Sub-array optimal distribution method and system based on quantum antelope optimizer

Abstract

The invention provides a sub-array optimal distribution method and system based on a quantum antelope optimizer, and belongs to the field of array signal processing. The invention aims to solve the problem of inaccurate estimation of distributed array performance attenuation and direction of arrival due to reduction of the number of snapshots and change of interference noise under the conditions of small sampling snapshots and impact noise. According to the method, the array structure is optimized under the impact noise condition, received signals are processed by constructing an infinite norm weighted fraction low-order covariance matrix, and the method is more suitable for the environment where the number of snapshots is reduced and the impact noise is severe; a quantum optimization mechanism is introduced, and the performance and search efficiency of an original algorithm in the distributed array research direction are improved based on an evolution strategy of a quantum rotation angle and a quantum rotation door; according to the method, the direction finding accuracy of the distributed array system can be improved, and the situation that the array performance influence factors in the actual direction finding application are not considered sufficiently and the performance improvement is not large due to the fact that the directional diagram of the array serves as the optimization target can be effectively avoided.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a method and system for optimal subarray distribution based on the quantum antelope optimizer. Background Technology

[0002] Distributed array technology is an emerging technology that utilizes multiple separate subarrays working collaboratively. It boasts significant advantages and broad application prospects, finding wide application in target detection, wireless communication, and electronic warfare. It offers advantages such as high-resolution beamforming, enhanced anti-jamming capabilities, and multi-target tracking. Each independent array or element can be deployed in real-time according to mission requirements, enabling dynamic control of array distribution in various complex environments, whereas traditional distributed arrays typically employ uniform, equally spaced distributions.

[0003] A review of existing literature revealed that Yang Minglei et al., in their paper "Distributed Array DOA Estimation Based on Preprocessing MUSIC Algorithm" published in *Guidance and Fuze* (2017, Vol. 38, No. 3, pp. 10-15), proposed a distributed array consisting of two identical uniform linear arrays. However, they did not discuss the different configurations of the distributed array in detail, but instead directly set the spacing between the two uniform linear arrays. Fu Sida et al., in their paper "Heterogeneous Distributed Array Optimization Based on Differential Evolution Algorithm" published in *Aerospace Electronic Countermeasures* (2023, No. 2, pp. 32-37), proposed optimizing the subarray distribution positions using a differential evolution algorithm. Their method of designing an algorithm with stronger convergence ability and faster convergence speed to optimize distributed arrays provides us with a promising approach. In their paper "Research on Distributed Array Raster Lobe Suppression Algorithm Based on Improved Genetic Algorithm" published in Fire Control Radar Technology (2017, Vol. 38, No. 3, pp. 10-15), An Zhengshuai et al. proposed an improved genetic algorithm to optimize the position distribution of subarrays. However, the final result can only suppress grating lobes and does not significantly improve the direction finding performance of the distributed array.

[0004] Literature review results indicate that existing distributed array layout optimization methods primarily focus on suppressing maximum sidelobe levels, but these methods do not significantly improve the direction-of-arrival (DOA) estimation performance of distributed arrays. This invention, based on a subarray optimal distribution method using a quantum antelope optimizer, improves the DOA estimation performance of distributed arrays, addressing the severe performance degradation issue under small snapshot conditions. Furthermore, this invention reduces computational complexity and improves algorithm efficiency even under small snapshot conditions, providing a novel approach for distributed array direction finding. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] To address the issue of inaccurate direction-of-arrival estimation due to performance degradation of distributed arrays under conditions of small sampling, fast snapshots, and impulsive noise, caused by the reduction in the number of snapshots and changes in interference noise.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a method for optimal subarray distribution based on the quantum antelope optimizer, comprising the following steps:

[0009] S100. Modeling of impact noise and source information in space, including,

[0010] A distributed array system is established, which includes multiple equidistant subarrays, each of which includes multiple equidistant array elements; far-field narrowband signals in space are incident on the distributed array system from multiple directions and construct an azimuth matrix.

[0011] S200. Construct an infinite norm weighted fractional low-order covariance matrix using the snapshot data received by the distributed array system, and perform direction estimation to obtain the root mean square error equation for the direction estimation, including:

[0012] A model for receiving snapshot signals in a distributed array system is constructed. After processing the received signal, an infinite norm weighted fractional low-order covariance matrix is ​​constructed from the received data. Then, DOA estimation is performed based on the MUSIC algorithm. The fractional low-order covariance matrix is ​​decomposed into signal subspace and noise subspace. The spatial spectrum function of the MUSIC algorithm based on the low-order matrix is ​​derived. Finally, the objective function is obtained.

