A low-cost and scalable phased array sparse optimization method

Abstract

The present invention discloses a low-cost scalable phased array sparse optimization method, comprising the following steps: step 1, setting array indicators to determine the scale; step 2, selecting the sparse rate; step 3, dividing the known scale array Q area; step 4, dividing the central symmetric unit in any area, randomly distributing the R1 unit array, and obtaining the basic population through regional scalable replication; step 5, repeating step 4 to obtain the population set, from which the maximum fitness is selected; step 6, performing algorithm optimization on the R1 unit; step 7, correcting the actual number of array elements; step 8, returning to step 5 to search for the best replacement until the number of iterations is met; step 9, verifying the optimization result, if the indicator is not reached, returning to the corresponding step according to the four-degree priority to re-optimize; step 10, evaluating the optimal array. The present invention greatly reduces the design scope of sparse array through equal regional scalable division, and the scalable layout improves the flexibility of array design, debugging and application in complex scenes.

Description

Technical Field

[0001] The present invention relates to sparse optimization of array antennas, and in particular to a low-cost scalable array sparse method design method for different engineering technical index requirements. Background Art

[0002] In the face of the sharp increase in performance requirements for future detection systems, phased array antenna arrays with multi-beam fast scanning, multi-target capture, strong anti-interference ability, and high reliability are bound to become the development trend of future array design. Today, phased arrays have gradually been applied to military radars and commercial radars. However, with the improvement of engineering and technical indicators, the operating frequency of radars is getting higher and higher, and the wavelength is getting shorter and shorter. Under the premise of meeting the half-wavelength array, the array element spacing is getting shorter and shorter, which makes the ULA (Uniform Linear Array) produce a large number of array elements, large power consumption and heat consumption, large electromagnetic coupling, increased signal processing complexity, complex engineering technology and other unavoidable cost and technical problems, resulting in complex array implementation process and increased implementation difficulty, which seriously restricts the development of large phased arrays. Therefore, sparse optimization of the array has become a necessary link to be considered when arranging the array. Sparse phased arrays are a low-cost solution with some equivalent performance. Sparse operation has the following main advantages: (1) reducing manufacturing costs; (2) increasing the spacing between array elements during array layout and reducing process difficulty; (3) reducing the influence of electromagnetic coupling between channels; and (4) increasing angular resolution with the same number of channels.

[0003] Global sparse technology is a sparse method with a low sparse rate and good sidelobe level suppression. However, global sparse technology still has some limitations, such as: (1) The array pattern obtained by global random sparse array is non-periodic. Such non-periodicity will increase the difficulty of routing during hardware layout and will also bring about errors in many aspects, resulting in a large deviation between the actual test effect and the simulation effect; (2) There is no scalability between multiple array regions. A global random sparse array can only be applied to engineering backgrounds with the same indicators, so the cost of sparse arrays is still high; (3) The curve of the antenna scanning pattern obtained by global random sparse at different angles is unstable, and the sidelobe level is difficult to unify; (4) Global random sparse array will lead to low error correction efficiency, and the error correction capability still needs to be improved. Therefore, it is necessary to further optimize the sparse operation, but there are relatively few scalable phased array sparse optimization methods studied domestically and internationally. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a low-cost scalable phased array sparse optimization method that can adapt to different engineering technical indicators by periodically and scalably dividing areas such as array areas, thereby greatly reducing the design range of sparse arrays, reducing the difficulty of design, debugging and application of arrays in complex scenarios.

[0005] The object of the present invention is achieved through the following technical solution: a low-cost scalable phased array sparse optimization method, comprising the following steps:

[0006] Step 1: Set the performance index of the phased array: the phased array adopts a uniform grid array distribution mode, and sets each array element to be an ideal omnidirectional array element with equal amplitude and phase; and set the initial sparse rate range, azimuth resolution, elevation resolution and maximum sidelobe level threshold FSLL of the phased array;

[0007] Step 2: Select a sparse rate within the sparse rate range;

[0008] Step 3: Divide the uniform grid array into Q regions, where the value range of Q is: η is the sparsity rate, Indicates rounding down, M is the number of antenna arrays in azimuth, and N is the number of antenna arrays in elevation. In initial operation, the maximum integer value within the Q range is taken;

