Sparse MIMO array optimization design method based on subarray structure constraint

Abstract

The application discloses a sparse MIMO array design method based on genetic optimization, which is used for realizing high-resolution virtual array construction under the condition of reducing the number of transmitting and receiving array elements, and comprises the following steps: firstly, multiple geometric subarray structure constraints are constructed according to array performance evaluation indexes; then, population and system parameter settings are initialized; secondly, a multi-objective constraint model is established with the optimization target of maximizing fitness; subsequently, the model is solved by using an improved genetic algorithm until the algorithm converges, and finally, a sparse MIMO array structure satisfying the performance optimization and the quantity constraint is obtained. Compared with the prior art, the application enhances the controllability of the array structure by introducing the geometric subarray constraint, and guarantees the expected aperture form of the virtual array; the improved genetic algorithm can realize global search under the condition of fixed antenna number, and avoids local optimization; compared with the traditional method, the application has good engineering implementation and algorithm universality.

Description

Technical Field

[0001] This invention discloses a sparse MIMO array optimization design method based on Geometric Subarray Constraint (GSC), which relates to the field of millimeter-wave imaging radar array design. Background Technology

[0002] Millimeter-wave MIMO imaging radar improves 2D DOA estimation performance by combining transmit and receive antennas to form a virtual array with a larger aperture. Traditional uniform linear or rectangular arrays trade off between component number and aperture, while sparse array design can expand the effective aperture without significantly increasing hardware costs. However, sparse array design is a discrete, non-convex optimization problem, prone to getting trapped in local optima. Furthermore, practical engineering constraints (such as PCB size, cascaded chip packaging rules, and antenna routing) must be considered, making traditional array design methods (based on main lobe width or side lobe level) difficult to directly meet practical requirements. Therefore, introducing subarrays containing desired structural features as constraints, ensuring the designed virtual array fully encompasses these subarrays, can significantly improve the engineering applicability of the array design and the final imaging performance.

[0003] Traditional millimeter-wave MIMO array systems typically employ uniform linear or rectangular arrays. By arranging multiple antennas at the transmitter and receiver and combining them with MIMO processing, a large-aperture virtual array can be formed, thereby improving angular resolution. However, when the number of antennas at the transmitter and receiver increases significantly, system complexity and hardware costs rise sharply. To balance performance and cost, a sparse array design is proposed, which aims to reduce the number of antennas while maintaining a similar spatial sampling density.

[0004] However, traditional sparse array optimization methods (such as simulated annealing, particle swarm optimization, genetic algorithms, etc.) are usually optimized directly based on the array pattern or the energy distribution of the virtual array. They lack geometric constraints and structural priors, resulting in array patterns that lack regularity, unstable side lobes of the pattern, and a tendency to get trapped in local optima.

[0005] Therefore, there is an urgent need for a method that combines geometric constraints with global optimization algorithms to quickly solve the optimal layout of sparse MIMO arrays while ensuring system constraints, thereby maintaining high angular resolution performance while reducing the number of antennas. Summary of the Invention

[0006] Technical Problem: The purpose of this invention is to provide a sparse MIMO array optimization design method based on subarray structure constraints. Under the condition of satisfying engineering physical constraints, the problem is how to construct a virtual array at the transmitter and receiver with the fewest possible number of antennas that can provide a large aperture, low sidelobes, and contain several expected geometric subarrays (to satisfy 2-D DOA and multi-target matching, etc.); and how to solve this discrete non-convex optimization problem with acceptable computational complexity.

[0007] Technical Solution: To address the aforementioned problems, this invention provides a sparse MIMO array optimization design method based on subarray structured constraints. This method imports the design objective into the optimization model using geometric subarrays as constraints, and employs an improved genetic algorithm (GA) to optimize the transmit and receive arrays. This ensures that the final virtual array systematically contains the expected geometric subarrays, meeting the design requirements of two-dimensional high-resolution imaging. Compared to traditional design methods that directly use main lobe width and side lobe level as constraints, this invention significantly reduces the number of antennas in the transmit and receive arrays while maintaining array performance, thereby reducing system complexity. It also exhibits better convergence and engineering feasibility, as detailed below:

[0008] Step 1: Define multiple geometric constraint subarrays to constrain the structural features of the desired virtual array;

[0009] Step 2: Establish the position matrix of the transmitting and receiving antennas on a two-dimensional uniform grid;

[0010] Step 3: Construct a virtual array using convolutional relationships;

[0011] Step 4: Calculate the completeness of the virtual array containing each subarray using the normalized similarity operator;

[0012] Step 5: Establish a multi-objective constraint model with the optimization objective of maximizing the completeness of each subarray contained in the virtual array;

[0013] Step 6: Use an improved genetic algorithm for array design and optimization;

[0014] Step 7: Output the optimal transmit and receive array configuration that satisfies the constraints.