[0013] S300. Initialize the quantum antelope population and obtain the local optimal measurement location and the global optimal measurement location, including:

[0014] After initializing a quantum antelope population in quantum space, it is determined whether there are predators around the antelopes. If not, a global search is performed; if so, a local search is performed. Then, the fitness value of each antelope is calculated and sorted to obtain the corresponding optimal measurement location.

[0015] S400, Update the quantum rotation angle and quantum position of each antelope according to its predation strategy, and then obtain the measured position, including,

[0016] Based on the biomimetic mechanism of the antelope, when the antelope is free from predators, it adopts Brownian motion and updates its quantum position through a quantum rotation gate. After discovering a predator, the antelope enters two stages: when it first discovers the predator, it escapes by flying like Levi, and after a long chase, it escapes by using Brownian motion. The quantum rotation angle and quantum position are updated accordingly for the two stages, thus obtaining the corresponding measured position.

[0017] S500: Calculate the updated measurement position fitness value, and update the local optimal position and the global optimal position;

[0018] S600: Determine whether the maximum number of iterations has been reached. If not, return to step S400. If it has been reached, terminate the iteration and output the distributed layout position information of the required array by converting the global optimal position into the output.

[0019] Further, in step S100, the following is included:

[0020] Assume the noise in the space satisfies Stable distribution of impulse noise, with characteristic index as ;

[0021] Existing in space Each wavelength is The far-field narrowband signals are respectively from the m-th azimuth angle The direction of the incident light onto the array, where the azimuth angle is... , , , Let m be the m-th azimuth angle; establish a distributed array system with a total number of array elements. All array elements are arranged in a straight line. Multiple array elements form a subarray. The array elements in the subarray are equally spaced, with a spacing of [missing information]. The number of subarrays is , No. The number of array elements in each subarray is , ,so Furthermore, the spacing between each subarray is equal to the spacing between a single array element. The integer multiples of the values ​​are used to obtain the parameters to be optimized, which are the spacings between the subarrays.

[0022] Further, in step S200, the following are included:

[0023] Distributed array system receives the first The model of the secondary snapshot signal is ,in , The maximum number of snapshots is given by the formula. , For a distributed array system to receive the Nth array element's... Second quick-snap signal, Let be the guiding matrix, where the first... The guide vectors are , The azimuth vector of the incoming wave. j represents the imaginary unit; d represents the spacing between each array element. For signal vectors, For a distributed array system to receive the Mth wavelength of the first wavelength Secondary signal vector Let be the independent and identically distributed impulse noise vectors of the array. Let N be the independent and identically distributed impulse noise vector of the Nth array element;

[0024] The signal received by the array is processed to obtain ,in Using the processed array Receive data construction The low-order covariance matrix R of the infinite norm weighted fraction of the second snapshot is: ,in For the first The low-order covariance matrix of the sub-shot data. for 3D matrix Its kth quick shot Line 1 Column elements are ,in To find conjugate, , , The parameters are the fractional low-order covariance matrix;

[0025] DOA estimation based on the MUSIC algorithm, focusing on the fractional low-order covariance matrix. Eigenvalue decomposition yields the signal subspace and the noise subspace. ,in It is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues. It is the impulse noise subspace spanned by the eigenvectors corresponding to small eigenvalues; It is a diagonal matrix composed of large eigenvalues. It is a diagonal matrix composed of small eigenvalues; Represents conjugate transpose;

[0026] The spatial spectral function of the MUSIC algorithm based on low-order matrices is derived as follows: After searching the spectral peaks, the first The azimuth estimate for this experiment is , , where T is the number of experiments;

[0027] Therefore, the objective function is obtained as follows: ,in For the potential solution of the array position structure, Indicates the distance between subarrays. Let be the number of information sources in space. For the first The accurate location value of each information source. For the first sequence The location estimate of each information source.

[0028] Further, in step S300, the following are included:

[0029] Initialize a quantum antelope population in quantum space. The quantum antelope population contains... Only one mountain antelope, the first The generation The first mountain antelope Quantum position Initialize randomly between [0,1], where , , Represents the total dimension; the measurement location is obtained as The measurement equation is ,in A random number that follows a uniform distribution between [0,1]. ; This represents the first [unit / item] in the generated herd of mountain antelopes. The generation The quantum position of a mountain antelope, that is The maximum number of iterations is ;

[0030] set up For hunting probability, For a random number in the range [0,1], when Less than the hunting probability When the time is right, it means there are no predators hunting around the grazing antelopes, so a global search is needed; otherwise, it means there are predators hunting, so a local search is needed.