[0009] Step 4: Perform a unit division operation on any area, so that the units R1, R2, R3, and R4 in the area are centrally symmetrically distributed; perform binary code random allocation on the antenna array elements in the sparse R1 area, and then flip the randomly arranged R1 area about the azimuth axis and the pitch axis to obtain R2 and R3, and then flip the center of R1 to obtain R4, and obtain the first area; and copy and lay out the area to obtain Q areas, and obtain a basic population G0;

[0010] Step 5: Repeat step 4 to generate several basic populations, generate the three-dimensional directional diagram of the initial population set according to the digital beamforming method, calculate the maximum sidelobe level in the three-dimensional directional diagram, and then calculate the normalized fitness value of each population, and find the maximum fitness value and record it as Q Mfit ; The basic population with the maximum fitness is taken as the optimal population of all generations, denoted by G best ;

[0011] Step 6: Use genetic algorithm to optimize R1 unit;

[0012] Step 7: Correct the actual number of array elements of R1 in each group;

[0013] Step 8: Keep the optimal array G in this iteration best, repeat steps 4 to 7. If the maximum number of iterations is reached, proceed to step 9;

[0014] Step 9: Verify whether the optimal antenna array design after algorithm optimization meets the corresponding index requirements in step 1. If so, the optimal array is obtained; otherwise, the array is re-optimized in four priority modes until the optimal array is obtained;

[0015] Step 10: Use MATLAB software to evaluate the output of the optimal array, capture the maximum sidelobe levels in different scanning directions in the three-dimensional directional diagram within the azimuth and elevation scanning ranges, and obtain the maximum sidelobe level evaluation diagram.

[0016] Furthermore, the specific implementation method of step 5 is: the directional pattern function of the planar array is expressed as:

[0017]

[0018] where f mn Equal to 0 or 1, indicating that there is no array element or there is array element distribution; represents the azimuth direction, θ represents the elevation direction, the maximum value of the array main beam is pointed to (φ0,θ0), d m Indicates the distance between the (m,n)th array element and the (0,0) reference array element in azimuth, d n It represents the distance between the (m,n)th array element and the (0,0) reference array element in the pitch direction, Δφ mn represents the phase difference between the (m,n)th array element and the (0,0)th reference array element, α mn is the excitation phase when the array main beam is pointing to the maximum value;

[0019] According to the definition of the maximum sidelobe level MSLL, it is taken as the sum of the maximum sidelobe level in azimuth and the maximum sidelobe level in elevation:

[0020]

[0021] Get a set of values ​​about MSLL, take the minimum value in the set as min(MSLL), and the maximum value as max(MSLL);

[0022] Calculate the normalized fitness value of each population:

[0023]

[0024] The fitness value is between 0 and 1, and then find the maximum fitness value among all populations and record it as Q Mfit .

[0025] Furthermore, in step 6, the optimization method is: setting the crossover probability P cand mutation probability P m ; For the normalized fitness values ​​of various populations, selection, crossover and mutation operations are performed successively;

[0026] Assume the maximum evolutionary number is G and the constrained crossover probability is P c , mutation probability P m , take out R1 from each initial population, use the "roulette" selection method, and take the relative fitness of each population as the probability of being selected. The formula is expressed as This decision condition is used to determine whether to retain its offspring; the selected R1 regions are divided into odd and even populations with a crossover probability P c Perform a crossover operation on the odd-numbered population and the even-numbered population, so that the odd-even paired individuals exchange their partial genes at the crossover position, thereby generating new population individuals; for each population after the crossover, then with the mutation probability P m Perform mutation operation.

[0027] Furthermore, in step seven, the correction method is: if the number of array elements after processing is different from the initial setting, then randomly select the difference array elements from the array elements, and force their working states to jump to the opposite state, that is, jump from "0" to "1", and from "1" to "0".

[0028] Furthermore, in step nine, the four priority modes are:

[0029] Priority 1, at the selected crossover probability P c , mutation probability P m If the upper limit of the value is not reached, the ratio The multiplication factor increases the original crossover probability P c , mutation probability P m Value, return to step six,;

[0030] Priority 2: If the number of random arrangement of the array does not exceed the constraint range, re-randomly generate the array distribution in the R1 unit and return to step 4;

[0031] Priority 3: Change the Q value within the constraint range, re-divide the expandable area, and return to step 3;

[0032] Priority 4: Change the sparsity rate η within the constraint range and return to step 2.

