Frequency control array variable beam shape synthesis method, system and device based on sparse reconstruction and medium

Abstract

The invention discloses a frequency control array variable beam shape synthesis method, system and device based on sparse reconstruction, and a medium. The method comprises the following steps: initializing parameters; uniformly sampling N points in the interval (0, Md) of the array element spacing and the interval (0, M delta f) of the frequency deviation; constructing discrete grid points Ai, j (theta, r) according to the initialization parameters and the discretization results Di and delta Fj; constructing a two-dimensional orthogonal basis matrix; mapping an expected beam directional diagram p (theta, r) into a transform domain, constructing a mapping matrix # imgabs0 # to map discrete grid points Ai, j (theta, r) into the transform domain, constructing a mapping matrix # imgabs1 # to construct a beam optimization problem, and solving the beam optimization problem; synthesizing a frequency control array beam directional diagram; the system, the equipment and the medium are used for implementing the method. According to the invention, various complex beam shapes can be generated, and the flexibility of beam forming is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of frequency-controlled array beamforming, and in particular relates to a frequency-controlled array variable beam shape synthesis method, system, device and medium based on sparse reconstruction. Background Art

[0002] The traditional phased array antenna is composed of a large number of radiating elements. Its working principle is to generate higher gain in a specific direction and lower gain in other directions through the mutual superposition of electromagnetic waves in space, thus forming a directional beam pattern. Unlike the phased array, the frequency-controlled array (see Figure 1) uses different transmission frequencies on each antenna element and adds a frequency offset much smaller than the carrier frequency to adjacent array elements. Since the transmission frequencies of different antennas are different, the phase superposition effect produced at different distances is also different, resulting in the phase superposition on some distance units to form a peak, and the phase cancellation on some distance units to form a trough. Therefore, the beam energy distribution of the frequency-controlled array is not only related to the angle, but also to the distance, thus forming a distance-angle dependent beam pattern. However, the beam pattern of the frequency-controlled array beam pattern is S-shaped, while the beam pattern of the phased array is linear (see Figure 2), which means that the beam pattern of the frequency-controlled array is coupled between distance and angle. Due to this coupled beam characteristic, the frequency-controlled array has limitations in many applications.

[0003] In the existing technical solutions, the main method to solve the problem of distance-angle coupling is to convert the traditional S-shaped frequency-controlled array beam pattern into a point beam to ensure that the beam forms a peak only at a specific target point, thereby decoupling the distance and angle. The basic principle of the existing methods is to synthesize point beams by redesigning the frequency deviation and breaking the linear relationship between the phase and distance dependence between adjacent array elements. They are mainly divided into the following two categories:

[0004] 1. Strategy based on nonlinear functions: This method uses a specific nonlinear function to design a frequency offset, thereby forming a point-like beam pattern at the target location, so that the beam energy is effectively concentrated in a specific area;

[0005] 2. Strategy based on optimization algorithm: First, the distance-angle two-dimensional area of ​​the frequency-controlled array beam pattern is divided into target area and non-target area. In order to concentrate the beam energy on the specific target area and minimize the sidelobes, the corresponding objective function and constraints are designed. However, since such problems are usually non-convex, the complexity of exhaustive search is extremely high. To this end, there are two common methods: one is to greatly reduce the complexity of system design through heuristic algorithms, thereby obtaining the optimal design frequency deviation; the other is to convert the non-convex problem into a convex optimization problem through mathematical methods, and then use the convex optimization algorithm to solve it.

[0006] The prior art literature proposes a symmetric frequency-controlled array beam pattern synthesis method based on multi-carrier frequency increment and convex optimization (H.Shao, J.Dai, J.Xiong, H.Chen and W.-Q.Wang, Dot-Shaped Range-AngleBeampattern Synthesis for Frequency DiverseArray[J].IEEE Antennas Wireless Propagation Letters, 2016, 15:1703-1706), which realizes the synthesis of single-point and multi-point beam shapes. This method is superior to the existing frequency-controlled array with logarithmic frequency deviation distribution in terms of transmission energy focusing, sidelobe suppression and array resolution performance.

