Array sidelobe level suppression method optimized by reconfigurable antenna unit

Abstract

The application discloses an array sidelobe level suppression method through reconfigurable antenna unit optimization selection, and belongs to the technical field of wide array beam scanning. The application further narrows the search space by effectively cutting unnecessary reconfigurable pattern element REP combination in a scanning beam, and obtains a better REP combination according to beam direction change, so as to realize array sidelobe level suppression based on reconfigurable antenna unit optimization selection with lower calculation complexity. The application can adaptively match a corresponding directional diagram mode according to application requirements with different scanning angles, can further effectively reduce the sidelobe of an array antenna, can realize a wider scanning angle, can increase the effective coverage range of an array system, and can effectively improve the power coverage range of the array system.

Description

Technical Field

[0001] This invention belongs to the field of wide array beam scanning technology, specifically relating to a method for suppressing array sidelobe levels through optimized selection of reconfigurable antenna elements. Background Technology

[0002] Array antennas possess excellent beamforming capabilities. By optimizing element excitation, they can flexibly synthesize pencil beam patterns (BPB) and shaped-beam patterns (SBP), and are widely used in many modern devices. In many array antenna applications, a low-peak wide-area scanning capability (Peak Sidelobe Level, PSLL) is often required as a fundamental condition, including wireless communication, navigation, and ground-based satellite signal receiving systems. Current work on this issue mainly falls into two categories: The first is to configure the array using wide-beam elements. This method allows the array to scan a wider range. However, wide beams reduce the average gain of the elements, resulting in a lower gain for the array. Therefore, high-gain applications require a large number of elements to configure the array. The second approach is to configure the array using reconfigurable element patterns (REPs), using different reconstruction patterns of array elements to scan a wide range. Optimal REP selection is a typical non-deterministic polynomial-hard (NP-hard) problem. Its solution can only be obtained through a global search. For an N-element array where each element has K REPs, it is necessary to evaluate K... N The possible combinations of REPs are searched to find the optimal combination. Even with small N and K, solving the REP selection problem using a global search method is computationally quite complex.

[0003] Currently, there is little research on how different REP selections should adapt to changes in beam direction. The most common practice for these arrays with wide scans is to coarsely select the REP, i.e., whose beam direction is closest to the desired beam direction. However, such a coarse selection method generally results in a relatively high PSLL value. Summary of the Invention

[0004] This invention provides a method for suppressing array sidelobe levels through optimized selection of reconfigurable antenna elements. By effectively cutting unnecessary reconfigurable mode element (REP) combinations in the scanning beam, the search space is further reduced, and a better REP combination is adaptively obtained according to the beam direction change, thereby achieving array sidelobe level suppression based on optimized selection of reconfigurable antenna elements with low computational complexity.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for suppressing array sidelobe levels through optimized selection of reconfigurable antenna elements, comprising the following steps:

[0007] Step 1: Parameter initialization, including:

[0008] Set the array size N and the number of reconfigurable pattern element REP types K;

[0009] Set the population size for the genetic algorithm. Maximum number of iterations generation gap Crossover probability Probability of mutation and the length of the rectangular window for each type. Among them, the category number ;

[0010] Initialize the population There are N individuals, each of which includes N genes. The N genes of each individual are initialized using random initialization, and the N initialized genes of each individual include K possible REPs.

[0011] Step 2, calculate the wide array beam scanning capability (PSLL) for each individual in the current generation, denoted as... and the smallest among contemporary individuals Recorded as ;

[0012] Step 3, determine if the algebra g is less than If yes, proceed to step 4; otherwise, proceed to step 7.

[0013] Step 4: Perform the selection, crossover, and mutation operations of the genetic algorithm:

[0014] Based on individual fitness From contemporary times Select from individuals Individual (i.e., by) (selecting the i-th individual with probability), and for the selected individual... Each individual performs a crossover operation;

[0015] The individuals that have undergone crossover are mutated using the mutation operation to obtain... Find the current most recent individual; and calculate the number of each type of REP for each current most recent individual, denoted as . ;

[0016] Step 5, for each Determine the current Whether the number of REPs is selected in the desired pencil beam PBP direction within an N-element array. The range of retrievable values If yes, proceed to step 7; otherwise, proceed to step 6.

