A method for suppressing the sidelobe of the radiation pattern of a whirling electromagnetic wave

Abstract

A vortex electromagnetic wave radiation pattern sidelobe suppression method, for the way of vortex electromagnetic wave generated by uniform circular array, first determines the multiple circle ring radius according to the beam pointing requirement, then takes the radiation pattern peak sidelobe ratio as the fitness function, and optimizes the amplitude excitation coefficient of each array element through particle swarm algorithm multiple iterations, and finally obtains the vortex electromagnetic wave radiation pattern with lower sidelobe. The present application can significantly suppress the vortex electromagnetic wave radiation pattern sidelobe, and provide technical support for the engineering application of vortex electromagnetic wave.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, and in particular to a method for suppressing sidelobes of vortex electromagnetic wave radiation patterns. Background Technology

[0002] In recent years, the application of vortex electromagnetic waves in radar imaging has attracted widespread attention from researchers both domestically and internationally. Unlike plane waves, whose equiphase surface is planar, the equiphase surface of vortex waves is spirally distributed in space. Radar imaging azimuth resolution depends on the observation angle range. Both real aperture array radar and synthetic aperture radar improve azimuth resolution by increasing the observation angle range; however, in forward-looking detection scenarios, the relative angle between the radar and the target is very small, making it difficult to obtain high azimuth resolution. The spiral phase of a vortex wave can be considered as a plane wave illuminating from different azimuth angles. Even when the relative angle between the radar and the target is small or even relatively stationary, high azimuth resolution can still be achieved through multiple illuminations.

[0003] Furthermore, the hollow nature of vortex wave radiation intensity allows for its application in near-field detection of high-speed platforms. Near-field detection of high-speed platforms utilizes a uniform circular array to generate vortex waves, and the beam tilt angle can be adaptively controlled by adjusting array parameters and modes. However, the sidelobe energy of vortex electromagnetic waves is excessively high, leading to wasted transmission energy in practical applications; therefore, measures are needed to suppress the sidelobes.

[0004] To address the sidelobe suppression problem of vortex wave radiation patterns, one approach is to optimize the radius of multiple circular array elements. However, since changing the radius of the circular elements alters the beam direction when other parameters are fixed, this method is not suitable for applications with specific beam direction requirements. Alternatively, a multi-circular amplitude weighting method can be used to suppress vortex wave sidelobes. Existing multi-circular amplitude weighting-based sidelobe suppression methods all employ equal amplitudes for array elements on the same circular element, which has limited sidelobe suppression effectiveness. Summary of the Invention

[0005] The purpose of this invention is to provide a method for suppressing sidelobes of vortex electromagnetic wave radiation patterns, which can significantly suppress sidelobes of vortex electromagnetic wave radiation patterns.

[0006] To achieve the above objectives, this invention provides a method for suppressing sidelobes in the radiation pattern of vortex electromagnetic waves. For the generation of vortex electromagnetic waves by a uniform circular array, the radius of the multiple rings is first determined according to the beam pointing requirements. Then, the peak sidelobe ratio of the radiation pattern is used as the fitness function. The amplitude excitation coefficients of each array element are optimized through multiple iterations using a particle swarm optimization algorithm, and finally, a vortex electromagnetic wave radiation pattern with lower sidelobes is obtained.

[0007] The method for suppressing sidelobes of vortex electromagnetic wave radiation patterns includes the following steps:

[0008] Step S1: Determine the radius of the multi-ring according to the desired beam direction;

[0009] Step S2: Generate the distribution grid δ0 = δ of the array element amplitude excitation coefficients at intervals Δδ. min :Δδ:δ max δ min ∈[0,1],δ max ∈[0,1], and set the number of particles N and the maximum number of iterations K;

[0010] Step S3: Initialize particle velocity and position, and initialize individual optimal solutions and optimal values, as well as global optimal solutions and optimal values;

[0011] Step S4: Based on the particle's current position [x1, x2, ..., x N ] M×N With the individual optimal solution [pbest1,pbest2,…,pbest] N ] M×N and the global optimal solution gbest M×1 The relationship between the particles is used to adjust their speed and position, and to update the individual optimal solution and optimal value, as well as the global optimal solution and optimal value.