[0007] Prior art literature proposes two frequency-controlled arrays with symmetrical logarithmic distribution of frequency offsets (Y.Xu and K.-M.Luk, Enhanced Transmit–Receive Beamforming for Frequency Diverse Array[J].IEEE Transactions on Antennas and Propagation, 2020, 68(7):5344-5352), aiming to achieve the maximum value in the required distance-angle region while exhibiting side lobes in areas of no interest. Secondly, the receiving process is designed to compensate for time-varying factors by utilizing multiple mixers corresponding to different frequencies. In order to maintain the shape of the main beam and simultaneously reduce the peak sidelobe level of the directional pattern, the optimization problem is formulated as a semidefinite programming problem. This method exhibits finely focused and symmetrically distributed transmit-receive beam patterns in the distance-angle domain.

[0008] However, since most existing methods are designed based on a single dimension, namely frequency deviation, they fail to fully utilize the dimension of array element spacing, which results in problems such as insufficient focusing performance of point beam synthesis, poor sidelobe suppression, uneven energy distribution of multiple point beams, and inability to synthesize two-dimensional variable beams. Summary of the invention

[0009] In order to overcome the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a frequency-controlled array variable beam shape synthesis method, system, device and medium based on sparse reconstruction, which fully utilizes the controllable degrees of freedom of the frequency-controlled array in the distance domain and the angle domain by simultaneously optimizing the two dimensions of array element spacing and frequency deviation, and can realize the synthesis of two-dimensional variable beam shapes, with more precise point beam focusing and enhanced sidelobe suppression effect; the present invention can generate a variety of complex beam shapes, greatly improving the flexibility of beamforming.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] A frequency-controlled array variable beam shape synthesis method based on sparse reconstruction comprises the following steps:

[0012] S1: Initialization parameters

[0013] Initialization parameters include but are not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r);

[0014] S2: Discretization of continuous intervals

[0015] According to the initialization parameters in step S1, N points are uniformly sampled in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset, which are respectively expressed as:

[0016]

[0017] Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively;

[0018] S3: Constructing discrete grid points

[0019] According to the initialization parameters in step S1 and the discretization result D in step S2 i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as:

[0020]

[0021] Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset;

[0022] S4: Construct a two-dimensional orthogonal basis matrix

[0023] According to the initialization parameters in step S1, a two-dimensional orthogonal basis matrix is ​​constructed, and the element Φ in the kth row and the lth column is k,l It is expressed as:

[0024]

[0025] Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively;

[0026] S5: Construct mapping matrix P and dic i,j

[0027] The desired beam pattern p(θ,r) defined in step S1 is mapped to the transform domain through the two-dimensional orthogonal basis matrix constructed in step S4 to construct a mapping matrix

[0028]

[0029] Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r);

[0030] The discrete grid points A constructed in step S3 are converted into the two-dimensional orthogonal basis matrix constructed in step S4. i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain to construct the mapping matrix

[0031]

[0032] Among them, dic i,j Represents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point;

[0033] S6: Construct the beam optimization problem and solve it

[0034] According to the mapping matrix P and dic constructed in step S5 i,j , construct the beam optimization problem:

[0035]

[0036] The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ;

[0037] S7: Synthesized frequency-steering array beam patterns

[0038] The discrete grid points A constructed in step S3 i,j (θ, r) and the weight matrix element s solved in step S6 i,j Substituting into the frequency controlled array factor AF(θ,r):

[0039]

[0040] Synthesize the final frequency-controlled array beam pattern.

[0041] The present invention also provides a frequency-controlled array variable beam shape synthesis system based on sparse reconstruction, comprising:

[0042] A parameter initialization module is used to initialize parameters, including but not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r);

[0043] The continuous interval discretization module is used to uniformly sample N points in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset according to the initialization parameters, which are respectively expressed as:

[0044]

[0045] Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively;

[0046] Discrete grid point construction module is used to construct the discrete grid point according to the initialization parameters and the discretization result D i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as:

[0047]

[0048] Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset;

[0049] The two-dimensional orthogonal basis matrix construction module is used to construct a two-dimensional orthogonal basis matrix according to the initialization parameters. The element Φ in the kth row and lth column k,l It is expressed as:

[0050]

[0051] Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively;

[0052] Mapping matrix P and dic i,j The construction module is used to map the desired beam pattern p(θ,r) defined in the transform domain through a two-dimensional orthogonal basis matrix to construct a mapping matrix

[0053]

[0054] Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r);

[0055] Through the two-dimensional orthogonal basis matrix, the discrete grid point A i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain to construct the mapping matrix

[0056]

[0057] Among them, dic i,j Represents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point;

[0058] Beam optimization problem construction and solution module, used to construct the mapping matrix P and dic i,j , construct the beam optimization problem:

[0059]

[0060] The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ;

[0061] The frequency-controlled array beam pattern synthesis module is used to construct discrete grid points A i,j (θ, r) and the weight matrix element s solved i,j Substituting into the frequency controlled array factor AF(θ,r):

[0062]

[0063] Synthesize the final frequency-controlled array beam pattern.

[0064] The present invention also provides a frequency-controlled array variable beam shape synthesis device based on sparse reconstruction, comprising:

[0065] Memory: a computer program storing the above-mentioned frequency-controlled array variable beam shape synthesis method based on sparse reconstruction, which is a computer-readable device;

[0066] Processor: used to implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction when executing the computer program.

[0067] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] 1. Achieve better beam focusing and sidelobe suppression effects:

[0070] Existing spot beam synthesis technology usually has difficulty in achieving high-precision beam focusing, and the sidelobe suppression effect is poor, which affects the accuracy of target detection. The present invention is based on sparse reconstruction theory to jointly optimize frequency offset and array element spacing. The desired spot beam and the constructed discretized grid are mapped through a two-dimensional orthogonal basis matrix, and the beam optimization problem is converted into a sparse linear combination problem, thereby realizing the synthesis of spot beams in the distance angle domain, significantly improving the focusing ability of the spot beam, and making the beam energy highly concentrated on the target point. At the same time, the synthesized spot beam also performs well in sidelobe suppression, which can effectively reduce the sidelobe level and reduce interference in non-target directions, thereby improving the overall performance and reliability of the system.

[0071] 2. Achieve full power beam when facing multiple point targets in the range angle domain:

[0072] When facing multiple target points in the distance angle domain, the existing point beam synthesis methods are usually unable to achieve full-power beams for each target point, and the beam energy is unevenly distributed. The present invention is based on sparse reconstruction theory to jointly optimize frequency offset and array element spacing. The desired multi-point beams and the constructed discretized grid are mapped by a two-dimensional orthogonal basis matrix, and the beam optimization problem is converted into a sparse linear combination problem, thereby realizing the synthesis of multi-point beams in the distance angle domain and achieving full-power beams at multiple target points. This method is particularly important in complex multi-target environments, and can significantly improve the detection and recognition capabilities of the system to meet the needs of high-precision, multi-target detection.

[0073] 3. Given the desired two-dimensional beam pattern, the synthesis of two-dimensional variable beam shape is achieved:

[0074] Most existing technologies perform beam optimization in a single dimension, which makes it difficult to achieve complex two-dimensional beam shapes. The present invention is based on sparse reconstruction theory to jointly optimize frequency offset and array element spacing. By mapping the given desired two-dimensional beam pattern and the constructed discretized grid through a two-dimensional orthogonal basis matrix, the beam optimization problem is converted into a sparse linear combination problem, thereby achieving the synthesis of two-dimensional variable beam shapes. This method can generate a variety of complex beam shapes, such as flat-top beams, curved beams, etc., which significantly improves the flexibility and adaptability of frequency-controlled array beamforming and meets the needs of different application scenarios.

[0075] In summary, the present invention uses discretization and sparse reconstruction methods to model the beam optimization problem as a sparse linear combination problem, which can simultaneously optimize the two dimensions of array spacing and frequency offset, thereby changing the energy distribution of the frequency-controlled array beam pattern. It has the advantages of good beam focusing performance, excellent sidelobe suppression effect, achieving full-power beams at multi-point targets in the distance angle domain, and generating a variety of complex beam shapes. The present invention significantly improves the flexibility and adaptability of beamforming to meet the needs of different application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] FIG. 1 is an array structure diagram of a phased array and a frequency-controlled array; FIG. 1( a ) is the array structure of a traditional phased array, and FIG. 1( b ) is the array structure of a uniform linear frequency-controlled array.

