Method for synthesizing directional pattern of movable antenna array based on improved fish eagle optimization algorithm

Abstract

The application provides a movable antenna array pattern synthesis method based on an improved fish eagle optimization algorithm, converts antenna positions and antenna weights into a joint variable vector, improves an update strategy on the basis of an original fish eagle optimization algorithm, introduces global search exploration based on levy flight in a first stage, and adds an adaptive probability mechanism to dynamically guide a search scheme for selecting between a global optimal value and a same-generation optimal value to strengthen exploration diversity, adopts Gaussian disturbance in a second stage to perform local fine exploration and dynamically attenuate an update step to further optimize a solution in the first stage, prevent premature convergence, and be applied to a pattern synthesis problem in a movable antenna array, consider engineering practical constraints such as a minimum spacing between antenna arrays and a maximum aperture range, and can effectively realize target enhancement, interference suppression and various practical application scenarios such as a shaped beam.

Description

Technical Field

[0001] This application relates to the field of array signal processing, and in particular to a method for pattern synthesis of movable antenna arrays based on an improved Osprey optimization algorithm. Background Technology

[0002] In key technology fields such as modern communication, radar detection, and electronic countermeasures, antenna arrays, as core signal transceiver units, directly determine the system's target detection accuracy, positioning accuracy, and anti-interference capability through their overall radiation pattern performance. This is one of the core factors affecting the overall system effectiveness. Traditional antenna arrays mostly employ fixed element layout designs, and their radiation pattern synthesis process primarily relies on optimizing and adjusting the amplitude and phase weights of the elements to achieve main lobe gain enhancement, side lobe level suppression, and suppression of signals from specific interference directions.

[0003] However, the spatial control freedom of the radiation pattern is greatly constrained by the fixed array structure: on the one hand, the positional distribution of the fixed array elements determines the effective utilization boundary of the array aperture, making it difficult to overcome the performance bottleneck caused by the spatial configuration through weight optimization; on the other hand, facing increasingly stringent application requirements such as multi-source interference in complex electromagnetic environments, wideband adaptation, and high-resolution beamforming, the traditional method of simply relying on weight adjustment often falls into performance saturation and cannot simultaneously meet the optimization requirements of multiple indicators such as main lobe gain, side lobe suppression, and interference null depth, which has obvious limitations in practical engineering applications.

[0004] To overcome the performance bottlenecks of traditional fixed antenna arrays, movable antenna arrays (MAAs) have emerged due to their core characteristic of dynamically adjustable element positions, providing a new technical path for flexible array pattern reconstruction and performance enhancement. By jointly optimizing the spatial positions of elements and complex excitation weights, MAAs can fully exploit the optimization potential of the spatial dimension with limited aperture resources, significantly improving pattern flexibility, interference suppression capabilities, and aperture utilization efficiency, thus becoming an important research direction for solving array performance optimization problems in complex scenarios.

[0005] However, it is important to note that the joint optimization problem of movable antenna arrays exhibits significant complexity: First, the coupling relationship between element positions and excitation weights makes the objective function strongly non-convex, resulting in numerous local optima. Second, the optimization variables include the element position coordinates and the real and imaginary parts of the weights, leading to high problem dimensionality and a large solution space. Third, the optimization process must simultaneously satisfy multiple constraints such as element aperture range, minimum spacing (to prevent element coupling), weight normalization, and interference direction suppression, further increasing the difficulty of solving the problem. Traditional analytical methods and gradient-based optimization algorithms, limited by their own solution mechanisms, struggle to effectively handle such complex optimization problems with high dimensionality, non-convexity, and multiple constraints. They often suffer from slow convergence speed, susceptibility to local optima, and poor constraint handling, failing to fully leverage the structural advantages of movable antenna arrays.

[0006] The Osprey Optimization Algorithm (OOA), inspired by the hunting behavior of ospreys in nature, mathematically models two core stages: global search and local exploitation. It boasts advantages such as simple structure, few control parameters, and strong global search capability. Compared to traditional intelligent optimization algorithms, OOA exhibits superior search performance in handling some non-convex optimization problems and has been initially applied in several engineering optimization fields with good results, providing a potential solution for the joint optimization problem of movable antenna arrays. However, our research team found that the original Osprey Optimization Algorithm still has significant shortcomings when applied to the application scenario of movable antenna array patterns: when facing complex optimization scenarios with high dimensions and multiple constraints, its step size update mechanism in the global search stage lacks randomness and adaptability, causing the algorithm to easily get trapped in local optima and making it difficult to explore the globally optimal region; simultaneously, the search accuracy in the local exploitation stage is insufficient, making it difficult to balance convergence speed and convergence accuracy. This results in insufficient stability when dealing with problems like movable antenna array pattern synthesis, which have stringent accuracy requirements for solutions.