[0012] Determine whether the peak sidelobe ratio (PSLR) corresponding to the current position of each particle is less than the individual optimal value. If yes, update the individual optimal solution and the optimal value. The optimal solution is the position x of the array element amplitude in the distribution grid δ0. i The optimal value is the peak sidelobe ratio (PSLR) of the radiation pattern corresponding to the amplitude excitation coefficient of the array element; if "no", then do not update.

[0013] Determine whether the individual optimal value of each particle is less than the global optimal value. If "yes", update the global optimal solution and optimal value; if "no", do not update.

[0014] Step S5: Determine whether the global optimal value is less than the threshold or the number of iterations has reached the upper limit. If "yes", output the global optimal solution as the array element amplitude excitation coefficient; if "no", return to step S4 and continue to optimize the array element amplitude excitation coefficient.

[0015] In step S1, the vortex wave radiation field generated by a single uniform circular array is as follows:

[0016]

[0017] Where l represents the mode, θ represents the pitch angle, φ represents the azimuth angle, f(θ,φ) represents the array element radiation pattern, N represents the number of array elements, δ represents the array element amplitude excitation coefficient, and i represents the complex unit. n = 0, 1, ..., N-1 is the azimuth angle of the nth array element, k = 2π / λ is the wave number, λ is the wavelength, a is the radius of the ring, and Jl (·) is the l-th order Bessel function, and its expression is:

[0018] The radiation field of the multi-ring vortex wave is:

[0019]

[0020] Where H is the number of rings, N h Let δ be the number of array elements in the h-th layer of the ring. hn Let be the amplitude excitation coefficient of the nth array element on the h-th layer of the ring;

[0021] Let x0(l) = kasinθ0 be the location of the maximum value of the Bessel function, which can be obtained through fitting:

[0022] x0(l) = 1.1l + 0.87, l∈[1,10]

[0023] x0(l)=1.03l+1.62,l∈[11,50]

[0024] For a single circular array, determine the mode l and the radius of the circular array based on the given beam pointing requirements:

[0025]

[0026] If multiple rings are used to generate vortex waves, the radii of the remaining rings are selected around the radius of the first ring.

[0027] The element spacing on each ring array is λ, so the number of elements in each ring array is ceil(2πa / λ), where ceil(·) is rounded up.

[0028] In step S3, the velocities of N particles [v1, v2, ..., v] are initialized using random numbers. N ] M×N and position [x1,x2,…,x] N ] M×N The particle position is the position of the array element amplitude excitation coefficient in the distributed grid δ0, where M is the total number of array elements in the multi-layer circular array, v i ,i=1…N and x i The vectors i = 1…N are all M×1 dimensional vectors; the optimized fitness function is the peak-to-side-lobe ratio (PSLR) of the radiation pattern; in the first iteration, the initial individual position is used as the individual optimal solution [pbest1, pbest2, …, pbest]. N ] M×N The peak-to-sidelobe ratio (PSLR) of the radiation pattern corresponding to the individual optimal solution is initialized as the individual optimal value. Where, p maxLet p' be the amplitude of the main lobe of the radiation pattern, and p′ be the amplitude of the highest side lobe of the radiation pattern. The minimum value of all individual optimal values ​​and their corresponding optimal solutions are taken as the global optimal value and the global optimal solution gbest. M×1 .

