CN114336089A - Large-scale wide-angle scanning phased array antenna layered design method - Google Patents
Large-scale wide-angle scanning phased array antenna layered design method Download PDFInfo
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Abstract
The invention discloses a layering design method of a large-scale wide-angle scanning phased array antenna, which comprises the following steps: establishing a phased array antenna layered design model, wherein each irregular subarray forms a module panel; constructing a candidate matrix of the module panel; determining the number of control units based on the relation between the minimum control node number and the scanning angle coverage; sampling target patterns under different scanning angles; determining an initial point vector based on the target pattern sample value; acquiring an array configuration model by a convex relaxation method based on the initial point vector; and solving the phase center of the panel of the module through a self-adaptive covariance matrix evolution strategy, and tiling the primary subarray panel. The phase center of the module panel is sparsely distributed on the basis of the original method, so that the antenna units are effectively saved, the manufacturing cost is reduced, the performance of the antenna of a large-scale array is further improved, wide-angle scanning can be realized, and the method has great significance in practical application.
Description
Technical Field
The invention belongs to the technical field of sparse cloth optimization design of array antennas, and particularly relates to a layering design method of a large-scale wide-angle scanning phased array antenna.
Background
Along with the wide application of the subarray technology in the design of the phased array antenna of modern radar, satellite communication and the like, the number and the complexity of the antennas are greatly increased to meet the requirements of multifunctional and multitask of communication, navigation, positioning and the like, and the problems of platform load, antenna layout, cost, electromagnetic compatibility control and the like are seriously challenged. How to reduce the number of the channels of the array surface as much as possible and ensure the performance of the array antenna has very important research significance. The thin array antenna adopts array arrangement with non-uniform intervals, array elements are sparsely placed, the same radiation characteristic as the original array is realized by the thin array, and the potential advantages brought by the thin array antenna are as follows: the resolution is improved, the mutual coupling effect of the antenna units is weakened, the structure of the antenna system is simplified, and the like.
With the rapid development of the subarray technology, the overlapped subarray flat pavement plate, the shift period subarray module and the irregular polymer type subarray structure are widely concerned and steadily developed. The overlapping and shifting subarray structures are overly complex, and irregular subarray structures exhibit greater flexibility while providing smaller size, lower weight, and higher reconfigurability. The method for large-scale antenna array layered design also enters the visual field of people, but the classical subarray layered design method focuses more on the division and design of a primary irregular subarray, and is only simply spliced for a secondary subarray module.
Disclosure of Invention
The invention aims to provide a layering design method of a large-scale wide-angle scanning phased array antenna, which not only realizes effective saving of antenna units and reduction of manufacturing cost, but also further improves the performance of the large-scale array antenna, can realize wide-angle scanning, and has great significance in practical application.
The technical solution for realizing the purpose of the invention is as follows: a large-scale array antenna subarray layered design method based on a self-adaptive covariance matrix evolution strategy (CMA-ES) and a heuristic iterative convex relaxation programming method (H-ICRP) comprises the following steps:
firstly, establishing a large-scale phased array antenna layered design model. The method aims to enable irregular subarrays to form a module panel at first, then the module panels are subjected to sparse array formation, and each control unit (namely a phase shifter, an amplifier or a time delayer) is arranged in a subarray layout, so that the phased array antenna array design with low cost and low complexity is realized, and the subarray structure is reasonably optimized to realize wide-angle scanning;
second, a candidate matrix L is constructed for the module panel. The in-plane rectangular grid is represented by a set of linearly independent vectors, and the entire wavefront aperture can be represented as a set a, and the individual sub-arrays therein can be represented as a set S. Set S is considered a subset of set a by set cover theory. Finally, through operations of translation, rotation and mirror symmetry, a binary inclusion relation of the sub-array set S and the array surface set A is obtained and is represented by a dictionary matrix L;
and thirdly, selecting the freedom degree. Selecting a suitable number of control units ldofThe finite field effect caused by quantization errors is effectively reduced, and the balance between the cost and the array performance is achieved;
and fourthly, sampling the target patterns under different scanning angles. In order to find an optimal starting point, a fully-filled array radiation directional diagram is adopted as a target in a mode matching model, an expected/reference mode is sampled on a (u, v) plane, the radiation performance is considered, and meanwhile, the inversion performance is improved through multi-task interaction by utilizing a static mode and a scanning mode;
and fifthly, obtaining an initial point vector. Calculating an initial point vector by MT-BCS by using the target pattern sampling value obtained in the step 4, and adding additional constraint x in order to obtain a better initial point vector and reduce overlapping and loopholesTL＝1T；
And sixthly, solving the convex relaxation model. Outputting array configuration meeting the accurate tiling requirement by using the good initial point vector obtained in the step 5;
and seventhly, solving the phase center of the module panel. And solving a group of phase centers by using a self-adaptive covariance matrix evolution (CMA-ES) strategy to perform large-scale tiling of the primary subarray panel.