[0007] Therefore, in view of the performance bottleneck of traditional fixed array pattern synthesis methods, the difficulty of solving the joint optimization problem of movable antenna arrays, and the inherent defects of the original Osprey optimization algorithm, it is urgent to propose a technical solution that combines an improved optimization algorithm with movable antenna array pattern synthesis in order to achieve a comprehensive improvement in array performance under complex electromagnetic environments. Summary of the Invention

[0008] This application provides a method for pattern synthesis of a movable antenna array based on an improved Osprey optimization algorithm. The improved Osprey optimization algorithm is used for generating patterns of movable antenna arrays, effectively solving the problems of easy getting trapped in local optima, slow convergence speed, and difficulty in constraint handling in existing pattern synthesis methods, and improving the pattern synthesis performance of movable antenna arrays in complex electromagnetic environments.

[0009] In a first aspect, embodiments of this application provide a method for pattern synthesis of a movable antenna array based on an improved Osprey optimization algorithm, comprising the following steps:

[0010] S1: Construct a one-dimensional movable antenna array model, in which multiple adjustable array elements in the one-dimensional movable antenna array model are arranged in a continuous linear aperture interval of a preset length;

[0011] S2: Initialize the osprey population and define the fitness of each osprey individual and set the objective function. Each osprey individual corresponds to a joint variable vector composed of the array element position, the real part and the imaginary part of the complex weight. The fitness of each osprey individual is the sum of the minimum value of the pattern gain term and the weighted penalty term. The objective function is to minimize the fitness of the osprey individual.

[0012] S3: Iteratively search the osprey population until the iteration conditions are met to output the final global optimum. In the global search phase of each iteration, a random step size is generated through the Levy flight mechanism and the osprey individual position is updated by combining the dynamic factor of target selection and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum. In the local search phase of each iteration, a Gaussian perturbation mechanism is used to search in the vicinity of the current global optimum. The osprey individual position is updated by combining the dynamic convergence step size strategy and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum.

[0013] S4: Draw the radiation pattern of the movable antenna array based on the final global optimal solution.

[0014] Secondly, embodiments of this application provide an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute a movable antenna array pattern synthesis method based on an improved Osprey optimization algorithm.

[0015] Thirdly, embodiments of this application provide a readable storage medium storing a computer program, the computer program including program code for controlling a process to execute the process, the process including the described movable antenna array pattern synthesis method based on the improved Osprey optimization algorithm.

[0016] The main contributions and innovations of this invention are as follows:

[0017] This invention introduces a movable antenna array structure into the pattern synthesis problem for the first time, significantly improving the flexibility and accuracy of array beamforming by combining a collaborative optimization mechanism of position variables and complex excitations. Furthermore, this invention innovatively introduces a two-stage search framework combining the Levy flight mechanism and Gaussian local perturbations, based on the update strategy of the traditional Osprey optimization algorithm. This enhances the diversity of solutions and improves the convergence rate and precision. Experimental results show that the proposed scheme based on the Improved Osprey Optimization Algorithm (IOOA) achieves higher maximum target gain and lower interference response in typical multi-target pattern synthesis tasks, outperforming existing heuristic and alternating optimization methods. In addition, simulations were conducted for discretized phase-only multi-beam and flat-top shaped beamforming, verifying the feasibility of IOOA in the pattern synthesis problem of MA arrays.

[0018] In other words, this scheme transforms antenna position and antenna weight into a joint variable vector. Based on the original Osprey optimization algorithm, it improves the update strategy. In the first stage, it introduces a global search exploration based on Levy flight and adds an adaptive probability mechanism to dynamically guide the search scheme between the global optimum and the peer optimum to enhance the exploration diversity. In the second stage, it uses Gaussian perturbation for local refinement exploration and dynamically attenuated update step size to further optimize the solution in the first stage to prevent premature convergence. It is applied to the pattern synthesis problem in mobile antenna arrays, taking into account engineering constraints such as minimum spacing between antenna arrays and maximum aperture range. It can effectively realize practical application scenarios such as target enhancement, interference suppression, and various shaped beams.

[0019] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0021] Figure 1 These are comparison diagrams of null patterns for single beams under different algorithms.