[0029] In step S4, the velocity of the i-th particle is updated using the following formula:

[0030] v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest-x i )

[0031] Where i = 1, 2, ..., N, and N is the total number of particles; v i It is an M×1 dimensional vector representing the particle's velocity; c1 and c2 are learning factors, where c1 = c2 = 2; rand() is a random number between (0, 1); pbest i It is an M×1 dimensional vector representing the individual optimal solution for the i-th particle; x i It is an M×1 dimensional vector representing the current position of the particle; gbest M×1 This is the globally optimal solution;

[0032] The position of the i-th particle is updated using the following formula:

[0033] x i =x i +v i i = 1, ..., N

[0034] Calculate the element amplitude excitation coefficient δ corresponding to the current position of each particle. i =δ0(x i ), i = 1, ..., N are the particle numbers, δ i It is an M×1 dimensional vector; the array element amplitude excitation coefficient δ i As the corresponding δ hn Substituting into the formula for the radiation field of vortex waves in a multi-ring array F l (θ,φ), that is, the element amplitude excitation coefficient of the first circular array is δ1=δ i (1,N0), the h-th (h=2,…,N) h The amplitude excitation coefficients of the elements of the circular array are: Calculate the vortex wave radiation pattern F l Peak sidelobe ratio of (θ,φ) Where p max p' represents the amplitude of the main lobe of the radiation pattern, and p' represents the amplitude of the highest side lobe of the radiation pattern.

[0035] This invention can significantly suppress the side lobes of the radiation pattern of vortex electromagnetic waves, providing technical support for the engineering application of vortex electromagnetic waves. Attached Figure Description

[0036] Figure 1 This is a flowchart of a method for suppressing sidelobes of vortex electromagnetic wave radiation pattern provided by the present invention.

[0037] Figure 2 This is a fitness curve graph of the particle swarm optimization algorithm iteration.

[0038] Figure 3 This is a comparison of two-dimensional radiation patterns before and after the optimization of the array element excitation amplitude. Detailed Implementation

[0039] The following is based on Figures 1-3 The preferred embodiments of the present invention will be described in detail below.

[0040] This invention provides a method for suppressing sidelobes in the radiation pattern of vortex electromagnetic waves. For the generation of vortex electromagnetic waves by a uniform circular array, the method first determines the radius of multiple rings according to the beam pointing requirements, then uses the peak sidelobe ratio of the radiation pattern as a fitness function, and optimizes the amplitude excitation coefficients of each array element through multiple iterations using a particle swarm optimization algorithm, finally obtaining a vortex electromagnetic wave radiation pattern with lower sidelobes.

[0041] This invention specifically includes the following steps:

[0042] Step S1: Determine the radius of the multi-ring according to the desired beam direction;

[0043] The vortex wave radiation field generated by a single uniform circular array is as follows:

[0044]

[0045] Where l represents the mode, θ represents the pitch angle, φ represents the azimuth angle, f(θ,φ) represents the array element radiation pattern, N represents the number of array elements, δ represents the array element amplitude excitation coefficient, and i represents the complex unit. n = 0, 1, ..., N-1 is the azimuth angle of the nth array element, k = 2π / λ is the wave number, λ is the wavelength, a is the radius of the ring, and J l (·) is the l-th order Bessel function, and its expression is:

[0046] The radiation field of the multi-ring vortex wave is:

[0047]

[0048] Where H is the number of rings, N h Let δ be the number of array elements in the h-th layer ring. hnLet be the amplitude excitation coefficient of the nth array element on the h-th layer of the ring;

[0049] Let x0(l) = kasinθ0 be the location of the maximum value of the Bessel function, which can be obtained through fitting:

[0050] x0(l) = 1.1l + 0.87, l∈[1,10]

[0051] x0(l)=1.03l+1.62,l∈[11,50]

[0052] For a single circular array, determine the mode l and the radius of the circular array based on the given beam pointing requirements:

[0053]

[0054] If multiple rings are used to generate vortex waves, the radii of the remaining rings are selected around the radius of the first ring.

[0055] The element spacing on each ring array is λ, so the number of elements in each ring array is ceil(2πa / λ), where ceil(·) is rounded up.

