Array Antenna Pattern Optimization Method Based on Multi-Constraint Convex Optimization

Abstract

This invention proposes a method for optimizing the radiation pattern of an array antenna based on multi-constraint convex optimization. The steps are as follows: full-wave simulation is performed to obtain the direction vector of the array antenna; parameters such as the target direction and sidelobe level are initialized; a multi-constraint convex optimization problem is constructed and solved to obtain the excitation vector; the beamwidth is updated and the convex optimization problem is solved again; the optimized excitation vector is obtained and the array antenna radiation pattern is calculated. This invention constructs a convex optimization problem for the array antenna radiation pattern through multiple constraints, avoiding the defect that the maximum radiation direction of the array antenna radiation pattern deviates from the target direction when the sidelobe level is low. Furthermore, updating the maximum or minimum value updates the range of beamwidth values. When the initial sidelobe level is too low, the beamwidth is reduced, ultimately optimizing the array antenna radiation pattern to the lowest achievable sidelobe level, avoiding radiation pattern distortion and improving optimization efficiency.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology and relates to an optimization method for the radiation pattern of an array antenna, specifically an array antenna radiation pattern optimization method based on multi-constraint convex optimization, which can be used for signal detection or multi-target identification. Background Technology

[0002] An array antenna is a special antenna consisting of at least two antenna elements arranged together and subjected to appropriate excitation to achieve predetermined radiation characteristics. The radiation pattern of an array antenna is an important way to describe its radiation characteristics, including characteristic parameters such as the maximum radiation direction, sidelobe level, and beamwidth. In practical applications, the mutual coupling between array antenna elements can affect the maximum radiation direction, sidelobe level, and beamwidth of the array antenna pattern, resulting in phenomena such as shifts in the maximum radiation direction, increased sidelobe levels, beamwidth broadening, and distortion caused by main lobe splitting. Increased sidelobe levels will significantly affect the signal threshold setting of the array antenna in signal detection fields, while shifts in the maximum radiation direction and beamwidth broadening will significantly affect the accuracy of multi-target recognition. Therefore, optimizing the array antenna pattern is an important method to obtain an array antenna pattern that meets preset conditions.

[0003] Optimization methods for array antenna patterns can be categorized into three types: optimization methods based on array antenna structure, optimization methods based on array antenna excitation coefficients, and optimization methods based on both the array antenna structure and excitation coefficients. Optimization methods based on array antenna excitation coefficients use the excitation coefficients of the array antenna as variables. The optimized excitation coefficients yield the pattern that satisfies certain characteristic parameters. Existing technologies, with a fixed array antenna structure, address the optimization problem of minimizing the main lobe beamwidth of the array antenna pattern under a given sidelobe level. For example, the literature "Ma Wei. Random Array Beam Design Method Based on Convex Optimization [J]. Electronic Information Countermeasures Technology, 2023, 38(01):49-53" proposes a random array antenna pattern optimization method. This method first establishes an array antenna model composed of ideal point sources, calculates the pattern of each element in the array, then equates the array antenna pattern optimization problem to a second-order cone optimization problem, thus constraining the sidelobe region of the array antenna pattern. Finally, by traversing the azimuth angles of the entire space, the narrowest beamwidth pattern under a given sidelobe level is obtained through a search. This method uses second-order cone constraints to jointly constrain the sidelobes and the azimuth of strong interference, solving the spatial spectrum estimation or direction finding problem of strong interference in a specific direction. However, since it does not constrain the maximum radiation direction of the main lobe, when the sidelobe level is low, the maximum radiation direction of the array antenna pattern will deviate from the target direction or the main lobe will be distorted. At the same time, since this method needs to search through all azimuth angles in space to obtain the narrowest beam pattern, the optimization efficiency is low. Summary of the Invention

[0004] The purpose of this invention is to overcome the defects of the prior art and propose an array antenna pattern optimization method based on multi-constraint convex optimization to solve the technical problems of the maximum radiation direction of the array antenna pattern deviating from the target direction or the main lobe being distorted and the optimization efficiency being low in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Obtain the direction vector A(θ) of the array antenna:

[0007] Full-wave simulation is performed on an array antenna composed of N non-periodic array elements with aperture size L and center frequency f, respectively. The active element radiation pattern of each array element is obtained, and the radiation patterns of all active elements are combined to form the direction vector A(θ) of the array antenna, where N≥2 and θ represents the elevation angle of the array antenna radiation pattern.