[0022] Figure 2 This is a comparison of null patterns of dual beams under different algorithms.

[0023] Figure 3 This is a comparison of discrete phase-only multibeam patterns under different algorithms.

[0024] Figure 4The figure shows the experimental results of the flat-top wide beam and cosecant square beam of the algorithm of this invention.

[0025] Figure 5 This is a performance comparison chart under different population sizes.

[0026] Figure 6 This is a performance comparison chart for different number of iterations.

[0027] Figure 7 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0028] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0029] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0030] Example 1

[0031] This solution provides a method for pattern synthesis of a movable antenna array based on an improved Osprey optimization algorithm, including the following steps:

[0032] S1: Construct a one-dimensional movable antenna array model, in which multiple adjustable array elements in the one-dimensional movable antenna array model are arranged in a continuous linear aperture interval of a preset length;

[0033] S2: Initialize the osprey population and define the fitness of each osprey individual and set the objective function. Each osprey individual corresponds to a joint variable vector composed of the array element position, the real part and the imaginary part of the complex weight. The fitness of each osprey individual is the sum of the minimum value of the pattern gain term and the weighted penalty term. The objective function is to minimize the fitness of the osprey individual.

[0034] S3: Iteratively search the osprey population until the iteration conditions are met to output the final global optimum. In the global search phase of each iteration, a random step size is generated through the Levy flight mechanism and the osprey individual position is updated by combining the dynamic factor of target selection and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum. In the local search phase of each iteration, a Gaussian perturbation mechanism is used to search in the vicinity of the current global optimum. The osprey individual position is updated by combining the dynamic convergence step size strategy and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum.

[0035] S4: Draw the radiation pattern of the movable antenna array based on the final global optimal solution.

[0036] This scheme introduces a movable antenna array structure into pattern synthesis. By jointly optimizing the element positions and complex excitation weights, compared to the traditional fixed array approach that only optimizes weights, this scheme significantly improves the spatial control freedom of the pattern, enabling the exploitation of more performance potential with limited aperture resources and adapting to complex scenario requirements. Furthermore, this scheme constructs a two-stage search strategy within the traditional Osprey optimization algorithm: a Levy flight global search and a Gaussian perturbation local search. The Levy flight mechanism enhances the ability to escape local optima globally, while the Gaussian perturbation combined with a dynamically decreasing step size achieves refined local search. The synergy of these two approaches allows the improved Osprey optimization algorithm to possess both breadth and depth exploration capabilities.

[0037] In step S1, this scheme constructs a one-dimensional movable antenna array model. The one-dimensional linear array (array elements are distributed along a single straight line) can achieve core functions such as target direction gain enhancement, interference direction nulling, and sidelobe suppression by adjusting the array element positions and excitation weights.

[0038] Specifically, this scheme arranges N adjustable array elements within a continuous linear aperture interval of length L. The number of array elements N directly determines the degrees of freedom of the one-dimensional movable antenna array model. By changing the relative positions of the adjustable array elements within the aperture interval, the effective aperture and element spacing distribution of the one-dimensional movable antenna array can be dynamically adjusted, thereby unlocking more performance potential.

[0039] In some embodiments, the length of the continuous linear aperture interval and the number of adjustable array elements are set so that multiple adjustable array elements are arranged within a continuous linear aperture interval of a preset length.

[0040] In some embodiments, the pattern gain is constructed based on the element position vector and the complex weight vector.

[0041] In some embodiments, the element position vector represents the arrangement of multiple adjustable elements along a continuous linear aperture interval. Specifically, the position of the nth adjustable element is set as x.n ,in Then the element position vector of the current one-dimensional movable antenna array is Where R represents a real number and satisfies physical constraints .

[0042] In some embodiments, the complex weight vector is a core vector that quantizes the excitation signal parameters of each tunable element in a one-dimensional movable antenna array, wherein the complex weight vector includes the excitation amplitude in the real part and the excitation phase in the imaginary part.

[0043] Specifically, the excitation amplitude of the real part represents the excitation signal strength of the nth adjustable element. By adjusting the excitation amplitude of different adjustable elements, the distribution of radiated energy of each adjustable element can be controlled. For example, increasing the excitation amplitude of the element corresponding to the target direction improves the main lobe gain; decreasing the excitation amplitude of the element corresponding to the side lobe direction suppresses the side lobe level.

