A wide-area sparse array multi-frequency point joint low-sidelobe beamforming method

Abstract

The application discloses a wide-area sparse array multi-frequency-point joint low-sidelobe beam forming method, and relates to the field of beam forming.The application firstly constructs a wide-area sparse array, and determines available working frequency bands and working frequency points;secondly, different frequency points of different frequency bands are selected for joint beam forming, the maximum sidelobe-to-main lobe ratio is calculated, and the frequency band and the number of frequency points that make the maximum sidelobe-to-main lobe ratio minimum are determined;finally, the final directivity pattern function is determined, and beam forming is performed.The application can make the wide-area sparse array form a low sidelobe, and can solve the problem of excessively high sidelobe of the wide-area sparse array during beam forming.

Description

TECHNICAL FIELD

[0001] The present application relates to a multi-frequency point joint low sidelobe beam forming method in the field of beam forming, and is particularly suitable for the beam forming of a wide-area sparse array. BACKGROUND

[0002] Most of the current beam forming methods are based on non-sparse arrays, and the feature is that the element spacing is half the wavelength. At this time, high sidelobes and grating lobes will not be generated during beam forming, and a corresponding beam forming method is used to generate low sidelobes. This system has the following limitations:

[0003] When the array is a wide-area sparse array, that is, the element spacing is tens or even hundreds or thousands of times of half the wavelength, a large number of high sidelobes and grating lobes will be generated.

[0004] It can be seen that if the current beam forming method is used, it cannot effectively suppress the sidelobes. SUMMARY

[0005] The purpose of the present application is to avoid the shortcomings in the background art and provide a low sidelobe beam forming method that can be applied to non-sparse arrays and sparse arrays. The pattern functions at different frequencies are combined in a coherent manner, so that the sidelobe gain is greatly reduced while the main lobe gain remains unchanged.

[0006] The purpose of the present application is achieved as follows:

[0007] A wide-area sparse array multi-frequency point joint low sidelobe beam forming method, comprising the following steps:

[0008] Step 1, constructing a wide-area sparse array, the total number of elements in the wide-area sparse array is M, determining the coordinates (x m ,y m ,z m ) of the mth element, and determining the available frequency range [f min ,f max ]; wherein m=1, 2,..., M, f min represents the lowest frequency point of the available frequency range, and f max represents the highest frequency point of the available frequency range;

[0009] Step 2, selecting N frequency points in the available frequency range [f min ,f max ], the ith frequency point f iN in the N frequency points is:

[0010]

[0011] wherein N=2,..., 10, i=1, 2,..., N;

[0012] Step 3, calculate the maximum side-lobe-to-main-lobe ratio ratio of N frequency points joint low side-lobe beam forming according to the following formula N :

[0013]

[0014] ΔR=x m cosθcosφ+y m cosθsinφ+z m sinθ

[0015] ΔR0=x m cosθ0 cosφ0+y m cosθ0 sinφ0+z m sinθ0

[0016] Wherein, c is the speed of light, φ is the azimuth angle, θ is the elevation angle, (θ0, φ0) is the beam pointing, S1 is the side-lobe interval of the pattern in the elevation direction, S2 is the side-lobe interval of the pattern in the azimuth direction;

[0017] Step 4, repeat step 2 and step 3 to obtain ratio of N=2,...,10 respectively N , select the N value that makes 20log 10 (ratio N ) minimum, set it as k', that is

[0018]

[0019] Then, in the range of N=2,...,k', select the minimum value of N that satisfies the following conditions:

[0020] 20log 10 (ratio N )-20log 10 (ratio k′ )<1, N=2,...,k'

[0021] The minimum value is the final determined frequency point number k of the multi-frequency point joint low side-lobe beam forming;

[0022] Step 5, calculate the pattern:

[0023]

[0024] Wherein, F k (φ,θ) is the pattern function of the k frequency point joint low side-lobe beam forming;

[0025] Complete the wide-area sparse array multi-frequency point joint low side-lobe beam forming.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. The principle of the method of the present invention is relatively simple, which can ensure that the wide-area sparse radar has a low sidelobe radiation pattern while meeting its own strong anti-interference capability, thereby improving the radar system's target detection performance.