[0033] The beneficial effects of the present invention are as follows: the present invention realizes scalable and low-cost phased array sparse optimization operation, and there is no need to perform global random sparse array on the phased array. By periodically and scalably dividing the array area and other areas, the design range of the sparse array is greatly reduced. The scalable layout reduces the design, debugging and application difficulties of the array in complex scenes, and can adapt to different engineering technical indicators, and achieves the compatibility of different scene designs. Under the premise of ensuring a low sparse rate, the present invention improves the sidelobe level suppression effect, improves the periodicity of the wide field scanning performance of the sparse array, achieves the purpose of reducing antenna elements and reducing costs, and has a high resolution in both azimuth and elevation, and solves the problem of unstable sidelobe level suppression effect caused by the asymmetry of the directional pattern obtained by the non-periodic global random sparse array in the current antenna array sparse operation. At the same time, it reduces the design cost of actual engineering applications, improves the error correction efficiency, and can accurately collect data, which has important application value and engineering significance in the fields of phased array radar image processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is an operation flow chart of the scalable phased array sparse optimization method of the present invention;

[0035] Figure 2 It is a schematic diagram of the scalable phased sparse array partitioning principle of the present invention;

[0036] Figure 3 A position distribution diagram of the optimal sparse array output by the present invention;

[0037] Figure 4 The normalized directional diagram of the optimal sparse array output by the present invention;

[0038] Figure 5 The azimuth direction diagram of the optimal sparse array output by the present invention;

[0039] Figure 6 The elevation direction pattern of the optimal sparse array output by the present invention;

[0040] Figure 7 It is the main lobe scanning-side lobe pattern of the optimal sparse array output by the present invention. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0042] like Figure 1 As shown, a low-cost and scalable phased array sparse optimization method of the present invention comprises the following steps:

[0043] Step 1: Set the performance index of the phased array: The phased array uses a uniform grid array distribution method, and sets each array element to be an ideal omnidirectional array element with equal amplitude and phase; and set the initial sparse rate range of the phased array η∈[η a ,η b ],(0<η a <η b <1), azimuth resolution, elevation resolution and maximum sidelobe level threshold FSLL;

[0044] This embodiment takes the working frequency of 77GHz as an example, sets the sparse rate range to 0.10-0.30, the sidelobe level threshold to no higher than -17dB, the azimuth angular resolution index to be approximately 0.7°, and the elevation angular resolution index to be approximately 2.1° (both the azimuth angular resolution index and the elevation angular resolution index are values ​​with only one decimal place). According to the wavelength formula It can be inferred that: the array element spacing The theoretical formula for the angular resolution of the known antenna array is: According to the constraint resolution value, combined with the resolution formula M≈101.6 / ρ x , N≈101.6 / ρ y Calculation infers that: the aperture of the array antenna is 28cm×9.3cm, the number of azimuth antenna arrays M is 144, and the number of elevation antenna arrays N is 48. When the array is full, the total number of antenna array elements (M, N) is L=M×N=6912.

[0045] Step 2: Select a sparse rate within the sparse rate range. In this embodiment, the initial sparse rate is η=0.25. According to the definition of sparse rate, Then the number of antenna array elements NL after sparseness is 1782;

[0046] Step 3: Divide the uniform grid array into Q regions. Considering the scalability purpose, the value of Q is selected according to the following constraints:

[0047] (1) Q is a positive integer not less than 2;

[0048] (2) Ensure that the actual number of array elements in each area after sparseness is not less than 4;

[0049] That is, the value range of Q is: Indicates rounding down; the actual value of Q can be set by the user. Generally, the maximum integer value within the range of Q is taken in the initial operation, because starting from the value of the maximum partition can achieve the maximum partition under the premise of meeting the index, so that the number of array elements in each area is the least. For the convenience of explanation, this embodiment takes Q=3; the uniform array is divided into 3×1 equal areas, thereby dividing into 3 completely identical areas q (1,1) ,q (1,2) ,q(,13) such that the array element parameters (m, n) when each unit is fully filled are (48, 48);