[0017] Step 6, determine the current individual's Is it less than If so, then redefine. The range of retrievable values And based on the redefined range of callable values Continue to step 5;

[0018] Otherwise, rearrange the genes of the current individual so that the individual corresponding to the rearranged genes... satisfy The range of retrievable values Then proceed to step 7;

[0019] Step 7, Update the next generation of individuals:

[0020] The latest Each individual is set as an individual in the (g+1)th generation, and from the (g)th generation... Select the first from among the individuals indivual The smallest individual is taken as the individual of the (g+1)th generation, and the (g+1)th generation is obtained. Individual;

[0021] Calculate the g+1 generation PSLL for each individual, based on Minimum update of individual PSLL and updating the genetic generation. Then, proceed to step 3;

[0022] Step 8, based on the current generation The smallest of the individuals The optimal selection result of reconfigurable antenna elements (i.e., the optimal PSLL result) is obtained by arranging the genes of individuals, and beam scanning is performed based on the optimal selection result of reconfigurable antenna elements to achieve the purpose of suppressing the array sidelobe level.

[0023] The technical solution provided by this invention brings at least the following beneficial effects:

[0024] For applications with different scanning angles, adaptive matching of the corresponding radiation pattern can further and effectively reduce the sidelobes of the array antenna, thereby achieving a wider scanning angle, increasing the effective coverage of the array system, and thus effectively improving the power coverage of the array system. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A schematic diagram of the REP fixed algorithm and the random selection algorithm;

[0027] Figure 2 For an AEP with a 32-element linear array having two reconfigurable modes, (2-a) is mode 1 and (2-b) is mode 2;

[0028] Figure 3 The results show the synthesis of two types of REP using different algorithms under different beam directions, where the beam direction of (3-a) is... The beam direction of (3-b) is The beam direction of (3-c) is The beam direction of (3-c) is ;

[0029] Figure 4 The PSLLs obtained by different algorithms for two types of REP under different beam directions are shown in (4-a), where (4-b) shows the PSLLs obtained by different algorithms and (4-c) shows the PSLL differences between the method of this invention and other comparative algorithms.

[0030] Figure 5 PSLL obtained by different algorithms for two types of REP under different beam directions, where the minimum angular distance in (5-a) is... , 5-(b) (5-c) . Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0032] Genetic Algorithms (GAs) are widely used to solve array synthesis problems due to their ability to effectively solve any combinatorial optimization problem. This invention improves the genetic algorithm by effectively cutting unnecessary REP combinations in the scanning beam. This allows for maintaining a high probability of optimal REP combinations while further narrowing the search space. Furthermore, it adaptively selects REP combinations based on changes in beam direction, further suppressing PSLL in the scanning PBP.

[0033] Consider a linear array antenna with N elements, assuming its position is... , The electric field strength of the array antenna can then be described as:

[0034] (1)

[0035] in, , and These are the excitation of the array element factor, the array factor, and the k-th REP of the n-th element, respectively. Indicates the incident direction of the signal source, the direction is in The changes between them, among which It is the wavelength of electromagnetic waves.

[0036] Vectorizing the above equation, we get:

[0037] (2)

[0038] in

[0039] (3)

[0040] in, Indicates array excitation, Indicates the array steering vector. Represents array REP, symbol This represents element-wise multiplication between two vectors.

[0041] Therefore, the problem of minimizing the PBP synthesis (PBPS) of PSLL by selecting the optimal REP combination can be formulated as follows:

[0042] (4)

[0043] in, The beam direction of the PBP. This is the sidelobe region. Therefore, the optimization problem is to simultaneously select the optimal... and optimal REP combination This minimizes the PSLL. Simplifying the problem, we can divide it into two sub-problems:

[0044] Subproblem 1:

[0045] (5)

[0046] Subproblem 2:

[0047] (6)

[0048] The first subproblem, the incentive optimization problem, is convex and can be solved using existing tools such as CVX. The second subproblem, the REP combinatorial selection problem, is nonconvex, making it quite difficult to obtain the optimal solution to problem (6).

[0049] The commonly used methods for solving the REP combinatorial selection problem are the REP fixed algorithm, which selects the same reconstruction mode for all array elements; or the random selection algorithm, which selects a reconstruction mode independently and randomly for each array element. Figure 1 The computational results for two methods of solving the REP combinatorial choice problem are presented. Figure 1 middle, This is represented as a fixed REP algorithm where all array elements are in mode 1. REP represents the fixed algorithm where all array elements are in mode 2, while RND represents the random selection algorithm where array elements are randomly selected independently in mode 1 or mode 2.

