A non-uniform feeding-based irregular array wide-angle scanning optimization method

Abstract

The application provides a non-uniform phase feeding based irregular array wide-angle scanning optimization method, and aims at the problems of gain decline and sidelobe deterioration caused by large-angle scanning of the relative wave path difference of the irregular array, constructs an array architecture parameter optimization model based on a complementary strategy of multi-type subarray non-uniform phase feeding, and uses the anisotropy of different shape subarrays and the complementarity of the non-uniform phase feeding switch state to maximize the normalized scanning radiant energy as the target; in the solving process, a separation optimization strategy based on alternating minimization is adopted, the mixed integer nonlinear programming problem is decomposed into two sub-problems of internal phase configuration optimization and non-uniform phase feeding switch state distribution optimization for alternating solving, and the optimal array architecture parameters are output according to the solving results; the application has the beneficial effects that the application effectively eliminates the scanning blind area of a specific azimuth angle, significantly improves the gain consistency of wide-angle scanning and reduces the sidelobe level.

Description

Technical Field

[0001] This invention relates to the fields of communication and radar technology, and in particular to an optimization method for wide-angle scanning of irregular arrays based on non-uniform phase feeding. Background Technology

[0002] With the ever-increasing demands of modern radar and communication systems for detection range, resolution, and anti-jamming capabilities, large-scale phased array antennas have become the mainstream form. To reduce system cost, lighten weight, and simplify the complexity of the feed network, a subarray-level architecture is typically adopted, combining several adjacent array elements into an irregular subarray that shares a single T / R component. While this irregular subarray architecture can suppress grating lobes at the physical level by breaking periodicity, the resulting large equivalent spacing leads to significant phase quantization errors, i.e., relative path difference (RWPD).

[0003] The presence of relative path difference (RWPD) disrupts the in-phase superposition condition within the subarray, causing the main lobe pointing of the subarray pattern to fail to follow the main lobe pointing deflection of the array factor. Particularly under large-angle scanning conditions (wide-angle scanning), the relative path difference (RWPD) increases sharply, leading to a significant decrease in array gain and deterioration of sidelobe levels. Therefore, achieving high-quality wide-angle scanning while maintaining the low-cost advantage of irregular subarray architectures is a pressing problem that needs to be solved.

[0004] Existing solutions mainly fall into two categories: one is based on wide-angle scanning antenna element designs, but this limits the physical size and form of the antenna elements, resulting in poor design flexibility; the other is based on fixed non-uniform phase feed (UFP) technology using a single square subarray, which improves scanning performance by introducing a preset phase delay into the feed network. However, UFP technology for square subarrays is limited by the geometric symmetry of the square subarray, and even with complementary strategies, at specific azimuth angles (such as... There are still blind spots in the scanning (see) Figure 7 (a)), and a higher proportion of square subarrays will reduce the randomness of the array surface, resulting in a weakening of the grating lobe suppression capability. Summary of the Invention

[0005] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide an optimization method for wide-angle scanning of irregular arrays based on non-uniform phase feeding, which solves the problems of large gain loss, scanning blind zone at a specific azimuth angle, and sidelobe level rise in the prior art.

[0006] To achieve the above and other related objectives, the present invention provides the following technical solution:

[0007] An optimization method for wide-angle scanning of irregular arrays based on non-uniform phase feeding includes the following steps: constructing a multi-type irregular subarray array model and defining normalized scanning radiation energy as an evaluation index, wherein the normalized scanning radiation energy is used to reflect the gain loss caused by the relative path difference; constructing an array architecture parameter optimization model based on the multi-type irregular subarray array model and a non-uniform phase feeding mutual compensation strategy of multi-type subarrays, wherein the optimization variables in the array architecture parameter optimization model include continuous variables and discrete variables, the continuous variables are the internal phase configuration vectors of each type of subarray when the non-uniform phase feeding state is turned on, and the discrete variables are the non-uniform phase feeding switching state distribution vectors of each subarray in the array;

[0008] The array architecture parameter optimization model is solved using a separation optimization strategy based on alternating minimization. The optimal array architecture parameters are output based on the solution results, and beam scanning is performed based on the optimal array architecture parameters to obtain excellent wide-angle scanning performance. The optimal array architecture parameters include the optimal internal phase configuration vector of each type of subarray and the optimal non-uniform feed phase switch state distribution vector of the entire array.

[0009] In one embodiment of the present invention, defining the normalized scan radiation energy as an evaluation index includes: for the first... An irregular subarray, which in the scanning direction The normalized scan radiation energy is defined as: ;in, The number of array elements within the subarray; For the first in the sub-array The relative path difference of each array element; the normalized scan radiation energy decreases monotonically as the gain loss caused by the relative path difference increases.

[0010] In one embodiment of the present invention, the optimization objective of the array architecture parameter optimization model is to maximize the minimum value of the normalized scan radiation energy synthesized by the whole array within the target scanning region by adjusting the array architecture parameters, while taking into account peak suppression and global energy efficiency improvement outside the target scanning region. The array architecture parameters include continuous variables and discrete variables among the optimization variables.

[0011] In one embodiment of the present invention, the array architecture parameter optimization model belongs to a mixed integer nonlinear programming problem. In the process of solving the array architecture parameter optimization model using a separation optimization strategy based on alternating minimization, the separation optimization strategy decomposes the mixed integer nonlinear programming problem into two sub-problems for alternating iterative solution.