[0050] Step Four: Perform unit division on any region so that the units R1, R2, R3, and R4 within the region are centrosymmetrically distributed; there are many types of block partitions with centrosymmetric characteristics. In this embodiment, a "field" character partition is adopted, as shown in Figure 2 ; for a uniformly arranged planar antenna array, take unit q (1,1) of R1 as an example (R1 is any one of the four selected regions). Under the constraint of η = 0.25, the number of antenna array elements in the R1 region after sparsification is reduced to 144. Perform random binary code assignment on it (the random binary code assignment here is to have determined the sparsity rate value, that is, the number of 0s and 1s has been determined, and only randomly distribute these 0s and 1s to the positions of the array elements). Use f mn to represent the setting state of the corresponding array element: f mn = 1 indicates that there is an array element arrangement at the corresponding position, f mn = 0 indicates that there is no array element arrangement at the corresponding position. Then, flip the randomly arranged R1 region about the azimuth axis and the elevation axis to obtain R2 and R3 respectively, and then flip the center of R1 to obtain R4, thus obtaining the first region q (1,1) ; and copy and tile the q (1,1) to obtain Q regions, obtaining a basic population G0. A population refers to the planar range composed of Q regions, and each region includes four units.

[0051] Step Five: Repeat Step Four to generate several basic populations. In this embodiment, the population size NP is set to 50. Then, repeat the operation of Step Four, re-perform random binary code assignment on the R1 region, and then perform flipping and tiling operations. After operating 50 times, an initial population set G0(i) is generated, [i = 1, 2,..., NP; NP = 50]. Generate the three-dimensional radiation pattern of the initial population set according to the digital beamforming method (DBF), calculate the maximum sidelobe level MSLL in the three-dimensional radiation pattern respectively, then calculate the normalized fitness value of each population, and find the maximum fitness value and denote it as Q Mfit ; regard the basic population with the maximum fitness as the optimal population of all generations, denoted as G best ;

[0052] The specific implementation method is as follows: The radiation pattern in this embodiment mainly represents the relationship between the magnitude of the energy flux density and the spatial direction. Therefore, a power-normalized radiation pattern is adopted. The radiation pattern function of the planar array is expressed as:

[0053]

[0054] where f mnEqual to 0 or 1, indicating that there is no array element or there is array element distribution; represents the azimuth direction, θ represents the elevation direction, the maximum value of the array main beam is pointed to (φ0,θ0), d m Indicates the distance between the (m,n)th array element and the (0,0) reference array element in azimuth, d n It represents the distance between the (m,n)th array element and the (0,0) reference array element in the pitch direction, Δφ mn represents the phase difference between the (m,n)th array element and the (0,0)th reference array element, α mn is the excitation phase when the array main beam is pointing to the maximum value;

[0055] According to the definition of the maximum sidelobe level MSLL, it is taken as the maximum sidelobe level in the azimuth direction of the pattern. Maximum sidelobe level in elevation sum:

[0056]

[0057] sidelobe1 and sidelobe2 represent the azimuth and elevation sidelobes respectively; a set of values ​​about MSLL is obtained, the minimum value in the set is recorded as min(MSLL), and the maximum value is recorded as max(MSLL);

[0058] Then calculate the normalized fitness value set Q of these fifty populations respectively fiti (i=1,2,...,NP;NP=50), the normalized fitness value is:

[0059]

[0060] The fitness value is between 0 and 1. The normalized fitness can clearly indicate the arrangement of the side lobe level of the selected population in the unit interval. Then find the maximum fitness value among all populations and record it as Q. Mfit .

[0061] Step 6: Use genetic algorithm to optimize R1 unit; the optimization method is: set the crossover probability P c and mutation probability P m ; For the normalized fitness values ​​of various populations, selection, crossover and mutation operations are performed successively;

[0062] Assume that the maximum evolutionary number is G = 200 and the crossover probability is constrained to P c , mutation probability P m The value range is

[0063] 0.8≤P c ≤1,0.05≤P m ≤1, the initial crossover probability value Pc is 0.8, the mutation probability value P m The above operation has obtained the normalized fitness value of each population, and then the R1 in each initial population is taken out, and the "roulette" selection method is adopted, and the relative fitness of each population is used as the probability of being selected. The formula is expressed as This decision condition is used to determine whether to retain its offspring; the selected R1 regions are divided into odd and even populations with a crossover probability P c = 0.8 to perform a crossover operation on the odd-numbered population and the even-numbered population, so that the odd-even paired individuals exchange their partial genes at the crossover position, thereby generating new population individuals; for each population after the crossover, then with the mutation probability P m =0.05 for mutation operation.