Compared with the prior art, the invention has the following remarkable advantages: (1) an adaptive covariance matrix evolution strategy (CMA-ES) is used in the hierarchical design of the large-scale wide-angle scanning array antenna, so that the performance of the large-scale array antenna is further improved, and the application background of the large-scale array antenna is widened; (2) the minimum array element spacing of the reconstructed area array is limited, so that the minimum array element spacing is prevented from being overlapped during secondary tiling, wide-angle scanning can be realized, and the method has great significance in practical application; (3) the side lobe performance lower than that of simple uniform tiling can be obtained, the use of array units is greatly reduced, effective saving of antenna units is realized, and the manufacturing cost is reduced.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
In fig. 1(a), the scanning angle θ is 0 °,
when the radiation pattern is on the basis of the irregular subarray module panel; in fig. 1(b), the scan angle θ is 0 °,
and on the basis of the irregular subarray module panel, a comparison graph of the uniform area array direction and the thin cloth reconstruction area array direction is obtained.
In fig. 2(a), the scanning angle θ is 15 °,
when the radiation pattern is on the basis of the irregular subarray module panel; in fig. 2(b), the scan angle θ is 15 °,
and on the basis of the irregular subarray module panel, a comparison graph of the uniform area array direction and the thin cloth reconstruction area array direction is obtained.
In fig. 3(a), the scanning angle θ is 25 °,
when the radiation pattern is on the basis of the irregular subarray module panel; in fig. 3(b), the scan angle θ is 25 °,
and on the basis of the irregular subarray module panel, a comparison graph of the uniform area array direction and the thin cloth reconstruction area array direction is obtained.
In fig. 4(a), the scanning angle θ is 35 °,
when the radiation pattern is on the basis of the irregular subarray module panel; in fig. 4(b), the scan angle θ is 35 °,
and on the basis of the irregular subarray module panel, a comparison graph of the uniform area array direction and the thin cloth reconstruction area array direction is obtained.
Fig. 5(a) and 5(b) are block panel tiles of a uniform area array and a sparse reconstruction area array.
Detailed Description
The invention provides a large-scale wide-angle scanning phased array antenna layered design method based on a self-adaptive covariance matrix evolution strategy (CMA-ES) and a heuristic iterative convex relaxation programming method (H-ICRP), which comprises the following steps:
firstly, establishing a large-scale phased array antenna layered design model; the irregular subarrays are firstly formed into a module panel, then the module panels are thinly arranged into an array, and each control unit (namely a TR component) is arranged in the arrangement of the subarrays and comprises a low-noise amplifier, a power amplifier, an amplitude limiter, a phase shifter and the like;
establishing a planar array of M x N antenna elements respectively disposed along the x-axis and the y-axis, any element in the plane being represented as a two-linear independent vector d1And d2Integer weighted linear combination of
rmn＝md1+nd2 (1)
In the case of a rectangular lattice, d1＝[1/2λ，0]TAnd d2＝[0，1/2λ]TAnd λ is the corresponding wavelength at the frequency of the array.
