non-uniform fast Fourier transform algorithm based on minimum mean square error. Through interpolation calculation, the sampling of non-uniform linear arrays can be converted into virtual uniform linear array sampling, and then FFT can be used for beamforming processing. However, the interpolation process inevitably introduces beam pattern calculation errors, which will affect the accuracy of amplitude and angle measurement. There are two main methods for simplifying amplitude ratio curve design: one is the frequency-invariant beamforming method introduced in the literature "Broadband Beamforming: Concepts and Techniques" (by Wei Liu and Stephan Weiss, Harbin Institute of Technology Press, 2019). By designing a constant beamwidth beamformer, the array can have the same beam pattern for input signals of different frequencies, and the amplitude ratio curve can be shared for angle measurements at different frequencies. The disadvantage is that the beamforming coefficient design is more complex and the performance of each beam, such as the main lobe ratio, is inconsistent. The other method, which is commonly used in engineering, is to interpolate the amplitude ratio curves at different frequencies and use a set of amplitude ratio curves to replace a series of amplitude ratio curves that differ at different frequencies. The disadvantage is that this approximation may introduce a large angle measurement error, especially in the lower frequency band (such as the P-band), where the beam pattern of different frequencies differs greatly, and this approximation error is particularly obvious. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies by providing a broadband linear array multi-beamforming method and an amplitude comparison angle measurement method. The beamforming process of the broadband linear array is implemented using one-dimensional spatial DFT, replacing the large amount of beamforming coefficients with a small number of spatial DFT control parameters. Simultaneously, an amplitude comparison curve is established for estimating the normalized spatial frequency. The azimuth angle is indirectly solved by estimating the normalized spatial frequency through amplitude comparison. This amplitude comparison curve can be identical across different beams, greatly simplifying the design of the amplitude comparison curve, and eliminating the angle measurement error caused by interpolation approximation.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A broadband linear array multibeamforming method, the method comprising:

[0008] Based on the array element location distribution information and array operating frequency information, a beamforming model expressed by one-dimensional spatial DFT and a normalized spatial frequency calculation model are established, and the beamforming coefficients are determined through one-dimensional spatial DFT analysis.

[0009] The digital acquisition signals of each element of the broadband linear array are converted into multiple narrowband amplitude and phase signals. Multi-beamforming is completed based on the beamforming coefficients. Peak detection is performed on the amplitude of the multi-beams, and relevant information of the detected signal is output. The detected signal is a spatial frequency domain peak signal whose amplitude exceeds a preset threshold. The relevant information includes frequency value, beam number, the beam it belongs to, and amplitude information of adjacent beams.

[0010] Furthermore, the calculation model process for normalized spatial frequency includes:

[0011] Select a reference element and obtain the distance of other elements relative to the reference element. For non-uniform linear arrays, select half the wavelength of the array's highest operating frequency as the virtual element spacing d (for uniform linear arrays, the actual element spacing can be directly taken).

[0012] The normalized spatial frequency calculation model is as follows:

[0013] ω=2π*d*sin(θ) / λ

[0014] Where θ is the incident azimuth angle of the signal, λ is the incident signal wavelength, d≤λ / 2, θ∈[-π / 2,π / 2], -π≤ω≤π;

[0015] The amplitude and phase signals of each array element, converted to a certain frequency, are denoted by x(n). The beamforming model expressed by the one-dimensional spatial discrete Fourier transform is as follows:

[0016]

[0017] Where n = 0, 1, 2, ..., N-1, the linear array has a total of N elements, ω m Here, M represents the homogenized frequency sampling points of the spatial DFT, M is the number of frequency domain samples in the spatial DFT output, and A is the number of samples in the frequency domain. n Y(ω) is the magnitude weighting coefficient of the array data. m The output is the beamforming result calculated using a one-dimensional spatial DFT.

[0018] Furthermore, the method outputs relevant information of the detected signal by performing two-dimensional joint peak search and detection processing along the beam dimension and frequency dimension.

[0019] Furthermore, the amplitude weighting coefficients of each element determine the beam's array gain, main lobe width, and main-to-side lobe ratio. By using the same amplitude weighting coefficients for each beam, consistent beam index parameters can be obtained. The phase weighting coefficients of each element are calculated by compensating for the phase difference between the beam pointing and each element.