[0008] (2) Initialize parameters:

[0009] The target direction and sidelobe level of the initial array antenna pattern are θ0 and P, respectively. SLL The number of iterations is k, the maximum number of iterations is K, and the convergence accuracy is Δθ. The excitation vector, beamwidth, main lobe region, and side lobe region of the array antenna in the k-th iteration are w, w, and w, respectively. k , Let k=1, and calculate the initial beamwidth, main lobe region, and side lobe region as follows: in, They represent Minimum and maximum values;

[0010] (3) Construct the expression for the multi-constraint convex optimization problem of the array antenna pattern:

[0011] The constraint function for constructing the array antenna pattern in the target direction θ0 is |F(w k ,θ0)-d|≤ε0、In the sidelobe region The constraint function is |F(w) k ,θ p The constraint function for the phase of the radiated electric field at θ0 is imagF(w)|≤P. k ,θ0)=0, in the main lobe region The constraint function is |F(w) k ,θ q )|≤real(F(w k The convex optimization problem of θ0):

[0012]

[0013] F(w k ,θ0)=A(θ0)w k

[0014] F(w k ,θ p )=A(θ p )w k

[0015] F(w k ,θ q )=A(θ q )w k

[0016] Wherein, minP represents the sidelobe region Minimize the upper bound constraint P, where imag represents finding the imaginary part of the complex number, real represents finding the real part of the complex number, and F(w) k ,θ0)F(w k ,θ q ), F(w k ,θ p ) represent the target direction θ0 and the main lobe region, respectively. Side lobe region The radiated electric field, where d represents a positive constant and ε0 represents the electric field with respect to F(w) k The parameters constrained by θ0) are θ q θ p These represent the elevation angles of the main lobe region and the side lobe region of the array antenna pattern, respectively.

[0017] (4) Calculate the array antenna pattern:

[0018] Solving the convex pattern optimization problem of the array antenna yields the excitation vector w of the array antenna. k and through w k Calculate the antenna radiation pattern F(w) using the direction vector A(θ) of the antenna array. k ,θ);

[0019] (5) Determine whether the main lobe of the array antenna pattern is distorted:

[0020] Determine the radiation pattern F(w) of the array antenna k Does the main lobe of (θ) exhibit distortion? If so, what is the range of beamwidth values? maximum value Update the value and use the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1 and execute step (4); otherwise, execute step (6).

[0021] (6) Determine whether the termination condition is met:

[0022] Determine the radiation pattern F(w) of the array antenna k Sidelobe level of θ) Or whether the convergence accuracy Δθ satisfies the termination condition. If yes, output the optimized activation vector w′ and execute step (8); otherwise, execute step (7).

[0023] (7) Update the range of beamwidth values:

[0024] judge Whether it holds true, and if so, by considering the range of beamwidth values. maximum value The update implementation for Otherwise, update by adjusting the beamwidth range. minimum value The update implementation for The update is performed using the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1, and execute step (4);

[0025] (8) Obtain the optimized results of the array antenna pattern:

[0026] The optimized array antenna pattern F(w′,θ) = A(θ)w′ is calculated based on w′ and the direction vector A(θ) of the array antenna.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] 1. When constructing the convex optimization problem of the array antenna pattern, this invention constrains the target direction, main lobe region, and side lobe region of the array antenna pattern, so that the maximum radiation direction is located in the target direction, thus avoiding the defect of the prior art where the maximum radiation direction of the array antenna pattern deviates from the target direction when the side lobe level is low.