[0031] The quantum position is obtained by determining the measurement position according to the measurement rules. Map it to array position Substituting these values ​​into the objective function to calculate the fitness, the fitness function becomes: ,in For the first The experiment The generation The distribution array corresponding to only one mountain antelope was obtained as the first Estimate the direction of arrival of the source wave; sort all fitness values, all antelopes up to the first... The optimal position obtained by the alternative search is denoted as the global optimal position. .

[0032] Further, in step S400, the following is included:

[0033] Based on the biomimetic mechanism of the antelope, when free-range grazing occurs in the absence of predators, each antelope exhibits Brownian motion; when Less than the hunting probability At that time, the first Only mountain antelope The update equation for the quantum rotation angle in real-time global search of quantum position is:

[0034]

[0035] in, The speed at which the mountain antelope moves. It is a random number in the range [0,1], the first... Only mountain antelope Vibranium exercise factor These are random numbers that follow a standard normal distribution. For the first The generation Only mountain antelope Quantum rotation angle for real-time global search of quantum position;

[0036] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The quantum position is:

[0037]

[0038] in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between;

[0039] when Greater than the hunting probability At that time, the first Only mountain antelopes conduct local searches; according to the biomimetic mechanism of mountain antelopes, after discovering a predator, mountain antelopes enter two stages: the first stage is when the mountain antelopes have just discovered the predator and use the Levi flight method to escape; the second stage is when the mountain antelopes become fatigued under the predator's frantic pursuit and escape using Brownian motion.

[0040] In the first stage, a motion direction factor is generated. ,in It is -1 or 1; the first Only mountain antelope Villev's flight factor is The expression for the Levi flight factor is: ,in For Levi's flight stride, Random numbers that are distributed according to a standard normal distribution. As an adjustable variable in the Levy flight factor; then the first stage of the... The first mountain antelope The update equation for the quantum rotation angle is:

[0041]

[0042] in, The speed at which the mountain antelope moves. It is a random number in the range [0,1].

[0043] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is:

[0044]

[0045] make As a fatigue algebra, when the number of iterations exceeds At this point, the antelope will become fatigued due to decreased physical strength, thus entering the second stage of escaping using Brownian motion, and thus achieving the second stage. Only mountain antelope The update equation for the quantum rotation angle is:

[0046]

[0047] in, The speed at which the mountain antelope moves. Brownian motion factor For variables representing the cumulative effect of predators, , Let it be one of the adjustable variables;

[0048] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is:

[0049]

[0050] in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between;

[0051] Through the first The generation Only mountain antelope Quantum position The measured position of the array position structure is obtained. Its measurement equation is ,in Let [0,1] be a random number that follows a uniform distribution. , ; will the first The generation The measured position of the mountain antelope is mapped to the corresponding array position. .

[0052] Further, in step S500, the following are included:

[0053] Calculate the first The generation The fitness level of the mountain antelope is If the fitness of the updated quantum position is less than the fitness of the original quantum position, then... If the new quantum position is not found, the original quantum position will be replaced by the new one; otherwise, the original quantum position will be preserved, i.e., let... , , , comparison until All measurement location fitness values ​​of the generation are obtained until The global optimal position of the generation is .

[0054] The subarray optimal distribution system based on the quantum antelope optimizer has a program module corresponding to the above steps, which executes the steps in the subarray optimal distribution method based on the quantum antelope optimizer when running.

[0055] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement steps of a subarray optimal distribution method based on a quantum antelope optimizer.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] (1) This invention selects to optimize the corresponding array structure under more complex environments such as impact noise conditions. By constructing an infinite norm weighted fractional low-order covariance matrix to process the received signal, it breaks through the application limitations of traditional methods and is more adaptable to harsh environments such as reduced snapshot number and impact noise.

[0058] (2) This invention adopts the quantum antelope algorithm, which introduces a quantum optimization mechanism compared with the traditional antelope optimization algorithm. By designing a new evolution strategy based on quantum rotation angle and quantum rotation gate, the performance of the original algorithm in the research direction of distributed array is improved and the search efficiency is increased.

[0059] (3) This invention explores the array structure based on the results, which can improve the direction finding accuracy of the distributed array system and effectively avoid the situation where the array's radiation pattern is used as the optimization target, resulting in insufficient consideration of the array performance factors in actual direction finding applications and little performance improvement.