[0020] Furthermore, when the linear array is a uniform linear array, the method uses the Fast Fourier Transform algorithm to calculate the one-dimensional spatial discrete Fourier transform, and can calculate and control the number and density of output beams through the spatial zero-padding Fast Fourier Transform algorithm, while controlling the antenna gain at the overlap of adjacent beams.

[0021] On the other hand, the present invention also provides an amplitude comparison angle measurement method, which is used to calculate the two-dimensional angle of the detected signal generated by any of the aforementioned methods, and includes the following steps:

[0022] Based on the beamforming coefficients, calculate the relationship between the spatial frequency offset of the incident signal and the amplitude response ratio of adjacent beams, and establish an amplitude ratio table.

[0023] The normalized spatial frequency offset value of the incident signal is obtained based on the amplitude ratio table and the relevant information of the detected signal. Combined with the normalized spatial frequency value corresponding to the beam, the normalized spatial frequency estimation of the incident radiation source signal is completed.

[0024] Based on the system frequency transformation relationship, the radio frequency value of the detected signal is determined, and the true azimuth angle of the detected signal is calculated based on the calculation model of the normalized spatial frequency and the estimation result of the normalized spatial frequency of the incident radiation source signal.

[0025] Furthermore, the process of establishing the amplitude ratio table includes:

[0026] Select the spatial frequency sampling range of one cycle of the spatial discrete Fourier transform, simulate the input signal, and calculate the relationship between the amplitude ratio of adjacent beams and the spatial frequency offset.

[0027] Calculate the amplitude ratio between adjacent beams to establish a table relating it to the spatial frequency offset.

[0028] Furthermore, the method stores only one table of amplitude ratios between spatial frequency sampling intervals.

[0029] Furthermore, the calculation of the true azimuth angle of the detected signal based on the calculation model of the normalized spatial frequency and the normalized spatial frequency estimation result of the incident radiation source signal specifically includes:

[0030] The true azimuth angle of the detected signal:

[0031]

[0032] Where d is the element spacing and f is the radio frequency value. Here, c represents the normalized spatial frequency, and c represents the speed of light.

[0033] The beneficial effects of this invention are as follows:

[0034] (1) The present invention uses the same array element amplitude weighting coefficient for beamforming processing of different frequencies and different directions. On the one hand, it simplifies the design of beamforming coefficients, and on the other hand, it enables each beam to have the same array gain, main-side lobe ratio and adjacent beam overlap gain, so that the receiver has relatively consistent detection performance for incident signals at various angles.

[0035] (2) Unlike the traditional direct amplitude comparison angle measurement method, the amplitude ratio table established in this invention is used to estimate the normalized spatial frequency of the incident signal. By uniformly sampling the output frequency of the one-dimensional spatial DFT, the beam amplitude response exhibits periodicity in the spatial frequency dimension and is not directly related to the radio frequency of the incident signal. Only the amplitude ratio curve between the two output frequency sampling points of the one-dimensional spatial DFT needs to be stored to complete the one-dimensional angle measurement of various incident angles and frequencies, which greatly simplifies the design and storage of the amplitude ratio curve.

[0036] (3) The beamforming coefficient and amplitude curve designed in this invention do not have large interpolation approximation processing, which can better ensure the accuracy of angle measurement.

[0037] (4) This invention is applicable to broadband linear arrays of various layouts, including uniform linear arrays and non-uniform linear arrays, and has a certain degree of versatility. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the broadband linear array multi-beamforming process provided in Embodiment 1 of the present invention;

[0039] Figure 2 This is a schematic diagram of the amplitude comparison and angle measurement processing flow provided in Embodiment 2 of the present invention;

[0040] Figure 3 This is the overall flowchart of Embodiment 3 of the present invention;

[0041] Figure 4 This is a simulation diagram of the antenna pattern of a 28-element linear array according to Embodiment 3 of the present invention;

[0042] Figure 5 This is a simulation effect diagram of the antenna pattern of a 28-element linear array at two frequencies in Embodiment 3 of the present invention. Detailed Implementation

[0043] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0044] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] Traditional broadband linear array beamforming and amplitude comparison angle measurement methods have problems such as large amounts of data for beamforming coefficients and amplitude comparison curves, and while approximate processing simplifies the design, it introduces additional angle measurement errors.

[0046] To address the aforementioned technical problems, the following embodiments of the broadband linear array multi-beamforming method and amplitude-to-angle measurement method of the present invention are proposed.

