Non-redundant dish-shaped array structure with good coverage effect in spherical harmonic space and design method

Abstract

The invention belongs to the technical field of array antennas, and particularly relates to a non-redundant dish-shaped array structure with a good coverage effect in a spherical harmonic space and a design method. In order to better realize sky chart reconstruction by observing the 21 cm spectral line of neutral hydrogen so as to research the large-scale structure of the universe, the geometric characteristics of an odd polygon are utilized, three of 15 array elements except a central array element form a group to form an isosceles triangle, five sub-arrays are sequentially obtained by rotating the sub-arrays, the total aperture of the array is limited, and meanwhile, the total aperture of the array is reduced. And optimizing the distance between a vertex array element and a center array element of the triangular sub-array and the distance between two array elements on the outer side of the triangular sub-array, and finally determining an optimal solution.

Description

Technical Field

[0001] This invention belongs to the field of array antenna technology, specifically relating to a non-redundant dish array structure and design method that has good coverage in spherical harmonic space. Background Technology

[0002] The 21-cm line of neutral hydrogen (frequency 1420.4 MHz) is an important tool for studying the large-scale structure of the universe. Originating from the hyperfine transition of the 1s ground state of hydrogen atoms, it reflects the distribution of neutral hydrogen at different redshifts. Traditional galactic redshift surveys only cover about 1% of the observable universe, while the 21-cm intensity mapping technique, without needing to detect individual galaxies, can rapidly cover a much wider area of ​​the sky by observing the combined radio emissions of multiple galaxies. This has become an efficient means of studying the large-scale structure of the universe, and large radio interferometers (FIGs) are the core equipment for realizing this technique.

[0003] To reconstruct the 21cm spectral line, the antenna is fixed at a specific declination. The Earth's rotation causes the sky to "drift" along the right ascension direction, and the visibility function is recorded as a function of time (or right ascension). The form of the spherical harmonic function naturally suits this characteristic—that is, the periodic variation of right ascension can be expressed through the e-exponential term of the spherical harmonic function. Through spherical harmonic transformation, the visibility function can be decomposed into different m-modes. Since the data from different m-modes are independent of each other, the originally massive linear system for sky map reconstruction is broken down into a series of independent small linear systems, each corresponding to only one m-mode, reducing the dimensionality by approximately 10. 6 This significantly reduces the complexity of numerical calculations, transforming the Tiantu reconstruction from "infeasible" to "efficient and feasible."

[0004] Different array structures exhibit different behaviors in spherical harmonic space. To verify the effectiveness of the array structure, the reconstruction matrix and error covariance matrix of the array structure after spherical harmonic transformation are calculated. Only if its coverage performance is good can the reliability of the array structure for the Tiantu reconstruction system be judged.

[0005] Peak sidelobe level (PSLL) is one of the core indicators for evaluating the performance of a signal or pulse waveform. It is defined as the ratio of the peak amplitude of the main lobe to the amplitude of the highest sidelobe (usually expressed in decibels dB; a lower value indicates better performance). A lower PSLL can better suppress various types of interference, resulting in a significant improvement in signal anti-interference capability, spatial resolution, target recognition capability, energy utilization efficiency, and other aspects.

[0006] To this end, this invention designs a non-redundant array that breaks the periodic redundancy of traditional arrays, enabling it to have good PSLL performance and good coverage performance in spherical harmonic space, thus providing technical support for our final sky map reconstruction. Summary of the Invention

[0007] To better reconstruct cosmic maps by observing the 21 cm spectral line of neutral hydrogen and thus study the large-scale structure of the universe, this invention provides a non-redundant dish array structure and design method with good coverage in spherical harmonic domain. Utilizing the geometric properties of odd-numbered polygons, the 15 array elements (excluding the central element) are grouped into isosceles triangles of three. By rotating these subarrays, five subarrays are obtained. While limiting the total array aperture, the distances between the vertex elements and the central element of the triangular subarrays, as well as the distances between the two outer elements of each triangular subarray, are optimized to determine the optimal solution. Examples show that this structure achieves better results than previous literature in both minimizing peak sidelobe levels and spherical harmonic domain coverage.