[0064] Step 7. To ensure that the sparsity η in the newly generated populations from step 3 to step 6 remains unchanged, the actual number of array elements of R1 in each population needs to be corrected. The correction method is: if the number of array elements after processing is different from the initial setting, the difference array elements are randomly selected from the array elements, and their working states are forced to jump to the opposite state, that is, from "0" to "1", and from "1" to "0".

[0065] Step 8: Keep the optimal array G in this iteration best , repeat steps 4 to 7. If the maximum number of iterations is reached, proceed to step 9;

[0066] Step 9: Verify whether the optimal antenna array design after algorithm optimization meets the corresponding index requirements in step 1. If it does, the optimal array is obtained; otherwise, the array is re-optimized in four priority modes until the optimal array is obtained. The four priority modes are:

[0067] Priority 1, at the selected crossover probability P c , mutation probability P m If the upper limit of the value is not reached, the ratio The multiplication factor increases the original crossover probability P c , mutation probability P m Value, return to step six,;

[0068] Priority 2: If the number of random arrangement of the array does not exceed the constraint range, re-randomly generate the array distribution in the R1 unit and return to step 4;

[0069] Priority 3: Change the Q value within the constraint range, re-divide the expandable area, and return to step 3;

[0070] Priority 4: Change the sparsity rate η within the constraint range and return to step 2.

[0071] Step 10: Use MATLAB software to evaluate the output of the optimal array. In the three-dimensional directional diagram within the azimuth and elevation scanning range, capture the maximum sidelobe level in different scanning directions and obtain the maximum sidelobe level evaluation diagram. The final output of the optimal array is as follows: Figure 3 As shown, the three-dimensional radiation pattern of the optimal array at 0° azimuth and 0° elevation is as follows Figure 4 As shown, the azimuth cross-section direction diagram is as follows Figure 5 As shown, the direction diagram of the pitch section is as follows Figure 6 shown.

[0072] observe Figure 5 and Figure 6 It can be seen that the optimal sparse array meets the requirements of 0.7° resolution in azimuth and 2.3° resolution in elevation, and the maximum sidelobe level in the radiation pattern is below -13dB.

[0073] Change the beam angle of the sparse array so that it changes gradually by 1° within ±60° in azimuth and by 1° within ±45° in elevation. The final output main lobe scanning pattern is as follows: Figure 7 As shown in the figure, it can be seen that the maximum sidelobe level of the optimal sparse array in the main lobe scanning domain is lower than -12.63dB, which meets the design requirements.

[0074] The final image shows that the maximum sidelobe level after processing by this antenna array sparse optimization method has a wide scanning range and stable scanning effect in both azimuth and elevation, and the sidelobe level suppression effect is good, meeting the initially set threshold level, so that the sidelobe level is suppressed below -11dB. When all array elements are ideal omnidirectional array elements with equal amplitude and phase, the technical index requirements are fully met. In the future, when applied in a specific engineering context, combined with the method of the present invention and after constrained power allocation to each array element, more stringent technical indicators can be achieved, which provides great engineering practical reference value for the current phased array design.