Considering a k-th sub-array composed of n elements, the sub-array factor can be expressed as:
where K1 … K is the index number for each sub-array,
is the excitation of the ith element located in the kth sub-array. k is a radical of02 π/λ is the wave number, ri kIs the spatial position vector of the ith element in the kth sub-array, u ═ sin θ cos φ, sin θ sin φ, θ ∈ [0, π]，φ∈[0，2π]。
Thus, a modular panel array factor consisting of K sub-arrays can be expressed as
rkIs the phase center of the kth sub-array. Assuming that the sensor unit patterns ep (u) are all the same, the overall sensor array antenna pattern is represented as:
in the formula, FpIs a super array factor composed of second level sub-arrays. In this case, if the phase shifters are placed on the primary sub-array only, the antenna pattern is swept to u0Can be expressed as
Secondly, constructing a module panel candidate matrix L;
the entire wavefront aperture can be represented as a set a, consisting of coefficients (m, n), and each subarray can be represented by a subset of a, set to B; according to the set coverage theory, the splicing problem can be expressed as a binary set coverage problem, namely, for oneGiven irregular sub-array of given shape, it can be rotated and turned to get different arrangement, all possible positions in the aperture can be used as candidate set to find S ═ B1，…，BκK represents the total number of candidate sets; the purpose is to find a proper subset, and to accurately fill the aperture set A;
generating a binary matrix L by encoding the sets A and S; each row and each column of L respectively represents a corresponding subset in S and a corresponding element in A; if the corresponding subset contains the corresponding element, the entry is 1; otherwise, the entry is 0; in this case, L can be viewed as a dictionary matrix, the rows of which are candidates;
in order to achieve a design structure of non-overlapping subarrays, the goal is to select the row subsets in the matrix L skillfully so that the number 1 appears exactly once in each column; thus, the subarray division matrix T may be generated as:
l (l < kappa) is the number of selected subarrays, Tln1 (row l and column n) denotes grouping the nth element into the nth subarray and vice versa. Mathematically, it can be reduced to an accurate coverage problem or a multiform stitching problem.
Thirdly, selecting the degree of freedom: selecting a suitable number of control units ldof；
In order to achieve a good balance between structural complexity and radiation performance, the sub-array technique of placing the control nodes (phase shifters, amplifiers, delays) at the sub-array level is reliable. However, the main problem with this structure is the quantization lobe. The larger the scan angle increase, the larger the quantization error due to the steeper phase excitation, which is the main cause of the limited field of view effect.
In order to reduce the influence of quantization error, control nodes need to be added, and the degree of freedom of users needs to be increased. One simple way is to use a smaller or mixed type of sub-array. The relationship between the minimum number of control nodes and the scan angle coverage can be expressed as
Wherein theta ismaxAnd phimaxIs the maximum scan angle in two planes, θ3And phi3Is the half-power beamwidth in both planes. Thus, the control node synthesis problem can be expressed as control over a constant/, with the larger the constant/the more control nodes.
Fourthly, sampling the target patterns under different scanning angles: in order to find an optimal starting point, a fully-filled array radiation directional diagram is adopted as a target in an array mode matching model, an expected/reference mode is sampled on a (u, v) plane, the radiation performance is considered, and meanwhile, the inversion performance is improved through multi-task interaction by utilizing a static mode and a scanning mode;
for the desired/reference pattern sampling, the sample points or directions are defined as follows:
θkand phikK-th sampling values of pitch angle and azimuth angle, K1＝K2K, the sampling point positions in the u-v domain corresponding to K are:
thereby obtaining a measurement vector F in a compressed sensing theory formed by K directional diagram sampling valuesrefI.e. by
Fref＝[Fref(u0，v0)，Fref(u1，v1)，…，Fref(uK-1，vK-1)]T (10)
Fifthly, obtaining an initial point vector:
the optimal radiation performance of the array can be achieved by a fully populated matrix. The array pattern matching problem can be expressed as:
T-Ψw＝e (13)
wMN×1＝LTh (14)
where ε is the fidelity index, rmnA position vector representing the nth column array element of the mth row, T (theta, phi) is a desired directional diagram, psi ≈ psi1，…，Ψ1]HWherein the ith element value is
w≈[w1，…，wMN]HIs the excitation vector, T and h are the sampling vector of the target pattern and the weighting vector of the sub-array, respectively, e is the residual value, LTIs the transpose of the dictionary matrix.
