Phase-only weighted beamforming method of planar array considering mutual coupling effect

Abstract

The invention discloses a phase-only weighted beamforming method for a planar array considering a mutual coupling effect, and the method comprises the steps: carrying out the simulation extraction of AEP of each unit through building a small array, i.e., a subarray of a target large array, and enabling the AEP of each unit of the extracted subarray to be approximately equivalent to the AEP of other units of the target large array through a calculation method of subarray extrapolation; substituting the algorithm into the algorithm to increase the robustness of the system; setting an upper and lower bound constraint function and an auxiliary variable of directional diagram synthesis, introducing parameters such as a scale factor and a Lagrange multiplier, and constructing a directional diagram synthesis mathematical expression and an augmented Lagrange function; iteratively updating the auxiliary variable, the scale factor, the feed phase of each unit of the antenna array and the value of the Lagrange multiplier, and solving the equation to obtain a phase-only comprehensive result; according to the method, the influence of the mutual coupling effect on the array performance is avoided, the feed phase is calculated through the classical ADMM algorithm and the BFGS algorithm, the solving process is simplified, and large-scale problems can be efficiently and accurately solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of array antennas, and particularly relates to a planar array phase-only weighted beamforming method considering mutual coupling effects. Background Art

[0002] In the fields of modern communication systems, radar, sonar, satellite communication, etc., antenna array technology is widely used in beamforming. In beamforming, the two common weighting methods are phase weighting and amplitude weighting. Amplitude-weighted beamforming changes the radiation direction and intensity of the signal by adjusting the signal amplitude of the antenna elements. This method requires adjusting the amplitude and phase of each element to obtain the ideal beam direction and shape. Different from amplitude weighting, phase-weighted beamforming realizes beam control only by adjusting the phase of each antenna element. Its key idea is to control the propagation direction of the signal in space through the phase difference, so as to realize the directional pointing of the beam without changing the amplitude of the signal. This method is usually simpler than the amplitude weighting method because it avoids amplitude adjustment and reduces the complexity of the system. The phase-only weighted beamforming technology has been widely used in applications such as communication systems, radar systems, satellite communication, sonar systems, and acoustic imaging. For example, in a wireless communication system, beamforming can effectively improve the signal quality and coverage. At present, the research on the phase-only weighted beamforming technology mainly uses intelligent evolutionary algorithms and traditional optimization algorithms for beamforming. However, the intelligent evolutionary algorithm has a large amount of calculation, a long calculation time, a slow convergence speed, difficult parameter adjustment, and high requirements for hardware. The results of the traditional optimization algorithm strongly depend on the initial value and fall into local optimal solutions in complex nonlinear problems. The research on the phase-only weighted beamforming method is of great significance for solving the problems of slow beamforming and large error in scenarios such as radar detection, wireless communication, and intelligent antenna systems.

[0003] Planar arrays have greatly improved in terms of beam control ability, coverage, signal quality, and flexibility compared to linear arrays. With the progress of modern radar and wireless communication technologies, planar arrays are becoming increasingly popular. However, at present, most of the research on the phase-only weighted beamforming technology remains at the linear array level, and it is impossible to perform phase-only beamforming on planar arrays, which cannot meet the requirements in some specific application scenarios, such as applications that require three-dimensional space coverage signals. Moreover, in the design of antenna arrays, considering mutual coupling, synthesizing the radiation pattern of array antennas is an important topic and a major challenge in the antenna field. The mutual coupling between antenna elements may affect the beam shape, gain, and radiation power of the array antenna, thus limiting the accuracy and effectiveness of the array in practical applications. On the one hand, for the phase-only weighted beamforming problem, most of the existing phase-only weighted beamforming methods do not consider the influence of the mutual coupling between array elements on the performance of the antenna array, and assume that each array element is in an ideal situation when synthesizing. On the other hand, the existing phase-only weighted beamforming methods considering the mutual coupling effect have high computational complexity and poor algorithm applicability due to different coupling conditions. Studying the phase-only weighted beamforming method for planar arrays considering the mutual coupling effect is of great significance for solving the problem of errors between beamforming and theory in practical engineering applications.

[0004] The patent application with the publication number CN0.109639329A discloses a method for rapid phase-only weighted beamforming. This method sets the desired antenna beam pattern, initializes the weight functions at all discrete angles, the amplitude weighting values and phase weighting values of all antenna elements, and obtains the initial phased array antenna beam pattern; then updates the phase weighting values of all antenna elements: the phase weighting of any antenna element is a variable, and the phase weighting values of other antenna elements are the values obtained from the previous iteration calculation. The new phase weighting value of this antenna element is calculated by minimizing the derivative of the beamforming problem; then a new antenna beam pattern is formed using the updated phase weighting vector, the beamforming error is calculated, and the weight function at each discrete angle is calculated until the update calculation of the weight function at all discrete angles is completed; finally, until the error between the array antenna beam pattern and the desired shape beam pattern meets the requirements, an optimized phase weighting vector is obtained. However, this method has only completed the phase-only weighted beamforming for linear arrays at present and cannot complete the phase-only beamforming for planar arrays. Moreover, this method does not consider the mutual coupling effect between elements, and due to different coupling conditions, the algorithm applicability is poor, making it difficult to meet the requirements of beamforming in practical engineering, so it is not applicable to a wide range of beamforming scenarios. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned existing technologies, the purpose of the present invention is to propose a planar array phase-only weighted beamforming method considering the mutual coupling effect. By establishing a small array, i.e., a sub-array of the target large array, the AEP of each unit is extracted, and then through the calculation method of sub-array extrapolation, the AEP of each unit of the extracted sub-array is approximately equivalent to the AEP of other units of the target large array. Then, the approximately equivalent AEP is brought into the classical ADMM algorithm and BFGS algorithm to increase the robustness of the system. Calculating the feeding phase through the classical ADMM algorithm and BFGS algorithm can simplify the solution process and efficiently and accurately process large-scale problems. By introducing a scaling factor, the degree of freedom of the algorithm can be improved to enhance the beam control ability of the array antenna, improve the speed and accuracy of phase-only beamforming, consider the mutual coupling between units, reduce the error between beamforming and theory, and improve the versatility of beamforming.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A planar array phase-only weighted beamforming method considering the mutual coupling effect specifically includes the following steps:

[0008] Step 1, obtain the AEP of each antenna unit in the sub-array of the antenna array: Set the sampling angle domain range Obtain the of K×S antenna array elements respectively, where q = 1, 2,..., Q, p = 1, 2,..., P, Q is the number of sampling points in the elevation direction, P is the number of sampling points in the azimuth direction, (k = 1, 2,…K), (s = 1, 2,…S), the number of sub-array elements is K×S, K is the number of elements arranged along the x-axis, and S is the number of elements arranged along the y-axis;

[0009] Step 2, approximately equivalent the AEP of each element of the sub-array to the of each element in the M×V element target large array; the number of elements in the target large array is M×V; M is the number of elements arranged along the x-axis, and V is the number of elements arranged along the y-axis (M>K, V>S);

[0010] Step 3, construct the upper limit U and lower limit L of the radiation power expectation with a dimension of Q×P corresponding to the angle domain range;

[0011] Step 4, combine the of each unit of the M×V element target large array obtained in Step 2 to

[0012] construct a mathematical expression for phase-only weighted beamforming;

[0013]

[0014] Among them, represents taking the real part, represents taking the imaginary part, and respectively represent the Lagrange multipliers for constraining the real part and the imaginary part;

[0015] Step 6: Set the maximum number of iterations T of the augmented Lagrangian function L(μ, φ, Z, λ) constructed in Step 5, and set the auxiliary variables scaling factor μ, the feeding phases φ of each element of the antenna array n , Lagrange multipliers initial values μ(t), φ n (t) and According to the initial values μ(t), φ n (t) and respectively perform iterative solutions on the current auxiliary variables scaling factor μ(t + 1), the feeding phases φ of each element of the antenna array n (t + 1) and the Lagrange multiplier matrix ;

[0016] Step 7: Define the residual ΔZ of the auxiliary variable Z, and determine whether the residual satisfies the iteration termination condition. If it is satisfied, output the phase φ n , if not, return to Step 6 to continue the iteration, retain the feeding phases φ of each element of the antenna array at the t-th iteration t , according to the residual ΔZ of the auxiliary variable, select the feeding phase φ corresponding to the minimum residual t , according to the feeding phase φ t and the feeding amplitude A n obtain the pattern data E of the phase-only beamforming t .

[0017] The obtained from the K × S antenna elements in the said Step 1 is expressed as follows:

[0018]

[0019] Among them, is the AEP of the k-th row and s-th column antenna element, is a two-dimensional matrix with dimensions Q × P, and is expressed as follows:

[0020]

[0021] Among them, represents the k-th row and s-th column antenna element at θ = θ q , The pointed direction pattern data, θ q is the q-th elevation variable in the angle domain of the direction pattern sampling, and is the p-th azimuth variable in the angle domain of the direction pattern sampling.

[0022] In step 2, the AEP of each element of the sub-array is approximately equivalent to the AEP of each element of the M×V-element target large array, which is expressed as follows:

[0023] 2.1) Divide the columns of the sub-array into the central column, the left columns of the central column, and the right columns of the central column; perform equivalent extrapolation of the AEP of the sub-array. The AEP of all elements in the left columns of the sub-array center equivalently replaces the AEP of all elements in the left 1 to (S - 1) / 2 columns of the target array. The AEP of all elements in the right columns of the sub-array center equivalently replaces the AEP of all elements in the right V - (S + 1) / 2 + 2 to V columns of the target array. The AEP of all elements in the central column of the sub-array equivalently replaces the AEP of all elements in the middle (S + 1) / 2 to V - (S + 1) / 2 + 1 columns of the target array, obtaining the AEP of each unit of the K×V-dimensional array equivalent along the column;

[0024] 2.2) According to the rows of the sub-array, divide the K×V-dimensional array obtained by equivalent along the column in step 2.1) into three parts, namely the central row, the upper rows of the central row, and the lower rows of the central row; the AEP of all elements in the upper rows of the sub-array center equivalently replaces the AEP of all elements in the upper 1 to (K - 1) / 2 rows of the target array. The AEP of all elements in the lower rows of the sub-array center equivalently replaces the AEP of all elements in the lower M - (K + 1) / 2 + 2 to M rows of the target array. The AEP of all elements in the central row of the sub-array equivalently replaces the AEP of all elements in the middle (K + 1) / 2 to M - (K + 1) / 2 + 1 rows of the target array; after the equivalent replacement of the AEP of the target array, perform spatial phase compensation to finally obtain the radiation field of the M×V-element target large array.