[0075] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A low-cost and scalable phased array sparse optimization method, characterized in that: The following steps are involved: Step 1: Set the performance index of the phased array: the phased array adopts a uniform grid array distribution mode, and sets each array element to be an ideal omnidirectional array element with equal amplitude and phase; and set the initial sparse rate range, azimuth resolution, elevation resolution and maximum sidelobe level threshold FSLL of the phased array; Step 2: Select a sparse rate within the sparse rate range; Step 3: Divide the uniform grid array into Q regions, where the value range of Q is: η is the sparsity rate, It means rounding down, M is the number of antenna arrays in azimuth, and N is the number of antenna arrays in elevation; Step 4: Perform a unit division operation on any area, so that the units R1, R2, R3, and R4 in the area are centrally symmetrically distributed; perform binary code random allocation on the antenna array elements in the sparse R1 area, and then flip the randomly arranged R1 area about the azimuth axis and the pitch axis to obtain R2 and R3, and then flip the center of R1 to obtain R4, and obtain the first area; and copy and lay out the area to obtain Q areas, and obtain a basic population G0; Step 5: Repeat step 4 to generate several basic populations, generate the three-dimensional directional diagram of the initial population set according to the digital beamforming method, calculate the maximum sidelobe level in the three-dimensional directional diagram, and then calculate the normalized fitness value of each population, and find the maximum fitness value and record it as Q Mfit ; The basic population with the maximum fitness is taken as the optimal population of all generations, denoted by G best ; Step 6: Use genetic algorithm to optimize R1 unit; Step 7: Correct the actual number of array elements of R1 in each group; Step 8: Keep the optimal array G in this iteration best , repeat steps 4 to 7. If the maximum number of iterations is reached, proceed to step 9; Step 9: Verify whether the optimal antenna array design after algorithm optimization meets the corresponding index requirements in step 1. If so, the optimal array is obtained; otherwise, the array is re-optimized in four priority modes until the optimal array is obtained; Step 10: Use MATLAB software to evaluate the output of the optimal array, capture the maximum sidelobe levels in different scanning directions in the three-dimensional directional diagram within the azimuth and elevation scanning ranges, and obtain the maximum sidelobe level evaluation diagram.

2. The low-cost scalable phased array sparse optimization method according to claim 1, characterized in that: The specific implementation method of step 5 is: the directional pattern function of the planar array is expressed as: where f mn Equal to 0 or 1, indicating that there is no array element or there is array element distribution; represents the azimuth direction, θ represents the elevation direction, the maximum value of the array main beam is pointed to (φ0,θ0), d m Indicates the distance between the (m,n)th array element and the (0,0) reference array element in azimuth, d n It represents the distance between the (m,n)th array element and the (0,0) reference array element in the pitch direction, Δφ mn represents the phase difference between the (m,n)th array element and the (0,0)th reference array element, α mn is the excitation phase when the array main beam is pointing to the maximum value; The maximum sidelobe level MSLL is taken as the sum of the maximum sidelobe level in azimuth and the maximum sidelobe level in elevation: Get a set of values ​​about MSLL, take the minimum value in the set as min(MSLL), and the maximum value as max(MSLL); Calculate the normalized fitness value of each population: The fitness value is between 0 and 1, and then find the maximum fitness value among all populations and record it as Q Mfit .

3. The low-cost scalable phased array sparse optimization method according to claim 1, characterized in that: In step 6, the optimization method is: setting the crossover probability P c and mutation probability P m ; For the normalized fitness values ​​of various populations, selection, crossover and mutation operations are performed successively; Assume the maximum evolutionary number is G and the constraint crossover probability is P c , mutation probability P m , take out R1 from each initial population, use the "roulette" selection method, and take the relative fitness of each population as the probability of being selected. The formula is expressed as This decision condition is used to determine whether to retain its offspring; the selected R1 regions are divided into odd and even populations with a crossover probability P c Perform a crossover operation on the odd-numbered population and the even-numbered population, so that the odd-even paired individuals exchange their partial genes at the crossover position, thereby generating new population individuals; for each population after the crossover, then with the mutation probability P m Perform mutation operation.

4. The low-cost scalable phased array sparse optimization method according to claim 1, characterized in that: In step seven, the correction method is: if the number of array elements after processing is different from the initial setting, then randomly select the difference array elements from the array elements, and force their working states to jump to the opposite state, that is, jump from "0" to "1", and from "1" to "0".

5. The low-cost scalable phased array sparse optimization method according to claim 1, characterized in that: In step nine, the four priority modes are: Priority 1, at the selected crossover probability P c , mutation probability P m If the upper limit of the value is not reached, the ratio The multiplication factor increases the original crossover probability P c , mutation probability P m Value, return to step 6; Priority 2: If the number of random arrangement of the array does not exceed the constraint range, re-randomly generate the array distribution in the R1 unit and return to step 4; Priority 3: Change the Q value within the constraint range, re-divide the expandable area, and return to step 3; Priority 4: Change the sparsity rate η within the constraint range and return to step 2.

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