[0060] (4) Compared with existing methods, the number of array elements in the subarray is not fixed, which can adapt to complex environments with different numbers of array elements in the subarray, making it more flexible and applicable to a wider range of situations. Attached Figure Description

[0061] Figure 1 This is a flowchart of the subarray optimal distribution method based on the quantum antelope optimizer in an embodiment of the present invention;

[0062] Figure 2 This is a schematic diagram illustrating the layout optimization of subarrays in a distributed array according to an embodiment of the present invention;

[0063] Figure 3 This is a graph showing the relationship between the number of snapshots and the estimated mean square error under different array structures in this embodiment of the invention.

[0064] Figure 4 This is a graph showing the relationship between the number of snapshots and the estimated success probability under different array structures in this embodiment of the invention.

[0065] Figure 5 This is a graph showing the relationship between the generalized signal-to-noise ratio and the estimated mean square error under different array structures in the embodiments of the present invention.

[0066] Figure 6 This is a graph showing the relationship between the generalized signal-to-noise ratio and the probability of successful estimation under different array structures in embodiments of the present invention.

[0067] Figure 7 This is a graph showing the relationship between the number of snapshots and the estimated success probability under array structures with different numbers of subarray elements in embodiments of the present invention. Detailed Implementation

[0068] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0069] Specific Implementation Plan 1: Combining Figure 1 and Figure 2 As shown, this invention provides a subarray optimal distribution method based on the quantum antelope optimizer, comprising the following steps:

[0070] S100. Model the impact noise and source information in space.

[0071] Noise in space to satisfy Stable distribution of impulse noise, with characteristic index as Existing in space Each wavelength is The far-field narrowband signals are respectively from the m-th azimuth angle The direction of the incident light onto the array, where the azimuth angle is... , , , Let m be the m-th azimuth angle; establish a distributed array system with a total number of array elements. All array elements are arranged in a straight line. Multiple array elements form a subarray. The array elements in the subarray are equally spaced, with a spacing of [missing information]. The number of subarrays is , No. The number of array elements in each subarray is , ,so Furthermore, the spacing between each subarray is equal to the spacing between a single array element. The integer multiples of the values ​​are used to obtain the spacing between each subarray as the parameter to be optimized.

[0072] S200. Using the snapshot data received by the distributed array system, an infinite norm weighted fractional low-order covariance matrix is ​​constructed for direction estimation, thereby obtaining the root mean square error equation for the direction estimation.

[0073] Distributed array system receives the first The model of the secondary snapshot signal is ,in , The maximum number of snapshots is given by the formula. , For a distributed array system to receive the Nth array element's... Second quick-snap signal, Let be the guiding matrix, where the first... The guide vectors are , The azimuth vector of the incoming wave. j represents the imaginary unit; d represents the spacing between each array element. For signal vectors, For a distributed array system to receive the Mth wavelength of the first wavelength Secondary signal vector Let be the independent and identically distributed impulse noise vectors of the array. Let N be the independent and identically distributed impulse noise vector of the Nth array element;

[0074] The signal received by the array is processed to obtain ,in Using the processed array Receive data construction The low-order covariance matrix of the infinite norm weighted fraction of the second snapshot: ,in For the first The low-order covariance matrix of the sub-shot data. for 3D matrix Its kth quick shot Line 1 Column elements are ,in To find conjugate, , , The parameters are the fractional low-order covariance matrix;

[0075] DOA estimation is performed using the MUSIC algorithm on the fractional low-order covariance matrix. Eigenvalue decomposition yields the signal subspace and the noise subspace. ,in It is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues. It is the impulse noise subspace spanned by the eigenvectors corresponding to small eigenvalues; It is a diagonal matrix composed of large eigenvalues. It is a diagonal matrix composed of small eigenvalues; Represents conjugate transpose;

[0076] The spatial spectral function of the MUSIC algorithm based on low-order matrices is derived as follows: After searching the spectral peaks, the first The azimuth estimate for this experiment is , , where T is the number of experiments;

[0077] By testing the direction-finding performance of distributed arrays with different layouts for information sources in space, the objective function is obtained as follows: ,in For the potential solution of the array position structure, Indicates the distance between subarrays. , Let be the number of information sources in space. For the first The accurate location value of each information source. For the first The experiment Location estimates of each information source;

[0078] S300. Initialize the quantum antelope population and obtain the local optimal measurement location and the global optimal measurement location.