[0044] Specifically, the excitation phase of the imaginary part represents the phase offset of the excitation signal of the nth adjustable array element. By adjusting the phase difference of the radiated electromagnetic waves of each adjustable array element, beam directional scanning (making the electromagnetic waves in the target direction "superimpose in phase" to enhance the signal strength) and interference direction nulling (making the electromagnetic waves in the interference direction "cancel out of phase" to suppress the interference signal) can be achieved by precisely controlling the phase relationship.

[0045] To satisfy the normalization constraint, under the far-field condition of narrowband signals, the pattern gain expression is as follows:

[0046] ;

[0047] ;

[0048] in This represents the pattern gain, where w is the complex weight vector. Indicates the guide vector. x n This represents the nth adjustable array element, where N is the number of adjustable array elements, 0 ≤ n ≤ N, and θ is the array scanning angle. The carrier wavelength is represented by C, and the complex number is represented by C. This is to perform the conjugate transpose operation on the complex weight vector.

[0049] That is, the steering vector is solved based on the array scanning angle, carrier wavelength and array element position vector, and the square of the inner product of the steering vector and the complex weight vector is taken as the pattern gain.

[0050] In some embodiments, a minimum spacing between adjustable array elements is defined to prevent coupling from occurring due to excessively small spacing between the adjustable array elements.

[0051] In step S2, the objective function of this scheme is to minimize the fitness of individual ospreys. The objective function is the minimum sum of the pattern gain and the total weighting function, where the total weighting function includes interference threshold constraints, array aperture constraints, minimum spacing constraints, and weight normalization constraints. The corresponding objective function content is as follows:

[0052] ;

[0053] in This represents the minimum value of the pattern gain within the target array scanning angle. This is the total term of the weighted function.

[0054] It should be noted that this scheme introduces interference threshold constraints, array aperture constraints, minimum spacing constraints, and weight normalization constraints as weighted function terms in the objective function. Specifically, the weighted function terms are... Represented as:

[0055] ;

[0056] ;

[0057] in , , , The positive penalty coefficients correspond to the constraint strengths of the interference threshold constraint, array aperture constraint, minimum spacing constraint, and weight normalization constraint, respectively; where L is the length of the continuous linear aperture interval. It is a set of 1 to K interference directions. This represents the pattern gain along the k-th interference direction, where K is the number of interference angles. I 0 indicates that the pattern gain in the Kth interference direction should not exceed this value, x n Let n be the position of the nth adjustable element, where 0 ≤ n ≤ N, and N is the number of adjustable elements. l min denoted as minimum spacing constraint, w represents complex weight vector.

[0058] It should be noted that, as shown in S1 above, this scheme has already constructed the pattern gain based on the array element position vector and the complex weight vector. Therefore, the pattern synthesis problem is transformed into the problem of minimizing the pattern gain, that is, the pattern synthesis problem model is as follows:

[0059] ;

[0060] ;

[0061] in The set of angles in the direction of the target. Let M be the scanning angle of the Mth target array, where M is the total number of scanning angles of the target array.

[0062] However, simply minimizing the pattern gain is insufficient to satisfy the problem of pattern synthesis. Therefore, this scheme further introduces interference threshold constraints, array aperture constraints, minimum spacing constraints, and weight normalization constraints to optimize the pattern synthesis problem. That is, the pattern synthesis problem model needs to satisfy the following four constraints:

[0063] ① Array aperture constraint to ensure that the antenna's movement range is within the preset aperture range: that is... , where x n Let N be the nth adjustable array element, 0≤n≤N, where N is the number of adjustable array elements and L is the length of the continuous linear aperture interval.

[0064] ② Minimum spacing constraint to prevent coupling between array elements due to excessively small spacing: that is, , where x n For the nth adjustable array element, l min For the minimum spacing, 0 ≤ n ≤ N, where N is the number of adjustable array elements;

[0065] ③ Weight normalization constraint to facilitate statistics and calculations: that is, ;

[0066] ④ Interference threshold constraint to achieve anti-interference function: that is, Let the set of interference angles in the problem model be . I0 indicates that the pattern gain of the Kth interference direction should not exceed this value.

[0067] Correspondingly, this scheme constructs a weighted function term for the above four constraints and introduces it into the problem model of pattern synthesis to obtain an unconstrained optimization problem in the following form, which serves as the objective function for improving the Osprey optimization algorithm.