[0077] FIG2 is a beam pattern of a phased array and a uniform linear frequency-controlled array; FIG2(a) is a beam pattern of a conventional phased array, and FIG2(b) is a beam pattern of a uniform linear frequency-controlled array.

[0078] Figure 3 The present invention is a flow chart of a frequency-controlled array variable beam shape synthesis method based on sparse reconstruction.

[0079] Figure 4 It is the frequency control array structural framework corresponding to the present invention.

[0080] FIG5 is a comparison of the spot beams synthesized by the present invention and the traditional symmetric logarithmic frequency deviation technology. FIG5(a) and FIG5(b) are two-dimensional plane diagrams of the spot beams synthesized by the present invention and the traditional symmetric logarithmic frequency deviation technology, respectively, and FIG5(c) and FIG5(d) are cross-sectional diagrams of the spot beams synthesized by the present invention and the traditional symmetric logarithmic frequency deviation technology along the angle domain at a distance of r = 150 km, respectively. FIG5(e) and FIG5(f) are cross-sectional diagrams of the spot beams synthesized by the present invention and the traditional symmetric logarithmic frequency deviation technology along the angle domain at an angle of θ = 0°, respectively.

[0081] FIG6 is a comparison of the multi-spot beams synthesized by the present invention and the traditional symmetric logarithmic frequency deviation technology. FIG6(a) shows a three-dimensional diagram of the multi-spot beam synthesized by the present invention, FIG6(b) is a corresponding two-dimensional plane diagram, FIG6(c) is a three-dimensional diagram of the multi-spot beam synthesized by the traditional symmetric logarithmic frequency deviation technology, and FIG6(d) shows a corresponding two-dimensional plane diagram.

[0082] Figure 7 is a comparison diagram between the synthesized flat-top beam diagram of the present invention and the expected flat-top beam diagram, wherein Figure 7(a) is a three-dimensional diagram of the expected flat-top beam, Figure 7(b) is a two-dimensional plane diagram of the expected flat-top beam, Figure 7(c) is a three-dimensional diagram of the synthesized flat-top beam of the present invention, and Figure 7(d) is a two-dimensional plane diagram of the synthesized flat-top beam of the present invention.

[0083] Figure 8 is a comparison diagram between the synthesized curved beam of the present invention and the desired curved beam, wherein Figure 8(a) is a three-dimensional diagram of the desired curved beam, Figure 8(b) is a two-dimensional plane diagram of the desired curved beam, Figure 8(c) is a three-dimensional diagram of the synthesized curved beam of the present invention, and Figure 8(d) is a two-dimensional plane diagram of the synthesized curved beam of the present invention. DETAILED DESCRIPTION

[0084] The technical solution adopted by the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0085] In existing research, the two-dimensional beamforming technology of frequency-controlled arrays mainly focuses on the synthesis of point beams, usually by optimizing the design in a single dimension to achieve S-shaped beam decoupling of the frequency-controlled array in the distance-angle dimension. However, this method fails to fully utilize the potential of the frequency-controlled array to synthesize two-dimensional beams in the distance-angle domain, thereby limiting its beamforming flexibility. To overcome this problem, the present invention proposes a frequency-controlled array beamforming method based on sparse reconstruction. This method can generate a two-dimensional variable-shape beam pattern by simultaneously optimizing the two dimensions of array element spacing and frequency offset, significantly improving the flexibility of frequency-controlled array beamforming to adapt to different radar and communication environment requirements.

[0086] FIG. 1 is an array structure diagram of a phased array and a frequency-controlled array; FIG. 1( a ) is the array structure of a traditional phased array, and FIG. 1( b ) is the array structure of a uniform linear frequency-controlled array.