[0056] Step S2: Generate the distribution grid δ0 = δ of the array element amplitude excitation coefficients at intervals Δδ. min :Δδ:δ max δ min ∈[0,1],δ max ∈[0,1], and set the number of particles N and the maximum number of iterations K.

[0057] Step S3: Initialize particle velocity and position, and initialize individual optimal solutions and optimal values, as well as global optimal solutions and optimal values;

[0058] Initialize the velocities of N particles [v1, v2, ..., v] using random numbers. N ] M×N and position [x1,x2,…,x] N ] M×N The particle position is the position of the array element amplitude excitation coefficient in the distributed grid δ0, where M is the total number of array elements in the multi-layer circular array, v i ,i=1…N and x i The vectors i = 1…N are all M×1 dimensional vectors; the optimized fitness function is the peak-to-side-lobe ratio (PSLR) of the radiation pattern; in the first iteration, the initial individual position is used as the individual optimal solution [pbest1, pbest2, …, pbest]. N ] M×N The peak-to-sidelobe ratio (PSLR) of the radiation pattern corresponding to the individual optimal solution is initialized as the individual optimal value. Where, pmax Let p' be the amplitude of the main lobe of the radiation pattern, and p′ be the amplitude of the highest side lobe of the radiation pattern. The minimum value of all individual optimal values ​​and their corresponding optimal solutions are taken as the global optimal value and the global optimal solution gbest. M×1 .

[0059] Step S4: Based on the particle's current position [x1, x2, ..., x N ] M×N With the individual optimal solution [pbest1,pbest2,…,pbest] N ] M×N and the global optimal solution gbest M×1 The relationship between the particles is used to adjust their speed and position, and to update the individual optimal solution and optimal value, as well as the global optimal solution and optimal value.

[0060] The velocity of the i-th particle is updated using the following formula:

[0061] v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest-x i )

[0062] Where i = 1, 2, ..., N, and N is the total number of particles; v i It is an M×1 dimensional vector representing the particle's velocity; c1 and c2 are learning factors, where c1 = c2 = 2; rand() is a random number between (0, 1); pbest i It is an M×1 dimensional vector representing the individual optimal solution for the i-th particle; x i It is an M×1 dimensional vector representing the current position of the particle; gbest M×1 This is the globally optimal solution;

[0063] The position of the i-th particle is updated using the following formula:

[0064] x i =x i +v i i = 1, ..., N

[0065] Calculate the element amplitude excitation coefficient δ corresponding to the current position of each particle. i =δ0(x i ), i = 1, ..., N are the particle numbers, δ i It is an M×1 dimensional vector. The array element amplitude excitation coefficient δ i As the corresponding δ hn Substituting into the formula for the radiation field of vortex waves in a multi-ring array F l(θ,φ), that is, the element amplitude excitation coefficient of the first circular array is δ1=δ i (1,N0), the h-th (h=2,…,N) h The amplitude excitation coefficients of the elements of the circular array are: Calculate the vortex wave radiation pattern F l Peak sidelobe ratio of (θ,φ) Where p max p' represents the amplitude of the main lobe of the radiation pattern, and p' represents the amplitude of the highest side lobe of the radiation pattern.

[0066] Determine if the PSLR corresponding to the current position of each particle is less than the individual optimal value. If yes, update the individual optimal solution and the optimal value. The optimal solution is the position x of the array element amplitude in the distribution grid δ0. i The optimal value is the radiation pattern PSLR corresponding to the array element amplitude excitation coefficient; if "no", then do not update;

[0067] Determine whether the individual optimal value of each particle is less than the global optimal value. If "yes", update the global optimal solution and optimal value; if "no", do not update.

[0068] Step S5: Determine whether the global optimal value is less than the threshold or the number of iterations has reached the upper limit. If "yes", output the global optimal solution as the array element amplitude excitation coefficient; if "no", return to step S4 and continue to optimize the array element amplitude excitation coefficient.