[0008] To achieve the above objectives, the present invention employs the following technical solution:

[0009] This invention provides a non-redundant dish array structure with good coverage in spherical harmonic space, comprising:

[0010] There are 16 array elements. One array element is placed at the center, and the remaining 15 array elements form 5 sub-arrays, which are distributed around the center.

[0011] Each subarray contains three array elements forming an isosceles triangle. Other subarrays are obtained by rotating the subarray around the center of the circle.

[0012] Through intelligent optimization algorithms, the spacing between the center of the circle and the inner array elements of the subarray, as well as the spacing between the inner and outer array elements of the subarray, are optimized simultaneously.

[0013] Furthermore, the included angle between the subarrays is 72°, which is obtained by rotating one of the subarrays counterclockwise at 72° intervals.

[0014] Furthermore, in the array structure, each antenna is a Tianlai dish antenna with a diameter of 6 meters and an effective diameter of 5.4 meters.

[0015] This invention also provides a design method for a non-redundant dish array structure with good coverage in spherical harmonic space, comprising the following steps:

[0016] S1. Select the number of subarrays, constrain the aperture size and minimum element spacing, and generate random initialization data;

[0017] S2. Establish a reference model of the array structure, determine the arrangement position of the array elements according to the different positions searched by the algorithm population in the initialization data, and calculate the initial fitness function.

[0018] S3. Start iteration. After each iteration, including after initialization, check the spacing of the new array element positions. If the spacing requirement is met, proceed directly to S4; otherwise, adjust the search position until the requirement is met and then proceed to S4.

[0019] S4. Calculate the orientation pattern of the array layout searched by each population, determine the fitness function of the corresponding layout position, and store the relevant data;

[0020] S5. If the algorithm has not reached the maximum number of iterations, then proceed to S4 for the next iteration search; otherwise, obtain the position searched by the population corresponding to the current best fitness function, which corresponds to the best array element arrangement position.

[0021] S6. Perform spherical harmonic transformation on the power of the beam pattern and calculate the instrument noise;

[0022] S7. Calculate the noise covariance matrix N, fill the beam matrix A, and calculate the generalized inverse matrix Ainv of the beam matrix.

[0023] S8. Calculate the reconstruction matrix Rec and the error covariance matrix C to evaluate the coverage performance of the array structure in spherical harmonic space.

[0024] Furthermore, the number of subarrays in S1 is 5, the constrained aperture size d3 = 17.6 meters, and the minimum element spacing is 8.8 meters.

[0025] Furthermore, the S3 mid-spacing determination specifically involves:

[0026] After obtaining the arrangement positions of all array elements, store the Euclidean distance between any two array elements in matrix form. Since the distance between array elements does not need to be considered, fill the diagonal elements of the matrix with infinity. Then, perform a judgment: if there is an Euclidean distance between two array elements that is less than the minimum array element spacing, return True; otherwise, return False.

[0027] If True is returned, first determine whether the distance between the inner array element and the center of the circle is less than the minimum array element spacing. If it is less than the minimum array element spacing, set it to be equal to the minimum array element spacing; otherwise, do not perform any operation. Then, re-determine whether the spacing between the inner and outer array elements in the subarray is too close. If it is less than the minimum array element spacing, set it to be equal to the minimum array element spacing; otherwise, do not perform any operation. Finally, perform the spacing judgment again. If the condition is still not met, it can be determined that the spacing of the outer array in the subarray does not meet the requirements. At this time, only the distance between the inner and outer array elements of the subarray needs to be adjusted to ensure that the spacing between them will not exceed the maximum aperture limit, nor will it be less than the minimum array element spacing.

[0028] If the return value is False, no adjustments are made.

[0029] Furthermore, the design method of the present invention is a multi-constraint problem, with the peak sidelobe level as the fitness function, while constraining the minimum array element spacing to the specific size of a single dish antenna, and fixing the maximum aperture for solving.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] 1. The array structure of the present invention is a non-redundant array structure with a redundancy of 1.0. The array factor beam pattern still has a low peak sidelobe level under large spacing constraints, strong signal anti-interference ability and target recognition ability, and high energy utilization efficiency.

[0032] 2. The array structure of the present invention includes both a compact baseline and a long baseline, thereby enabling the array structure to cover information of both lower and higher order moduli in the spherical harmonic domain, such as the reconstruction matrix and the error covariance matrix, thus achieving better sky map reconstruction results.