[0025] In step 2, the of each element in the M×V-element target large array is

[0026]

[0027] Among them, is the AEP of the antenna element in the m-th row and v-th column, is a two-dimensional matrix with dimensions Q×P, which is expressed as follows:

[0028]

[0029] Among them, represents the direction pattern data of the antenna element in the m-th row and v-th column at θ = θ q , The pointed direction pattern data, θ qis the q-th elevation variable in the direction pattern sampling angle domain, and is the p-th azimuth variable in the direction pattern sampling angle domain.

[0030] In step 3, the expected upper limit U of the radiation power with the dimension of Q×P in the corresponding angle domain is constructed as follows:

[0031]

[0032] where represents the expected upper limit of the radiation power at θ = θ q , θ is the q-th elevation variable in the direction pattern sampling angle domain, q and is the p-th azimuth variable in the direction pattern sampling angle domain;

[0033] The expected lower limit L of the radiation power with the dimension of Q×P in the corresponding angle domain is constructed as follows:

[0034]

[0035] where represents the expected lower limit of the radiation power at θ = θ q , θ is the q-th elevation variable in the direction pattern sampling angle domain, q and is the p-th azimuth variable in the direction pattern sampling angle domain.

[0036] The specific method of step 4 is:

[0037] Introduce a scaling factor μ and define an auxiliary variable: where A n represents the feeding amplitude of each element of the antenna array, φ n represents the feeding phase of each element of the antenna array, n = 1, 2,... M×V, N represents the number of target antenna array elements N = M×V, T represents the transpose;

[0038] Combine the direction pattern expectation function and the auxiliary variable

[0039]

[0040] The method for iteratively solving the current auxiliary variable n (t + 1), the feeding phase φ of each element of the antenna array of the Lagrange multiplier matrix

[0041] 6.1) Iteratively solve the current auxiliary variables

[0042]

[0043] Set the initial value of the feeding phase φ of each array element:

[0044]

[0045] Let φ mv be converted into an N×1 dimensional matrix φ n Substitute it into the augmented Lagrangian function, φ n =[φ 1 , φ 2 ,..., φ n ,..., φ N T , The expression after ignoring the terms unrelated to Z in the augmented Lagrangian function L(μ(t), φ(t), Z, λ(t)) is as follows:

[0046]

[0047] where n = 1, 2,... M×V, N represents the number of target antenna array elements, ρ represents the penalty parameter, represents the radiation field of the antenna element in the m-th row and v-th column A = [A 1 , A 2 ,..., A n ,..., A N T represents the feeding amplitude of each array element of the antenna array, φ = [φ 1 , φ 2 ,..., φ n ,..., φ N T represents the feeding phase of each array element of the antenna array, [][] T represents the transpose;

[0048] The solution of Z(t + 1) is given by the following formula:

[0049]

[0050] where, represents the upper limit of the expected radiation power, represents the lower limit of the expected radiation power, arg() represents taking the phase angle;

[0051] 6.2) Iteratively solve the current scaling factor μ and the feeding phase φ values of each array element of the antenna array, the method is as follows:

[0052] ​​​

[0053] 6.2.1) Define three auxiliary functions \(W(\varphi)\), \(H(\varphi)\), and \(G\) respectively:

[0054] Decouple \(\{\mu(t + 1),\varphi(t + 1)\}\) and rewrite it as

[0055] \(W(\varphi)\), \(H(\varphi)\), and \(G\) are

[0056]

[0057] where \(\rho\) represents the penalty parameter, represents the radiation field of the \(m\)-th row and \(v\)-th column antenna element, \(A\) represents the feeding amplitude of each element of the antenna array, \(\varphi\) represents the feeding phase of each element of the antenna array, H represents the conjugate transpose, * represents taking the complex conjugate;

[0058] 6.2.2) When \(\varphi\) is given, the scale factor \(\mu\) of the two auxiliary functions \(W(\varphi)\) and \(H(\varphi)\) is expressed as follows:

[0059]

[0060] Construct the following non - linear optimization problem:

[0061]

[0062] 6.2.3) Update the value of the feeding phase \(\varphi\) of each element of the \(M\times V\) - element target large - scale array. Obtain the current feeding phase \(\varphi(t + 1)\) of the antenna array through the MATLAB function "fminunc", which is expressed as follows:

[0063]

[0064] where \(\varphi(t)\) is the feeding phase of each element before updating, and fminunc is the matlab function used to solve the minimum value of a non - linear multi - variable function;

[0065] 6.2.4) Update the scale factor \(\mu\) according to the current feeding phase \(\varphi(t + 1)\) to obtain the current scale factor \(\mu(t + 1)\):

[0066]

[0067] 6.3 Iteratively solve the current Lagrange multiplier The value of, the formula is as follows:

[0068]

[0069]

[0070] Among them, and respectively represent the Lagrange multipliers of the real part and the imaginary part of the constraint obtained in the current iteration.

[0071] The residual ΔZ of the auxiliary variable Z defined in step 7 is expressed as follows:

[0072]

[0073] Among them, ΔZ is the introduced auxiliary variable, is the expression after ignoring the terms irrelevant to Z in the augmented Lagrangian function L(μ, φ, Z, λ).

[0074] The judgment of whether the residual satisfies the iteration termination condition in step 7 is: ΔZ ≤ Δ or t + 1 = T;

[0075] Among them, Δ is the residual set by the user himself, t = 1, 2,..., T, and T represents the maximum number of iterations. According to the residual ΔZ of the auxiliary variable, the feeding phase φ corresponding to the minimum residual is selected t .