[0012] In one embodiment of the present invention, the step of using a separation optimization strategy based on alternating minimization to solve the array architecture parameter optimization model and outputting the optimal array architecture parameters according to the solution results includes: randomly initializing the non-uniform feed phase switch state distribution vector, internal phase configuration vector, and iteration count; phase subproblem update: fixing the current non-uniform feed phase switch state distribution vector, transforming the original mixed integer nonlinear programming problem into an optimization problem containing only continuous variables, and using a sequential quadratic programming algorithm to solve the updated internal phase configuration vectors of each type of subarray;

[0013] State subproblem update: Fix the updated internal phase configuration vector of each type of subarray, transform the optimization problem containing only continuous variables into a large-scale 0-1 combinatorial optimization problem, and use a discrete genetic algorithm to solve the updated non-uniform feed phase switch state distribution vector of the entire array; alternately iterate the phase subproblem update and state subproblem update, and output the optimal array architecture parameters based on the alternating iteration solution results.

[0014] In one embodiment of the present invention, fixing the current non-uniform feed phase switch state distribution vector transforms the original mixed-integer nonlinear programming problem into an optimization problem containing only continuous variables, and using a sequential quadratic programming algorithm to solve for the updated internal phase configuration vectors of each type of subarray, includes: fixing the current non-uniform feed phase switch state distribution vector; after fixing the current non-uniform feed phase switch state distribution vector, the optimization variable is the internal phase parameter of each type of subarray when the non-uniform feed phase is turned on; determining the phase optimization objective function based on the optimization variable; solving the phase optimization objective function using a sequential quadratic programming algorithm; and obtaining the optimal internal phase configuration vector corresponding to the current switch state distribution vector of each type of subarray after the solution.

[0015] In one embodiment of the present invention, fixing the updated internal phase configuration vectors of each type of subarray transforms the optimization problem containing only continuous variables into a large-scale 0-1 combinatorial optimization problem, and using a discrete genetic algorithm to solve the updated non-uniform feed phase switch state distribution vector of the entire array. This includes: fixing the current updated optimal internal phase configuration vector; after fixing the current updated optimal internal phase configuration vector, the optimization variable is the non-uniform feed phase switch state distribution vector of the entire array; determining the switch state optimization objective function based on the optimization variable; solving the switch state optimization objective function using a discrete genetic algorithm; and obtaining the optimal non-uniform feed phase switch state distribution vector corresponding to the current internal phase configuration vector of each type of subarray.

[0016] In one embodiment of the present invention, the step of alternately iterating the phase subproblem update and the state subproblem update, and outputting the optimal array architecture parameters based on the alternating iterative solution results, includes: constructing the distribution equation of the normalized scanning radiation energy of the entire array based on the current internal phase configuration vector and the non-uniform feed phase switch state distribution vector;

[0017] Based on the distribution equation of the normalized scan radiation energy of the entire array, the minimum value within the target scan area, the maximum value outside the target scan area, and the global scan energy efficiency are determined. The minimum value within the target scan area, the maximum value outside the target scan area, and the global scan energy efficiency are then weighted to obtain a comprehensive objective function. The change in the comprehensive objective function between two adjacent iterations is calculated. If the change is less than a set threshold or the iteration count reaches the maximum number of iterations, the iteration stops and the optimal array architecture parameters are output; otherwise, the iteration returns to the phase subproblem and continues.

[0018] As described above, the irregular array wide-angle scanning optimization method based on non-uniform phase feeding of the present invention has the following beneficial effects: 1. The present invention eliminates the scanning blind zone: The present invention utilizes the anisotropic complementarity of multiple types of subarrays in azimuth angle scanning, combined with the correction of scanning gain distribution by UFP switching state, effectively solving the problem of a single square subarray in a specific azimuth angle (such as... There is a gain collapse problem;

[0019] 2. This invention improves solution efficiency: For complex mixed-integer nonlinear programming problems, this invention proposes an alternating optimization strategy. Compared with joint global search, this invention significantly reduces computational complexity, thereby enabling the rapid acquisition of approximate optimal solutions that are suitable for large-scale arrays.

[0020] 3. This invention possesses excellent electrical performance indicators: the optimized array performs well within a wide-angle scanning range (e.g., scanning angle reaches...). (At that time), the directional coefficient is maintained above 19 dBi, and the peak sidelobe level is controlled below -12 dB, thus achieving consistency and robustness of full-area scanning. Attached Figure Description

[0021] Figure 1 The diagram shows the effect of applying non-uniform subarray feeding of multiple types of subarrays to an L-shaped subarray in the irregular array wide-angle scanning optimization method based on non-uniform feeding disclosed in the embodiments of the present invention.

[0022] Figure 2 The diagram shows the overall flowchart of the irregular array wide-angle scanning optimization method based on non-uniform phase feeding disclosed in the embodiments of the present invention.

[0023] Figure 3The flowchart shown is a separation optimization strategy based on alternating minimization in the irregular array wide-angle scanning optimization method based on non-uniform feed disclosed in the embodiments of the present invention.

[0024] Figure 4 The diagram shows the UFP switch state distribution and internal phase mapping before and after optimization in the irregular array wide-angle scanning optimization method based on non-uniform phase feeding disclosed in this embodiment of the invention.

[0025] Figure 5 The image shows a comparison of the full array synthesized NSRP distribution before and after optimization in the irregular array wide-angle scanning optimization method based on non-uniform feed disclosed in this embodiment of the invention.

[0026] Figure 6 The diagram shown is the array pattern under a typical wide-angle scanning state in the irregular array wide-angle scanning optimization method based on non-uniform phase feeding disclosed in the embodiments of the present invention.

[0027] Figure 7 The figure shows a comparison curve of the scanning performance parameters (directivity coefficient, peak sidelobe level) of the irregular array wide-angle scanning optimization method based on non-uniform phase feeding disclosed in the embodiments of the present invention with other architectures under different azimuth planes. Detailed Implementation

[0028] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. It should be noted that, unless otherwise specified, the following embodiments and features described herein can be combined with each other.