[0033] 3. The array structure of the present invention has independent baselines that are quite uniform in the horizontal direction, rather than concentrated in a certain direction. Its beams are uniformly covered in the spherical harmonic domain without obvious holes, and the average value of the error covariance matrix is ​​low. This provides an important idea for the design of array antennas in sky map reconstruction and has significant implications for promoting the widespread application of array antenna technology. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the non-redundant disk array structure of the present invention;

[0035] Figure 2 The two-dimensional planar beam pattern optimized for the array factor of the structure designed in this invention at 1420.4 MHz;

[0036] Figure 3 The three-dimensional beam pattern optimized for the array factor of the structure designed in this invention at 1420.4 MHz;

[0037] Figure 4 This is a schematic diagram of the reconstruction matrix of the structure designed in this invention during a mid-latitude sky survey at 1420.4 MHz;

[0038] Figure 5 This is a schematic diagram of the error covariance matrix of the structure designed in this invention during a mid-latitude sky survey at 1420.4 MHz;

[0039] Figure 6 This is a schematic diagram of the reconstruction matrix of the structure designed in this invention during a polar survey at 1420.4 MHz;

[0040] Figure 7This is a schematic diagram of the error covariance matrix of the structure designed in this invention during polar surveys at 1420.4 MHz. Detailed Implementation

[0041] To further illustrate the technical solution of the present invention, the present invention will be further described below through embodiments.

[0042] Example 1

[0043] Taking a 16-element array antenna as an example, this embodiment presents a non-redundant dish array structure design method with good coverage in spherical harmonic space, which includes the following steps:

[0044] S1. Select the number of subarrays, constrain the aperture size and minimum element spacing, and generate random initialization data;

[0045] The number of subarrays is selected as 5, the aperture size is constrained to d3 = 17.6 meters (the maximum pole diameter of the array structure), the minimum element spacing is 8.8 meters, the dish antenna is a Tianlai dish antenna with an antenna diameter of 6 meters and an effective aperture factor of 0.9, that is, an effective diameter of 5.4 meters.

[0046] S2. Establish a reference model of the array structure, determine the arrangement of array elements and calculate the initial fitness function according to the different positions searched by each bat in the algorithm population in the initialization data.

[0047] The five subarrays are obtained by rotating a single subarray at 72° intervals. The core subarray is the subarray in the due east direction, and the array element positions are (d1,0), (17.6,d2 / 2), and (17.6,-d2 / 2).

[0048] The optimization dimensions are two: first, the distance d1 from the center of the circle to the inner element of the subarray; and second, the distance d2 between the two outer elements of the subarray.

[0049] In the array structure, the positions of all array elements are obtained by rotating the matrix around the center of a single subarray to determine the positions of all array elements. The rotation interval is... num=5 represents the number of subarrays determined.

[0050] Since amplitude and phase excitation are not discussed, the array factor of the array structure can be expressed as:

[0051]

[0052] Where N is the total number of array elements excluding the center. This represents the offset of the nth array element from the reference point along the x-axis. This represents the offset of the nth element from the reference point along the y-axis, where 1 represents the phase when the center of the circle is taken as the reference point. θ is the azimuth angle, θ is the polar angle, and j is the imaginary unit.

[0053] The single antenna beam is selected as a Bessel beam, and its expression is:

[0054] ;

[0055] in, The angle is the angle between the observation direction and the beam pointing axis. For wavelength, For the effective aperture of a single antenna, This represents a first-order Bessel function.

[0056] The spacing between any two array elements can be expressed as:

[0057] ;

[0058] in, This indicates the calculation of the Euclidean distance; This indicates the position of the n1th array element. This represents the position of the n2th array element, and dmin is the minimum array element spacing constraint.

[0059] The initial fitness function is:

[0060] ,

[0061] in, This represents the maximum value of the matrix factor modulus; The first zero trap represents the matrix factor.

[0062] S3. Start iteration. After each iteration, including after initialization, check the spacing of the new array element positions. If the spacing requirement is met, proceed directly to S4; otherwise, adjust the search position until the requirement is met and then proceed to S4.

[0063] After obtaining the arrangement positions of all array elements, store the Euclidean distance between any two array elements in matrix form, fill the diagonal elements of the matrix with infinity, and then judge whether there is an Euclidean distance between two array elements that is less than the minimum array element spacing. If so, return True; otherwise, return False.