[0068] Furthermore, the fitness of each individual osprey is set as the sum of the minimum value of the pattern gain term and the weighted penalty term, expressed as:

[0069] ;

[0070] ;

[0071] ;

[0072] Let be the fitness of the i-th individual osprey. The gain of the orientation pattern for the i-th individual osprey. Let M be the Mth array scanning angle, where M is the total number of array scanning angles. Let K be the k-th interference direction, where K represents the total number of interference directions.

[0073] This scheme transforms the APV and AWV of a one-dimensional movable antenna array into a joint representation in the real number domain, and decomposes the AWV into its real and imaginary parts and concatenates them with the APV to form a joint variable. The joint variable This represents the i-th solution to the problem. That is, in this solution, each individual osprey is defined as a joint variable vector composed of the array element positions and the real and imaginary parts of the complex weights, as follows:

[0074] ;

[0075] in and Joint variables The lower and upper bounds of the range of each dimension variable. Indicates taking out The real part, Indicates taking out The imaginary part, This indicates that the position of the i-th individual osprey is transposed.

[0076] Furthermore, by uniformly sampling the initial osprey population to generate P osprey individuals, the solution for the entire osprey population can be represented by a matrix. ,in Let P be the transpose of the joint variable for the i-th osprey individual, 0 ≤ i ≤ P, and initialize the fitness of all osprey individuals as follows: ,in Let P be the fitness of the i-th osprey individual, 0 ≤ i ≤ P. Considering that the osprey's position in the search space is updated in each iteration, the fitness of the osprey in each iteration is... and It is also constantly being updated.

[0077] After constructing an osprey population, this scheme uses an improved osprey optimization algorithm for iterative searching to obtain the optimal solution. In the global search phase, the scheme generates random step sizes using the Levy distribution, which ensures that the algorithm fully explores the current high-quality region while occasionally escaping the region where the local optimum is located by using longer step sizes, thus expanding the search range and avoiding premature convergence to a suboptimal solution. In the local search phase, the selection of update targets is controlled by a probability factor that decreases with the number of iterations. In the early stage of iteration, update targets are randomly selected with a higher probability to strengthen global exploration; in the later stage of iteration, the algorithm moves closer to the current optimal solution with a higher probability, smoothly transitioning to local exploration.

[0078] Specifically, in the iterative global search phase, after selecting and updating the target based on the dynamic factors of target selection, a random step size is generated according to the Levy flight mechanism. The individual ospreys are then updated with the updated target and the random step size. The update formula is as follows:

[0079] ;

[0080] ;

[0081] ;

[0082] in Let be the joint variable vector of the i-th osprey individual in the t-th iteration. It is the joint variable vector updated after the global search phase of the i-th osprey individual in the t-th iteration. For Handmard product, It is the Levy step size vector generated for all joint variable vectors. Here are the parameters of the Levy distribution, taking values ​​in the range [1,2]. and Follows a normal distribution. It is the step size factor in the global search phase.

[0083] Furthermore, the fitness of the new position is calculated. If the fitness increases, the current position of the osprey is updated using a greedy formula to obtain the current global optimal solution, specifically expressed as:

[0084] ;

[0085] in Let be the joint variable vector of the i-th osprey individual in the t-th iteration. It is the joint variable vector updated after the global search phase of the i-th osprey individual in the t-th iteration. Let represent the fitness updated after the global search phase of the i-th osprey individual in the t-th iteration. Let represent the fitness of the i-th individual osprey in the t-th iteration.

[0086] After the global search phase searches for the current global optimum in the current iteration, a local search phase is then used to find the current global optimum. Centered on the solution, a Gaussian perturbation strategy is used to perform a fine search in its neighborhood, and a dynamically decreasing step size is combined to achieve adaptive adjustment of the local solution space.

[0087] Specifically, in the local search phase of each iteration, a Gaussian perturbation mechanism is used to search near the current global optimum. The specific formula for updating the individual osprey's position and calculating the fitness of the new position, combined with a dynamic convergence step size strategy, is as follows:

[0088] ;

[0089] ;

[0090] ,and

[0091] in It is the current globally optimal solution. It is the joint variable vector updated during the global search phase of the i-th osprey individual in the t-th iteration. It is the joint variable vector updated during the local search phase of the i-th osprey individual in the t-th iteration. For the perturbation step size, Let $\mathbf{ ... and Joint variables The lower and upper bounds of the range of each dimension variable. It is a random vector with a mean of 0. It is a learning factor in the local search phase. It is the Handmard product.