[0029] This invention relates to an optimization method for wide-angle scanning of irregular arrays based on non-uniform phase feeding, and uses an L-shaped subarray as an example to illustrate the technical mechanism of the invention; Figure 1 (b) demonstrates the L-shaped subarray without the introduction of non-uniform phase feed (i.e., without the introduction of phase extension lines, corresponding to...). Figure 1 (a) shows the scanning performance, where the sampling point values ​​represent the main lobe gain of the subarray in the corresponding direction. It can be seen that, limited by the anisotropy and irregularity of the L-shaped subarray geometry, its gain distribution is uneven at different azimuth angles (different radii from the center); and affected by the relative path difference (RWPD) effect, the gain decreases sharply with increasing pitch angle (different concentric circles from the center outwards); and after introducing non-uniform phase feeding (such as... Figure 1 (c) and Figure 1 (e) shows that the RWPD distribution center shifts from the normal direction, thus forming a differentiated scanning pattern (as shown in the figure). Figure 1 (d) and Figure 1(f) This shows that the scanning envelope of the subarray can be reshaped by adjusting the non-uniform phase feed (UFP) configuration of the subarray;

[0030] The core of this invention lies in the global optimization of the UFP values ​​and switching states of all irregular subarrays on the array surface, and the effective elimination of scanning blind spots by utilizing the performance complementarity between different subarrays. To improve the modularity of engineering implementation, each type of subarray is set to contain only two states: no UFP state (no phase extension line) and optimized UFP state (introducing a specific phase extension line).

[0031] Based on the above principles, this invention provides an array architecture parameter optimization method. This method, given an irregular array configuration, comprehensively utilizes the anisotropic radiation characteristics of multiple types of subarrays (such as L-shaped, T-shaped, Z-shaped, etc.) and the scanning capability correction brought by UFP switches to balance the RWPD distribution of the array at different scanning angles, thereby achieving consistent wide-angle scanning across the entire area. The core of the optimization lies in the collaborative solution of the internal phase configuration (continuous variable) of each type of subarray and the UFP switch state distribution of the entire array (discrete variable).

[0032] To achieve the above objectives, the present invention adopts the following technical solution, the process of which is as follows: Figure 2 As shown, the details are as follows:

[0033] Step 101: Construct a multi-type irregular subarray model and define normalized scanning radiation energy as an evaluation index.

[0034] Specifically, a multi-type irregular subarray model is constructed, and the normalized scan radiation energy (NSRP) is defined as an evaluation index. The normalized scan radiation energy (NSRP) is used to quantify the energy summation efficiency of the subarray in a specific scanning direction, reflecting the gain loss caused by RWPD.

[0035] More specifically, this invention uses the MATLAB software platform to construct a multi-type irregular subarray array model. When constructing the multi-type irregular subarray array model in the software: 1. Establish the basic dimensions and coordinate system of the array: set rows=16, cols=16, indicating that the entire array surface consists of 16×16 array elements; 2. Classify the array elements using subarray_id_matrix: each subarray corresponds to a unique number. The function of this matrix is ​​to establish the "array element-subarray" hierarchical relationship, that is, to determine which subarray each array element belongs to. This step is equivalent to completing the topological partitioning of the irregular subarray array in the software; 3. Specify the type label of each array element in its subarray using type_matrix. The advantage of this representation is that it can distinguish the geometric shape of the subarray and accurately map it to the specific array element inside the subarray when assigning internal phase; 4. Record the rotation direction of each subarray using orientation_matrix, with values ​​of 0, 1, 2, and 3, corresponding to 0°, 90°, 180°, and 270° rotations, respectively.

[0036] Therefore, this model not only simply records the subarray type, but also includes three layers of information: "shape type - internal element number - spatial rotation state," making the multi-type irregular subarray array model fully computable. Based on this model, the subarray distribution of the entire array is analyzed through the function analyze_subarray_distribution. This function takes the aforementioned subarray_id_matrix, type_matrix, orientation_matrix, and the current UFP state distribution ufp_map as input, and records the number of each type of subarray in the array. In this way, when calculating the power distribution later, it is not necessary to repeatedly calculate for each element and each subarray. Instead, it is only necessary to calculate the power distribution once for each representative subarray and then sum it by weight by quantity, thereby significantly reducing the computational complexity.

[0037] It should also be noted that the definition and calculation of NSRP are as follows: In the function `calculate_subarray_power_linear`, the wavenumber is first determined based on the given operating frequency, and then the scanning angle range is discretized to construct direction cosine u and v grids; for a given subarray shape, the position indices of the elements participating in radiation are obtained, and the planar coordinates of each element are calculated in combination with the element spacing. Then, for each scanning direction, the geometric phase term of each array element is calculated. The internal excitation phase is superimposed, and the complex amplitudes of all array elements are summed to obtain the array field pattern in that direction; its square mode abs(pattern).^2 is the linear radiation power of the subarray in that scanning direction;

[0038] In this invention, NSRP can be understood as the scanning radiation capability distribution formed after the linear power is normalized to its peak value. The linear power distribution of all subarray categories is weighted and averaged to obtain the linear radiation power distribution of the array in each scanning direction. Then, it is normalized based on the maximum power of the entire region to obtain a normalized scanning radiation power distribution map in dB form, i.e., the NSRP distribution map. This normalization process evaluates whether good coherent superposition can be maintained inside the subarray under a given scanning direction and how much the scanning capability in that direction has decreased relative to the optimal direction.

[0039] Step 102: Construct an array architecture parameter optimization model based on the non-uniform feed mutual compensation strategy of multiple types of subarrays according to the multi-type irregular subarray array model.