[0079] Initialize a quantum antelope population in quantum space. The quantum antelope population contains... Only one mountain antelope, the first The generation The first mountain antelope Quantum position Initialize randomly between [0,1], where , , Represents the total dimension; the measurement location is obtained as The measurement equation is ,in A random number that follows a uniform distribution between [0,1]. ; This represents the first [unit / item] in the generated herd of mountain antelopes. The generation The quantum position of a mountain antelope, that is The maximum number of iterations is ;

[0080] For hunting probability, For a random number in the range [0,1], when Less than the hunting probability When the quantum position is within a certain range, it indicates that there are no predators hunting in the vicinity of the grazing antelope, thus requiring a global search; conversely, it indicates that predators are hunting, requiring a local search. The quantum position is then used to obtain the measured position according to the measurement rules. Map it to array position Substituting these values ​​into the objective function to calculate the fitness, the fitness function becomes: ,in For the first The experiment The generation The distribution array corresponding to only one mountain antelope was obtained as the first The estimated direction of arrival (DOA) of the source was calculated; all fitness values ​​were sorted, and since the difference between the estimated and accurate DOA values ​​of the source should be as small as possible, smaller fitness values ​​were preferred. All antelopes up to the [number missing] [number missing] were ranked. The optimal position obtained by the alternative search is denoted as the global optimal position. ;

[0081] S400: Update the quantum rotation angle and quantum position of each antelope according to its hunting strategy, and then obtain the measured position.

[0082] Based on the biomimetic mechanism of the antelope, when free-range grazing occurs in the absence of predators, each antelope exhibits Brownian motion; when Less than the hunting probability At that time, the first Only mountain antelope The update equation for the quantum rotation angle in real-time global search of quantum position is:

[0083]

[0084] in, The speed at which the mountain antelope moves. It is a random number in the range [0,1], the first... Only mountain antelope Vibranium exercise factor These are random numbers that follow a standard normal distribution. For the first The generation Only mountain antelope Quantum rotation angle for real-time global search of quantum position;

[0085] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The quantum position is:

[0086]

[0087] in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between;

[0088] when Greater than the hunting probability At that time, the first The antelope conducts a localized search. Based on the antelope's biomimetic mechanism, it goes through two phases after spotting a predator. The first phase involves the antelope immediately fleeing using a Levi-like flight maneuver. The second phase involves the antelope becoming fatigued from the predator's relentless pursuit and fleeing using Brownian motion. Because it has ample energy in the first phase, immediately after spotting the predator and attempting to shake it off, a directional movement factor is generated. ,in It is -1 or 1; the first Only mountain antelope Villev's flight factor is The expression for the Levi flight factor is: ,in For Levi's flight stride, Random numbers that are distributed according to a standard normal distribution. As an adjustable variable in the Levy flight factor; then the first stage of the... The first mountain antelope The update equation for the quantum rotation angle is:

[0089]

[0090] in, The speed at which the mountain antelope moves. It is a random number in the range [0,1].

[0091] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is:

[0092]

[0093] make As a fatigue algebra, when the number of iterations exceeds At this point, the antelope will become fatigued due to decreased physical strength, thus entering the second stage of escaping using Brownian motion, and thus achieving the second stage. Only mountain antelope The update equation for the quantum rotation angle is:

[0094]

[0095] in, The speed at which the mountain antelope moves. is the Brownian motion factor, which is a random number following a standard normal distribution. For variables representing the cumulative effect of predators, , Let it be one of the adjustable variables;

[0096] The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is:

[0097]

[0098] in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between;

[0099] Through until the The generation Only mountain antelope Quantum position The measured position of the array position structure is obtained. Its measurement equation is ,in Let [0,1] be a random number that follows a uniform distribution. , ; will the first The generation The measured position of the mountain antelope is mapped to the corresponding array position. ;

[0100] S500: Calculate the updated measurement position fitness value, and update the local optimum and global optimum.

[0101] Calculate the first The generation The fitness level of the mountain antelope is If the fitness of the updated quantum position is less than the fitness of the original quantum position, then... If the new quantum position is 0, the original quantum position will be replaced by the new one; otherwise, the original quantum position will be preserved. , , , comparison until All measurement location fitness values ​​of the generation are obtained until The global optimal position of the generation is ;

[0102] S600, Determine if the maximum number of iterations has been reached. If it is not achieved, then... Return to step S400; if the target is reached, terminate the iteration and output the distributed layout position information of the required array by converting the global optimal position into the output.

[0103] Specific implementation scheme two: The present invention provides a subarray optimal distribution system based on the quantum antelope optimizer. The system has a program module corresponding to the above steps, and executes the steps in the subarray optimal distribution method based on the quantum antelope optimizer when running.

[0104] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0105] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, the steps of a subarray optimal distribution method based on a quantum antelope optimizer.

[0106] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.