[0087] FIG2 is a beam pattern of a phased array and a uniform linear frequency-controlled array; FIG2(a) is a beam pattern of a conventional phased array, and FIG2(b) is a beam pattern of a uniform linear frequency-controlled array.

[0088] The technical solution flow chart framework adopted by the present invention is as follows Figure 3 As shown, the corresponding frequency-controlled array structure framework is as follows Figure 4 The present invention proposes a frequency-controlled array variable beam shape synthesis method based on sparse reconstruction, comprising the following steps:

[0089] S1: Initialization parameters

[0090] Initialization parameters include but are not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r);

[0091] S2: Discretization of continuous intervals

[0092] According to the initialization parameters in step S1, N points are uniformly sampled in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset, which are respectively expressed as:

[0093]

[0094] Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively;

[0095] By replacing the continuous domain with discretized sampling, the search space of the beam optimization problem is greatly reduced.

[0096] S3: Constructing discrete grid points

[0097] According to the initialization parameters in step S1 and the discretization result D in step S2 i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as:

[0098]

[0099] Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset;

[0100] S4: Construct a two-dimensional orthogonal basis matrix

[0101] According to the initialization parameters in step S1, a two-dimensional orthogonal basis matrix is ​​constructed, and the element Φ in the kth row and the lth column is k,l It is expressed as:

[0102]

[0103] Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively;

[0104] The beam pattern is mapped from the range angle domain to the transform domain by constructing a two-dimensional orthogonal basis to fully utilize the sparsity in the transform domain.

[0105] S5: Construct mapping matrix P and dic i,j

[0106] The desired beam pattern p(θ,r) defined in step S1 is mapped to the transform domain through the two-dimensional orthogonal basis matrix constructed in step S4 to construct a mapping matrix

[0107]

[0108] Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r);

[0109] The discrete grid points A constructed in step S3 are converted into the two-dimensional orthogonal basis matrix constructed in step S4. i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain to construct the mapping matrix

[0110]

[0111] Among them, dic i,jRepresents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point;

[0112] S6: Construct the beam optimization problem and solve it

[0113] According to the mapping matrix P and dic constructed in step S5 i,j , construct the beam optimization problem:

[0114]

[0115] The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ;

[0116] In the transform domain, the beam optimization problem is modeled as a sparse linear combination problem, and the optimal weight of each grid point is determined by minimizing the reconstruction error.

[0117] S7: Synthesized frequency-steering array beam patterns

[0118] The discrete grid points A constructed in step S3 i,j (θ, r) and the weight matrix element s solved in step S6 i,j Substituting into the frequency controlled array factor AF(θ,r):

[0119]

[0120] Synthesize the final frequency-controlled array beam pattern.

[0121] The energy distribution of the frequency-controlled array beam pattern can be changed by simultaneously adjusting the array spacing and frequency offset.

[0122] Simulation parameter settings:

[0123] Carrier center frequency f0 = 5 GHz, number of arrays M = 64, frequency offset Δf = 1 kHz, array spacing d = 0.03 m, number of array elements M = 64, number of sampling points N = 64, number of orthogonal bases K = 64, total observation area (θ, r) is {-90°≤θ≤90°, 0km≤r≤300km}

[0124] Example 1

[0125] Simulation conditions:

[0126] Set p(θ, r) as a spot beam, with the target point located at (0°, 150 km), and apply p(θ, r) and the specific values ​​of the above simulation parameter settings to the technical solution proposed in the present invention.

[0127] Simulation results and analysis:

[0128] Referring to FIG. 5(a) and FIG. 5(b), the two-dimensional plane diagram of the spot beam synthesized by the method of the present invention (FIG. 5(a)) is compared with the two-dimensional plane diagram of the spot beam synthesized by the traditional symmetric logarithmic frequency deviation technology (FIG. 5(b)). The results show that the energy of the spot beam synthesized by the method of the present invention is highly concentrated at the target point (0°, 150km), showing excellent directional ability and beam focusing. In contrast, the energy distribution of the spot beam synthesized by the traditional symmetric logarithmic frequency deviation technology method is more dispersed, the main lobe width is wider, and there are obvious side lobes, which indicates that its focusing performance is not as good as that of the present invention.