[0069] The parameters set in this implementation example are: radar carrier frequency of 10 GHz, selectable ring radius that is an integer multiple of the wavelength λ, element spacing on the ring of λ, vortex wave mode of 4, and desired beam pointing of 11°. According to the formula, the radius of a single ring array is approximately 4λ. In practical applications, the number of rings is generally 2 to 3. In this simulation, the number of rings is set to 3, and the ring radii are 3λ, 4λ, and 5λ respectively. During the simulation, the radiation pattern used is... The array elements are set with a PSLR threshold of -20dB, a maximum number of iterations of 200, and a grid distribution of the array element amplitude excitation coefficients of [0.4:0.01:1].

[0070] like Figure 2 The figure shows the fitness curve of the particle swarm optimization algorithm iteration. Fitness is the peak-to-side-lobe ratio (PSLR) of the radiation pattern. As can be seen from the figure, the PSLR is -20.2 dB when the number of iterations reaches 81 in this simulation. Directional array elements are used. get Figure 3The figure shows a comparison of two-dimensional radiation patterns obtained by the method of the present invention, with the array element excitation amplitude shown by the dashed line being 1 and the array element excitation amplitude shown by the solid line. It can be seen from the figure that the beam pointing is 11° before and after optimization, and the beam width is not significantly widened. The PSLR of the unoptimized radiation pattern is -16.7dB, and the PSLR of the optimized radiation pattern is -20.2dB. Therefore, the method of the present invention can effectively suppress the sidelobes of the vortex wave radiation pattern.

[0071] It should be noted that, in the embodiments of the present invention, the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the embodiments and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0072] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for suppressing sidelobes in the radiation pattern of vortex electromagnetic waves, characterized in that, To address the method of generating vortex electromagnetic waves using a uniform circular array, the radius of the multiple rings is first determined based on the beam pointing requirements. Then, the peak-to-sidelobe ratio of the radiation pattern is used as the fitness function. The amplitude excitation coefficients of each array element are optimized through multiple iterations using a particle swarm optimization algorithm, ultimately resulting in a vortex electromagnetic wave radiation pattern with lower sidelobes. Includes the following steps: Step S1: Determine the radius of the multi-ring according to the desired beam direction; Step S2: Generate the distribution grid of the array element amplitude excitation coefficients at intervals Δδ. δ0=δ min :Δδ:δ max δ min ∈[0,1],δ max ∈[0,1], and set the number of particles N and the maximum number of iterations K, as well as the total number of array elements M of the multi-layer circular array; Step S3: Initialize particle velocity and position, and initialize individual optimal solutions and optimal values, as well as global optimal solutions and optimal values; Step S4: Based on the particle's current position [x1, x2, ..., x N ] M×N With the individual optimal solution [pbest1,pbest2,…,pbest] N ] M×N and the global optimal solution gbest M×1 The relationship between the particles is used to adjust their speed and position, and to update the individual optimal solution and optimal value, as well as the global optimal solution and optimal value. Determine if the peak-to-sidelobe ratio (PSLR) at the current position of each particle is less than the individual optimal value. If yes, update the individual optimal solution and the optimal value. The optimal solution is the position x of the element amplitude in the distribution grid δ0. i The optimal value is the peak sidelobe ratio (PSLR) of the radiation pattern corresponding to the amplitude excitation coefficient of the array element; if "no", then do not update. Determine whether the individual optimal value of each particle is less than the global optimal value. If "yes", update the global optimal solution and optimal value; if "no", do not update. Step S5: Determine whether the global optimal value is less than the threshold or the number of iterations has reached the upper limit. If "yes", output the global optimal solution as the array element amplitude excitation coefficient; if "no", return to step S4 and continue to optimize the array element amplitude excitation coefficient.

