Continuous non-uniform subarray division method based on discrete difference optimization algorithm

Abstract

A discrete differential evolution algorithm-based continuous non-uniform subarray division method comprises the following implementation steps of: firstly, establishing an array antenna uniform linear array model; secondly, initializing discrete differential evolution algorithm parameters; then, randomly generating an initial population and calculating a fitness value; then, variation, crossover, discrete distribution and selection operations are executed in sequence; and finally, judging whether an iteration evolution termination condition is met or not, if so, outputting a subarray division scheme with the minimum fitness value, and if not, continuing iteration. The method can accurately obtain a reasonable sub-array division scheme, overcomes grating lobes and grating zero point effects, has global search and fast convergence characteristics, and is applied to the technical field of array antenna sub-array division.

Description

Technical Field

[0001] This invention relates to the field of array antenna subarray partitioning technology, specifically to a method for partitioning continuous non-uniform subarrays. Background Technology

[0002] In multifunctional array antennas, the array typically consists of tens of thousands of elements. If beamforming is performed at the element level, each antenna element corresponds to a receiving channel, and the received signal undergoes multiple RF amplifications, frequency conversions, analog-to-digital converters, and subsequent digital signal processing. This results in prohibitively high hardware costs, making it impractical in terms of scale and cost. A common approach is to divide the tens of thousands of elements into several subarrays according to specific rules. Elements within a subarray share a single receiving channel. The subarray's internal units use analog beamforming technology for the first stage of beamforming. Then, the beams output from the subarrays are acquired by an ADC and digitally formed into a beam. After subarray division, the number of subarrays is much smaller than the number of elements, significantly reducing the required receiving channels. Subsequent array signal processing at the subarray level reduces computational load, accelerates convergence, and significantly lowers hardware consumption.

[0003] Currently, large-scale multi-functional arrays often employ uniform subarray division, meaning each subarray has the same number of elements. However, the periodic distribution of the subarray phase centers in a uniform subarray structure leads to severe grating lobe and grating null effects. Grating lobes reduce antenna directivity, hindering anti-interception capabilities; grating nulls cause main lobe distortion and reduced antenna gain. Continuous non-uniform subarray structures, by breaking the periodicity of the subarray phase centers, effectively mitigate grating lobe and grating null effects, becoming a primary method for addressing this problem. A continuous subarray is one where there are no overlapping elements between subarrays, and each subarray is a full-element structure; a non-uniform array is one where the number of elements in each subarray is different.

[0004] However, existing non-uniform subarray partitioning techniques still have significant limitations. Existing partitioning algorithms mostly rely on traditional methods such as genetic algorithms, particle swarm optimization, or enumeration. Among these, the crossover and mutation operations in genetic algorithms easily lead to premature loss of population diversity, making it difficult to traverse the entire feasible solution space when dealing with discrete subarray allocation problems in large-scale arrays, and prone to getting trapped in local optima. Particle swarm optimization algorithms have insufficient convergence accuracy in discrete decision domains, and the optimized subarray size configurations are often suboptimal solutions with limited grating lobe suppression effects. Furthermore, while enumeration, as a brute-force search scheme, can theoretically traverse all possible subarray partitioning combinations to obtain the global optimum, the number of feasible subarray partitioning solutions grows exponentially with the number of array elements, leading to a geometric increase in computational cost.

[0005] Generally, given the number of antenna array elements, the desired number of subarrays, and related array operating parameters, there is a pressing need for an efficient global optimization algorithm to achieve ideal subarray partitioning. The continuous non-uniform subarray partitioning method based on the discrete difference optimization algorithm proposed in this invention addresses this technical challenge. Summary of the Invention

[0006] The problem this invention aims to solve is: given the number of antenna array elements, the number of subarrays to be divided, and related array operating parameters, how to perform continuous non-uniform subarray partitioning while overcoming grating lobe and grating null effects. The method for solving this technical problem is a continuous non-uniform subarray partitioning method based on a discrete difference optimization algorithm, the implementation steps of which are as follows:

[0007] (1) The array to be divided is a uniform linear array, and the total number of array elements is... Array element spacing for , Indicates the wavelength of the incoming signal;

[0008] (2) The subarray partitioning pattern used in this method is a centrally symmetric structure; let The individual element array needs to be divided into Individual formations, The number is even; in this mode, the number of elements in the symmetrical subarrays remains the same, for example, the first and second elements are the same. The second subarray is related to the first one. The number of elements in each subarray is the same; therefore, in practical implementation, only the previous one needs to be optimized. The partitioning scheme for the subarray is given, and the second half of the scheme can be automatically generated based on the principle of symmetry, which reduces the population-individual dimension of the optimization problem. ;