Sixthly, solving a convex relaxation model:
the selection of rows in the matrix L can be expressed as
L is a binary dictionary matrix,/dofIs a constant number representing the total number of sub-arrays/patches that will be used to cover the array aperture. x is the selection vector of the selection candidate (1 indicates selected, 0 indicates unselected). 1 is a full 1 vector.
Expressing binary constraint as a minimization problem based on convex set difference theory
Thus, the expression may be expressed as
It is clear that the objective function 1Tx-xTx-0 is not a convex function. Therefore, it is linearized by a first order Taylor decomposition using a relaxation method, which can be expressed as (k +1) th iteration
Then, the sub-array tiling problem for the (k +1) th iteration can be expressed as:
wherein x0(k ═ 0) is the initial point vector.
And seventhly, solving the phase center of the module panel:
rkis the phase center of the kth sub-array. In general, the equivalent phase center of a two-dimensional sub-array can be expressed as
Wherein xiAnd yiIs the ith element on the x-axis and y-axis. n is the sum of the elements in a sub-array.
The CMA-ES algorithm needs to adjust a dynamic step size parameter sigma of multivariate normal distribution and a dynamic positive definite covariance matrix C to guide the direction of mutation evolution of the population, and the basic equation is as follows:
in the formula (I), the compound is shown in the specification,
is the kth population in the g +1 generation; m is(g)∈RM×1Is the mean of the multivariate normal distribution that produces the population of the g-th generation; sigma(g)And C(g)∈RM×MRespectively, the step size and covariance matrix of the multivariate normal distribution that produced the population of the g-th generation, C(0)Is an M × M identity matrix, and M is the number of optimized variables.
The selected fitness function value is set as:
fcost＝PSLLdB+c0(dtarget-min(dmin，dtarget))2 (21)
wherein f iscostFor the fitness function value, PSLL is the highest sidelobe level value corresponding to the array, dminIs the actual minimum cell pitch, atargetA minimum cell pitch required for practice, c0And performing interval expansion processing on a group of optimized thin cloth array element positions to obtain a proper module panel phase center for large-scale tiling.
In order to verify the correctness and the effectiveness of the invention, a large-scale planar array multi-beam scanning pattern comprehensive problem is analyzed below, the operation environment is (CPU 1.8GHz, 8.00GB RAM, Matlab2018a), and it is assumed that a module panel used as a secondary sub-array for array arrangement is formed by accurately tiling a 4-unit L-shaped domino structure, the panel is a rectangular uniform planar array, the number of antenna units in the x and y directions is M-8, and N-8, respectively. When the modules are uniformly spread, the number of the module panels is set to be 100, the modules are thinned, the number of the module panels after being thinned is reduced to 60, the thinning rate is 40%, and the aperture of the array is slightly enlarged. The aperture D of the uniform array is 36 lambda, and the array element interval is 0.5 lambda. The present invention optimally designs a non-uniformly distributed area array, and can balance the control unit and array performance, and the aperture D of the thin-cloth array is 40 lambda, and the minimum interval of array elements is 0.55 lambda, so that the reconstructed thin-cloth area array can be made to be in the range of [ +/-45 deg. °]And the directional diagram is kept in the sweep angle range, grating lobes are not generated, and beam scanning is realized. The performance of the radiation pattern of the reconstructed sparse array is superior to that of the uniformly distributed area array radiation pattern. In the calculation of the preferred initial point, the desired partyThe number of samples of the graph is 442 and 419, and the prior parameter of the MT-BCS is considered to be beta1＝β2The stop threshold is set to 10 for 1. Fig. 1(a) -4 (a) show radiation patterns with better performance obtained based on better initial point vectors, which are formed by accurately tiling 8 × 8 sub-array panels in a 4-unit L-type domino structure under different scanning angles. In order to more clearly see the effect of the sparse array of the secondary panel, the comparison between the directional diagram of the reconstructed sparse array and the radiation directional diagram of the uniformly tiled array is performed under different scanning angles in fig. 1(b) to 4(b), and the grating lobe suppression effect of the combination of the layered array factors on the overall true area directional diagram can be seen. As can be seen from the figure, the angle was [ + -45 DEG, 45 DEG)]In the range of the sweep angle, in the array factor pitching direction synthetic directional diagram, the highest side lobe of the radiation directional diagram of the reconstructed thin-cloth area array is always below-20 dB and is far superior to that of the original uniform area array. Fig. 5 shows a schematic diagram of splicing a reconstructed sparse area array and an original uniform area array based on an irregular subarray divided into 8 × 8 panels. It can be seen that the aperture of the reconstructed sparse area array is slightly enlarged compared with the original uniform area array. In addition, the scanning electrical properties at different angles for the two tiling schemes are shown in table 1.