2. The vortex electromagnetic wave radiation pattern sidelobe suppression method as described in claim 1, characterized in that, In step S1, the vortex wave radiation field generated by a single uniform circular array is as follows: Where l represents the mode, θ represents the elevation angle, φ represents the azimuth angle, and f(θ,φ) represents the array element pattern. N′ represents the number of array elements, δ represents the array element amplitude excitation coefficient, and i represents the complex unit. n = 0, 1, ..., N′-1 is the azimuth angle of the nth array element, k = 2π / λ is the wave number, λ is the wavelength, a is the radius of the ring, and J l (·) is the l-th order Bessel function, and its expression is: The radiation field of the multi-ring vortex wave is: Where H is the number of rings, N h Let δ be the number of array elements in the h-th layer of the ring. hn Let be the amplitude excitation coefficient of the nth array element on the h-th layer of the ring; Let x0(l) = kasinθ0 be the location of the maximum value of the Bessel function, which is obtained through fitting: x0(l)＝1.1l+0.87,l∈[1,10] x0(l)＝1.03l+1.62,l∈[11,50] For a single circular array, determine the mode l and the radius of the circular array based on the given beam pointing requirements: If multiple rings are used to generate vortex waves, the radii of the remaining rings are selected around the radius of the first ring. The element spacing on each ring array is λ, so the number of elements in each ring array is ceil(2πa / λ), where ceil(·) is rounded up.

3. The vortex electromagnetic wave radiation pattern sidelobe suppression method as described in claim 2, characterized in that, In step S3, the velocities of N particles [v1, v2, ..., v] are initialized using random numbers. N ] M×N and position [x1,x2,…,x] N ] M×N The particle position is the position of the array element amplitude excitation coefficient in the distributed grid δ0, where M is the total number of array elements in the multi-layer circular array, v i ,i=1…N and x i All i = 1…N are M×1 dimensional vectors; the optimized fitness function is the peak-to-side-lobe ratio (PSLR) of the radiation pattern; in the first iteration, the initial individual position is used as the individual's optimal solution [pbest1, pbest2, …, pbest]. N ] M×N The peak-to-sidelobe ratio (PSLR) of the radiation pattern corresponding to the individual optimal solution is initialized as the individual optimal value. Where, p max Let p' be the amplitude of the main lobe of the radiation pattern, and p′ be the amplitude of the highest side lobe of the radiation pattern. The minimum value of all individual optimal values ​​and their corresponding optimal solutions are taken as the global optimal value and the global optimal solution gbest. M×1 .

4. The vortex electromagnetic wave radiation pattern sidelobe suppression method as described in claim 3, characterized in that, In step S4, the velocity of the i-th particle is updated using the following formula: v i =v i +c1×rand()×(pbest i -x i )+c2×rand()×(gbest-x i ) Where i = 1, 2, ..., N, and N is the total number of particles; v i It is an M×1 dimensional vector representing the particle's velocity; c1 and c2 are learning factors, where c1 = c2 = 2; rand() is a random number between (0, 1); pbest i It is an M×1 dimensional vector representing the individual optimal solution for the i-th particle; x i It is an M×1 dimensional vector representing the current position of the particle; gbest M×1 This is the globally optimal solution; The position of the i-th particle is updated using the following formula: x i =x i +v i ,i=1,…,N Calculate the element amplitude excitation coefficient δ corresponding to the current position of each particle. i =δ0(x i ), i = 1, ..., N are the particle numbers, δ i It is an M×1 dimensional vector; the array element amplitude excitation coefficient δ i As the corresponding δ hn Substituting into the formula for the radiation field of vortex waves in a multi-ring array F l (θ,φ), that is, the element amplitude excitation coefficient of the first circular array is δ1=δ i (1, N0), the amplitude excitation coefficient of the h-th circular array element is Calculate the vortex wave radiation pattern F l Peak sidelobe ratio of (θ,φ) Where p max p' represents the amplitude of the main lobe of the radiation pattern, and p' represents the amplitude of the highest side lobe of the radiation pattern.

Images