[0076] The feeding phase φ of each element of the antenna array in the t-th iteration in step 7 t , is expressed as follows:

[0077] φ t = [φ t,1 , φ t,2 ,..., φ t,n ,..., φ t,N T

[0078] According to the feeding phase φ t and the feeding amplitude A n the corresponding pattern data E t is obtained, which is expressed as follows:

[0079]

[0080] Among them, ρ represents the penalty parameter, and E t represents the total radiation field of the M×V element target array, that is, the pattern data of only phase beamforming, represents the radiation field of the antenna element in the m-th row and v-th column, A n represents the feeding amplitude of each element of the antenna array, and φ t,n represents the feeding phase of the n-th antenna element in the t-th iteration.

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] ​First, the present invention simulates and extracts the AEP of each unit by establishing a small array, i.e., a sub-array of the target large array, and then approximates and equivalent the AEP of each unit of the extracted sub-array to that of other units of the target large array through the calculation method of sub-array extrapolation, which can solve the influence of mutual coupling effect on the array performance and make the antenna array have better adaptability and robustness in different application scenarios.

[0083] Second, the present invention optimizes the phase only of the planar array antenna through the phase-only weighted beamforming method based on the ADMM algorithm to achieve efficient and accurate beam control. Compared with the traditional amplitude-phase beamforming, this method greatly simplifies the hardware design, reduces the system complexity and cost, and greatly simplifies the solution process, and can efficiently and accurately process large-scale problems.

[0084] Third, by introducing the scaling factor μ, the present invention improves the algorithm degree of freedom, enables the algorithm to adaptively adjust according to the changes of the environment or data, so as to maintain good performance in dynamic scenarios, and the result can more finely fit the desired radiation pattern.

[0085] In summary, the present invention solves the problems that most of the existing phase-only weighted beamforming can only be applied to linear arrays and cannot perform beamforming on planar arrays, and is susceptible to mutual coupling effects, high computational complexity, poor algorithm applicability, etc.; it can be used in applications such as communication, radar, sonar systems, and medical imaging that require high-precision beam pointing and three-dimensional space coverage of signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is the implementation flowchart of the present invention.

[0087] Figure 2 is the implementation flowchart of the sub-array extrapolation of the present invention.

[0088] Figure 3 is the sub-array structure of the planar array phase-only weighted beamforming method of the present invention; wherein, Figure 3 (a) is the top view of the array, Figure 3 (b) is the bottom view of the array.

[0089] Figure 4 is the target array structure of the planar array phase-only weighted beamforming method of the present invention; wherein, Figure 4 (a) is the top view of the array, Figure 4 (b) is the bottom view of the array.

[0090] Figure 5 is the comparison diagram of the radiation patterns of the 13×13 element array of the present invention under different methods in the plane.

[0091] Figure 6For generating nulls in sidelobes in the present invention, in is the comparison diagram of radiation patterns.

[0092] Figure 7 For generating nulls in sidelobes in the present invention, the three-dimensional radiation pattern obtained by the subarray extrapolation method in MATLAB; among them, Figure 7 (a) is the side view of the three-dimensional radiation pattern, Figure 7 (b) is the top view of the three-dimensional radiation pattern, Figure 7 (c) is the residual curve.

[0093] Figure 8 For generating nulls in sidelobes in the present invention, the three-dimensional radiation pattern obtained by HFSS simulation. Detailed implementation manners

[0094] In order to more clearly describe the solution and effect of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0095] It should be noted that the step numbers in the specification and claims of the present invention are only for clearly describing the implementation solutions of the present invention for easy understanding, and their sequence numbers are not limited.

[0096] A method for phase-only weighted beamforming of a planar array considering mutual coupling effects, referring to Figure 1 , the implementation steps of this example are as follows:

[0097] Step 1: Obtain the AEP of each antenna element in the subarray array.

[0098] The antenna array, as Figure 3 shown, where Figure 3 (a) is the radiation surface of the array, Figure 3 (b) is the feeding surface of the array, including 49 antenna elements with a center frequency of 10 GHz. These 49 antenna elements are uniformly arranged along the x-axis with a spacing of d = 0.0175 m and along the y-axis with a spacing of d = 0.0172 m to form a 7×7 planar array, and the phase center of the 1st element is located at the origin.

[0099] In this step, the of each antenna element in the antenna array is obtained through simulation software.

[0100] Using the Ansys HFSS simulation software, set the operating frequency to 10 GHz, set the feeding phase of 49 antenna elements to 0°, set the feeding amplitude of the antenna element in the k-th row and s-th column to 1 W respectively, and set the feeding amplitude of the remaining elements to 0 W, and obtain the It is a two-dimensional matrix with dimensions of K×S, and is expressed as follows:

[0101]

[0102] Among them, is the AEP of the antenna element in the k-th row and s-th column. It is a two-dimensional matrix with dimensions of Q×P, and is expressed as follows:

[0103]

[0104] Among them, represents the pattern data of the antenna element in the k-th row and s-th column in the direction of θ = θ q , θ q is the q-th elevation variable in the pattern sampling angle domain, is the p-th azimuth variable in the pattern sampling angle domain.

[0105] Step 2: Obtain the AEP of the target planar array element through the subarray extrapolation calculation method based on the AEP idea.