[0009] (3) Set the number of individuals in the population according to the discrete difference optimization algorithm. Maximum number of generations Mutation operators Cross operator Upper bound condition for the number of elements in each subarray Lower bound condition for the number of elements in each subarray All of the above parameters are constants;

[0010] (4) Initialize the number of generations ;

[0011] (5) Randomly generate the initial population, that is, randomly generate P individuals of dimension D. ,in It is the j-th component of the i-th individual in the initial population, representing the number of elements in the j-th subarray. The superscript represents the generation number, which is generated as follows:

[0012]

[0013] in, Represents a random number between 0 and 1. This indicates a truncation / rounding operation. , ;

[0014] (6) For each individual in the contemporary era The fitness value is obtained by calculating the fitness value. The specific calculation steps are as follows:

[0015] The first step is to determine the individual population from the initial population. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ,in ;

[0016] The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ;

[0017] The third step is to record the individual with the lowest fitness value as... ;

[0018] (7) Perform mutation operation. The mutation operation adopts the DE / best / 1 strategy and is performed on each individual in the parent generation. Mutation occurs, resulting in mutated individuals. , This represents the j-th component of the i-th mutated individual. The calculation method is as follows:

[0019]

[0020] in, Represents individuals of generation g Variable individuals, The individual with the lowest fitness value among the individuals of generation g. It is a mutation operator. For difference individual vectors, , This represents the index of an individual randomly selected from the g-th generation population. ;

[0021] (8) Perform crossover operation, parent individual and mutated individuals Cross-combination to form cross individuals , The j-th component of the i-th crossover individual is calculated as follows:

[0022]

[0023] in, equals interval A random positive integer value, and Keeping the i-th individual unchanged, This represents the j-th component of the i-th individual in the g-th generation. It is the crossover probability;

[0024] (9) Perform discrete allocation operation, the specific operation is as follows:

[0025] The first step is to calculate each crossover individual. Each component The absolute weight is calculated as follows:

[0026]

[0027] in, Indicates taking the absolute value;

[0028] The second step is to initialize each crossover individual. Set a D-dimensional mapping individual If the value of this individual element is all 1, it means that each subarray is assigned only 1 element. Therefore, the number of remaining elements is... ;

[0029] The third step is to perform the allocation operation, based on the previously calculated crossover individuals. Absolute weight of each component The remaining array elements are allocated as follows:

[0030]

[0031] in, Indicates rounding down;

[0032] The fourth step is to update the number of remaining array elements after allocation. , ,at this time ;

[0033] The fifth step is to make a judgment. If If the discrete allocation operation ends, jump to (10); if Proceed to step six;

[0034] Step 6: Perform redistribution and extract overlapping individuals. Absolute weight of each component and The fractional part of the product , The method for calculating the j-th component is as follows:

[0035]

[0036] Will Sort in descending order to obtain the descending sorted index. ,satisfy:

[0037]

[0038] Use the remaining array elements Distributed equally The first two in descending order Each subarray remains unchanged, while the others remain the same.

[0039]

[0040] (10) Perform the selection operation, the specific operation is as follows:

[0041] The first step is to assign individuals based on each discrete distribution. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ;

[0042] The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ;

[0043] The third step is to map each discrete individual fitness value With each individual of generation g fitness value A one-to-one comparison was performed, and individuals with lower fitness values ​​were retained:

[0044]

[0045] in This represents a successful entry into the [number]th [stage / section]. A formal individual of the era;

[0046] Step 4, record Formal individuals of the generation fitness value And the individual with the smallest fitness value is denoted as ;

[0047] (11) Perform an iteration termination check:

[0048] like ,make Jump to step (7);

[0049] like Then Output as the final subarray partitioning form.

[0050] The beneficial effects of this invention are: given the number of antenna array elements, the number of subarrays to be divided, and the relevant array operating parameters, it can accurately obtain a reasonable subarray division scheme, overcome the grating lobe and grating null effects, and the algorithm has global search and efficient convergence characteristics. The calculation process is simple and easy to implement, and it can be widely applied in the field of array antenna subarray division technology. Attached Figure Description

[0051] Figure 1 This is a schematic diagram illustrating the overall steps of the method implementation;

[0052] Figure 2 This is a schematic diagram of a uniform linear array antenna model. Detailed Implementation