[0029] 2. This invention updates the beamwidth range by updating the maximum or minimum value of the beamwidth range. When the initial sidelobe level is too low, the beamwidth is reduced to ultimately optimize the array antenna pattern at the lowest sidelobe level that the array antenna can achieve, thus avoiding pattern distortion. At the same time, this update method avoids the low optimization efficiency caused by the existing technology that requires searching through all azimuth angles in space to obtain the narrowest beamwidth pattern. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0031] Figure 2 This is a diagram showing the optimization results of the present invention at different initial sidelobe levels;

[0032] Figure 3 The diagram shows the optimization results of this invention in different initialization target directions;

[0033] Figure 4 This is a diagram showing the optimized results of the present invention when the initial sidelobe level is too low. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0035] Reference Figure 1 The present invention includes the following steps:

[0036] Step 1) Obtain the direction vector A(θ) of the array antenna:

[0037] Full-wave simulation is performed on an array antenna composed of N non-periodic array elements with aperture size L and center frequency f, respectively. The active element radiation pattern of each array element is obtained, and the radiation patterns of all active elements are combined to form the direction vector A(θ) of the array antenna, where N≥2 and θ represents the elevation angle of the array antenna radiation pattern.

[0038] The array antenna used in this invention is a linear structure composed of N non-periodic array elements. Each array element includes a dielectric substrate, a metal radiating patch printed on the upper surface of the dielectric substrate, and a metal ground plane on the lower surface. The number of array elements is N = 37, the aperture size is L = 660 mm, and the center frequency is f = 10 GHz.

[0039] Step 2) Initialize parameters:

[0040] The target direction and sidelobe level of the initial array antenna pattern are θ0 and P, respectively. SLLThe number of iterations is k, the maximum number of iterations is K, and the convergence accuracy is Δθ. The excitation vector, beamwidth, main lobe region, and side lobe region of the array antenna in the k-th iteration are w, w, and w, respectively. k , Let k=1, and calculate the initial beamwidth, main lobe region, and side lobe region as follows: in, They represent Minimum and maximum values;

[0041] Initial beamwidth Main lobe region Side lobe region The calculation formulas are as follows:

[0042]

[0043]

[0044]

[0045]

[0046] λ=c / f

[0047]

[0048]

[0049]

[0050]

[0051] in, They represent the cases when k=1, respectively. The minimum and maximum values ​​of γ = 1.2, BW represents the zero-power beamwidth of the main lobe of the Chebyshev excitation pattern, c is the speed of electromagnetic wave propagation in free space, λ is the wavelength, cosh is the hyperbolic cosine function, arccosh is the inverse hyperbolic cosine function, sin is the sine function, cos is the cosine function, arccos is the inverse cosine function, v and x are constants, and ∪ represents the union.

[0052] The maximum number of iterations K is calculated using the following formula:

[0053]

[0054] in, This indicates rounding up, and log is the logarithmic function.

[0055] The maximum value of the initial beamwidth range is given by using the zero-power beamwidth of the main lobe of the Chebyshev excitation pattern, which avoids the need to manually set the initial beamwidth range. The maximum number of iterations is given by Δθ, which ensures a sufficient search for the beamwidth.

[0056] Step 3) Construct the expression for the multi-constraint convex optimization problem of the array antenna pattern:

[0057] The constraint function for constructing the array antenna pattern in the target direction θ0 is |F(w k ,θ0)-d|≤ε0、In the sidelobe region The constraint function is |F(w) k ,θ p The constraint function for the phase of the radiated electric field at θ0 is imagF(w)|≤P. k ,θ0)=0, in the main lobe region The constraint function is |F(w) k ,θ q )|≤real(F(w k The convex optimization problem of θ0):

[0058]

[0059] F(w k ,θ0)=A(θ0)w k

[0060] F(w k ,θ p )=A(θ p )w k

[0061] F(w k ,θ q )=A(θ q )w k

[0062] Wherein, minP represents the sidelobe region Minimize the upper bound constraint P, where imag represents finding the imaginary part of the complex number, real represents finding the real part of the complex number, and F(w) k ,θ0)F(w k ,θ q ), F(w k ,θ p ) represent the target direction θ0 and the main lobe region, respectively. Side lobe region The radiated electric field, where d represents a positive constant, taken as d = 100, and ε0 represents the electric field of F(w) k The parameters constrained by ε0 and θ0 are taken as ε0 = 1. q θp These represent the elevation angles of the main lobe region and the side lobe region of the array antenna pattern, respectively.