[0129] Figure 5(c) and Figure 5(d) respectively show the cross-sectional views of the point beam synthesized by the method of the present invention and the traditional symmetric logarithmic frequency deviation technology along the angle domain when r = 150 km. The comparison shows that the side lobes of the beam generated by the method of the present invention are almost invisible in the cross-sectional view of the angle domain, which effectively suppresses the side lobes; while the traditional method has a more concentrated energy in the angle domain, but has a higher side lobe.

[0130] Figure 5(e) and Figure 5(f) respectively show the cross-sectional views of the point beam synthesized by the method of the present invention and the traditional symmetric logarithmic frequency deviation technology along the range domain when θ=0°. From the comparison, it can be seen that the side lobes of the beam generated by the method of the present invention are almost invisible in the cross-sectional view of the range domain, which effectively suppresses the side lobes; in contrast, the energy distribution of the range domain of the traditional method is relatively wide, with obvious side lobes.

[0131] Therefore, the spot beam generated by the method of the present invention has better focusing, lower side lobes and narrower beam width. These characteristics make the method of the present invention show significant practical advantages in application scenarios requiring high precision and high resolution.

[0132] Example 2

[0133] Simulation conditions:

[0134] Set p(θ, r) as a multi-spot beam, with the target points located at (20°, 150 km) and (-40°, 150 km) respectively. Apply p(θ, r) and the specific values ​​of the above simulation parameter settings to the technical solution proposed in the present invention.

[0135] Simulation results and analysis:

[0136] FIG6(a) shows a three-dimensional diagram of the multi-spot beams synthesized by the method of the present invention. It can be seen that the method achieves higher energy focusing at each target point, lower side lobes, narrower beam width, and can achieve full-power beams at multiple target points. FIG6(b) shows the corresponding two-dimensional plane diagram, which clearly shows the spot beams formed at the target points of (20°, 150km) and (-40°, 150km). In contrast, FIG6(c) and FIG6(d) show the traditional symmetric logarithmic frequency deviation technology. Although this method can also form spot beams at the target points of (20°, 150km) and (-40°, 150km), the power distribution of different target points is uneven, the beam focusing is poor, and there are obvious side lobes, which affect the overall performance and effect. This comparison shows the superiority of the method of the present invention in multi-target positioning applications.

[0137] Example 3

[0138] Simulation conditions:

[0139] Set p(θ, r) to a flat-top beam, where the flat-top beam region is defined as {(θ, r): -30°≤θ≤30°, 100km≤r≤200km}, and apply p(θ, r) and the specific values ​​of the above simulation parameter settings to the technical solution proposed in the present invention.

[0140] Simulation results and analysis:

[0141] Figures 7(a) and 7(b) respectively show the three-dimensional graph and two-dimensional plane graph of the desired flat-top beam pattern. It can be seen from the figures that the area of ​​the flat-top beam is defined as {(θ, r): -30°≤θ≤30°, 100km≤r≤200km}. In this area, the desired beam presents an ideal flat-top shape, and the energy is evenly distributed within this range. Figures 7(c) and 7(d) respectively show the three-dimensional graph and two-dimensional plane graph of the synthesized flat-top beam by the method of the present invention. It can be seen that the generated beam pattern achieves an energy distribution that is approximately flat-topped within the defined area, and the amplitude of the beam is significantly higher than that of other areas. Although the synthesized beam has side lobes at the edge compared to the ideal flat-top beam, the overall energy concentration effect is still very close to the desired distribution, showing good beam focusing capability and spatial coverage effect.

[0142] Example 4

[0143] Simulation conditions:

[0144] p(θ, r) is set as a curved beam, and the specific values ​​of p(θ, r) and the above simulation parameter settings are applied to the technical solution proposed in the present invention.

[0145] Simulation results and analysis:

[0146] Figures 8(a) and 8(b) show the three-dimensional graph and two-dimensional plane graph of the desired curve graph, respectively. It can be seen that the beam energy is distributed along a specific curve and maintains a uniform energy distribution on the curve. Figures 8(c) and 8(d) show the three-dimensional graph and two-dimensional plane graph of the synthesized curved beam of the method of the present invention, respectively. Although the energy distribution of the synthesized beam on the preset curve is uneven, it is still strictly distributed along the curved path. This result proves the superior performance of this method in complex beam shape control.