[0015] in,

[0016] In step 1, the first Each geometric constraint submatrix is ​​represented as size matrix , The elements in the set are binary sets. When an element is "1", it indicates that an element exists at the corresponding position; when an element is "0", it indicates that the position was not selected; set of geometrically constrained subarrays. It includes predefined structural feature constraints, including horizontal linear arrays, pitch linear arrays, and tilt linear arrays. The number of defined geometric constraint subarrays.

[0017] The transmitting antenna position matrix With the receiving antenna position matrix They respectively satisfy:

[0018] ,

[0019] parameter These represent the row and column dimensions of the transmitting and receiving antenna arrays, respectively, and their values ​​are determined by the circuit board wiring conditions and the array aperture size.

[0020] In step 3, the transmitting antenna position matrix With the receiving antenna position matrix The virtual array matrix is ​​obtained by performing two-dimensional convolution calculation. Size is To ensure Since it's also a binary matrix, after convolution, the non-zero positions are set to 1. The row and column dimensions satisfy:

[0021] .

[0022] In step 4, a normalized similarity operator is used. Calculate the virtual array matrix Includes each The completeness is calculated as follows:

[0023] ,

[0024] in and These are the Frobenius inner product and norm, respectively.

[0025] ,

[0026] ,

[0027] in, express The OK List the elements, express The OK List the elements, express The OK List the squares of the moduli of each element.

[0028] Step 5 establishes a multi-objective constraint model with the optimization objective of maximizing the weighted sum of all integrity values. The optimization objective function includes constraint terms to limit the antenna number deviation, and its expression is:

[0029]

[0030] in for The corresponding normalized weighting coefficients, and This indicates the number of non-zero elements in the matrix. For the threshold, and These represent the expected number of transmit and receive antennas, respectively.

[0031] Step 6, the improved genetic algorithm, includes encoding, crossover, mutation, and selection steps, wherein:

[0032] coding: and Indicates the first For the transmit and receive antenna position matrix, its elements are sequentially expanded into row vectors. and The two are concatenated to form a vector. Assume the population size is... Then the entire population is represented as ;

[0033] Mutation: in terms of probability In the same area or Randomly swap the positions of the two antennas;

[0034] Crossover: based on probability Exchange complete or sub-block.

[0035] In step 6, the new individuals generated by the crossover and mutation operations are merged with the original population to form a temporary population. Temporary population Each individual Reconstructed into a matrix and And calculate fitness:

[0036] ,

[0037] in .

[0038] In step 6, a roulette wheel selection method is used to update the next generation of the population, and the selection probability is defined as:

[0039] ,

[0040] in For the first The fitness of an individual for The population size; this mechanism allows individuals with low fitness to have a chance to pass on their genes to the next generation, maintaining genetic diversity while also effectively preventing premature convergence.

[0041] In step 7, when a certain The optimization process terminates when the fitness reaches a preset threshold or the maximum number of iterations is reached, and the output is displayed. As the optimal transmit and receive array configuration.

[0042] Beneficial effects: Compared with the prior art, this invention enhances the controllability of the array structure by introducing geometric subarray constraints, ensuring the expected aperture shape of the virtual array; the improved genetic algorithm can achieve global search under the condition of fixed number of antennas, avoiding local optima; compared with traditional methods, this invention can maintain the same angular resolution while reducing the number of antennas; it is applicable to millimeter-wave imaging radar systems and has good engineering feasibility and algorithm versatility. Attached Figure Description

[0043] Figure 1 This is an overall flowchart of the sparse MIMO array optimization design method based on geometric subarray constraints proposed in this invention.

[0044] Figure 2 The flowchart for the improved genetic algorithm.

[0045] Figure 3 The fitness convergence curve.

[0046] Figure 4 This is a comparison diagram of the transmitting and receiving arrays, in which... Figure 4 (a) in the diagram represents the TX / RX array element of the TI MMWCAS-RF EVM. Figure 4 (b) in the figure represents the TX / RX array element designed by the method of the present invention.

[0047] Figure 5 This is a comparison chart of virtual arrays, in which... Figure 5 (a) in the image represents the virtual array of the TI MMWCAS-RF EVM. Figure 5 (b) in the figure represents the virtual array designed by the method of the present invention. Detailed Implementation

[0048] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0049] This invention can be implemented in many different forms and should not be considered as limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully express the scope of the invention to those skilled in the art.