[0050] Genetic algorithms simulate biological evolution through the genetic mechanisms of natural selection and Darwinian evolution. Their basic idea is to evolve a group of candidate solutions into better solutions, and they are widely used to solve search problems. The population evolves through selection, crossover, mutation, and recombination operations. This invention improves the genetic algorithm to effectively reduce the REP combination space and select the optimal REP combination.

[0051] For a PBPS problem with an array of N elements, where each element has K REPs, the specific implementation steps for selecting REP combinations using a genetic algorithm include:

[0052] Population initialization: Set the population size to [value]. (Preset values; specific values ​​depend on the application scenario). Each individual has N genes (array elements), and each gene has K distinct possible values ​​(REPs). Genes are randomly initialized, and the initialized genes should include all K possible REPs. The maximum number of generations to evolve is set. .

[0053] Selection operation: For generation g (with an initial value of 1), select a subset of individuals to generate generation (g+1), and evaluate their fitness values ​​to obtain a better solution (PSLL: That is, selection. Each individual undergoes the following crossover and mutation operations, where... This is the generation gap ratio. (Definition) Describes the PSLL of the i-th individual and ,definition Let represent the fitness of the i-th individual. Current total fitness , Here is ,by The probability is used to select the i-th individual to generate the (g+1)-th generation.

[0054] Crossover operation: Crossing over two adjacent parent individuals in the g-th generation (i.e., those selected in the selection operation) (g+1) individuals are crossbred to generate offspring of the (g+1)th generation. The crossbringing probability is... Uniform crossover is used, meaning that the genes of two crossover individuals are exchanged with equal probability.

[0055] Mutation operation: For any individual in generation g, the two types of mutations occur with equal probability, i.e., 50%:1). A set of randomly located genes (out of a total of N genes) ) with probability 1) Mutation occurs; 2) A set of random continuous genes, with probability Reverse the order. Among them... This represents the probability of mutation.

[0056] Recombination operation: The (g+1)th generation individuals are formed by crossover and mutation operations. The lowest PSLL for each individual and the g-th generation It consists of individual entities.

[0057] REP combination space contraction strategy:

[0058] Each element has K possible REP choices, so the REP combination size is K. N REPs with beam directions closer to the desired PBP direction are more likely to be selected for synthesizing a better PBP; conversely, REPs with beam directions farther from the desired PBP direction will be used less frequently. Assume the desired PBP direction is... The specific process for selecting REP combinations is as follows:

[0059] Determine the number of choices for the k-th REP: Let express The normalized power beam pattern of the k-th REP in the direction, and the beam direction of the k-th REP is... The desired beam direction of the PBP is .definition , Then N array elements are arranged in order to The number of selected k-th REPs for the desired PBP direction is initialized as follows:

[0060] (7)

[0061] To improve the robustness of genetic algorithms, allow In a length of The rectangular window changes. For ease of application, It is set to an even number. Therefore, The adjustable range is ,Right now ,in and The minimum and maximum quantities are defined as follows:

[0062] (8)

[0063] Modify formula (8) Range or rearrangement of an individual's genes: Let the minimum PSLL obtained by the g-th generation individual be defined as Given formula (8) The scope does not satisfy the individual REP combination. The constraints can be handled in the following two ways: 1) The individual's PSLL is lower than 2) The individual's PSLL is higher than For case 1, the definition will be redefined in formula (8). Constraints, and for case 2, the individual's genes are rearranged to meet the requirements. Constraints. For the i-th individual, assume it has... A different REP.

[0064] Scenario 1: A new The constraints are defined as follows:

[0065] (9)

[0066] Case 2: For any k-th REP of the i-th individual, its current number may be less than the allowed lower bound, i.e. Or greater than the upper limit of allowable limits, i.e. In this case, adjust the number of the k-th gene, for example... You can choose from a range of options, that is... , and The definition is as follows:

[0067] (10)

[0068] In the integer field The number of adjustments to the k-th REP is randomly selected, i.e. . A positive value indicates that the k-th REP needs to be deleted, while a negative value indicates that the k-th REP needs to be added. To ensure that the total number of REPs remains unchanged, we have: .if The random selection is always the kth REP. A gene is replaced with another REP. When the k-th REP is adjusted, the related genes in the individual will remain unchanged in subsequent operations. This process is repeated until the desired result is achieved. constraint.