[0053] First, establish a uniform linear array model of the antenna array, such as Figure 2 As shown; initialize the discrete differential evolution algorithm parameters, including the number of individuals in the population. Maximum number of generations Mutation operators Crossover operator CR, upper bound condition , lower bound condition The process involves: randomly generating an initial population; calculating the fitness of the initial population and recording the individual with the smallest fitness value; performing a mutation operation to obtain mutated individuals; performing a crossover operation by combining the mutated individuals with their parents to obtain crossover individuals; performing a discrete allocation operation on the crossover individuals to obtain discretely allocated individuals; performing a selection operation on the discretely allocated individuals and their parents, retaining individuals with smaller fitness values ​​for the next generation; evolving to the maximum number of generations to obtain the final population, with the individual with the smallest fitness function value being output as the final subarray partition. The overall steps are as follows: Figure 1 As shown. The specific implementation steps are as follows:

[0054] (1) The array to be divided is a uniform linear array, and the total number of array elements is... Array element spacing for , Indicates the wavelength of the incoming signal;

[0055] (2) The subarray partitioning pattern used in this method is a centrally symmetric structure; let The individual element array needs to be divided into Individual formations, The number is even; in this mode, the number of elements in the symmetrical subarrays remains the same, for example, the first and second elements are the same. The second subarray is related to the first one. The number of elements in each subarray is the same; therefore, in practical implementation, only the previous one needs to be optimized. The partitioning scheme for the subarray is given, and the second half of the scheme can be automatically generated based on the principle of symmetry, which reduces the population-individual dimension of the optimization problem. ;

[0056] (3) Set the number of individuals in the population according to the discrete difference optimization algorithm. Maximum number of generations Mutation operators Cross operator Upper bound condition for the number of elements in each subarray Lower bound condition for the number of elements in each subarray All of the above parameters are constants;

[0057] (4) Initialize the number of generations ;

[0058] (5) Randomly generate the initial population, that is, randomly generate P individuals of dimension D. ,in It is the j-th component of the i-th individual in the initial population, representing the number of elements in the j-th subarray. The superscript represents the generation number, which is generated as follows:

[0059]

[0060] in, Represents a random number between 0 and 1. This indicates a truncation / rounding operation. , ;

[0061] (6) For each individual in the contemporary era The fitness value is obtained by calculating the fitness value. The specific calculation steps are as follows:

[0062] The first step is to determine the individual population from the initial population. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ,in Normalized subarray pattern refers to a pattern in which each subarray is treated as an independent element under a specific subarray partitioning scheme, and the phase center of the subarray is regarded as the position of the independent element. The far-field normalized pattern is then called the normalized subarray pattern.

[0063] The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ;

[0064] The third step is to record the individual with the lowest fitness value as... ;

[0065] (7) Perform mutation operation. The mutation operation adopts the DE / best / 1 strategy and is performed on each individual in the parent generation. Mutation occurs, resulting in mutated individuals. , This represents the j-th component of the i-th mutated individual. The calculation method is as follows:

[0066]

[0067] in, Represents individuals of generation g Variable individuals, The individual with the lowest fitness value among the individuals of generation g. It is a mutation operator. For difference individual vectors, , This represents the index of an individual randomly selected from the g-th generation population. ;

[0068] (8) Perform crossover operation, parent individual and mutated individuals Cross-combination to form cross individuals , The j-th component of the i-th crossover individual is calculated as follows:

[0069]

[0070] in, equals interval A random positive integer value, and Keeping the i-th individual unchanged, This represents the j-th component of the i-th individual in the g-th generation. It is the crossover probability;

[0071] (9) Perform discrete allocation operation, the specific operation is as follows:

[0072] The first step is to calculate each crossover individual. Each component The absolute weight is calculated as follows:

[0073]

[0074] in, Indicates taking the absolute value;

[0075] The second step is to initialize each crossover individual. Set a D-dimensional mapping individual If the value of this individual element is all 1, it means that each subarray is assigned only 1 element. Therefore, the number of remaining elements is... ;

[0076] The third step is to perform the allocation operation, based on the previously calculated crossover individuals. Absolute weight of each component The remaining array elements are allocated as follows:

[0077]

[0078] in, Indicates rounding down;

[0079] The fourth step is to update the number of remaining array elements after allocation. , ,at this time ;

[0080] The fifth step is to make a judgment. If If the discrete allocation operation ends, jump to (10); if Proceed to step six;

[0081] Step 6: Perform redistribution and extract overlapping individuals. Absolute weight of each component and The fractional part of the product , The method for calculating the j-th component is as follows:

[0082]

[0083] Will Sort in descending order to obtain the descending sorted index. ,satisfy:

[0084]

[0085] Use the remaining array elements Distributed equally The first two in descending order Each subarray remains unchanged, while the others remain the same.