[0064] If True is returned, first determine whether the distance between the inner array element and the center of the circle is less than the minimum array element spacing. If it is less than the minimum array element spacing, set it to be equal to the minimum array element spacing; otherwise, do not perform any operation. Then, re-determine whether the spacing between the inner and outer array elements in the subarray is too close. If it is less than the minimum array element spacing, set it to be equal to the minimum array element spacing; otherwise, do not perform any operation. Finally, perform the spacing judgment again. If the condition is still not met, it can be determined that the spacing of the outer array in the subarray does not meet the requirements. At this time, only the distance between the inner and outer array elements of the subarray needs to be adjusted to ensure that the spacing between them will not exceed the maximum aperture limit, nor will it be less than the minimum array element spacing.

[0065] If the return value is False, it means that the distance between any array elements is greater than dmin, which meets the spacing requirement, and no adjustment is made.

[0066] S4. Calculate the orientation pattern of the array layout searched by each population, determine the fitness function of the corresponding layout position, and store the relevant data;

[0067] When the array elements meet the spacing requirements, the orientation pattern of the arrangement form corresponding to each population of the algorithm is obtained according to the above calculation formulas of array factor and fitness function, and the fitness function of the corresponding arrangement position is determined; stored, and the current iteration number, fitness function, and the corresponding array element position parameters corresponding to the fitness function are printed.

[0068] S5. If the algorithm has not reached the maximum number of iterations, then proceed to S4 for the next iteration search; otherwise, obtain the position searched by the population corresponding to the current best fitness function, which corresponds to the best array element arrangement position.

[0069] If the algorithm does not reach the maximum number of iterations, it proceeds to S4 for the next iteration search. If and only if the fitness function in this iteration is less than the previously stored optimal fitness function, the global optimal fitness function is modified to the fitness function of this iteration, and the position of the globally optimal bat individual is adjusted to the position searched by the algorithm population in this iteration; otherwise, no modification is made. When the algorithm reaches the maximum number of iterations, the current best fitness function and the corresponding search position are obtained, which corresponds to the optimal array element arrangement position.

[0070] S6. Perform spherical harmonic transformation on the power of the beam pattern and calculate the instrument noise;

[0071] The power pattern of the beam is represented as follows:

[0072] ;

[0073] According to the formula for the inverse spherical harmonic transformation, when m≥0, we have:

[0074] ;

[0075] in, It is a spherical harmonic function. and The distribution represents the spherical harmonic coefficients of the real part of the beam expansion and the spherical harmonic coefficients of the imaginary part of the beam expansion, where i is the imaginary unit and * is the conjugate symbol. Let be a sphere, and let be a surface integral element.

[0076] According to the properties of spherical harmonic functions, we have:

[0077] ;

[0078] The following equation can be derived:

[0079] ;

[0080] The above equation yields the spherical harmonic coefficients in the positive and negative m modes after spherical harmonic transformation of the beam power pattern.

[0081] The instrument noise standard deviation depends on the system temperature T, in Kelvin, the number of observation days (n days), and the frequency bandwidth. The units are megahertz, the maximum order of the spherical harmonic function lmax, and the number of scans per declination. The calculation expression is as follows:

[0082] ;

[0083] Where t is the integration time for a single sample, we have ;

[0084] In this embodiment, the system temperature is T=100K. =1MHz, lmax=1500, It depends on the specific sky survey strategy.

[0085] S7. Calculate the noise covariance matrix N, fill the beam matrix A, and calculate the generalized inverse matrix Ainv of the beam matrix.

[0086] After calculating the noise standard deviation, the beams are divided into autocorrelation beams and crosscorrelation beams, and noise is added to different beams.

[0087] For autocorrelation beams, the magnitude of the added noise is inversely proportional to the square root of the number of autocorrelation beams, and also inversely proportional to the square root of the normalized value of the proportion of observation time of a single point in the total time.

[0088] For cross-correlation beams, the magnitude of the added noise is inversely proportional to the square root of the number of redundant baselines, and also inversely proportional to the square root of the normalized value of the proportion of observation time in a single direction to the total time.