[0047] Example 1

[0048] Reference Figure 1 ,like Figure 1 The diagram shown is a schematic of the broadband linear array multibeamforming process provided in this embodiment. The method specifically includes the following steps:

[0049] Step 1, Establishing a one-dimensional spatial DFT model:

[0050] Based on the array element position distribution information and the array operating frequency range, a beamforming processing mathematical model expressed by one-dimensional spatial DFT and a calculation formula for normalized spatial frequency are established.

[0051] Step 2, Beamforming factor design:

[0052] By using one-dimensional spatial DFT simulation and combining specific application requirements, the beamforming coefficients of each beam design are determined, which serve as the amplitude weighting coefficients of the array data for each beam design. The phase weighting coefficients are determined by calculating the phase difference that needs to be compensated for in beam pointing.

[0053] Step 3, Beamforming and Detection Processing:

[0054] The signals acquired by each element of the broadband linear array are corrected and transformed into multiple narrowband amplitude and phase signals. Based on the beamforming coefficients determined in step 2, multi-beamforming processing is completed. Then, peak detection is performed on the multi-beam amplitude to output information such as the frequency value, beam number, the beam in which the signal is located, and the amplitude of adjacent beams.

[0055] Example 2

[0056] This embodiment provides an amplitude-based angle measurement method for calculating the true azimuth of the incident signal generated by the broadband linear array multibeamforming method provided in the aforementioned embodiment.

[0057] Reference Figure 2 ,like Figure 2 The diagram shown is a schematic of the amplitude comparison and angle measurement processing flow provided in this embodiment. The method specifically includes the following steps:

[0058] Step 1, establish an amplitude ratio table:

[0059] Based on the determined beamforming coefficients, the relationship between the spatial frequency offset of the incident signal (relative to the neighboring frequency domain sampling points of the one-dimensional spatial DFT output) and the amplitude response ratio of the adjacent beams is calculated through simulation, and an amplitude ratio table is established.

[0060] Step 2, Normalized spatial frequency estimation:

[0061] Based on the amplitude ratio table and the detected signal information from step 1, the normalized spatial frequency offset value of the incident signal is obtained by looking up the table. Then, combined with the normalized spatial frequency value corresponding to the beam, the final normalized spatial frequency estimation of the incident radiation source signal is completed.

[0062] Step 3, Calculate the true location:

[0063] The radio frequency value of the output signal in step 1 is determined, and then the true orientation of the incident signal is calculated based on the normalized spatial frequency calculation formula determined in step 1 and the spatial frequency estimation result of the radiation source signal output in step 2.

[0064] Example 3

[0065] This embodiment uses a general broadband non-uniform linear array model as an example for illustration, referring to... Figure 3 ,like Figure 3The following is a flowchart of the overall process of this embodiment.

[0066] Step 1: Select the leftmost element as the reference element and obtain the distance D of other elements relative to the reference element. n If half the wavelength of the array's highest operating frequency is selected as the virtual element spacing d, then the normalized spatial frequency can be expressed as:

[0067] ω=2π*d*sin(θ) / λ

[0068] Where θ is the incident azimuth angle of the signal and λ is the incident signal wavelength. Obviously, for d≤λ / 2 and θ∈[-π / 2,π / 2], we have -π≤ω≤π.

[0069] Assuming that the signals acquired by each array element are corrected and transformed, and the amplitude and phase signals converted to a certain frequency are represented by x(n) (where n = 0, 1, 2, ..., N-1, and the linear array has a total of N array elements), then the beamforming process of the broadband linear array can be represented by one-dimensional spatial DFT as follows:

[0070]

[0071] ω m =(2m-M)*π / M,m=0,1,2,…,M-1

[0072] Where, ω m Here, M represents the homogenized frequency sampling points of the spatial DFT, M is the number of frequency domain samples in the spatial DFT output, and A is the number of samples in the frequency domain. n Y(ω) is the magnitude weighting coefficient of the array data. m The output is the beamforming result calculated using a one-dimensional spatial DFT.

[0073] Step 2: Amplitude weighting coefficient A for each matrix's metadata n The array gain, main lobe width, and main-to-side lobe ratio of the beam are determined and can be selected through optimization calculations based on actual application requirements. Parameter M determines the number and density of output beams; obviously, the denser the beams, the higher the overlap gain of adjacent beams, which can be selected according to actual needs. The M frequency domain samples of the spatial DFT output are generally not all necessary. Constrained by the effective angle measurement range of the array and the effective value range of ω for different frequency signals in step 1, only a few frequency domain samples are usually selected as beamforming results for detection and amplitude-to-angle comparison processing.