[0063] In constructing the convex optimization problem of the array antenna pattern, this invention constrains the target direction, main lobe region, and sidelobe region of the array antenna pattern, ensuring that the maximum radiation direction is located in the target direction. This avoids the defect in existing technologies where the maximum radiation direction of the array antenna pattern deviates from the target direction when the sidelobe level is low. The constraint function is imagF(w k When θ0)=0 makes the phase of the radiated electric field in the target direction zero, the constraint function |F(w) in the main lobe region is... k ,θ q )|≤real(F(w k The constraint function |F(w,θ0)) with the target direction k The maximum radiation direction is located in the target direction, and the constraint function |F(w)| ≤ ε0 is used to ensure that the maximum radiation direction is located in the target direction. k ,θ p The constraint |≤P is used to constrain the sidelobe level of the array antenna pattern.

[0064] Step 4) Calculate the array antenna pattern:

[0065] Solving the convex pattern optimization problem of the array antenna yields the excitation vector w of the array antenna. k and through w k Calculate the antenna radiation pattern F(w) using the direction vector A(θ) of the antenna array. k ,θ);

[0066] F(w k The formula for calculating θ is:

[0067] F(w k ,θ)=A(θ)w k .

[0068] Step 5) Determine if the main lobe of the array antenna pattern is distorted:

[0069] Determine the radiation pattern F(w) of the array antenna k If the main lobe of (θ) is distorted, then the beamwidth range is used. maximum value Update the value and use the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1 and execute step (4); otherwise, execute step (6).

[0070] For the range of beamwidth values maximum value The update formula for performing the update is:

[0071]

[0072] Through the updated value range Calculate the main lobe region of the array antenna pattern and the side lobe region The calculation formulas are as follows:

[0073]

[0074]

[0075] Determine the radiation pattern F(w) of the array antenna k Whether the main lobe of F(w,θ) is distorted refers to determining whether F(w) is distorted. k If the main lobe of θ is monotonically increasing on the left and monotonically decreasing on the right in the target direction θ0, then no distortion has occurred; otherwise, distortion has occurred.

[0076] The system determines whether the main lobe of the radiation pattern is distorted. If the main lobe is distorted, the maximum value of the beamwidth range is reduced, thereby reducing the beamwidth in the next optimization and preventing the main lobe of the final array antenna radiation pattern from being distorted.

[0077] Step 6) Determine if the termination condition is met:

[0078] Determine the radiation pattern F(w) of the array antenna k Sidelobe level of θ) Or whether the convergence accuracy Δθ satisfies the termination condition. If yes, output the optimized activation vector w′ and execute step (8); otherwise, execute step (7).

[0079] By determining whether the termination condition is met, the narrowest radiation pattern of the array antenna under the initial sidelobe level can be obtained if the maximum number of iterations is reached and the sidelobe level is satisfied. Alternatively, if the initial sidelobe level is too low and the sidelobe level of the array antenna radiation pattern cannot reach the initial sidelobe level, the iteration process can be terminated by the size of the beamwidth range. Finally, the array antenna radiation pattern under the lowest sidelobe level that the array antenna can achieve is obtained.

[0080] Step 7) Update the range of beamwidth values:

[0081] judge Whether it holds true, and if so, by considering the range of beamwidth values. maximum value The update implementation for Otherwise, update by adjusting the beamwidth range. minimum value The update implementation for The update is performed using the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1, and execute step (4);

[0082] For the maximum value and minimum value The update formulas are as follows:

[0083]

[0084]

[0085] This invention updates the beamwidth range by updating the maximum or minimum value of the beamwidth range. When the initial sidelobe level is too low, the beamwidth is reduced to ultimately optimize the array antenna pattern to the lowest achievable sidelobe level, avoiding pattern distortion. This update method also avoids the low optimization efficiency of existing technologies that require searching all azimuth angles in space to find the narrowest beamwidth pattern. Pattern distortion occurs when the beamwidth is too large during optimization. After identifying pattern distortion, reducing the beamwidth avoids the problem of main lobe distortion in the final pattern. By updating the maximum or minimum value of the beamwidth range to the previous generation's beamwidth to reduce the range, the beamwidth that meets the conditions can be quickly found, thereby improving optimization efficiency.