[0069] As one possible implementation, the specific steps of the array sidelobe level suppression method with reconfigurable antenna element optimization provided in this embodiment of the invention include:

[0070] Step S1: Parameter initialization, including:

[0071] Set the array size N and the number of REP species K; set the population size. Maximum number of iterations generation gap Crossover probability Probability of mutation Length of rectangular window ; and initialization algebra ;

[0072] Step S2, calculate PSLL, i.e. ,definition ;

[0073] Step S3, if If the condition is met, proceed to step S4; otherwise, proceed to step S7.

[0074] Step S4: Perform the selection, crossover, and mutation operations of the genetic algorithm.

[0075] Select by choosing an operation. Individual;

[0076] The selection in the selection operation Each individual performs a crossover operation;

[0077] The mutation operation is used to mutate the individuals that have undergone the crossover operation;

[0078] Calculate the k-th mutation of each individual. The number of REPs is recorded as follows: ;

[0079] Step S5, determine If the quantity is within the range defined by formula (8), proceed to step S7; otherwise, proceed to step S6.

[0080] Step S6, determine the obtained PSLL ( Is it lower than If (i.e.) Then, according to formula (9), redefine... Constraints are applied, and then step S7 is executed; if not (i.e.) Then, according to case 2 (formula (10)), the individual's genes are rearranged to meet the requirements. Set constraints, and then proceed to step S7;

[0081] Step S7, update the next generation of individuals:

[0082] The latest individual is designated as generation g+1, and generation g+1 is constructed through recombination operations. The individuals, i.e., the (g+1)th generation individuals, are formed by crossover and mutation operations. The lowest PSLL for each individual and the g-th generation Composed of individual entities;

[0083] Simultaneously updated and updating the genetic generation. Then, continue with step S3;

[0084] Step S8, output the optimal PSLL, that is The gene arrangement of the lowest individual.

[0085] To further verify the performance of the method of this invention, simulation verification was conducted through test experiments. This test experiment used a 32-element half-wavelength uniformly distributed linear array with two types of REPs. The Active Element Pattern (AEP) was simulated using full-wave simulation, considering the mutual coupling effect between array elements. The angular resolution was set to... The beamwidth of the synthesized PBP in the simulation is defined as the minimum angular distance from the beam direction to the sidelobe region, denoted as . . Figure 2 (2-a) and (2-b) in the figure show REP mode 1 and REP mode 2 with different elements, respectively. All simulations in this test used these two AEPs.

[0086] The specific parameter configurations in this test experiment are as follows: population size. The maximum number of generations of evolution generation gap Crossover probability Probability of mutation Length of rectangular window Beam direction beamwidth The sidelobe regions are respectively , , and .

[0087] The specific element selection modes of different algorithms for the two types of REPs under different beam directions in this test experiment are shown in Table 1. The two types of REPs were tested using different algorithms under different beam directions. The PSLL obtained from the data is shown in Table 2.

[0088] Table 1

[0089]

[0090] Table 2

[0091]

[0092] Figure 3 The synthesis results of different algorithms under different beam directions are presented as synthesis results. Figure 3 The synthesis results shown indicate that, for all cases, although all compared algorithms can synthesize beam patterns pointing in the desired direction, the method of this invention always achieves the lowest PSLL. Furthermore, Table 1 shows the element selection modes of different algorithms under different beam directions, demonstrating that different PBPs can be synthesized by selecting different REP modes for array elements using different algorithms. For the REP fixed algorithm, in... Figure 3 In (3-a), when the beam direction is hour, Performance is better than In the other three cases, The performance is inferior to ,Right now This is mainly because the beam pattern pointing in REP mode 1 is different from the desired beam pointing, i.e. If they are similar, then It can synthesize beam patterns with better performance, while for other beam directions, Synthetic beam pattern performs better.

[0093] To more clearly demonstrate the performance, Table 2 shows the PSLL obtained using different algorithms in different beam directions. The results in Table 2 show that the method of the present invention achieves the lowest PSLL under all different conditions. Compared to... , And "RED" can further suppress PSLL. In the direction, the suppression is approximately 0.55 dB, 19.16 dB, and 4.05 dB compared to other algorithms; in In the direction, the suppression is approximately 1.41dB, 0.44dB, and 3.68dB compared to other algorithms; in In the direction, the suppression is approximately 2.85dB, 1.14dB, and 0.82dB compared to other algorithms; in In the direction of the algorithm, the suppression is approximately 4.26 dB, 3.76 dB, and 0.40 dB compared to other algorithms. Therefore, it is demonstrated that the REP selection scheme proposed in this invention is effective in further suppressing PSLL.