[0092] Furthermore, the fitness of the new position is calculated. If the fitness increases, the current position of the osprey is updated using a greedy formula to obtain the current global optimal solution, specifically expressed as:

[0093] ;

[0094] in Let be the joint variable vector of the i-th osprey individual in the t-th iteration. It is the joint variable vector updated during the local search phase of the i-th osprey individual in the t-th iteration. This represents the fitness of the i-th osprey individual in the t-th iteration after the local search phase update. Let represent the fitness of the i-th individual osprey in the t-th iteration.

[0095] In some embodiments, the iteration condition of this scheme is to reach the number of iterations, that is, when the preset maximum number of iterations T is reached, the iterative search is terminated and the current global optimal solution is output. If the current number of iterations t is less than the maximum number of iterations T, the number of iterations is incremented by 1 and the iterative search continues.

[0096] In step S4, the antenna position vector and complex weights of the final global optimal solution are used as the design result of the current movable antenna array and the radiation pattern is plotted.

[0097] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0098] The performance of IOA in array pattern synthesis was evaluated using Matlab simulations. The basic parameters of the movable antenna array were also analyzed. The normalization value is 1 and the array element position is... In IOOA, all parameters are set to [unit]. , , =1.9, =0.2, =0.9. All experiments were run on a 4.0 GHz personal computer, using Matlab R 2023b as the simulation platform.

[0099] Figure 1 The image shows a comparison of null patterns of a single beam under different algorithms, considering an MA array where N=8 and D=8. , = The IOOA parameters are set to P=30 and T=800. =0.01. The beam target direction is 90° and the interference direction is set to... Simulation results were compared with those of the Zero Forcing (ZF) algorithm, Firefly Algorithm (FA), and Alternating Optimization (AO) algorithm. The figures clearly show that the proposed method, along with ZF, FA, and AO, achieves nearly 99.9% of the full array gain, while satisfying the null trap threshold in the interference direction. However, the proposed method maintains a lower sidelobe pattern compared to other algorithms, and its runtime of 9.7 seconds is faster than FA (10.9 seconds) and AO (106.2 seconds). Although the ZF algorithm's runtime is <1 second, the resulting MA array aperture exceeds 28mm. Furthermore, the sidelobes are too high, and the radiation pattern obtained from a specific closed solution cannot constrain the sidelobe suppression and aperture range.

[0100] Figure 2 This paper presents a comparison of the bidirectional graph performance under different optimization schemes, with the beam target set as follows: The interference direction is set to The IOA parameter is set to P =30, T =1200, =0.1. As can be seen from the figure, all the comparison schemes can effectively generate deep nulls in the specified interference directions. The method proposed in this paper can achieve 87% of the full array gain, while the FA, AO-SCA, and FPA schemes achieve 82%, 56%, and 55% of the full array gain, respectively. In terms of computational efficiency, IOOA only requires 4.9 seconds, significantly faster than FA (9.8 seconds) and AO-SCA (33.3 seconds). It should be noted that the zero-forcing (ZF) algorithm cannot meet the dimensionality matching condition between the number of array elements and the number of interference directions, thus it cannot be used in multi-beam scenarios.

[0101] Figure 3 The feasibility of synthesizing reconfigurable MA arrays under discrete pure phase constraints was verified, demonstrating that the beam direction or shape can be changed simply by adjusting the phase excitation. This means all beams share the same antenna position and excitation amplitude. Let the quantization bit depth be... C and define Q =2 C The candidate phase weights can then be enumerated as follows: In this experiment, a configuration was considered. N =7, D =5 , = The MA array is targeted with two low-sidelobe pen-tip beam patterns, with the main lobes pointing at 90° and 120° respectively. The normalized sidelobe level is required to not exceed -9 dB. Other relevant parameters are set as follows: C =4, P =30, T =1200. For example... Figure 3 As shown, both obtained beam patterns meet the given requirements, while the pattern obtained by the comparison algorithm exceeds the expected sidelobe level. Furthermore, the method proposed in this invention produces a narrower main lobe, corresponding to better focusing performance. Finally, the proposed method executes in only 18.5 seconds, while the mixed-integer programming method, due to the use of a mixed-integer programming solver, takes over 6000 seconds.

[0102] Figure 4 This demonstrates the performance of the IOOA algorithm in common shaped beam scenarios, considering a radiation pattern with a flat-top main lobe and squared cosecant, assuming the MA array is... , and , where the IOOA parameter P =120, T=18000. The expected level fluctuation in the main lobe region within the range of [70°, 110°] is no more than 0.32 dB, and the highest peak value of the side lobes is no more than -30 dB. The proposed method can strictly meet the shape expectation of the main lobe and the requirements for side lobe suppression, with runtimes of 383.8 seconds and 428.3 seconds, respectively.