[0040] Specifically, an array architecture parameter optimization model based on a complementary strategy of UFP for multiple types of subarrays is established. The optimization model belongs to the mixed integer nonlinear programming (MINLP) problem. The optimization variables of the optimization model include: (1) continuous variables: the internal phase configuration vector of each type of subarray when UFP is enabled; (2) discrete variables: the distribution vector of the UFP switching state of each subarray in the array (0 indicates UFP is off, 1 indicates UFP is on). The optimization objective of the optimization model is to maximize the minimum value of the full array synthetic normalized scan radiation energy (NSRP) in the target scanning area, while taking into account peak suppression outside the target area and global energy efficiency improvement.

[0041] More specifically, the array architecture parameter optimization model of this invention is also established in the MATLAB software environment. Its establishment is based primarily on three aspects: 1. Different types of irregular subarrays have different NSRP distributions under different scanning directions, thus possessing natural spatial complementarity; 2. The equivalent phase distribution inside the same type of subarray differs between UFP-off and UFP-on states, resulting in different scanning envelopes, thus exhibiting complementarity in operating states; 3. The goal of array wide-angle scanning optimization is not to maximize gain in a single direction, but rather to maximize the performance in the worst-case direction within the target scanning region, suppress abnormally high responses outside the region, and increase the concentration of scanning energy within the target region. Based on these three points, a joint optimization model of "geometric complementarity of multiple types of subarrays + UFP state complementarity + comprehensive evaluation of the target region" is formed.

[0042] The specific optimization model establishment process is as follows: 1. First, it is necessary to define the optimization variables: The optimization variables are divided into two categories: continuous variables and discrete variables. The continuous variables are the internal phase configurations of each type of subarray when the UFP is enabled, namely Phase_L, Phase_T, and Phase_Z. Each type of subarray corresponds to 4 array element internal phases, for a total of 12 continuous variables. The discrete variables are the UFP switching states of all subarrays in the entire array, namely current_state_vector, with a length equal to the total number of subarrays num_subs=64. Each variable can only take the value 0 or 1, where 1 indicates that the subarray is enabled for UFP and 0 indicates that the subarray is in normal feeding state. These two types of variables together determine the final architecture parameters of the array, thus constituting a mixed integer nonlinear programming problem as a whole.

[0043] 2. Next, the objective function needs to be defined: First, based on the current continuous phase and discrete state, the number of various "shape type - rotation direction - UFP state" combinations on the array surface is counted to obtain the data subarray_stats. For each combination, the NSRP calculation is performed using Supplement 2. Thus, any set of optimization variables can be mapped to an NSRP distribution map covering the entire scan area, thereby transforming the array architecture design problem into a clear numerical optimization problem. The specific evaluation method for this NSRP distribution map is divided into several cost components:

[0044] The first term is the minimum lift cost, cost_min_lift. First, all power samples P_inside are extracted within the target optimization region, and the minimum value min_power_inside is calculated. Then, it is normalized using the peak value max_power of the entire region, resulting in normalized_min = min_power_inside / max_power. Subsequently, it is compared with a preset target threshold target_min_ratio = 0.6. If the minimum value is lower than this threshold, a positive cost is generated; otherwise, the cost is zero. In this way, the optimization process prioritizes lifting the worst scanning direction in the target region, thereby eliminating blind spots.

[0045] The second term is the out-of-band suppression cost, cost_side_suppress. First, the average power within the target region, mean_power_inside, is calculated, and then the maximum power outside the target region, max_power_outside, is calculated. The ratio of the two is used as the out-of-band suppression index, reflecting whether there is an excessively strong response outside the target scanning region. The third term is the energy efficiency cost, cost_efficiency, which is defined as 1-efficiency, where efficiency = total_power_inside / total_power_all, used to measure what proportion of the total scanning energy is concentrated within the target optimization region. Finally, the three terms are linearly combined using weights w_min_lift = 4.0, w_side_suppress = 3.0, and w_efficiency = 3.0 to obtain the total cost function, score. The smaller the total cost, the better the optimization result.

[0046] Step 103: The array architecture parameter optimization model is solved using a separation optimization strategy based on alternating minimization. The optimal array architecture parameters are output based on the solution results, and beam scanning is performed based on the optimal array architecture parameters to obtain excellent wide-angle scanning performance.

[0047] Specifically, a separation optimization strategy based on alternating minimization is used to solve the array architecture parameter optimization model. This strategy decomposes the original mixed-integer nonlinear programming (MINLP) problem into two subproblems for alternating iterative solutions: Subproblem I: With the current UFP switch state distribution fixed, the Sequential Quadratic Programming (SQP) algorithm is used to optimize the internal phase configuration of each type of subarray; Subproblem II: With the current internal phase configuration fixed, the Discrete Genetic Algorithm (Discrete GA) is used to optimize the UFP switch state distribution of the entire array. Finally, the optimal array architecture parameters are output. These optimal parameters include the optimal internal phase configuration vectors of each type of subarray and the optimal UFP switch state distribution vector of the entire array. Based on these parameters, excellent wide-angle scanning performance can be obtained during beam scanning.

[0048] Furthermore, to further explain steps 101 to 103 above, the key to this invention lies in the anisotropy and complementarity of multiple types of subarrays, and the subarray scanning gain correction brought about by the introduction of UFP. The specific process is as follows:

[0049] 1. Definition and Optimization Objective of NSRP: In a subarray architecture, due to the lack of independent phase shifting capability within the subarray, there is an error between the actual feed phase and the ideal scanning phase gradient, namely, the relative path difference (RWPD). The relative path difference (RWPD) causes the main lobe of the subarray pattern to deviate, resulting in gain loss. To quantify this loss, this invention introduces NSRP as an evaluation index. Each subarray, in the scanning direction The NSRP definition on the above is: ,in, The number of array elements within the sub-array. For the first in the sub-array For each array element's RWPD (considering the introduced UFP internal phase), the lower the NSRP value, the greater the gain loss.