[0089] Assuming there is no correlation between noises from different baselines, the noise covariance matrix is ​​a diagonal matrix whose size is twice the square of the number of beams. The noise value of the same beam is added at the position of the adjacent even and odd indices in the noise covariance matrix, corresponding to the positive and negative m modes in the spherical harmonic domain.

[0090] Since the different m-modes are uncorrelated after spherical harmonic transformation, the A matrix is ​​filled with different m-modes, and its rows depend on the number of beams, with a size of twice the number of beams; the column size is lmax.

[0091] For different m-modulus values, the generalized inverse matrix Ainv of matrix A is calculated through singular value decomposition. To ensure computational stability, very small singular values ​​are truncated before inversion. The truncation threshold consists of a relative threshold and an absolute threshold. Its specific expression is:

[0092] ;

[0093] Where, N m Let A represent the noise covariance matrix under different m-modes. m This represents the beam matrix under different m-modes.

[0094] To ensure the stability of the results when calculating the generalized inverse matrix, this embodiment uses a relative threshold of 0.02 and an absolute threshold of 0.01.

[0095] S8. Calculate the reconstruction matrix Rec and the error covariance matrix C to evaluate the coverage performance of the array structure in the spherical harmonic space.

[0096] The specific expression for the reconstructed matrix is:

[0097] ;

[0098] The specific expression for the error covariance matrix is:

[0099]

[0100] in," " indicates conjugate transpose.

[0101] The non-redundant dish array structure designed in this embodiment has good coverage in spherical harmonic space, such as... Figure 1 As shown, there are 16 array elements. One array element is placed at the center of the circle, and the remaining 15 array elements form 5 subarrays, which are distributed around the center of the circle. The three array elements in each subarray form an isosceles triangle. Other subarrays are obtained by rotating the subarrays around the center of the circle. The included angle between each subarray is 72°.

[0102] Example 2

[0103] This embodiment further illustrates the effects of the present invention through the following simulation:

[0104] Experimental platform: Intel Core i7-12700 processor, 64-bit operating system Windows 11 Education Edition with a base frequency of 2.10GHz, Python 3.11, PyCharm Professional Edition 2025.1.2.

[0105] (1) Simulation parameters

[0106] The intelligent optimization algorithm selected is the bat algorithm, and the number of bat populations is... Maximum number of iterations Loudness parameter Pulse emission rate The resolution is 5 points per degree.

[0107] Simulation conditions: Total number of array elements: 16, element spacing must not be less than 6 meters, fixed d3 = 17.6 meters.

[0108] Sky survey strategy:

[0109] ① Mid-latitude sky survey: The antenna beam points to 31 sampling points from declination 29.38 degrees to 59.38 degrees, with spherical harmonic resolution parameters of... ,wavelength Meters, number of scans for each pointer Do not enable self-correlated beaming.

[0110] ② Polar Sky Survey: The antenna beam points from 75° to 90° declination, with a total of 16 sampling points and a spherical harmonic resolution parameter of [parameter missing]. ,wavelength Meters, number of scans for each pointer Do not enable self-correlated beaming.

[0111] (2) Simulation content

[0112] Table 1 shows the optimal array element positions of the non-redundant disk structure of the present invention at 1420.4 MHz.

[0113] Table 1 Optimal Array Element Positions

[0114] Array element number Array element position Array element number Array element position Array element number Array element position 1 (8.966, 0.000) 7 (-7.254, 5.270) 13 (2.771, -8.5270) 2 (17.020, 4.480) 8 (-16.403, 6.380) 14 (9.520, -14.803) 3 (17.020, -4.480) 9 (-11.136, 13.629) 15 (0.999, -17.572) 4 (2.771, 8.527) 10 (-7.254, -5.270) 16 (0.000，0.000) 5 (0.999, 17.572) 11 (-11.136, -13.629) 6 (9.52, 14.803) 12 (-16.403, -6.38)

[0115] Figure 2 and Figure 3The images show the array factor pattern and three-dimensional gain pattern of the structure designed in this invention at 1420.4 MHz, respectively. Its peak sidelobe level reaches -3.15 dB, which is higher than the 16-element Tianlai dish array in the paper "Sky reconstruction from transitvisibilities: PAON-4 and Tianlai dish array". The PSLL is reduced by about 2.53 dB. This is because the Tianlai dish array has 108 independent baselines with a redundancy of 1.11, while the array structure designed in this invention is a non-redundant array with 120 independent baselines, reaching the theoretical maximum value, and the redundancy is reduced to 1. In such a phased array with ultra-large spacing, the PSLL is relatively sensitive to redundancy. Therefore, this invention has achieved a greater breakthrough in PSLL.