[0028] 2. This invention has good reference value given the current scarcity of low sidelobe beamforming technology for wide-area sparse radar. Attached Figure Description

[0029] Figure 1 This is a flowchart of an embodiment of the present invention;

[0030] Figure 2 This is the maximum sidelobe-to-main-lobe ratio after combining different frequency points in different frequency bands according to the embodiments of the present invention;

[0031] Figure 3 This is the radiation pattern of the combined beamforming at seven frequency points from 2 to 2.4 GHz in an embodiment of the present invention. Detailed Implementation

[0032] like Figure 1 As shown, a method for multi-frequency joint low sidelobe beamforming using a wide-area sparse array is proposed. First, a wide-area sparse array is constructed, and the available operating frequency bands and operating frequencies are determined. Second, joint beamforming is performed on different frequencies within different selected frequency bands to calculate the maximum sidelobe-to-main-lobe ratio. The frequency bands and the number of frequencies that minimize this ratio are then determined. Finally, the final radiation pattern function is determined, and beamforming is performed. Specifically, the method includes the following steps:

[0033] Step 1: Construct a wide-area sparse array. The total number of array elements in the wide-area sparse array is M. Determine the coordinates (x, y) of the m-th array element. m ,y m ,z m ), determine the available frequency band range [f min ,f max ]; where m = 1, 2, ..., M, f min Indicates the lowest frequency point of the available frequency band, f max Indicates the highest frequency point in the available frequency band;

[0034] Step 2, within the available frequency band range [f min ,f max Select N frequency points from the [N frequency points], and the i-th frequency point f among the N frequency points. iN for:

[0035]

[0036] Where N = 2, ..., 10, i = 1, 2, ..., N;

[0037] Step 3: Calculate the maximum sidelobe-to-main-lobe ratio (ratio) when N frequency points are used for joint low-sidelobe beamforming according to the following formula. N :

[0038]

[0039] ΔR=x m cosθcosφ+y m cosθsinφ+z m sinθ

[0040] ΔR0=x m cosθ0cosφ0+y m cosθ0sinφ0+z m sinθ0

[0041] Where c is the speed of light, φ is the azimuth angle, θ is the elevation angle, (θ0, φ0) is the beam direction, S1 is the sidelobe interval of the elevation direction of the radiation pattern, and S2 is the sidelobe interval of the azimuth direction of the radiation pattern; || indicates taking the modulus of the result, and max() indicates the maximum value in the result. If the zero-power point of the main lobe of the elevation radiation pattern is 2ψ0, then...

[0042] S1={θ|θ min ≤θ≤θ0-ψ0∪θ0+ψ0≤θ≤θ max}

[0043] Where, θ min It is the origin of the side lobe, θ max It is the end point of the side lobe; if the zero-power point of the main lobe in the azimuth pattern is but Where, φ min It is the origin of the side lobe, φ max It is the end point of the side lobe;

[0044] Step 4: Repeat steps 2 and 3 to obtain the ratios for N = 2, ..., 10 respectively. N Select the one that makes 20log 10 (ratio N Take the minimum value of N and set it as k′, that is...

[0045]

[0046] Here, argmin() represents the value of the independent variable when the function value is minimized. By repeatedly comparing the differences, a number of frequency points that make the maximum sidelobe and main lobe relatively small can be selected, which can reduce the amount of computation while ensuring a certain sidelobe reduction effect.