[0050] like Figure 1 and Figure 2 As shown, Figure 1 This is a schematic diagram illustrating the overall process of the sparse MIMO array optimization design method based on geometric subarray constraints proposed in this invention. Figure 2 This is a schematic diagram of the array structure search and optimization process based on the improved genetic algorithm proposed in this invention. The method includes the following steps:

[0051] Step 1: Define multiple geometric constraint submatrices , used to constrain the structural characteristics of the desired virtual array;

[0052] Specifically, the geometric subarray It includes predefined structural feature constraints, such as horizontal linear arrays, pitch linear arrays, and tilt linear arrays. The matrix elements are binary sets. When an element in the matrix is ​​"1", it means that there is a matrix element at the corresponding position; when an element in the matrix is ​​"0", it means that the position has not been selected.

[0053] Step 2: Initialize population and system parameter settings;

[0054] Specifically, the position matrix of the transmitting and receiving antennas is established on a two-dimensional uniform grid. and They respectively satisfy:

[0055] ,

[0056] parameter These represent the row and column dimensions of the transmitting and receiving arrays, respectively, and their values ​​are determined by the circuit board wiring conditions and the array aperture size.

[0057] Will and Vectorization and For the first For the transmitting and receiving arrays, gene sequences Assume the population size is... Then the entire population can be represented as ;

[0058] Through convolutional relationships To construct a virtual array, in order to ensure Since it's also a binary matrix, after convolution, the non-zero positions are set to 1. The row and column dimensions satisfy:

[0059] ,

[0060] Using the normalized similarity operator The degree of completeness of a virtual array containing subarrays is represented by the following calculation method:

[0061] ,

[0062] in and These are the Frobenius inner product and norm, respectively.

[0063] ,

[0064] ,

[0065] Step 3: Establish a multi-objective constraint model with maximizing fitness as the optimization objective;

[0066] Specifically, the optimization objective function includes constraint terms to limit the antenna number deviation, and its expression is:

[0067]

[0068] in for The corresponding normalized weighting coefficients, and This indicates the number of non-zero elements in the matrix. For the threshold, and These represent the expected number of transmit and receive antennas, respectively.

[0069] Step 4: Use an improved genetic algorithm for array design and optimization;

[0070] Specifically, the improved genetic algorithm includes crossover, mutation, and selection steps, wherein:

[0071] Mutation: in terms of probability In the same area ( or Randomly swap the positions of the two antennas;

[0072] Crossover: based on probability Exchange complete or sub-block.

[0073] New individuals generated by crossover and mutation operations are merged with the original population to form a temporary population. Temporary population Each individual Reconstructed into a matrix and And calculate fitness:

[0074] ,

[0075] in .

[0076] Based on fitness The size of the next generation of the population is updated using Roulette Selection, and the selection probability is defined as:

[0077] ,

[0078] in For the first The fitness of an individual for Population size.

[0079] Step 5: Output the optimal transmit and receive array configuration that satisfies the constraints.

[0080] Specifically, when a certain The fitness level reaches the preset threshold The optimization process may terminate when the maximum number of iterations is reached, and the output will be displayed. As the optimal transmit and receive array configuration.

[0081] To verify the beneficial effects of the present invention, the following experiments were conducted:

[0082] The array design of the Texas Instruments (TI) MMWCAS-RF-EVM was selected as a comparison. The hardware configuration of the TI MMWCAS-RF-EVM includes 12 transmit antennas (TX) and 16 receive antennas (RX), such as... Figure 4 As shown in (a), in the two-dimensional DOA estimation scenario, its virtual array is an 86-element uniform linear array (ULA) in the azimuth (horizontal) dimension and a 4-element sparse linear array in the pitch (vertical) dimension, as follows. Figure 5 As shown in (a).

[0083] To achieve the same angular resolution as the original system while reducing the number of array elements, this paper selects an 86-element azimuth array and a 4-element elevation array as geometrically constrained subarrays. The input is then used as the basis for the optimization design of the proposed GSC algorithm.

[0084] The grid size settings for the transmit / receive array are as follows:

[0085] ,

[0086] Among them, the array element spacing Take half the wavelength.

[0087] The iteration termination condition is: when the error threshold is reached. And the optimal individual fitness Stop iterating when the time comes.

[0088] The convergence curve of the algorithm is as follows Figure 3 As shown in the figure, the fitness value of the optimal individual and the average fitness of the entire population gradually increase during the iteration process, eventually converging to the optimal solution.