[0116] Figure 4 This diagram illustrates the reconstruction matrix of the structure designed in this invention during a mid-latitude sky survey at 1420.4 MHz. Since only cross-correlation signals were used, the region below l=100 (the autocorrelation beam coverage area) is blank. Furthermore, under the same survey strategy, the reconstruction matrix coverage area of ​​the array structure designed in this invention differs slightly from that of the Tianlai dish array. This is because different baselines have different coverage areas in the spherical harmonic domain, and the array structure designed in this invention differs from the Tianlai dish array in the baseline direction. At higher orders (l), the truncation value of the reconstruction matrix of this invention reaches approximately l=1200, slightly higher than that of the Tianlai dish array. This is because the longest baseline in the structure of this invention is slightly larger than that of the Tianlai dish array, and the cross-correlation beams of long baselines are closer to higher orders (l) in the spherical harmonic space. Moreover, the reconstruction matrix of this invention during mid-latitude sky surveys shares two similar watersheds with the Tianlai dish array class, where m>l... At point m, the reconstructed matrix is ​​truncated, while at point m... <l And m>l At certain locations, the reconstruction matrix values ​​are higher, indicating that the SkyMap may have better reconstruction results in these areas.

[0117] Figure 5 This is a schematic diagram of the error covariance matrix of the structure designed in this invention during a mid-latitude sky survey at 1420.4 MHz. Its coverage area is close to the reconstructed matrix. However, unlike the reconstructed matrix, at m=l... Although a similar watershed can still be seen at this point, the magnitude of the error values ​​on both sides of the watershed is not as clearly distinguishable as that of the reconstruction matrix. Since this invention uses the same sky survey strategy as the Tianlai dish array, it will also obtain an instrument noise of approximately 9.96 mK. Similar to the Tianlai dish array, the overall error value is smaller when the order l is less than 800, and larger when the order l is greater than 800. In addition, both have the same gap in the lower right corner of the covered triangular region, which indicates that the error is extremely large at (l, m). The difference is that, near the gap region, the error value of the Tianlai dish array is close to 25, while the error value of the array structure designed in this invention is close to 10. In addition, the error covariance matrix of this embodiment is lower than that of the Tianlai dish array in almost all aspects of the covered area. If the high error region in the lower right corner is excluded, the average error will not exceed 6.2.

[0118] Figure 6 and Figure 7 These are schematic diagrams of the reconstruction matrix and error covariance matrix of the structure designed in this invention during a polar survey at 1420.4 MHz. In the polar cap region, the resolution nside=1024 is increased to avoid distortion that may be caused by using the Healpix pixelation method in the polar region; since the observed declination points from 75° to 90°, it can be clearly seen that at m=l When the reconstructed matrix is ​​truncated, the error covariance is greater than or equal to m. Significant errors occurred at this point. Compared to the mid-latitude sky survey, the coverage area in spherical harmonic space is less than half that of the mid-latitude sky survey. However, this is because the reconstruction of polar sky maps only requires this part of the information.

[0119] Comparing the reconstruction matrices and error covariance matrices of the array structure designed in this invention and the Tianlai dish array structure in polar surveys, it can be found that their shapes are similar. The reconstruction matrices of both are close to triangles, while the error covariance matrices are closer to right trapezoids. The polar survey coverage of the array structure designed in this invention is similar to that of the Tianlai dish array in terms of both reconstruction matrix and error covariance matrix. For the reconstruction matrix, the performance of the two is also quite similar. However, in terms of error covariance matrix, this invention still has a lower average error, which is consistent with the mid-latitude survey effect and is within our expectations. The error covariance matrix of the Tianlai dish array begins to show a significant high error (red) region when l is greater than 500, while the error covariance matrix of the array structure designed in this invention only shows a significant high error region when l is greater than 700. Near the edge region, the error covariance of both gradually increases, but the area of ​​the gradually increasing region is still smaller for this invention than for the Tianlai dish array, which fully demonstrates that this invention has better spherical harmonic space coverage at different frequencies. Furthermore, at a frequency of 1250MHz, the PSLL achieved by this structure is -2.90dB, which is still higher than that of the Tianlai dish array structure, demonstrating the robustness of the present invention.