[0050] The optimization objective of this invention is to adjust the array architecture parameters (internal phase configuration) within the target scanning area. and UFP switch state distribution This aims to make the NSRP distribution of the entire array synthesis as flat as possible and its value as high as possible, thus eliminating the "weakest link" effect; specifically, the three components of the objective function are: the minimum value within the target scanning region... (Maximize to eliminate blind spots in the target area scan), maximum value outside the target scan area. (Minimize to suppress leakage energy peaks outside the target region), and global scan energy efficiency. (To maximize the proportion of scanning energy in the target area), where, These are the array architecture parameters.

[0051] 2. Separation Optimization Strategy Based on Alternating Minimization: To determine the optimal array architecture parameters, this invention constructs a mixed-integer nonlinear programming problem. Considering the large problem size and the difficulty of direct solution, this invention proposes a separation optimization strategy based on alternating minimization, such as... Figure 3 As shown, the algorithm flow is as follows:

[0052] 1) Initialization: Randomly initialize the UFP switch state distribution vector and internal phase configuration vector Set the iteration count ;

[0053] 2) Phase subproblem update (Step 1): Fix the current switch state distribution vector The original mixed-integer nonlinear programming problem is transformed into an optimization problem with only continuous variables, and the Sequential Quadratic Programming (SQP) algorithm is used to solve for the updated internal phase configuration vector. The specific process is as follows (corresponding to) Figure 3 Sub-problem I (process)

[0054] 21) Fix the current switch state distribution vector : in the In this iteration, the current UFP switch state is determined by the state vector. Given that the 64 subarrays in this embodiment can be represented as: ,in, Indicates the first UFP state of each subarray This indicates that UFP is enabled. This indicates that the UFP is disabled; based on the current state vector. A mapping relationship between subarray numbers and UFP states is established. Combined with the array's subarray number matrix, subarray type matrix, and rotation direction matrix, the distribution of various types of subarrays on the array is statistically analyzed, yielding the following results: The statistics record the number of each "subarray type - rotation direction - UFP state" combination in the array; for example, L_O0_UFP1 represents the number of L-shaped subarrays with UFP enabled at 0°; T_O1_UFP0 represents the number of T-shaped subarrays with UFP disabled at 90°; due to the state vector Since the variables are fixed, the above statistics remain unchanged throughout the phase optimization process, thus fixing the discrete variables in the original problem and retaining only the continuous phase variables for optimization.

[0055] 22) Set optimization variables Fixed state vector Then, the optimization variables are the internal phase parameters of various subarrays when UFP is enabled, totaling 12 continuous variables, which can be expressed as: ,in: , , Let L, T, and Z represent the internal phase configurations of the L-shaped, T-shaped, and Z-shaped subarrays respectively in the UFP-enabled state; at this time, the phase optimization objective function can be expressed as: That is, in the current state vector Under fixed conditions, by adjusting the 12-dimensional internal phase vector This optimizes the overall scanning performance of the array in the target scanning area.

[0056] 23) Solving with SQP algorithm: Under a fixed state vector Then, the phase optimization problem can be expressed as: The constraints are satisfied: ,in, and The upper and lower boundaries of the internal phase variables are represented respectively. The fmincon function in MATLAB and the SQP algorithm are used to solve the problem. The working mechanism of the SQP algorithm can be summarized as follows: In each iteration, the original objective function is first approximated twice near the current phase point, and the constraints are linearized to construct a local quadratic programming subproblem. Then, the quadratic programming subproblem is solved to obtain the search direction and step size. The phase variables are then updated accordingly to gradually approach the local optimum. Since the number of continuous variables in this invention is small, and the variable boundaries are clear and the objective function is continuous and computable, SQP is suitable for fast solution in this stage.

[0057] 24) Calculate the updated phase vector Once the SQP algorithm converges, the current state vector is obtained. The corresponding optimal internal phase configuration: ,Right now: ,in, , and These represent the optimal internal phase configuration vectors corresponding to the L-shaped, T-shaped, and Z-shaped subarrays, respectively; [The following is a separate, unrelated sentence:] ... Then, it is used as the input parameter for subproblem II for subsequent UFP switch state distribution optimization.

[0058] 3. State Subproblem Update (Step 2): Fix the updated internal phase vector The problem is transformed into a large-scale 0-1 combinatorial optimization problem, and solved using a discrete genetic algorithm (Discrete GA) to obtain the updated switch state vector. The specific process is as follows (corresponding to) Figure 3 Sub-problem II process):

[0059] 31) Fix the current internal phase vector In subproblem II, the optimal internal phase vector obtained in the previous stage is... Given the optimal phases of three types of subarrays in the UFP-enabled state: ,in: , , These three sets of internal phases remain fixed in this stage and will not participate in subsequent optimizations.

[0060] 32) Set optimization variables After fixing the continuous phase variables in the optimization problem, the optimization variable becomes the state vector of the entire array UFP switches. ,in, Indicates the first Each sub-unit activates UFP. This indicates that the UFP is off; thus, the original hybrid optimization problem, which simultaneously involved continuous phase and discrete switching, is transformed into a combinatorial optimization problem focusing only on the discrete UFP switching states; for any candidate state vector First, establish the mapping relationship between "subarray number - UFP state": ufp_map=containers.Map(unique_ids,s); then, combining the subarray type matrix, rotation direction matrix, and the current candidate UFP state, count the number of each "subarray type - rotation direction - UFP state" combination to obtain the statistics: For example, if some L-shaped subarrays facing 180° in a candidate solution have UFP enabled, the count of the corresponding field L_O2_UFP1 increases; if some Z-shaped subarrays facing 270° have UFP disabled, the count of the corresponding field Z_O3_UFP0 increases; fixed internal phase Then, the objective function for optimizing the switching states can be expressed as:

[0061] 33) Solution using Discrete Genetic Algorithm: The discrete GA optimization problem can be expressed as: The GA function is used in the MATLAB Global Optimization Toolbox: intcon=1:64; lb=zeros(1,64); ub=ones(1,64); options=optimoptions('ga','Display','off','PopulationSize',100,'MaxGenerations',200);

[0062] 34) Calculate the updated switch state vector The current internal phase vector is obtained after GA convergence. The corresponding optimal UFP switch state: ,Will As the input to Step 1 of the next iteration, the alternating optimization loop continues until the entire alternating minimization algorithm converges.