[0103] Figure 5 It shows different numbers of array elements N and interference threshold The maximum-min gain varies with P The changes. To demonstrate optimal performance at different population sizes, T The gain was uniformly set to 2500, and 100 Monte Carlo simulations were performed to obtain the average gain value. The results show that, except... Except in cases where the population size P As the beamforming gain changes from 10 to 40, the gain is significantly improved. Specifically, for ,when P When the value is increased from 10 to 40, the gain increases from 7.3 to 8.1. ), and an upgrade from 6.3 to 7.3 ( This can be attributed to the fact that a larger population size allows for a more comprehensive characterization of the feasible region. However, for A smaller population size of approximately 10 is sufficient to ensure convergence; further increases... P The resulting performance improvement is negligible.

[0104] Figure 6 Showing in different N and Under the condition that the maximum-min gain changes with the number of iterations, where P The value was fixed at 30, and 100 Monte Carlo simulations were performed, with the average value taken. It can be clearly seen that for all configurations, the max-min gain exhibits a continuous upward trend in the early iteration stages, subsequently reaching saturation, indicating that the proposed algorithm has achieved stable convergence. At that time, the gain converged after approximately 400 generations. In contrast, at... conditions, and Convergence requires 1500 and 2000 generations respectively. This is because the higher dimensionality significantly prolongs the convergence process of the algorithm.

[0105] Example 2

[0106] This embodiment also provides an electronic device, see reference. Figure 7It includes a memory 404 and a processor 402, the memory 404 storing a computer program and the processor 402 being configured to run the computer program to perform the steps in the embodiments of the movable antenna array pattern synthesis method of any of the above-described improved Osprey optimization algorithms.

[0107] Specifically, the processor 402 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0108] The memory 404 may include a large-capacity memory 404 for data or instructions. The memory 404 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 402.

[0109] The processor 402 reads and executes computer program instructions stored in the memory 404 to implement any of the improved Osprey optimization algorithms in the above embodiments for the mobile antenna array pattern synthesis method.

[0110] Optionally, the electronic device may further include a transmission device 406 and an input / output device 408, wherein the transmission device 406 is connected to the processor 402, and the input / output device 408 is connected to the processor 402.

[0111] The transmission device 406 can be used to receive or send data via a network. Specific examples of the network described above may include wired or wireless networks provided by the communication provider of the electronic device. In one example, the transmission device includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 406 may be a Radio Frequency (RF) module used for wireless communication with the Internet.

[0112] Input / output device 408 is used to input or output information. In this embodiment, the input information may be a movable antenna array, etc., and the output information may be a radiation pattern, etc.

[0113] Optionally, in this embodiment, the processor 402 can be configured to perform the following steps via a computer program:

[0114] S1: Construct a one-dimensional movable antenna array model, in which multiple adjustable array elements in the one-dimensional movable antenna array model are arranged in a continuous linear aperture interval of a preset length;

[0115] S2: Initialize the osprey population and define the fitness of each osprey individual and set the objective function. Each osprey individual corresponds to a joint variable vector composed of the array element position, the real part and the imaginary part of the complex weight. The fitness of each osprey individual is the sum of the minimum value of the pattern gain term and the weighted penalty term. The objective function is to minimize the fitness of the osprey individual.

[0116] S3: Iteratively search the osprey population until the iteration conditions are met to output the final global optimum. In the global search phase of each iteration, a random step size is generated through the Levy flight mechanism and the osprey individual position is updated by combining the dynamic factor of target selection and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum. In the local search phase of each iteration, a Gaussian perturbation mechanism is used to search in the vicinity of the current global optimum. The osprey individual position is updated by combining the dynamic convergence step size strategy and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum.

[0117] S4: Draw the radiation pattern of the movable antenna array based on the final global optimal solution.

[0118] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated here.