[0086] Step 8) Obtain the optimized results of the array antenna pattern:

[0087] The optimized array antenna pattern F(w′,θ) is calculated based on w′ and the direction vector A(θ) of the array antenna:

[0088] F(w′,θ)=A(θ)w′.

[0089] The technical effects of the present invention will be further explained below with reference to simulation results:

[0090] 1. Experimental conditions and contents:

[0091] The hardware platform for the simulation experiment of this invention is: a 32-core Intel(R) Xeon(R) Gold 5215 CPU with a main frequency of 2.50GHz and 1024GB of memory.

[0092] The software platform for the simulation experiment of this invention is HFSS2022R1 and MATLAB2021b.

[0093] Simulations were performed to evaluate the optimization effect of this invention under different initial sidelobe levels, different initialization target directions, and when the initial sidelobe level was too low. The results are as follows: Figure 2 , 3 As shown in Figure 4;

[0094] 2. Analysis of experimental results:

[0095] Reference Figure 2 The vertical axis represents the normalized radiated electric field in dB, and the horizontal and vertical axes represent the elevation angles in degrees. With the target radiation pattern at θ0 = 0°, and initial sidelobe levels set to -35dB, -25dB, and -15dB respectively, the optimized normalized radiation pattern of the array antenna is as follows: Figure 2 As shown, the beamwidths are 7.78°, 5.80° and 3.80°, respectively. The sidelobe level is exactly equal to the initial sidelobe level. The array antenna pattern with the narrowest beamwidth under the given sidelobe level is obtained. The maximum radiation direction of the pattern all points to the target direction.

[0096] Reference Figure 3 The vertical axis represents the normalized radiated electric field in dB, and the horizontal and vertical axes represent the elevation angle in degrees. The initial sidelobe level is P. SLL With a voltage of -25dB, the optimized normalized radiation patterns of the array antenna at target directions of -40°, -20°, and 0° are as follows: Figure 3 As shown, the beamwidths are 11.80°, 6.36°, and 5.80°, respectively, and the maximum radiation direction is pointing towards the target direction, and the initial sidelobe level condition is satisfied.

[0097] Reference Figure 4 The vertical axis represents the normalized radiated electric field in dB, and the horizontal and vertical axes represent the elevation angle in degrees. When the initial sidelobe level is too low, for example, if the sidelobe level is set to P... SLL = -1000dB. Since the sidelobe level is too low, the array antenna cannot be realized. The method of the present invention obtained the array antenna pattern with the lowest sidelobe level that the array can achieve. At this time, the beamwidth is 16.68° and the sidelobe level is -67.6dB.

[0098] The experimental results above show that the present invention iteratively optimizes the array antenna pattern through a multi-constraint convex optimization algorithm. Given a target direction, it can obtain the array antenna pattern with the narrowest beamwidth under different initial sidelobe levels. Given a sidelobe level, it can obtain the narrowest array antenna pattern under different target directions. In addition, when the initial sidelobe level is too low, it can obtain the array antenna pattern with the lowest achievable sidelobe level.