[0047] Next, within the range N = 2, ..., k′, select the smallest value of N that satisfies the following condition:

[0048] 20log 10 (ratio N )-20log 10 (ratio k′ ) < 1, N = 2, ..., k′

[0049] The minimum value is the number of frequency points k that is finally determined to form a multi-frequency joint low sidelobe beam;

[0050] Step 5, calculate the radiation pattern:

[0051]

[0052] ΔR=x m cosθcosφ+y m cosθsinφ+z m sinθ

[0053] ΔR0=x m cosθ0 cosφ0+y m cosθ0 sinφ0+z m sinθ0

[0054] Among them, F k (φ,θ) is the pattern function formed by the combined low sidelobe beams of k frequency points;

[0055] Complete the formation of low sidelobe beamformation at multiple frequency points using a wide-area sparse array.

[0056] The effectiveness of this method can be further illustrated by the following simulation comparison experiments:

[0057] 1. Experimental Scenario:

[0058] A wide-area sparse linear array is constructed with M = 20 array elements and d = 100m spacing between array elements. The coordinates of the first array element are (0,0,0) and the coordinates of the m-th array element are (100m,0,0), where m = 1,2,3,…,20 and the beam pointing θ0 = 0°.

[0059] 2. Simulation content:

[0060] Joint beamforming simulations were performed using 2-10 frequency points across five frequency bands: 2-2.2 GHz, 2-2.4 GHz, 2-2.6 GHz, 2-2.8 GHz, and 2-3 GHz. The maximum sidelobe and main lobe after combining different frequency points across different frequency bands were calculated as follows: Figure 2As shown; the radiation pattern formed by the joint beam at 7 frequency points in the 2-2.4 GHz band is as follows. Figure 3 As shown.

[0061] 3. Simulation Result Analysis:

[0062] from Figure 2 As can be seen, the five frequency bands can achieve the effect of minimizing the ratio of the maximum sidelobe to the main lobe at frequencies of 4, 6, 7, 8, and 10, respectively.

[0063] from Figure 3 As can be seen, the combined beamforming method of the present invention can generate lower sidelobes when forming wide-area sparse array beams, which is of great significance for improving the detection efficiency of targets.

Claims

1. A method for wide-area sparse array multi-frequency point joint low sidelobe beamforming, characterized in that, Includes the following steps: Step 1: Construct a wide-area sparse array. The total number of array elements in the wide-area sparse array is M. Determine the coordinates (x, y) of the m-th array element. m ,y m ,z m ), determine the available frequency band range [f min ,f max ]; where m = 1, 2, ..., M, f min Indicates the lowest frequency point of the available frequency band, f max Indicates the highest frequency point in the available frequency band; Step 2, within the available frequency band range [f min ,f max Select N frequency points from the [N frequency points], and the i-th frequency point f among the N frequency points. iN for: Where N = 2, ..., 10, i = 1, 2, ..., N; Step 3: Calculate the maximum sidelobe-to-main-lobe ratio (ratio) when N frequency points are used for joint low-sidelobe beamforming according to the following formula. N : ΔR=x m cosθcosφ+y m cosθsinφ+z m sinθ ΔR0=x m cosθ0cosφ0+y m cosθ0sinφ0+z m sinθ0 Where c is the speed of light, φ is the azimuth angle, θ is the elevation angle, (θ0,φ0) is the beam direction, S1 is the sidelobe interval of the elevation direction of the radiation pattern, and S2 is the sidelobe interval of the azimuth direction of the radiation pattern. Step 4: Repeat steps 2 and 3 to obtain the ratios for N = 2, ..., 10 respectively. N Select the one that makes 20log 10 (ratio N Take the minimum value of N and set it as k′, that is... Next, within the range N = 2, ..., k′, select the smallest value of N that satisfies the following condition: 20log 10 (ratio N )-20log 10 (ratio k′ )<1,N=2,...,k′ The minimum value is the number of frequency points k that is finally determined to form a multi-frequency joint low sidelobe beam; Step 5, calculate the radiation pattern: Among them, F k (φ,θ) is the pattern function formed by the combined low sidelobe beams of k frequency points; Complete the formation of low sidelobe beamformation at multiple frequency points using a wide-area sparse array.

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