[0089] Figure 4 (b) Shows the optimized transmission array With receiver array Spatial distribution; Figure 5 (b) is its corresponding virtual array The area marked by the red box indicates: all geometric subarrays. All of these have been fully integrated into the final virtual array structure. Furthermore, two additional virtual array elements were obtained in the elevation dimension, further improving the angular resolution. Compared to the original TI MMWCAS-RF-EVM system (12-TX / 16-RX), the designed sparse array uses only 10 transmit antennas and 14 receive antennas (10-TX / 14-RX), achieving equivalent aperture performance while reducing the number of array elements, fully validating the effectiveness of the proposed algorithm.

[0090] It should be noted that the above-described embodiments only illustrate some implementation methods of the present invention, and their description should not be construed as limiting the scope of the present invention. It should be pointed out that those skilled in the art can make several improvements without departing from the concept of the present invention, and these improvements should all fall within the protection scope of the present invention.

Claims

1. A sparse MIMO array optimization design method based on subarray structured constraints, characterized in that, Includes the following steps: Step 1: Define multiple geometric constraint subarrays to constrain the structural features of the desired virtual array; Step 2: Establish the position matrix of the transmitting and receiving antennas on a two-dimensional uniform grid; Step 3: Construct a virtual array using convolutional relationships; Step 4: Calculate the completeness of the virtual array containing each subarray using the normalized similarity operator; Step 5: Establish a multi-objective constraint model with the optimization objective of maximizing the completeness of each subarray contained in the virtual array; Step 6: Use an improved genetic algorithm for array design and optimization; Step 7: Output the optimal transmit and receive array configuration that satisfies the constraints.

2. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 1, characterized in that: In step 1, the first Each geometric constraint submatrix is ​​represented as size matrix , The elements in the set are binary sets. When an element is "1", it indicates that an element exists at the corresponding position; when an element is "0", it indicates that the position was not selected; set of geometrically constrained subarrays. It includes predefined structural feature constraints, including horizontal linear arrays, pitch linear arrays, and tilt linear arrays. The number of defined geometric constraint subarrays.

3. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 2, characterized in that: The transmitting antenna position matrix With the receiving antenna position matrix They respectively satisfy: ， parameter These represent the row and column dimensions of the transmitting and receiving antenna arrays, respectively, and their values ​​are determined by the circuit board wiring conditions and the array aperture size.

4. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 3, characterized in that: In step 3, the transmitting antenna position matrix With the receiving antenna position matrix The virtual array matrix is ​​obtained by performing two-dimensional convolution calculation. Size is To ensure Since it's also a binary matrix, after convolution, the non-zero positions are set to 1. The row and column dimensions satisfy: 。 5. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 4, characterized in that: In step 4, a normalized similarity operator is used. Calculate the virtual array matrix Includes each The completeness is calculated as follows: ， in and These are the Frobenius inner product and norm, respectively. ， ， in, express The OK List the elements, express The OK List the elements, express The OK List the squares of the moduli of each element.

6. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 5, characterized in that: Step 5 establishes a multi-objective constraint model with the optimization objective of maximizing the weighted sum of all integrity values. The optimization objective function includes constraint terms to limit the antenna number deviation, and its expression is: in for The corresponding normalized weighting coefficients, and This indicates the number of non-zero elements in the matrix. For the threshold, and These represent the expected number of transmit and receive antennas, respectively.

7. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 6, characterized in that: Step 6, the improved genetic algorithm, includes encoding, crossover, mutation, and selection steps, wherein: coding: and Indicates the first For the transmit and receive antenna position matrix, its elements are sequentially expanded into row vectors. and The two are concatenated to form a vector. Assume the population size is... Then the entire population is represented as ; Mutation: in terms of probability In the same area or Randomly swap the positions of the two antennas; Crossover: based on probability Exchange complete or sub-block.

8. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 7, characterized in that: In step 6, the new individuals generated by the crossover and mutation operations are merged with the original population to form a temporary population. Temporary population Each individual Reconstructed into a matrix and And calculate fitness: ， in .

9. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 8, characterized in that: In step 6, a roulette wheel selection method is used to update the next generation of the population, and the selection probability is defined as: ， in For the first The fitness of an individual for The population size; this mechanism allows individuals with low fitness to have a chance to pass on their genes to the next generation, maintaining genetic diversity while also effectively preventing premature convergence.

10. The sparse MIMO array optimization design method based on subarray structured constraints as described in claim 9, characterized in that: In step 7, when a certain The optimization process terminates when the fitness reaches a preset threshold or the maximum number of iterations is reached, and the output is displayed. As the optimal transmit and receive array configuration.

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