Claims

1. A method for optimizing the radiation pattern of an array antenna based on multi-constraint convex optimization, characterized in that, Includes the following steps: (1) Obtain the direction vector A(θ) of the array antenna: Full-wave simulation is performed on an array antenna composed of N non-periodic array elements with aperture size L and center frequency f, respectively. The active element radiation pattern of each array element is obtained, and the radiation patterns of all active elements are combined to form the direction vector A(θ) of the array antenna, where N≥2 and θ represents the elevation angle of the array antenna radiation pattern. (2) Initialize parameters: The target direction and sidelobe level of the initial array antenna pattern are θ0 and P, respectively. SLL The number of iterations is k, the maximum number of iterations is K, and the convergence accuracy is Δθ. The excitation vector, beamwidth, main lobe region, and side lobe region of the array antenna in the k-th iteration are w, w, and w, respectively. k , Let k=1, and calculate the initial beamwidth, main lobe region, and side lobe region as follows: in, They represent Minimum and maximum values; (3) Construct the expression for the multi-constraint convex optimization problem of the array antenna pattern: The constraint function for constructing the array antenna pattern in the target direction θ0 is |F(w k ,θ0)-d|≤ε0、In the sidelobe region The constraint function is |F(w) k ,θ p The constraint function for the phase of the radiated electric field at θ0 is imagF(w)|≤P. k ,θ0)=0, in the main lobe region The constraint function is |F(w) k ,θ q )|≤real(F(w k The convex optimization problem of θ0): F(w k ,θ0)=A(θ0)w k F(w k ,i p )=A(θ p )w k F(w k ,i q )=A(θ q )w k Wherein, minP represents the sidelobe region Minimize the upper bound constraint P, where imag represents finding the imaginary part of the complex number, real represents finding the real part of the complex number, and F(w) k ,θ0)F(w k ,θ q ), F(w k ,θ p ) represent the target direction θ0 and the main lobe region, respectively. Side lobe region The radiated electric field, where d represents a positive constant and ε0 represents the electric field with respect to F(w) k The parameters constrained by θ0) are θ q θ p These represent the elevation angles of the main lobe region and the side lobe region of the array antenna pattern, respectively. (4) Calculate the array antenna pattern: Solving the convex pattern optimization problem of the array antenna yields the excitation vector w of the array antenna. k and through w k Calculate the antenna radiation pattern F(w) using the direction vector A(θ) of the antenna array. k ,θ); (5) Determine whether the main lobe of the array antenna pattern is distorted: Determine the radiation pattern F(w) of the array antenna k If the main lobe of (θ) is distorted, then the beamwidth range is used. maximum value Update the value and use the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1 and execute step (4); otherwise, execute step (6). (6) Determine whether the termination condition is met: Determine the radiation pattern F(w) of the array antenna k The sidelobe level P of θ) s k Or whether the convergence accuracy Δθ satisfies the termination condition. If yes, output the optimized activation vector w′ and execute step (8); otherwise, execute step (7). (7) Update the range of beamwidth values: judge Whether it holds true, and if so, by considering the range of beamwidth values. maximum value The update implementation for Otherwise, update by adjusting the beamwidth range. minimum value The update implementation for The update is performed using the updated value range. Calculate the main lobe region of the array antenna pattern and the side lobe region Then, let k = k + 1, and execute step (4); (8) Obtain the optimized results of the array antenna pattern: The optimized array antenna pattern F(w′,θ) = A(θ)w′ is calculated based on w′ and the direction vector A(θ) of the array antenna.

2. The method according to claim 1, characterized in that, The initial beamwidth mentioned in step (2) Main lobe region Side lobe region The calculation formulas are as follows: λ=c / f in, They represent the cases when k=1, respectively. The minimum and maximum values ​​of , γ represents a constant greater than 1, BW represents the zero-power beamwidth of the main lobe of the Chebyshev excitation pattern, c is the speed of electromagnetic wave propagation in free space, λ is the wavelength, cosh is the hyperbolic cosine function, arccosh is the inverse hyperbolic cosine function, sin is the sine function, cos is the cosine function, arccos is the inverse cosine function, v and x are constants, and ∪ represents the union.

3. The method according to claim 2, characterized in that, The maximum number of iterations K mentioned in step (2) is calculated using the following formula: in, This indicates rounding up, and log is the logarithmic function.

4. The method according to claim 1, characterized in that, The array antenna pattern F(w) described in step (4) k The formula for calculating θ is: F(w k ,θ)=A(θ)w k 。 5. The method according to claim 1, characterized in that, The range of beamwidth values ​​mentioned in step (5) maximum value The update is performed using the following formula:

6. The method according to claim 1, characterized in that, The updated value range mentioned in step (5) Calculate the main lobe region of the array antenna pattern and the side lobe region The calculation formulas are as follows:

7. The method according to claim 1, characterized in that, The determination of the array antenna pattern F(w) in step (5) k Whether the main lobe of F(w,θ) is distorted refers to determining whether F(w) is distorted. k If the main lobe of θ is monotonically increasing on the left and monotonically decreasing on the right in the target direction θ0, then no distortion has occurred; otherwise, distortion has occurred.

8. The method according to claim 1, characterized in that, The step (7) described above involves adjusting the beamwidth range. maximum value The update implementation for The update, and by adjusting the range of beamwidth values minimum value The update implementation for The update, where the maximum value and minimum value The update formulas are as follows:

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