[0119] Generally, various embodiments can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects of the invention can be implemented in hardware, while others can be implemented by firmware or software executed by a controller, microprocessor, or other computing device, but the invention is not limited thereto. Although various aspects of the invention may be shown and described as block diagrams, flowcharts, or using some other graphical representation, it should be understood that, by way of non-limiting example, these blocks, apparatuses, systems, techniques, or methods described herein can be implemented in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0120] Embodiments of the present invention can be implemented by computer software, which may be executable by a data processor of a mobile device, such as a processor entity, or by hardware, or by a combination of software and hardware. Computer software or programs (also referred to as program products), including software routines, applets, and / or macros, can be stored in any device-readable data storage medium, and they include program instructions for performing specific tasks. A computer program product may include one or more computer-executable components configured to perform embodiments when the program is run. One or more computer-executable components may be at least one piece of software code or a portion thereof. Additionally, it should be noted that any block in the logical flow of the figures may represent a program step, or interconnected logical circuitry, blocks and functions, or a combination of program steps and logical circuitry, blocks and functions. The software may be stored on physical media such as memory chips or blocks of storage implemented within a processor, magnetic media such as hard disks or floppy disks, and optical media such as, for example, DVDs and their data variants, CDs, etc. The physical medium is a non-transient medium.

[0121] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for pattern synthesis of a movable antenna array based on an improved Osprey optimization algorithm, characterized in that, Includes the following steps: S1: Construct a one-dimensional movable antenna array model, in which multiple adjustable array elements in the one-dimensional movable antenna array model are arranged in a continuous linear aperture interval of a preset length; S2: Initialize the osprey population and define the fitness of each osprey individual and set the objective function. Each osprey individual corresponds to a joint variable vector composed of the array element position, the real part and the imaginary part of the complex weight. The fitness of each osprey individual is the sum of the minimum value of the pattern gain term and the weighted penalty term. The objective function is to minimize the fitness of the osprey individual. S3: Iteratively search the osprey population until the iteration conditions are met to output the final global optimum. In the global search phase of each iteration, a random step size is generated through the Levy flight mechanism and the osprey individual position is updated by combining the dynamic factor of target selection and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum. In the local search phase of each iteration, a Gaussian perturbation mechanism is used to search in the vicinity of the current global optimum. The osprey individual position is updated by combining the dynamic convergence step size strategy and the fitness of the new position is calculated. If the fitness increases, the current osprey individual position is updated to obtain the current global optimum. S4: Draw the radiation pattern of the movable antenna array based on the final global optimal solution.

2. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, The radiation pattern gain is constructed based on the element position vector and the complex weight vector. The element position vector represents the arrangement position of multiple adjustable elements along a continuous linear aperture interval. The complex weight vector is the core vector that quantizes the excitation signal parameters of each adjustable element in a one-dimensional movable antenna array. The complex weight vector includes the real part of the excitation amplitude and the imaginary part of the excitation phase.

3. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, The objective function is the minimum sum of the pattern gain and the total term of the weighting function, where the total term of the weighting function includes interference threshold constraints, array aperture constraints, minimum spacing constraints, and weight normalization constraints.

4. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, The objective function is: ； ； in This represents the minimum value of the pattern gain within the target array scanning angle. Let w be the total term of the weighting function, where w is the complex weight vector, and x is the weight vector. n This represents the nth adjustable array element, where N is the number of adjustable array elements.

5. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 4, characterized in that, ； in , , , The positive penalty coefficients correspond to the constraint strengths of the interference threshold constraint, array aperture constraint, minimum spacing constraint, and weight normalization constraint, respectively; where L is the length of the continuous linear aperture interval. It is a set of 1 to K interference directions. This represents the pattern gain along the k-th interference direction, where K is the number of interference angles. I 0 indicates that the pattern gain in the k-th interference direction should not exceed this value, x n Let n be the position of the nth adjustable element, where 0 ≤ n ≤ N, and N is the number of adjustable elements. l min denoted as minimum spacing constraint, w represents complex weight vector.

6. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, During the iterative global search phase, after selecting and updating the target based on the dynamic factors of target selection, a random step size is generated according to the Levy flight mechanism to update the individual ospreys with the updated target and the random step size.

7. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, The iteration condition is to reach the preset maximum number of iterations, that is, when the preset maximum number of iterations is reached, the iterative search is terminated and the current global optimal solution is output.

8. The method for pattern synthesis of a movable antenna array based on the improved Osprey optimization algorithm according to claim 1, characterized in that, The antenna position vector and complex weights of the final global optimal solution are used as the design result of the current movable antenna array, and the radiation pattern is plotted.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to execute the movable antenna array pattern synthesis method based on the improved Osprey optimization algorithm as described in any one of claims 1 to 8.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program, which includes program code for controlling a process to execute the process, the process including the movable antenna array pattern synthesis method based on the improved Osprey optimization algorithm according to any one of claims 1 to 8.

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