[0107] Simulation Experiment

[0108] This invention overcomes the limitations of existing methods that mostly use the array pattern as the optimization target, instead using the distributed array structure as the optimization target, and effectively overcomes the influence of harsh environments such as small snapshots and impulse noise. The quantum antelope optimization mechanism is abbreviated as QMGO below. Simulation of the subarray optimal distribution method based on the quantum antelope optimizer begins with parameter settings, where the distributed system (including corresponding hardware, where each array element receives a signal, transmits the data through the channel, and sends it to the processor for information processing) has a total number of array elements. Total number of subarrays The number of array elements in each subarray , The spacing between the array elements in the sub-array The overall arrangement of each subarray is as follows: Figure 2 Number of sources The value is 4, and the incident directions are respectively , , , Fractional low-order covariance matrix parameters The noise is additive impulse noise, with a characteristic index of [missing information]. The generalized signal-to-noise ratio is 3dB. The parameters for QMGO are then set as follows: (List of antelope numbers) The dimension of each antelope is Maximum number of iterations Hunting probability The speed of the mountain antelope Motion direction factor Based on the current iteration number To determine whether a number is even or odd, when If it is an odd number ,when If it is an even number fatigue algebra The two adjustable variables are respectively , The classic MUSIC method is used for estimating the direction of arrival of the signal source, with the algorithm's spectral peak search step size set to 0.1° and the number of received data snapshots set to 20.

[0109] After setting the above parameters, the final distributed array system layout structure was obtained by conducting multiple tests and selecting the optimal values. The spacing between adjacent subarrays is [missing information]. To verify the superiority of the obtained subarray layout structure, the obtained layout structure and the subarray spacing are both... , , Three uniformly spaced array structures, along with a uniform linear array, were jointly simulated and compared. These are referred to below as 10x spacing, 30x spacing, 50x spacing, and the uniform linear array (ULA), respectively. The direction-finding performance of these array structures was tested under harsh conditions, including small snapshots, impact noise, and low signal-to-noise ratio.

[0110] Let the total number of subarrays be... The number of elements in the subarrays are respectively , , The overall arrangement of each subarray remains the same. Figure 2 With other parameters remaining unchanged, the spacing between adjacent subarrays is obtained as follows: ,in The direction-finding performance was tested under harsh conditions such as small snapshots and impact noise when the number of subarray elements was not completely the same.

[0111] Figure 3 In the experiment, the influence of the number of sampling snapshots on the direction-finding accuracy of different array structures was investigated under impulse noise and a generalized signal-to-noise ratio of 15dB. 200 independent experiments were conducted for each number of snapshots. As shown in the figure, under impulse noise and small snapshot conditions, the array structure proposed in this invention maintains a sufficiently small root mean square error (RMSE). Furthermore, as the number of snapshots decreases, the RMSE of all array structures increases. The array structure proposed in this invention has the smallest RMSE, indicating that the proposed array layout structure can adapt to the application conditions of small snapshots.

[0112] Figure 4In this study, the impact of the number of sampling snapshots on the success probability of direction finding estimation for different array structures was investigated under impulsive noise and a generalized signal-to-noise ratio of 15 dB. The study defined a successful estimation as an error of less than 1.5° between the estimated value and the target. 200 experiments were conducted independently for each number of snapshots. As shown in the figure, under both impulsive noise and small snapshot conditions, the array structure proposed in this invention maintained a high success probability of estimation. With decreasing snapshot numbers, the success probability of estimation decreased for all array structures. The array structure proposed in this invention exhibited the highest success probability, indicating that the proposed layout structure can adapt to the application conditions of small snapshots.

[0113] Figure 5 In the experiment, 15 snapshots were selected for the impulse noise downsampling, and 200 experiments were conducted independently for each generalized signal-to-noise ratio (SNR). As shown in the figure, the root mean square error (RMSE) increases as the SNR decreases. However, under the same number of snapshots and low SNR conditions, the array structure proposed in this invention exhibits higher direction-finding performance compared to other structures.

[0114] Figure 6 In this study, the number of snapshots under impulse noise was set to 15. The influence of the generalized signal-to-noise ratio (SNR) on the success probability of direction finding estimation for different array structures was investigated. It was determined that a successful estimation was defined as an error of less than 1.5° between the estimated value and the target. 200 independent experiments were conducted for each SNR. As shown in the figure, the success probability decreases with decreasing SNR. However, under the same number of snapshots and a low SNR condition, the array structure proposed in this invention exhibits higher direction finding performance compared to other structures.

[0115] Figure 7 In the process, it can be found that when the number of array elements in each subarray is not exactly the same, the performance is better as the number of snapshots increases. Compared with other situations, the present invention still has better performance. The present invention can adapt to complex environments with different numbers of array elements in subarrays under a certain number of snapshots.