[0106] 2.1) Divide the columns of the subarray into the central column, the left columns of the central column, and the right columns of the central column; perform equivalent extrapolation of the subarray AEP. The AEP of all elements in the left columns of the subarray center equivalently replaces the AEP of all elements in the left 1 to (S - 1) / 2 columns of the target array, the AEP of all elements in the right columns of the subarray center equivalently replaces the AEP of all elements in the right V - (S + 1) / 2 + 2 to V columns of the target array, and the AEP of all elements in the central column of the subarray equivalently replaces the AEP of all elements in the middle (S + 1) / 2 to V - (S + 1) / 2 + 1 columns of the target array, to obtain the AEP of each element of the K×V-dimensional array equivalent along the column;

[0107] 2.2) According to the rows of the subarray, divide the K×V-dimensional array obtained by equivalent along the column in step 2.1) into three parts, namely the central row, the upper rows of the central row, and the lower rows of the central row; the AEP of all elements in the upper rows of the subarray center equivalently replaces the AEP of all elements in the upper 1 to (K - 1) / 2 rows of the target array, the AEP of all elements in the lower rows of the subarray center equivalently replaces the AEP of all elements in the lower M - (K + 1) / 2 + 2 to M rows of the target array, and the AEP of all elements in the central row of the subarray equivalently replaces the AEP of all elements in the middle (K + 1) / 2 to M - (K + 1) / 2 + 1 rows of the target array; perform spatial phase compensation after the equivalent replacement of the target array AEP, and finally obtain the radiation field of the M×V-element target large array.

[0108] After the equivalent replacement of the target array AEP, spatial phase compensation is performed, and finally the radiation field of the target array is obtained, as Figure 2 shown.

[0109] In the M×V element target large array, each unit's is expressed as follows:

[0110]

[0111] Among them, is the AEP of the antenna element in the m-th row and v-th column, which is a two-dimensional matrix with dimensions of Q×P and is expressed as follows:

[0112]

[0113] Among them, represents the pattern data of the antenna element in the m-th row and v-th column at θ = θ q , pointing in the direction, θ q is the q-th elevation variable in the pattern sampling angle domain, is the p-th azimuth variable in the pattern sampling angle domain.

[0114] Step 3: Based on the target form of only phase beamforming, construct a pattern desired function with dimensions of Q×P for the corresponding angle domain range, including the upper limit U of the desired radiation power and the lower limit L of the desired radiation power;

[0115] Construct the upper limit U of the desired radiation power with dimensions of Q×P for the corresponding angle domain range, which is expressed as follows:

[0116]

[0117] Among them, represents the upper limit of the desired radiation power at θ = θ q , pointing in the direction, θ q is the q-th elevation variable in the pattern sampling angle domain, is the p-th azimuth variable in the pattern sampling angle domain.

[0118] Construct the lower limit L of the desired radiation power with dimensions of Q×P for the corresponding angle domain range, which is expressed as follows:

[0119]

[0120] Among them, represents the lower limit of the desired radiation power at θ = θ q , pointing in the direction, θ q is the q-th elevation variable in the pattern sampling angle domain, is the p-th azimuth variable in the direction pattern sampling angle domain.

[0121] Step 4: Construct the mathematical expression of phase-only weighted beamforming:

[0122] Introduce a scaling factor μ and define auxiliary variables: where A n represents the feeding amplitude of each element of the antenna array, φ n represents the feeding phase of each element of the antenna array, n = 1, 2,... M×V, N represents the number of target antenna array elements N = M×V, [] T represents the transpose;

[0123] Combine the desired function of the direction pattern and the auxiliary variables to establish the following mathematical expression:

[0124]

[0125] Step 5: Construct the augmented Lagrangian function L(μ, φ, Z, λ) and iteratively solve to obtain the current auxiliary variable Z n , the scaling factor μ, the feeding phase φ of each element of the antenna array t and the Lagrange multiplier values.

[0126] Introduce a penalty parameter ρ and a Lagrange multiplier λ, and construct the augmented Lagrangian function L(μ, φ, Z, λ) based on the mathematical expression of phase-only weighted beamforming constructed in Step 4:

[0127]

[0128] where, represents taking the real part, represents taking the imaginary part, and represent the Lagrange multipliers for the constraint real part and the constraint imaginary part respectively;

[0129] Step 6: Set the maximum number of iterations T of the augmented Lagrangian function L(μ, φ, Z, λ) constructed in Step 5, and set the auxiliary variable scaling factor μ, the feeding phase φ of each element of the antenna array n , the Lagrange multiplier initial values μ(t), φ n (t) and According to the initial values μ(t), φ n (t) and respectively for the current auxiliary variable Scaling factor μ(t + 1), feeding phase φ of each element of the antenna array n (t + 1) and the Lagrange multiplier matrix are iteratively solved;

[0130] 6.1) Iteratively solve the current auxiliary variable

[0131]

[0132] Set the initial value of the feeding phase φ of each element,

[0133]

[0134] Convert φ mv to an N×1 dimensional matrix φ n and substitute it into the augmented Lagrangian function. φ n =[φ 1 , φ 2 ,..., φ n ,..., φ N T , the expression after ignoring the terms irrelevant to Z in the augmented Lagrangian function L(μ(t), φ(t), Z, λ(t)) is as follows:

[0135]

[0136] where n = 1, 2,... M×V, N represents the number of target antenna array elements, ρ represents the penalty parameter, represents the radiation field of the antenna element in the m-th row and v-th column. A = [A 1 , A 2 ,..., A n ,..., A N T represents the feeding amplitude of each element of the antenna array, φ = [φ 1 , φ 2 ,..., φ n ,..., φ N T represents the feeding phase of each element of the antenna array, [][] T represents the transpose;