Table 1 scanning electrical property comparison table
The basic idea of the invention is that firstly, a heuristic iterative convex relaxation programming method (H-ICRP) is utilized to ensure that a given irregular subarray is accurately tiled into a module panel, and then the sparse arraying is carried out on the panels. By reducing the number of control units (phase shifters, amplifiers and T/R modules) to the number of sub-arrays per module panel, the feed network is simplified, cost is effectively saved, and an effective tradeoff is established between radiation performance and engineering convenience. Considering that the original irregular subarray hierarchical design method simply splices together the module panels, the method introduces an adaptive covariance matrix evolution strategy (CMA-ES). The phase center of the module panel is sparsely distributed on the basis of the original method, so that the antenna units are effectively saved, the manufacturing cost is reduced, the performance of the antenna of a large-scale array is further improved, wide-angle scanning can be realized, and the method has great significance in practical application.
Claims (10)
1. A large-scale wide-angle scanning phased-array antenna layered design method is characterized by comprising the following steps:
establishing a phased array antenna layered design model, wherein each irregular subarray forms a module panel;
constructing a candidate matrix of the module panel;
determining the number of control units based on the relation between the minimum control node number and the scanning angle coverage;
sampling target patterns under different scanning angles;
determining an initial point vector based on the target pattern sample value;
acquiring an array configuration model by a convex relaxation method based on the initial point vector;
and solving the phase center of the panel of the module through a self-adaptive covariance matrix evolution strategy, and tiling the primary subarray panel.
2. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: the establishing of the phased array antenna layered design model specifically comprises the following steps:
establishing a planar array of M x N antenna elements respectively disposed along the x-axis and the y-axis, any element in the plane passing through two linearly independent vectors d1And d2The integer weighted linear combination of (a) is expressed as:
rmn＝md1+nd2 (1)
in the case of a rectangular lattice, d1＝[1/2λ，0]TAnd d2＝[0，1/2λ]Tλ is the wavelength corresponding to the frequency of the array;
determining the subarray factor of the kth subarray as follows:
where K1 … K is the index number for each sub-array,
is the excitation of the ith element located in the kth sub-array; k is a radical of02 pi/lambda is the wave number, u is (sin θ cos phi, sin θ sin phi), theta is e [0, pi]，φ∈[0，2π]，ri kIs the spatial position vector of the ith element in the kth sub-array, and n is the number of the elements of the kth sub-array;
determining the module panel array factor formed by K sub-arrays as:
rkis the phase center of the kth sub-array; assuming that the sensor unit patterns ep (u) are all the same, the overall sensor array antenna pattern is:
in the formula, FpIs a super array factor composed of second level sub-arrays; if the phase shifter is placed on the primary sub-array only, the antenna pattern is scanned to u0The treatment time is as follows:
3. the hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: the candidate matrix for constructing the module panel is specifically:
another set a, representing the entire wavefront aperture, is composed of coefficients (m, n), each subarray being represented by a subset of a,is set to be B; all possible positions within the aperture are taken as candidate set S ═ B1,…,BκK represents the total number of candidate sets;
coding the sets A and S to generate a binary candidate matrix L; each row and each column of L respectively represents a corresponding subset in S and a corresponding element in A; if the corresponding subset contains the corresponding element, the entry is 1; otherwise, the entry is 0;
selecting a subset of rows in the candidate matrix L such that the number 1 appears once in each column; determining a subarray division matrix T as:
4. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: the relationship between the minimum control node number and the scanning angle coverage is as follows:
wherein theta ismaxAnd phimaxIs the maximum scan angle in two planes, θ3And phi3Is the half-power beamwidth in both planes.
5. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: the sampling of the target pattern at different scan angles is performed by using a fully populated array radiation pattern as a target and using stationary and scanning modes to sample the desired/reference mode in the (u, v) plane.
6. The hierarchical design method of the large-scale wide-angle scanning phased array antenna according to claim 5, characterized in that: said sampling of the desired/reference pattern in the (u, v) plane specifically comprises:
for the desired/reference pattern sampling, a sample point or direction is defined:
θkand phikK-th sampled values, K, of pitch and azimuth angles, respectively1＝K2The sampling point positions in the (u, v) plane domain are:
obtaining a measurement vector F consisting of K directional diagram sampling valuesrefComprises the following steps:
Fref＝[Fref(u0,v0),Fref(u1,v1),…,Fref(uK-1,vK-1)]T (10)
7. the hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: determining an initial point vector based on target pattern sample values calculates an initial point vector by MT-BCS and adds an additional constraint xTL＝1TThe array pattern match is expressed as:
T-Ψw＝e (13)
wMN×1＝LTh (14)
where ε is the fidelity index, rmnA position vector representing the nth column array element of the mth row, T (theta, phi) is a desired directional diagram, psi ≈ psi1，…，ΨI]HWherein the ith element value is
w≈[w1，…，wMN]HIs the excitation vector, T and h are the sampling vector of the target pattern and the weighting vector of the sub-array, respectively, e is the residual value, LTIs a transpose of the candidate matrix L.
8. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 7, characterized in that: the obtaining of the array configuration model by the convex relaxation method based on the initial point vector specifically includes:
the rows in the candidate matrix L are represented as:
based on the convex set difference theory, the array configuration model is expressed as:
thus, in conjunction with equation (15), the array configuration model can be expressed as
The objective function is represented as (k +1) th iteration by linearizing it by a relaxation method with a first order Taylor decomposition
The array configuration model for the (k +1) th iteration is:
wherein k is 0, x0Is the initial point vector.
9. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 1, characterized in that: solving the module panel phase center through the adaptive covariance matrix evolution strategy specifically comprises:
optimizing the position of the array element of the module panel by a self-adaptive covariance matrix evolution strategy;
based on the optimized location of the kth module panel, determining the kth module panel phase center as:
wherein xiAnd yiIs the ith element on the x-axis and y-axis; n is the sum of the elements in a sub-array.
10. The hierarchical design method for large-scale wide-angle scanning phased array antenna according to claim 9, characterized in that: optimizing the position of the array element of the module panel through the adaptive covariance matrix evolution strategy specifically comprises the following steps:
optimizing the array element position of the module panel by an adaptive covariance matrix evolution strategy, wherein the adaptive covariance matrix evolution strategy equation is as follows:
in the formula (I), the compound is shown in the specification,
is the kth population in the g +1 generation; m is(g)∈RM×1Is the mean of the multivariate normal distribution that produces the population of the g-th generation; sigma(g)And C(g)∈RM×MRespectively, the step size and covariance matrix of the multivariate normal distribution that produced the population of the g-th generation, C(0)An M multiplied by M identity matrix, wherein M is the number of the optimized variables;
the fitness function value of the adaptive covariance matrix evolution strategy is set as:
fcost＝PSLLdB+c0(dtarget-min(dmin,dtarget))2 (21)
fcostfor the fitness function value, PSLL is the highest sidelobe level value corresponding to the array, dminTo the actual minimum cell pitch, dtargetA minimum cell pitch required for practice, c0Are weight coefficients.
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