[0116] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for optimal subarray distribution based on the quantum antelope optimizer, characterized in that, Includes the following steps: S100. Modeling of impact noise and source information in space, including, Establish a distributed array system arranged on the same straight line, the array system comprising multiple equidistant subarrays, each subarray comprising multiple equidistant array elements; Far-field narrowband signals in space are incident on the distributed array system from multiple directions and construct an azimuth matrix; S200. Construct an infinite norm weighted fractional low-order covariance matrix using the snapshot data received by the distributed array system, and perform direction estimation to obtain the root mean square error equation for the direction estimation. include, A model for receiving snapshot signals in a distributed array system is constructed. After processing the received signal, an infinite norm weighted fractional low-order covariance matrix is ​​constructed from the received data. Then, DOA estimation is performed based on the MUSIC algorithm. The fractional low-order covariance matrix is ​​decomposed into signal subspace and noise subspace. The spatial spectrum function of the MUSIC algorithm based on the low-order matrix is ​​derived. Finally, the objective function is obtained. S300. Initialize the quantum antelope population and obtain the local optimal measurement location and the global optimal measurement location, including: After initializing a quantum antelope population in quantum space, it is determined whether there are predators around the antelopes. If not, a global search is performed; if so, a local search is performed. Then, the fitness value of each antelope is calculated and sorted to obtain the corresponding optimal measurement location. S400, Update the quantum rotation angle and quantum position of each antelope according to its predation strategy, and then obtain the measured position, including, Based on the biomimetic mechanism of the antelope, when the antelope is free from predators, it adopts Brownian motion and updates its quantum position through a quantum rotation gate. After discovering a predator, the antelope enters two stages: when it first discovers the predator, it escapes by flying like Levi, and after a long chase, it escapes by using Brownian motion. The quantum rotation angle and quantum position are updated accordingly for the two stages, thus obtaining the corresponding measured position. S500: Calculate the updated measurement position fitness value, and update the local optimal position and the global optimal position; S600: Determine whether the maximum number of iterations has been reached. If not, return to step S400. If it has been reached, terminate the iteration and output the distributed layout position information of the required array by converting the global optimal position into the output.

2. The subarray optimal distribution method based on the quantum antelope optimizer according to claim 1, characterized in that: In step S100, the following are included: Assume the noise in the space satisfies Stable distribution of impulse noise, with characteristic index as ; Existing in space Each wavelength is The far-field narrowband signals are respectively from the m-th azimuth angle The direction of the incident light onto the array, where the azimuth angle is... , , , Let m be the m-th azimuth angle; establish a distributed array system with a total number of array elements. All array elements are arranged in a straight line. Multiple array elements form a subarray. The array elements in the subarray are equally spaced, with a spacing of [missing information]. The number of subarrays is , No. The number of array elements in each subarray is , ,so Furthermore, the spacing between each subarray is equal to the spacing between a single array element. The integer multiples of the values ​​are used to obtain the parameters to be optimized, which are the spacings between the subarrays.

3. The subarray optimal distribution method based on the quantum antelope optimizer according to claim 2, characterized in that: Step S200 includes, Distributed array system receives the first The model of the secondary snapshot signal is ,in , The maximum number of snapshots is given by the formula. , For a distributed array system to receive the Nth array element's... Second quick-snap signal, Let be the guiding matrix, where the first... The guide vectors are , The azimuth vector of the incoming wave. ; j represents the imaginary unit; d represents the spacing between each array element. For signal vectors, For a distributed array system to receive the Mth wavelength of the first wavelength Secondary signal vector Let be the independent and identically distributed impulse noise vectors of the array. Let N be the independent and identically distributed impulse noise vector of the Nth array element; The signal received by the array is processed to obtain ,in Using the processed array Receive data construction The low-order covariance matrix R of the infinite norm weighted fraction of the second snapshot is: ,in For the first The low-order covariance matrix of the sub-shot data. for 3D matrix Its kth quick shot Line 1 Column elements are ,in To find conjugate, , , The parameters are the fractional low-order covariance matrix; DOA estimation based on the MUSIC algorithm, focusing on the fractional low-order covariance matrix. Eigenvalue decomposition yields the signal subspace and the noise subspace. ,in It is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues. It is the impulse noise subspace spanned by the eigenvectors corresponding to small eigenvalues; It is a diagonal matrix composed of large eigenvalues. It is a diagonal matrix composed of small eigenvalues; Represents conjugate transpose; The spatial spectral function of the MUSIC algorithm based on low-order matrices is derived as follows: After searching the spectral peaks, the first The azimuth estimate for this experiment is , , where T is the number of experiments; Therefore, the objective function is obtained as follows: ,in For the potential solution of the array position structure, Indicates the distance between subarrays. , Let be the number of information sources in space. For the first The accurate location value of each information source. For the first sequence The location estimate of each information source.