[0137] The solution of Z(t + 1) is given by the following formula:

[0138]

[0139] where, represents the upper limit of the radiation power expectation, represents the lower limit of the radiation power expectation, arg() represents taking the phase angle;

[0140] ​​​6.2) Iteratively solve the values of the current scaling factor μ and the feeding phases φ of each element of the antenna array as follows:

[0141]

[0142] 6.2.1) Define three auxiliary functions W(φ), H(φ), and G respectively:

[0143] Decouple {μ(t + 1), φ(t + 1)}, which can be rewritten as

[0144] W(φ), H(φ), and G are

[0145]

[0146] where ρ represents the penalty parameter, represents the radiation field of the antenna element in the m-th row and v-th column, A represents the feeding amplitude of each element of the antenna array, φ represents the feeding phase of each element of the antenna array, H represents the conjugate transpose, * represents taking the complex conjugate;

[0147] 6.2.2) When φ is given, the scaling factor μ in terms of two auxiliary functions M(φ) and N(φ) is expressed as follows:

[0148]

[0149] Construct the following non - linear optimization problem:

[0150]

[0151] 6.2.3) Update the values of the feeding phases φ of each element of the M×V - element target large array, and obtain the current feeding phase φ(t + 1) of the antenna array through the MATLAB function "fminunc", which is expressed as follows:

[0152]

[0153] where φ(t) is the feeding phase of each element before update, and fminunc is the matlab function used to solve the minimum value of a non - linear multi - variable function;

[0154] 6.2.4) Update the scaling factor μ according to the current feeding phase φ(t + 1) to obtain the current scaling factor μ(t + 1):

[0155]

[0156] 6.3 Iteratively solve the current Lagrange multiplier The value of, and the formula is as follows:

[0157]

[0158] Among them, and respectively represent the Lagrange multipliers of the real and imaginary parts of the constraint obtained in the current iteration;

[0159] Step 7: Define the auxiliary variable Z n The residual ΔZ of

[0160]

[0161] is expressed as follows: Among them, ΔZ is the introduced auxiliary variable, is the expression after ignoring the terms unrelated to Z in the augmented Lagrangian function L(μ, φ, Z, λ).

[0162] Judge whether the residual satisfies the iteration termination condition ΔZ ≤ Δ or t + 1 = T.

[0163] Among them, Δ is the residual set by the user himself, t = 1, 2,..., T, and T represents the maximum number of iterations. If it is satisfied, output the phase φ n , if not satisfied, return to Step 6 to continue the iteration, and retain the feeding phase φ of each element of the antenna array at the t-th iteration t , which is expressed as follows:

[0164] φ t = [φ t,1 , φ t,2 ,..., φ t,n ,..., φ t,N T

[0165] According to the feeding phase φ t and the feeding amplitude A n obtain the corresponding pattern data E t , which is expressed as follows:

[0166]

[0167] Among them, ρ represents the penalty parameter, and E t represents the total radiation field of the N-element target array, that is, the pattern data of only phase beamforming, represents the radiation field of the antenna element in the m-th row and v-th column, A n represents the feeding amplitude of each element of the antenna array, and φ t,n represents the feeding phase of the n-th antenna element in the t-th iteration. According to the residual ΔZ of the auxiliary variable, select the feeding phase φ corresponding to the minimum residual t , according to the feeding phase φ t and the feeding amplitude A nObtain the pattern data E of only phase beamforming t 。

[0168] The effects of the present invention can be further illustrated by the following simulation experiments.

[0169] I. Simulation experiment conditions

[0170] Using Ansys HFSS simulation software, set to include 49 antenna elements and 169 antenna elements. The feeding phase of each antenna element is 0°. Arrange these 49 antenna elements and 169 antenna elements along the x-axis with a spacing d = 0.0175m and along the y-axis with a spacing d = 0.0172m to form 7×7 and 13×13 planar arrays. Among them, the phase center of the No. 1 element is located at the origin, and the operating frequency is 10GHz;

[0171] II. Simulation experiment content

[0172] Simulation experiment 1: Under the above experimental conditions, use the method of the present invention to perform subarray extrapolation calculation based on the AEP idea to generate the radiation pattern of the antenna array. In this simulation experiment, set the feeding phase of 169 antenna elements to 0° and set the feeding amplitude of 169 antenna elements to 1W. As Figure 5 shown, it is the comparison diagram of the radiation patterns of the 169-element array in the plane under different methods of the present invention. It can be seen from Figure 5 that the method proposed in this paper is more accurate than using the pattern multiplication theorem in the traditional method.

[0173] Simulation experiment 2: Under the above experimental conditions, use the method of the present invention to perform only phase weighted beamforming for generating nulls in the sidelobes. Suppress the entire three-dimensional space sidelobes below -19dB, and generate a -45dB deep null in θ = 36° to 41°. The main lobe region is [-9° to 9°], and the sidelobe regions are [-90° to -10°], [10° to 35°] and [42° to 90°]. As Figures 6 - 8 shown, among them, Figure 6 is the result comparison diagram of the radiation pattern obtained by subarray extrapolation in MATLAB and the radiation pattern obtained by HFSS simulation at ; Figure 7 The three-dimensional radiation pattern obtained by subarray extrapolation in MATLAB, where Figure 7 (a) is the side view, Figure 7 (b) is the top view; Figure 8 is the three-dimensional radiation pattern obtained by HFSS simulation. It can be seen from Figure 7 and Figure 8 that in this simulation experiment of only phase weighted beamforming for generating nulls in the sidelobes It can also achieve a null depth of -40 dB, starting from Figures 6 - 8 It can be seen that, compared with the traditional amplitude-phase beamforming for planar arrays, the method proposed in the present invention greatly simplifies the hardware design, reduces the system complexity and cost, and greatly simplifies the solution process, and can quickly and accurately achieve the nulling-only phase weighting beamforming of the sidelobes of the planar array.