[0063] Before determining convergence, it is necessary to explain the fitness function used in the optimization process. , and joint objective function The calculation method is as follows: 1. Fitness composition: In each phase or state optimization phase, firstly, based on the current internal phase vector and UFP state vector Constructing a full array of NSRP distributions: ;in, The number of subarrays is counted. The corresponding field in the middle; This represents the normalized scan radiation energy of the subarray under a given internal phase. , The scanning angle range;

[0064] 2. Local index calculation: 1) Minimum value within the target scanning area: ; ; TARGET_MIN_RATIO sets the minimum acceptable ratio relative to the maximum NSRP. In this invention, it is set to 0.6, meaning that if the minimum value within the target area is less than 0.6 of the global maximum value, a positive cost is incurred; 2) Maximum value suppression outside the target scanning area: ; 3) Global scan energy efficiency: ;

[0065] 3. Total Cost Function: The total fitness is obtained by weighting the above indicators according to their respective weights. ;in, , , and Set them to 0.4, 0.3 and 0.3 respectively (manual parameter adjustment) to ensure that the three local indicators are taken into account and balanced;

[0066] 4. Convergence criterion: In the first... After completing Step 1 and Step 2 in the next iteration, first calculate the change in the objective function. ,in, Indicates the first The comprehensive objective function value corresponding to the next iteration includes the total cost after weighting the minimum value of the target region, peak suppression, and global energy efficiency. Indicates the first The comprehensive objective function value after the next iteration; then the change... With preset convergence threshold (In this invention, it is set as follows) ) compare, if or reaching the maximum number of iterations. (Set to 200 in this invention) indicates that the algorithm has converged, the iteration has stopped, and the current optimal internal phase vector has been output. and the optimal UFP switch state vector : , Otherwise, let Return to Step 1 to continue the next iteration.

[0067] In practical applications, the following specific embodiment further illustrates the actual application process of the present invention. This embodiment takes a 16×16 element multi-type quadrature lattice irregular array as the overall object, and focuses on the L-shaped quadrature subarray as the representative, to illustrate how the irregular array wide-angle scanning optimization technology based on non-uniform phase feeding completes modeling, solving, and verification in practical applications. In this embodiment, the entire array surface consists of 16×16 elements, totaling 256 elements, with an operating frequency of 30GHz, corresponding to a wavelength of 10mm, and an element spacing of 0.5λ. The array surface is divided into 64 quadrature subarrays in a quadrature lattice manner, and each subarray is uniquely numbered by subarray_id_matrix. The subarray types include L-shaped, T-shaped, and Z-shaped, and each subarray also has 4 possible rotation orientations, which are recorded by orientation_matrix. To describe the position of the array elements inside the subarray, type_matrix is ​​used to mark each array element. For example, the four array elements inside the L-shaped subarray are denoted as L1, L2, L3, and L4 respectively. For the L-shaped subarray, its basic geometry is represented in the code as Shape_L=[111;100], which means that there are three array elements in the first row and one array element on the left side of the second row, forming a typical L-shaped structure.

[0068] In practical applications, the above array topology model is first established in MATLAB, and the scanning angle sampling range is set. The calculation range for the entire region is theta∈[-90°,90°] and phi∈[-90°,90°], with 181 sampling points for each region. The target optimization region (wide-angle range) is theta∈[-60°,60°] and phi∈[-90°,90°]. This allows for the calculation of the radiation power across the entire scanning spherical range, but the performance uniformity within the wide-angle scanning target region is the primary focus. Subsequently, a set of 4-dimensional internal phases is initialized for each of the L-shaped, T-shaped, and Z-shaped subarrays as the initial phase configuration for the UFP in the on state. Simultaneously, the initial UFP switching states of 64 subarrays are randomly generated, with approximately 50% of the subarrays in the on state. Taking the L-shaped subarray as an example, if the state of an L-shaped subarray is 1, it means that its four internal array elements introduce the corresponding L-shaped internal phase vector; if the state is 0, it means that its four internal array elements are all fed with zero-phase power.

[0069] In the benchmark verification phase, all subarrays are initially set to UFP (Unified Phase Filtering) off, constructing a "UFP-off" benchmark array. Under this condition, the L-shaped subarray is scanned without any additional phase compensation, relying solely on its geometry. The normalized scan radiation power distribution of this benchmark array is calculated, and the normalized minimum, inside-outside power ratio, and energy efficiency within the optimized region are output. For the L-shaped subarray, this step is equivalent to obtaining its baseline scan envelope under conditions without UFP compensation. It is typically observed that as the elevation angle increases, the NSRP (Negative Radiated Power Distribution) of the L-shaped subarray decreases significantly due to the increase in RWPD (Rapid Wave Power Distribution), and lower value regions are formed in certain azimuth directions.