[0074] Step 3: Based on the beamforming coefficients determined in Step 2, select a spatial frequency sampling range for one period of the spatial DFT, simulate the input signal, and calculate the relationship between the amplitude ratio of adjacent beams and the spatial frequency offset (relative to neighboring frequency sampling points). For example, simulate the spatial frequency ω∈[ω... m ,ωm+1 ] Calculate the amplitude ratio |Y(ω) between adjacent beams m+1 )| / |Y(ω m This establishes its relationship with the spatial frequency offset value (Δω=ω-ω). m Relationship table.

[0075] As one implementation method, the ratio table in this embodiment can be used for spatial frequency estimation of signals with arbitrary incident frequency and azimuth angle, and the entire system only needs to store one copy.

[0076] Step 4: The signals acquired by each array element are transformed and corrected to be converted into multiple narrowband amplitude and phase signals. Based on the beamforming coefficients determined in Step 2, multi-beam calculation is completed. Then, two-dimensional joint peak search and detection is performed along the beam dimension and frequency dimension, and the frequency value (usually the intermediate frequency), beam number, amplitude of the beam and adjacent beams of the detected signal are output.

[0077] Step 5: Based on the amplitude ratio table established in Step 3 and the detected signal amplitude data output in Step 4, determine the normalized spatial frequency offset value Δω by looking up the table. Based on the beam number of the detected signal in Step 4 (corresponding to a spatial DFT output frequency sampling point ω), p Complete the normalized spatial frequency estimation of the incident radiation source signal:

[0078]

[0079] Step 6: Based on the detected signal frequency value output in Step 4, and according to the system frequency transformation relationship, obtain its corresponding radio frequency value f. Then, using the normalized spatial frequency estimate output in Step 5, and following the spatial frequency calculation formula determined in Step 1, calculate the true location of the radiation source signal.

[0080]

[0081] in, Here, c represents the normalized spatial frequency, and c represents the speed of light.

[0082] Reference Figure 4 ,like Figure 4 The diagram shows the simulation effect of the antenna pattern of a 28-element linear array in this embodiment. The beam design method of this embodiment is used to demonstrate the antenna pattern effects for different frequencies and directions. Relative to the normalized spatial frequency, its beam performance (including main lobe width, main-to-side lobe ratio, and gain at beam overlap) is exactly the same. Therefore, a set of amplitude ratio curves can be used to directly estimate the normalized spatial frequency, and then solve for the azimuth angle.

[0083] Reference Figure 5 ,like Figure 5The figure shown is a simulation of the antenna pattern of a 28-element linear array at two frequencies in this embodiment. At different frequencies, the antenna pattern calculated directly relative to the azimuth angle is very different, and the antenna pattern of different directional beams at the same frequency is also different (starting from the center beam, the beams closer to the sides have wider main lobes). Therefore, using the traditional direct amplitude comparison and angle measurement method, the receiver must store all these different amplitude comparison curves, which is quite complicated.

[0084] Example 4

[0085] Another common example is the multi-beamforming and amplitude-to-angle measurement processing of broadband uniform digital linear arrays. The process is largely the same as that of the aforementioned non-uniform broadband linear arrays, with the main difference being in the following steps:

[0086] Step 1: The element spacing of a uniform linear array is designed to be no less than half the wavelength of the maximum operating frequency, based on the consideration of eliminating grating lobes. This can be directly used for normalized spatial frequency calculation. For uniform linear arrays, one-dimensional spatial DFT calculation can be accelerated using the FFT algorithm.