[0120] The foregoing has shown and described the main features and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0121] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A non-redundant dish array structure with good coverage effect in spherical harmonics space, characterized in that, The application relates to an array structure and a method for optimizing the array structure. 16 array elements, one array element is placed at the center of a circle, and the other 15 array elements form five sub-arrays and are distributed around the center of the circle; Three array elements in each sub-array form an isosceles triangle, and other sub-arrays are obtained by rotating the sub-array around the center of the circle; The distance from the center of the circle to the inner array element in the sub-array and the distance between the inner and outer array elements in the sub-array are simultaneously optimized through an intelligent optimization algorithm.

2. The 16-element non-redundant dish array structure with good coverage effect in spherical harmonics space according to claim 1, characterized in that, The included angle between the sub-arrays is 72 degrees.

3. The 16-element non-redundant dish array structure with good coverage effect in spherical harmonics space according to claim 1, characterized in that, In the array structure, a single antenna is a Tianlai disc-shaped antenna with an aperture of 6 meters and an effective aperture of 5.4 meters.

4. A method for designing a non-redundant dish array structure with good coverage in spherical harmonics space, characterized in that, The method comprises the following steps: S1, selecting the number of sub-arrays, constraining the aperture size and the minimum array element spacing, and generating random initialization data; S2, establishing a reference model of the array structure, determining the arrangement position of the array elements according to different positions searched by the algorithm population in the initialization data, and calculating the initialization fitness function; S3, starting iteration, after each iteration, including the initialization, the distance between the new array element positions is judged, if the distance meets the distance requirement, it is directly transferred to S4; otherwise, the search position is adjusted until the requirement is met and then transferred to S4; S4, calculating the directional diagram of the array arrangement searched by each population, determining the fitness function of the corresponding arrangement position, and storing the related data; S5, if the algorithm has not reached the highest iteration number, the next iteration search is performed in S4; otherwise, the position searched by the population corresponding to the current best fitness function is obtained, and the position corresponds to the best array element arrangement position; S6, performing spherical harmonic transformation on the power of the beam directional diagram, and calculating the instrument noise; S7, calculating the noise covariance matrix N, filling the beam matrix A, and calculating the generalized inverse matrix Ainv of the beam matrix; S8, calculating the reconstruction matrix Rec and the error covariance matrix C, and evaluating the coverage performance of the array structure in the spherical harmonic space.

5. The method of claim 4, wherein the non-redundant design of a spherical array structure with good coverage in the spherical harmonics space is characterized by In S1, the number of sub-arrays is 5, the aperture size d3 is 17.6 meters, and the minimum array element spacing is 8.8 meters.

6. The method of claim 4, wherein the non-redundant design of a spherical array structure with good coverage in the spherical harmonics space is characterized by, In S3, the distance judgment is specifically as follows: After obtaining the arrangement positions of all array elements, the Euclidean distance between any two array elements is stored in the form of a matrix, the elements on the diagonal of the matrix are filled with infinity, and then the judgment is performed, if the Euclidean distance between two array elements is less than the minimum array element spacing, True is returned, otherwise, False is returned; if True is returned, firstly, it is determined whether the distance between the inner array element and the center of the circle in the generated array element position is less than the minimum array element spacing, if yes, the distance is directly equal to the minimum array element spacing, otherwise, no operation is performed; subsequently, it is determined whether the distance between the inner array element and the outer array element in the sub-array is too close, if yes, the distance is directly equal to the minimum array element spacing, otherwise, no operation is performed; finally, the distance judgment is performed again, if the condition is still not met, it is determined that the distance between the outer array elements in the sub-array does not meet the requirement, at this time, only the distance between the inner and outer array elements in the sub-array is adjusted, so that the distance between the two array elements does not exceed the maximum aperture limit and is not less than the minimum array element spacing; if False is returned, no adjustment is performed.

7. The method of designing a non-redundant dish array structure with good coverage in spherical harmonics according to any one of claims 4-6, wherein, The design method is a multi-constraint problem, taking the peak side lobe level as the fitness function, while constraining the minimum element spacing and fixing the maximum aperture to solve.

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