[0070] The alternating optimization process of this invention then begins: First, the UFP state distribution on the current array surface is fixed, and SQP optimization is performed on the internal phases of the three types of subarrays. Taking the L-shaped subarray as an example, its four internal phase variables are incorporated into a 12-dimensional continuous optimization vector and solved together with the T-shaped and Z-shaped subarrays. Each time the objective function is called, the L-shaped subarray is divided into two cases: different rotation orientations and different UFP states. If a group of L-shaped subarrays currently has UFP enabled, the rotate_phase function is called to rearrange the L-shaped phase vector according to its rotation direction, and then its power distribution is calculated together with the rotated L-shaped structure to ensure that the correspondence between the array elements and the specific UFP configuration is accurate. If the group of L-shaped subarrays has UFP disabled, its power distribution is calculated directly using the zero-phase vector. After SQP optimization, a set of L-shaped internal phases that are more suitable for the current state distribution is obtained. The physical meaning of this phase is that it can shift the high-gain region of the L-shaped subarray during wide-angle scanning to the originally weaker direction, thereby enhancing the compensation capability for the low NSRP region.

[0071] After obtaining the optimized internal phase, the phase is kept fixed, and the discrete genetic algorithm optimization stage begins. At this point, the algorithm needs to decide whether to enable UFP for each L-shaped, T-shaped, and Z-shaped subarray on the array surface. Taking the L-shaped subarray as an example, if enabling UFP for a certain L-shaped subarray under the current fixed phase can significantly improve the NSRP of its corner domain, the genetic algorithm will tend to keep its state at 1. Conversely, if the L-shaped subarray is more conducive to reducing the overall cost of the array when it is closed, its state may be optimized to 0. Since the state optimization is based on the overall effect of the array, the final result is not that all L-shaped subarrays are uniformly enabled or disabled, but rather that a non-uniform distribution is formed that is coordinated with the position, rotation orientation, and other types of subarrays.

[0072] In this embodiment, after approximately 5 to 10 rounds of alternating optimization (depending on the initialization method), convergence is achieved, outputting the final optimal state distribution and optimal internal phase. Furthermore, the optimization results are mapped to an element-level internal phase matrix, allowing a clear view of which subarrays are in the active state and the corresponding phase values ​​for their four internal elements. Figure 4 (b) shows that the UFP activation rate on the array surface is about 64.1%, indicating that not all subarrays need to introduce phase compensation, but global performance balance is achieved by partially turning on and partially turning off. For the L-shaped subarray, its optimized role is no longer to improve the subarray gain in a certain direction in isolation, but to form a multi-mode complementary architecture together with the T-shaped and Z-shaped subarrays.

[0073] During the performance verification phase, NSRP distribution diagrams were plotted before and after optimization, as follows: Figure 5 As shown in the figure; the results show that, compared with the UFP fully off reference array, the array optimized by this invention significantly shrinks the low-value region within the target scanning area and significantly increases the normalized minimum value, indicating that the original weak scanning direction has been effectively compensated; at the same time, the abnormally high response outside the region is suppressed, indicating that there is no significant out-of-band deterioration caused by the in-band improvement. Further radiation pattern simulation shows that, under typical wide-angle scanning conditions, such as when the scanning elevation angle reaches 60°, the directivity coefficient of the optimized array can still be maintained above 19dBi, the peak sidelobe level is controlled below -12dB, and the performance on different azimuth sections is more consistent, such as Figure 6 As shown.

[0074] It should also be noted that the implementation results analysis was conducted using a simulation verification based on a 16×16 element quadruple lattice (L / T / Z-shaped) irregular array: 1. Optimized UFP distribution: as shown in the figure. Figure 4 As shown, after alternating optimization, the array surface exhibits a specific non-uniform distribution state; the activation rate of the subarray UFP is approximately 64.1%, which means that some subarrays are configured to introduce additional internal phase delay (on state), while others maintain the traditional feeding state (off state); this mixed distribution reflects the algorithm's automatic trade-off and balance between "improving large-angle scanning capability" and "maintaining small-angle gain";

[0075] 2. Comparison of NSRP before and after optimization: such as Figure 5 As shown, before optimization ( Figure 5 (a): The NSRP distribution is extremely uneven, especially in the large pitch angle region where there is a significant low-value area (dark blue area), indicating severe scanning gain loss in this region; after optimization ( Figure 5 (b) The NSRP coverage within the target scanning area was significantly improved, with low-value areas being greatly enhanced and the overall distribution becoming flatter and more uniform. This indicates that the scanning blind zone was successfully eliminated through the complementarity of multiple subarray types and UFP states;

[0076] 3. Wide-angle scanning effect and electrical performance indicators: Based on the optimized array architecture parameters, beamforming simulation of the array is performed to verify its actual electrical performance; such as Figure 6The scan pattern shown, and Figure 7 The performance parameter curves shown indicate that under wide-angle scanning conditions (e.g., scanning to the pitch angle), The architecture proposed in this invention is shown in different azimuth angle sections. The results show excellent consistency across the entire spectrum. Specifically: 1) Directivity: Throughout the wide-angle scanning range, the directivity coefficient remains above 19 dBi. Compared to architectures without a UFP and single square subarray UFP architectures, this invention exhibits the slowest gain attenuation and the widest effective scanning area at large angles; 2) Peak Sidelobe Level (PSLL): Throughout the full scanning range, the PSLL is consistently controlled below -12 dB, with some angles exceeding -14 dB. No malignant grating lobes or abnormally high sidelobes were observed, demonstrating the effectiveness of this optimization technique in suppressing sidelobe elevation.

[0077] In summary, this invention significantly improves the wide-angle scanning performance of large-scale irregular arrays through its original multi-type subarray UFP complementary strategy and efficient alternation optimization algorithm, providing a new technical approach for the design of high-performance phased array antennas.

[0078] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. All equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this invention should still be covered by the claims of this invention.