[0087] Step 2: For the selection of amplitude weighting coefficients for uniform linear arrays, there are various theoretically mature window functions available to meet different requirements in terms of array gain, main lobe width, main lobe-to-side lobe ratio, etc. Through spatial zero-padding FFT calculation, the number and density of output beams can be controlled, and the antenna gain at the overlap of adjacent beams can also be controlled.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A broadband linear array multi-beamforming and amplitude-to-angle measurement method, characterized in that, The broadband linear array multibeamforming method includes: Based on the array element location distribution information and array operating frequency information, a beamforming model expressed by one-dimensional spatial DFT and a normalized spatial frequency calculation model are established, and the beamforming coefficients are determined through one-dimensional spatial DFT analysis. The digital acquisition signals of each element of the broadband linear array are converted into multiple narrowband amplitude and phase signals. Multi-beamforming is completed based on the beamforming coefficients. Peak detection is performed on the amplitude of the multi-beams, and relevant information of the detected signal is output. The detected signal is a spatial frequency domain peak signal whose amplitude exceeds a preset threshold. The relevant information includes frequency value, beam number, the beam it belongs to, and amplitude information of adjacent beams. The amplitude comparison angle measurement method is used to calculate the two-dimensional angle of the detected signal generated by the broadband linear array multibeamforming method. The amplitude comparison angle measurement method includes: Based on the beamforming coefficients, calculate the relationship between the spatial frequency offset of the incident signal and the amplitude response ratio of adjacent beams, and establish an amplitude ratio table. The normalized spatial frequency offset value of the incident signal is obtained based on the amplitude ratio table and the relevant information of the detected signal. Combined with the normalized spatial frequency value corresponding to the beam, the normalized spatial frequency estimation of the incident radiation source signal is completed. Based on the system frequency transformation relationship, the radio frequency value of the detected signal is determined, and the true azimuth angle of the detected signal is calculated based on the calculation model of the normalized spatial frequency and the estimation result of the normalized spatial frequency of the incident radiation source signal.

2. The broadband linear array multi-beamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The calculation model process for normalized spatial frequency includes: Select a reference element and obtain the distance of other elements relative to the reference element. For non-uniform linear arrays, select half the wavelength of the array's highest operating frequency as the virtual element spacing. For uniform linear arrays, directly take the actual element spacing. The normalized spatial frequency calculation model is as follows: in, The azimuth angle of the signal incident. The wavelength of the incident signal, d For the spacing between array elements, , , ; The amplitude and phase signals of each array element are converted to a certain frequency using the signal collected by the array elements. The beamforming model expressed using the one-dimensional spatial discrete Fourier transform is as follows: ； in, The linear array has a total of N elements. Here, M represents the homogenized frequency sampling points of the spatial domain DFT, and M is the number of frequency domain samples in the spatial domain DFT output. The magnitude weighting coefficients for the array data. The output beamforming result is calculated using a one-dimensional spatial DFT.

3. The broadband linear array multi-beamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The broadband linear array multi-beamforming method outputs relevant information of the detected signal by performing two-dimensional joint peak search and detection processing along the beam dimension and frequency dimension.

4. The broadband linear array multibeamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The amplitude weighting coefficients of each element determine the array gain, main lobe width, and main-to-side lobe ratio of the beam. Using the same amplitude weighting coefficients for each beam ensures consistent beam parameters. The phase weighting coefficients of each element are calculated by compensating for the phase difference between the beam pointing and each element.

5. The broadband linear array multibeamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, When the linear array is a uniform linear array, the broadband linear array multi-beamforming method uses the fast Fourier transform algorithm to calculate the one-dimensional spatial discrete Fourier transform.

6. The broadband linear array multi-beamforming and amplitude-to-angle measurement method as described in claim 5, characterized in that, The broadband linear array multi-beamforming method calculates and controls the number and density of output beams using a spatial zero-padding fast Fourier transform algorithm, while simultaneously controlling the antenna gain at the overlap of adjacent beams.

7. The broadband linear array multibeamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The process of establishing the amplitude ratio table includes: Select the spatial frequency sampling range of one cycle of the spatial discrete Fourier transform, simulate the input signal, and calculate the relationship between the amplitude ratio of adjacent beams and the spatial frequency offset. Calculate the amplitude ratio between adjacent beams to establish a table relating it to the spatial frequency offset.

8. The broadband linear array multibeamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The amplitude comparison angle measurement method stores only one table of amplitude ratios between spatial frequency sampling intervals.

9. The broadband linear array multibeamforming and amplitude-to-angle measurement method as described in claim 1, characterized in that, The calculation of the true azimuth angle of the detected signal based on the normalized spatial frequency calculation model and the normalized spatial frequency estimation result of the incident radiation source signal specifically includes: The true azimuth angle of the detected signal: ； Where d is the element spacing. This is the radio frequency value. Here, c represents the normalized spatial frequency, and c represents the speed of light.

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