[0086]

[0087] (10) Perform the selection operation, the specific operation is as follows:

[0088] The first step is to assign individuals based on each discrete distribution. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ;

[0089] The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ;

[0090] The third step is to map each discrete individual fitness value With each individual of generation g fitness value A one-to-one comparison was performed, and individuals with lower fitness values ​​were retained:

[0091]

[0092] in This represents a successful entry into the [number]th [stage / section]. A formal individual of the era;

[0093] Step 4, record Formal individuals of the generation fitness value And the individual with the smallest fitness value is denoted as ;

[0094] (11) Perform an iteration termination check:

[0095] like ,make Jump to step (7);

[0096] like Then Output as the final subarray partitioning form.

Claims

1. A method for partitioning a continuous non-uniform subarray based on a discrete difference optimization algorithm, the implementation steps of which are: (1) The array to be divided is a uniform linear array, and the total number of array elements is... Array element spacing for , Indicates the wavelength of the incoming signal; (2) The subarray partitioning pattern used in this method is a centrally symmetric structure; let The individual element array needs to be divided into Individual formations, The number is even; in this mode, the number of elements in the symmetrical subarrays remains the same, for example, the first and second elements are the same. The second subarray is related to the first one. The number of elements in each subarray is the same; therefore, in practical implementation, only the previous one needs to be optimized. The partitioning scheme for the subarray is given, and the second half of the scheme can be automatically generated based on the principle of symmetry, which reduces the population-individual dimension of the optimization problem. ; (3) Set the number of individuals in the population according to the discrete difference optimization algorithm. Maximum number of generations Mutation operators Cross operator Upper bound condition for the number of elements in each subarray Lower bound condition for the number of elements in each subarray All of the above parameters are constants; (4) Initialize the number of generations ; (5) Randomly generate the initial population, that is, randomly generate P individuals of dimension D. ,in It is the j-th component of the i-th individual in the initial population, representing the number of elements in the j-th subarray. The superscript represents the generation number, which is generated as follows: in, Represents a random number between 0 and 1. This indicates a truncation / rounding operation. , ; (6) For each individual in the contemporary era The fitness value is obtained by calculating the fitness value. The specific calculation steps are as follows: The first step is to determine the individual population from the initial population. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ,in ; The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ; The third step is to record the individual with the lowest fitness value as... ; (7) Perform mutation operation. The mutation operation adopts the DE / best / 1 strategy and is performed on each individual in the parent generation. Mutation occurs, resulting in mutated individuals. , This represents the j-th component of the i-th mutated individual. The calculation method is as follows: in, Represents individuals of generation g Variable individuals, The individual with the lowest fitness value among the individuals of generation g. It is a mutation operator. For difference individual vectors, , This represents the index of an individual randomly selected from the g-th generation population. ; (8) Perform crossover operation, parent individual and mutated individuals Cross-combination to form cross individuals , The j-th component of the i-th crossover individual is calculated as follows: in, equals interval A random positive integer value, and Keeping the i-th individual unchanged, This represents the j-th component of the i-th individual in the g-th generation. It is the crossover probability; (9) Perform discrete allocation operation, the specific operation is as follows: The first step is to calculate each crossover individual. Each component The absolute weight is calculated as follows: in, Indicates taking the absolute value; The second step is to initialize each crossover individual. Set a D-dimensional mapping individual If the value of this individual element is all 1, it means that each subarray is assigned only 1 element. Therefore, the number of remaining elements is... ; The third step is to perform the allocation operation, based on the previously calculated crossover individuals. Absolute weight of each component The remaining array elements are allocated as follows: in, Indicates rounding down; The fourth step is to update the number of remaining array elements after allocation. , ,at this time ; The fifth step is to make a judgment. If If the discrete allocation operation ends, jump to (10); if Proceed to step six; Step 6: Perform redistribution and extract overlapping individuals. Absolute weight of each component and The fractional part of the product , The method for calculating the j-th component is as follows: Will Sort in descending order to obtain the descending sorted index. ,satisfy: Use the remaining array elements Distributed equally The first two in descending order Each subarray remains unchanged, while the others remain the same. (10) Perform the selection operation, the specific operation is as follows: The first step is to assign individuals based on each discrete distribution. Calculate the normalized subarray pattern under the corresponding subarray partitioning method. ; The second step is to normalize the subarray orientation pattern for each individual. Find the highest sidelobe level in the radiation pattern. As the fitness value of this individual ; The third step is to map each discrete individual fitness value With each individual of generation g fitness value A one-to-one comparison was performed, and individuals with lower fitness values ​​were retained: in This represents a successful entry into the [number]th [stage / section]. A formal individual of the era; Step 4, record Formal individuals of the generation fitness value And the individual with the smallest fitness value is denoted as ; (11) Perform an iteration termination check: like ,make Jump to step (7); like Then Output as the final subarray partitioning form.

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