Claims

1. A planar array phase-weighted beamforming method taking mutual coupling effects into account, characterized in that: The steps include: Step 1: Get the AEP of each antenna element in the antenna array subarray: Set the sampling angle domain range Get the AEP of K×S antenna elements respectively Where q=1,2,...,Q,p=1,2,...,P, Q is the number of sampling points in elevation, P is the number of sampling points in azimuth, (k=1,2,...K),(s=1,2,...S), the number of sub-array elements is K×S, K is the number of units arranged along the x-axis, S is the number of units arranged along the y-axis; Step 2: Use the AEP of each element of the subarray to approximate the AEP of each element in the M×V element target large array (m=1,2,…M),(v=1,2,…V), the number of target large array elements is M×V; M is the number of elements arranged along the x-axis, and V is the number of elements arranged along the y-axis (M>K,V>S); Step 3: Construct the corresponding angle domain The dimension of the range is Q×P, the expected upper limit U and the expected lower limit L of the radiated power; Step 4: Combine the AEP of each unit of the M×V target large array obtained in step 2 Construct the mathematical expression of phase-only weighted beamforming; Step 5: Introduce the penalty parameter ρ and the Lagrangian multiplier λ, and construct the augmented Lagrangian function L(μ, φ, Z, λ) based on the mathematical expression of phase-weighted beamforming only: in, represents the real part, represents the imaginary part, and denote the Lagrange multipliers of the real part of the constraint and the imaginary part of the constraint respectively; Step 6: Set the maximum number of iterations T of the augmented Lagrangian function L(μ, φ, Z, λ) constructed in step 5, and set the auxiliary variables Proportional factor μ, antenna array element feeding phase φ n , Lagrange multipliers The initial value of μ(t), φ n (t) According to the initial value μ(t), φ n (t) For the current auxiliary variables Proportional factor μ(t+1), antenna array element feed phase φ n (t+1) and the Lagrange multiplier matrix Perform iterative solution; Step 7: Define the residual ΔZ of the auxiliary variable Z, and determine whether the residual satisfies the iteration termination condition. If so, output the phase φ n If it is not satisfied, return to step 6 to continue the iteration and retain the feeding phase φ of each element of the antenna array in the tth iteration t , according to the residual ΔZ of the auxiliary variable, select the feeding phase φ corresponding to the minimum residual t , according to the feeding phase φ t With the feeding amplitude A n Get the directional pattern data E of only phase beamforming t .

2. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: The AEP of the K×S antenna elements in step 1 It is expressed as follows: in, is the AEP of the antenna element in row k and column s, is a two-dimensional matrix of dimension Q×P, expressed as follows: in, It means that the antenna array element in row k and column s is at θ = θ q , Directional pattern data, θ q is the qth elevation variable in the pattern sampling angle domain, It is the pth azimuth variable in the directional pattern sampling angle domain.

3. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: The AEP of each element of the subarray described in step 2 is used to approximate the AEP of each element of the M×V element target large array, which is expressed as follows: 2.1) Divide the columns of the subarray into the central column, the column to the left of the central column, and the column to the right of the central column; perform equivalent extrapolation of the subarray AEP, the AEP of all the array elements in the central left column of the subarray equivalently replaces the AEP of all the array elements in the left 1 to (S-1) / 2 columns of the target array, the AEP of all the array elements in the central right column of the subarray equivalently replaces the AEP of all the array elements in the right V-(S+1) / 2+2 to V columns of the target array, the AEP of all the array elements in the central column of the subarray equivalently replaces the AEP of all the array elements in the middle (S+1) / 2 to V-(S+1) / 2+1 columns of the target array, and obtains the AEP of each unit of the K×V dimensional array equivalent to that along the column; 2.2) According to the rows of the subarray, the K×V dimensional array equivalently obtained along the columns in step 2.1) is divided into three parts, namely the center row, the upper row of the center row, and the lower row of the center row; the AEP of all the array elements in the upper row of the subarray center is equivalent to replacing the AEP of all the array elements in the upper 1 to (K-1) / 2 rows of the target array, the AEP of all the array elements in the lower row of the subarray center is equivalent to replacing the AEP of all the array elements in the lower M-(K+1) / 2+2 to M rows of the target array, and the AEP of all the array elements in the center row of the subarray is equivalent to replacing the AEP of all the array elements in the middle (K+1) / 2 to M-(K+1) / 2+1 rows of the target array; after the target array AEP is equivalently replaced, spatial phase compensation is performed to finally obtain the radiation field of a large target array of M×V elements.

4. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: The AEP of each element in the M×V element target large array described in step 2 It is expressed as follows: in, is the AEP of the antenna element in the mth row and vth column, is a two-dimensional matrix of dimension Q×P, expressed as follows: in, It means that the antenna array element in the mth row and vth column is at θ=θ q , Directional pattern data, θ q is the qth elevation variable in the pattern sampling angle domain, It is the pth azimuth variable in the directional pattern sampling angle domain.

5. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: Construct the corresponding angle domain in step 3 The expected upper limit U of the radiated power with a range dimension of Q×P is expressed as follows: in, Indicates that when θ=θ q , The expected upper limit of the radiated power in the direction, θ q is the qth elevation variable in the pattern sampling angle domain, is the pth azimuth variable in the directional pattern sampling angle domain; Construct the expected lower limit L of the radiated power corresponding to the angular domain range with the dimension of Q×P, which is expressed as follows: in, Indicates that when θ=θ q , The expected lower limit of the radiated power in the direction, θ q is the qth elevation variable in the pattern sampling angle domain, It is the pth azimuth variable in the directional pattern sampling angle domain.

6. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: The specific method of step 4 is: Introduce the proportional factor μ and define the auxiliary variables: Among them A n Indicates the feeding amplitude of each element of the antenna array, φ n represents the feeding phase of each element of the antenna array, n=1,2,...M×V, N represents the number of target antenna array elements N=M×V, [] T represents transpose; Combining the directional pattern expectation function and auxiliary variables Create the following mathematical expression:

7. The method for planar array phase-weighted beamforming taking mutual coupling effects into account according to claim 1, characterized in that: In step 6, the current auxiliary variable is iteratively solved Proportional factor μ(t+1), antenna array element feed phase φ n (t+1) and the Lagrange multiplier matrix The method is: 6.1) Iterate to solve the current auxiliary variable Set the initial value of each array element feed phase φ: φ mv Convert to N×1 dimensional matrix φ n Substitute the augmented Lagrangian function, φ n =[φ1,φ2,...,φ n ,...,φ N ] T , ignoring the expression of the terms unrelated to Z in the augmented Lagrangian function L(μ(t),φ(t),Z,λ(t)), it is expressed as follows: Where n = 1, 2, ... M × V, N represents the number of target antenna array elements, ρ represents the penalty parameter, The radiation field A of the mth row and vth column antenna element is A=[A1,A2,...,A n ,...,A N ] T represents the feeding amplitude of each element of the antenna array, φ=[φ1,φ2,...,φ n ,...,φ N ] T Indicates the feeding phase of each element of the antenna array, [] T represents transpose; The solution for Z(t+1) is given by: in, represents the expected upper limit of radiated power, Indicates the expected lower limit of radiation power, arg() indicates the phase angle; 6.2) Iteratively solve the current proportional factor μ and the value of the feed phase φ of each element of the antenna array as follows: 6.2.1) Define three auxiliary functions W(φ), H(φ), and G respectively: Decoupling {μ(t+1),φ(t+1)} can be rewritten as W(φ),H(φ),G are: Among them, ρ represents the penalty parameter, represents the radiation field of the antenna array element in the mth row and vth column, A represents the feeding amplitude of each element in the antenna array, φ represents the feeding phase of each element in the antenna array, [] H represents the conjugate transpose, [] * represents taking the complex conjugate; 6.2.2) When φ is given, the scaling factor μ using two auxiliary functions W(φ) and H(φ) is expressed as follows: The following nonlinear optimization problem is constructed: 6.2.3) Update the value of the feed phase φ of each element of the M×V element target large array, and obtain the current feed phase φ(t+1) of the antenna array through the MATLAB function "fminunc", which is expressed as follows: Where φ(t) is the feeding phase of each array element before updating, and fminunc is a MATLAB function used to solve the minimum value of nonlinear multivariate functions; 6.2.4) Update the proportional factor μ according to the current feeding phase φ(t+1) to obtain the current proportional factor μ(t+1): 6.3 Iterative solution of the current Lagrange multiplier The value of is as follows: in, and Respectively represent the Lagrange multipliers of the real and imaginary parts of the constraints obtained in the current iteration.

8. A planar array phase-weighted beamforming method taking mutual coupling effects into account according to claim 1, characterized in that , the residual ΔZ of the auxiliary variable Z defined in step 7 is expressed as follows: Among them, ΔZ is the introduced auxiliary variable, is the expression after ignoring the irrelevant terms with Z in the augmented Lagrangian function L(μ,φ,Z,λ).

9. A planar array phase-weighted beamforming method taking mutual coupling effects into account according to claim 1, characterized in that , the determination of whether the residual meets the iteration termination condition in step 7 is: ΔZ≤Δor t+1=T; where Δ is the residual set by the user, t=1,2,...,T, T represents the maximum number of iterations, and the feeding phase φ corresponding to the minimum residual is selected according to the residual ΔZ of the auxiliary variable t .

10. A planar array phase-weighted beamforming method taking mutual coupling effects into account according to claim 1, characterized in that , the feeding phase φ of each element of the antenna array for the tth iteration described in step 7 t , which is expressed as follows: f t =[φ t,1 ,f t,2 ,...,f t,n ,...,f t,N ] T According to the feeding phase φ t With the feeding amplitude A n Get the corresponding directional pattern data E t , which is expressed as follows: Among them, ρ represents the penalty parameter, E t Represents the total radiation field of the N-element target array, that is, the directional pattern data of only phase beamforming, A represents the radiation field of the antenna array element in the mth row and vth column, n Indicates the feeding amplitude of each element of the antenna array, φ t,n represents the feeding phase of the nth antenna element in the tth iteration.

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