4. The subarray optimal distribution method based on the quantum antelope optimizer according to claim 3, characterized in that: Step S300 includes, Initialize a quantum antelope population in quantum space. The quantum antelope population contains... Only one mountain antelope, the first The generation The first mountain antelope Quantum position Initialize randomly between [0,1], where , , Represents the total dimension; the measurement location is obtained as The measurement equation is ,in A random number that follows a uniform distribution between [0,1]. ; This represents the first [unit / item] in the generated herd of mountain antelopes. The generation The quantum position of a mountain antelope, that is The maximum number of iterations is ; set up For hunting probability, For a random number in the range [0,1], when Less than the hunting probability When the time is right, it means there are no predators hunting around the grazing antelopes, so a global search is needed; otherwise, it means there are predators hunting, so a local search is needed. The quantum position is obtained by determining the measurement position according to the measurement rules. Map it to array position Substituting these values ​​into the objective function to calculate the fitness, the fitness function becomes: ,in For the first The experiment The generation The distribution array corresponding to only one mountain antelope was obtained as the first Estimate the direction of arrival of the source wave; sort all fitness values, all antelopes up to the first... The optimal position obtained by the alternative search is denoted as the global optimal position. .

5. The subarray optimal distribution method based on the quantum antelope optimizer according to claim 4, characterized in that: In step S400, the following are included: Based on the biomimetic mechanism of the antelope, when free-range grazing occurs in the absence of predators, each antelope exhibits Brownian motion; when Less than the hunting probability At that time, the first Only mountain antelope The update equation for the quantum rotation angle in real-time global search of quantum position is: in, The speed at which the mountain antelope moves. It is a random number in the range [0,1], the first... Only mountain antelope Vibranium exercise factor These are random numbers that follow a standard normal distribution. For the first The generation Only mountain antelope Quantum rotation angle for real-time global search of quantum position; The first [item] is obtained through quantum rotating gate update. Only mountain antelope The quantum position is: in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between; when Greater than the hunting probability At that time, the first Only mountain antelopes conduct local searches; according to the biomimetic mechanism of mountain antelopes, after discovering a predator, mountain antelopes enter two stages: the first stage is when the mountain antelopes have just discovered the predator and use the Levi flight method to escape; the second stage is when the mountain antelopes become fatigued under the predator's frantic pursuit and escape using Brownian motion. In the first stage, a motion direction factor is generated. ,in It is -1 or 1; the first Only mountain antelope Villev's flight factor is The expression for the Levi flight factor is: ,in For Levi's flight stride, Random numbers that are distributed according to a standard normal distribution. As an adjustable variable in the Levy flight factor; then the first stage of the... The first mountain antelope The update equation for the quantum rotation angle is: in, The speed at which the mountain antelope moves. It is a random number in the range [0,1]. The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is: make As a fatigue algebra, when the number of iterations exceeds At this point, the antelope will become fatigued due to decreased physical strength, thus entering the second stage of escaping using Brownian motion, and thus achieving the second stage. Only mountain antelope The update equation for the quantum rotation angle is: in, The speed at which the mountain antelope moves. Brownian motion factor For variables representing the cumulative effect of predators, , Let it be one of the adjustable variables; The first [item] is obtained through quantum rotating gate update. Only mountain antelope The update equation for the quantum position is: in, A random number that follows a uniform distribution between [0,1]. This represents the probability of flipping the qubit when the quantum rotation angle is 0; its value is... The constants between; Through the first The generation Only mountain antelope Quantum position The measured position of the array position structure is obtained. Its measurement equation is ,in Let [0,1] be a random number that follows a uniform distribution. , ; will the first The generation The measured position of the mountain antelope is mapped to the corresponding array position. .

6. The subarray optimal distribution method based on the quantum antelope optimizer according to claim 5, characterized in that: Step S500 includes, Calculate the first The generation The fitness level of the mountain antelope is If the fitness of the updated quantum position is less than the fitness of the original quantum position, then... If the new quantum position is not found, the original quantum position will be replaced by the new one; otherwise, the original quantum position will be preserved, i.e., let... , , , comparison until All measurement location fitness values ​​of the generation are obtained until The global optimal position of the generation is .

7. A subarray optimal distribution system based on the quantum antelope optimizer, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-6 above, and executes the steps in the subarray optimal distribution method based on the quantum antelope optimizer described above when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the subarray optimal distribution method based on the quantum antelope optimizer as described in any one of claims 1-6.

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