[0094] To demonstrate scanning capabilities, Figure 4 All algorithms in arrive Angular resolution is The PSLL obtained from scanning within the range is plotted. Figure 5 (5-a) shows the PSLL obtained by each algorithm in different beam directions. Figure 5 Figure (5-b) shows the PSLL difference between the proposed method and other comparative algorithms. The results show that the proposed method always achieves the minimum PSLL value. On average across all beam directions, compared to… , Compared to the "RND" algorithm, the method of this invention can further suppress PSLL by approximately 2.23 dB, 2.79 dB, and 2.82 dB. When the beam direction is from... Scanned In terms of direction, the method of the present invention is the same as The PSLL difference increases, and The PSLL difference decreases.

[0095] To verify the combining performance of PBP with other beamwidth settings, i.e., using different beamwidth values . Figure 5 The PSLL obtained by different algorithms under different scan directions is shown. Figure 4 The results given in (4-a) further demonstrate that the method of this invention can achieve the lowest PSLL under different beamwidths and beam directions. Statistically, its performance is superior to the REP selection algorithm, i.e., the "RND" algorithm; it is also superior to the REP fixing algorithm, i.e. , algorithm.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0097] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for suppressing array sidelobe levels through optimized selection of reconfigurable antenna elements, characterized in that, Includes the following steps: Step 1: Parameter initialization: Set the array size N and the number of reconfigurable pattern element REP types K; Set the population size for the genetic algorithm. Maximum number of iterations generation gap Crossover probability Probability of mutation ; Initialize the population There are N individuals, each of which includes N genes. The N genes of each individual are initialized using random initialization, and the N initialized genes of each individual include K possible REPs. Step 2, calculate the wide array beam scanning capability (PSLL) for each individual in the current generation, denoted as... and the smallest among contemporary individuals Recorded as ; Step 3, determine if the algebra g is less than If so, proceed to step 4; Otherwise, proceed to step 7; Step 4: Perform the selection, crossover, and mutation operations of the genetic algorithm: Based on individual fitness From contemporary times Select from individuals Individuals, and the selected Each individual performs a crossover operation; The individuals that have undergone crossover are mutated using the mutation operation to obtain... The most current individual; And calculate the latest number of each type of REP for each individual, denoted as . Category number ; Step 5, for each Determine the current Whether the number of REPs is selected in the desired pencil beam PBP direction within an N-element array. The range of retrievable values If yes, proceed to step 7; otherwise, proceed to step 6. Step 6, determine the current individual's Is it less than If so, then redefine. The range of retrievable values And based on the redefined range of callable values Continue to step 5; Otherwise, rearrange the genes of the current individual so that the individual corresponding to the rearranged genes... satisfy The range of retrievable values Then proceed to step 7; Step 7, Update the next generation of individuals: The latest Each individual is set as an individual of generation g+1, and from generation g... Select the first from among the individuals indivual The smallest individual is taken as the individual of the (g+1)th generation, and the (g+1)th generation is obtained. Individual; Calculate the g+1 generation PSLL for each individual, based on Minimum update of individual PSLL and updating the genetic generation. Then, proceed to step 3; Step 8, based on the current generation The smallest of the individuals The optimal selection result of reconfigurable antenna elements is obtained by arranging the genes of individuals, and beam scanning is performed based on the optimal selection result of reconfigurable antenna elements.

2. The method as described in claim 1, characterized in that, fitness Specifically: ； in, This represents the maximum PSLL among contemporary individuals.

3. The method as described in claim 1, characterized in that, In step 5, The range of retrievable values Specifically set as follows: calculate Initial value: ； Among them, parameters ,parameter , This indicates the desired beam direction of the PBP. express Normalized power beam pattern of the k-th REP in the direction, This indicates the beam direction of the k-th REP; based on initial value setting Minimum quantity and maximum quantity : ， ； in, This represents the length of the rectangular window of the preset k-th REP.

4. The method as described in claim 1, characterized in that, Step 6, Redefine The range of retrievable values Specifically: ,in, This represents the preset rectangular window length of the k-th REP. .

5. The method as described in claim 1, characterized in that, In step 6, the specific steps of rearranging the genes of the current individual are as follows: Set upper and lower limits for the number of REP modulations for any k-th gene: ； in, , This indicates adjusting the number of the k-th gene. The lower and upper limits; In modulation quantity range The number of adjustments randomly selected from the k-th REP ,and ; For each gene of the current individual, if Then, the random selection is always the kth REP. One gene, replaced with another REP; if If so, then add the k-th REP to the genes of the current individual.

Images