Claims

1. A method for optimizing wide-angle scanning of irregular arrays based on non-uniform phase feeding, characterized in that, Includes the following steps: A multi-type irregular subarray model is constructed, and normalized scanning radiation energy is defined as an evaluation index, wherein the normalized scanning radiation energy is used to reflect the gain loss caused by the relative path difference; Based on the multi-type irregular subarray array model, an array architecture parameter optimization model based on the multi-type subarray non-uniform feed mutual compensation strategy is constructed. The optimization variables in the array architecture parameter optimization model include continuous variables and discrete variables. The continuous variables are the internal phase configuration vectors of each type of subarray when the non-uniform feed phase state is turned on, and the discrete variables are the non-uniform feed phase switching state distribution vectors of each subarray in the array. The array architecture parameter optimization model is solved using a separation optimization strategy based on alternating minimization. The optimal array architecture parameters are output based on the solution results, and beam scanning is performed based on the optimal array architecture parameters to obtain excellent wide-angle scanning performance. The optimal array architecture parameters include the optimal internal phase configuration vector of each type of subarray and the optimal non-uniform feed phase switch state distribution vector of the entire array. The array architecture parameter optimization model belongs to the mixed integer nonlinear programming problem. In the process of solving the array architecture parameter optimization model using the separation optimization strategy based on alternating minimization, the separation optimization strategy decomposes the mixed integer nonlinear programming problem into two sub-problems for alternating iterative solution. The process employs a separation optimization strategy based on alternating minimization to solve the array architecture parameter optimization model, and outputs the optimal array architecture parameters based on the solution results, including: Randomly initialize the non-uniform phase feed switch state distribution vector, internal phase configuration vector, and iteration count; Phase subproblem update: Fix the current non-uniform feed phase switch state distribution vector, transform the original mixed integer nonlinear programming problem into an optimization problem containing only continuous variables, and use the sequential quadratic programming algorithm to solve the updated internal phase configuration vector of each type of subarray; State subproblem update: Fix the updated internal phase configuration vector of each type of subarray, transform the optimization problem containing only continuous variables into a large-scale 0-1 combinatorial optimization problem, and use a discrete genetic algorithm to solve the updated non-uniform feed phase switch state distribution vector of the entire array; The phase subproblem update and the state subproblem update are solved iteratively and alternately. The optimal array architecture parameters are output based on the results of the alternating iteration.

2. The irregular array wide-angle scanning optimization method based on non-uniform phase feeding according to claim 1, characterized in that: The definition of normalized scan radiation energy as an evaluation index includes: For the An irregular subarray, which in the scanning direction The normalized scan radiation energy is defined as: ； in, The number of array elements within the subarray; For the first in the sub-array The relative path difference of each array element; the normalized scan radiation energy decreases monotonically as the gain loss caused by the relative path difference increases.

3. The irregular array wide-angle scanning optimization method based on non-uniform phase feeding according to claim 1, characterized in that: The optimization objective of the array architecture parameter optimization model is to maximize the minimum normalized scan radiation energy synthesized by the entire array within the target scanning region by adjusting the array architecture parameters, while also taking into account peak suppression and global energy efficiency improvement outside the target scanning region. The array architecture parameters include continuous and discrete variables among the optimization variables.

4. The irregular array wide-angle scanning optimization method based on non-uniform phase feeding according to claim 1, characterized in that: The fixed current non-uniform feed phase switch state distribution vector transforms the original mixed-integer nonlinear programming problem into an optimization problem containing only continuous variables. A sequential quadratic programming algorithm is then used to solve for the updated internal phase configuration vectors of each type of subarray, including: The current non-uniform feed phase switch state distribution vector is fixed, and after fixing the current non-uniform feed phase switch state distribution vector, the optimization variable is the internal phase parameter when the non-uniform feed phase of each type of subarray is turned on. The phase optimization objective function is determined according to the optimization variable. The phase optimization objective function is solved using a sequential quadratic programming algorithm, and the optimal internal phase configuration vector corresponding to the current switching state distribution vector of each type of subarray is obtained from the solution.

5. The irregular array wide-angle scanning optimization method based on non-uniform phase feeding according to claim 4, characterized in that: The fixed, updated internal phase configuration vectors of each type of subarray transform the optimization problem containing only continuous variables into a large-scale 0-1 combinatorial optimization problem. A discrete genetic algorithm is then used to solve the updated non-uniform feed phase switch state distribution vector of the entire array, including: The current updated optimal internal phase configuration vector is fixed, and after fixing the current updated optimal internal phase configuration vector, the optimization variable is the full array non-uniform feed phase switch state distribution vector, and the switch state optimization objective function is determined according to the optimization variable; The objective function is optimized based on the switching state and solved using a discrete genetic algorithm. The optimal non-uniform feed phase switching state distribution vector corresponding to the current internal phase configuration vector of each type of subarray is obtained from the solution.

6. The irregular array wide-angle scanning optimization method based on non-uniform phase feeding according to claim 5, characterized in that: The step of alternately iterating through the phase subproblem update and the state subproblem update, and outputting the optimal array architecture parameters based on the results of the alternate iterations, includes: The normalized scanning radiation energy distribution equation for the entire array is constructed based on the current internal phase configuration vector and the non-uniform phase feed switch state distribution vector. The minimum value within the target scanning area, the maximum value outside the target scanning area, and the global scanning energy efficiency are determined based on the distribution equation of the normalized scanning radiation energy of the entire array. The minimum value within the target scanning area, the maximum value outside the target scanning area, and the global scanning energy efficiency are then weighted according to their respective weights to obtain a comprehensive objective function. Calculate the change in the combined objective function between two consecutive iterations. If the change is less than a set threshold or the iteration count reaches the maximum number of iterations, stop the iteration and output the optimal array architecture parameters; otherwise, return to the phase subproblem and continue iterating.

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