[0147] In summary, the present invention proposes a frequency-controlled array variable beam shape synthesis method based on sparse reconstruction, which mainly solves the problems of the existing decoupling methods in the single beam optimization dimension and the poor beam focusing and sidelobe suppression effects. The implementation process includes: first, discretizing the continuous interval and constructing a discrete grid matrix; second, using a two-dimensional orthogonal basis to map the target beam and the discrete grid matrix from the distance-angle domain to the transform domain; then, reconstructing the optimization problem through sparsity; finally, performing a convex optimization solution to obtain the frequency-controlled array beam diagram. The present invention realizes more efficient and flexible frequency-controlled array beamforming to adapt to different communication environments and needs, and provides theoretical support for subsequent applications.

[0148] The key points and protection points of the present invention are:

[0149] 1. Construct discrete grid points and a two-dimensional orthogonal basis to model the two-dimensional beam pattern fitting problem as a sparse linear combination problem:

[0150] First, the continuous intervals of array element spacing and frequency offset are discretized and sampled to construct discrete grid points. Then, a two-dimensional orthogonal basis is constructed to map the target beam pattern and discrete grid points from the distance-angle domain to the transform domain. In the transform domain, the problem is modeled as a sparse linear combination problem, and the optimal weight of each grid point is determined by minimizing the reconstruction error, thereby achieving accurate fitting of the two-dimensional beam pattern.

[0151] 2. Under the frequency-controlled array system with multi-carrier frequency increments, frequency-controlled array distance-angle dimension variable beam shape synthesis is achieved through dual-dimensional optimization:

[0152] By adjusting the array spacing and frequency offset to change the beam energy distribution in the distance-angle dimension, the generated beam pattern can be flexibly controlled in both the distance and angle dimensions. This dual-dimensional optimization can not only generate high-precision spot beams, but also synthesize a variety of complex beam shapes, achieving more efficient and flexible frequency-controlled array beamforming.

[0153] The present invention also provides a frequency-controlled array variable beam shape synthesis system based on sparse reconstruction, comprising:

[0154] A parameter initialization module is used to implement the initialization parameters in step 1, and the initialization parameters include but are not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r);

[0155] The continuous interval discretization module is used to implement the uniform sampling of N points in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset according to the initialization parameters in step S1 in step 2, which are respectively expressed as:

[0156]

[0157] Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively;

[0158] Discrete grid point construction module, used to implement the initialization parameters in step S1 and the discretization result D in step S2 in step 3 i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as:

[0159]

[0160] Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset;

[0161] A two-dimensional orthogonal basis matrix construction module is used to implement the construction of a two-dimensional orthogonal basis matrix according to the initialization parameters in step S1 in step 4, and the element Φ in the kth row and the lth column k,l It is expressed as:

[0162]

[0163] Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively;

[0164] Mapping matrix P and dic i,j A construction module is used to implement the two-dimensional orthogonal basis matrix constructed by step S4 in step 5, map the desired beam pattern p(θ,r) defined in step S1 into the transform domain, and construct a mapping matrix

[0165]

[0166] Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r);

[0167] The discrete grid points A constructed in step S3 are converted into the two-dimensional orthogonal basis matrix constructed in step S4. i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain to construct the mapping matrix

[0168]

[0169] Among them, dic i,j Represents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point;

[0170] The beam optimization problem construction and solution module is used to implement the mapping matrix P and dic constructed in step S5 in step 6 i,j , construct the beam optimization problem:

[0171]

[0172] The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ;

[0173] The frequency-controlled array beam pattern synthesis module is used to implement the discrete grid point A constructed in step S3 in step 7. i,j (θ, r) and the weight matrix element s solved in step S6 i,j Substituting into the frequency controlled array factor AF(θ,r):

[0174]

[0175] Synthesize the final frequency-controlled array beam pattern.

[0176] The present invention also provides a frequency-controlled array variable beam shape synthesis device based on sparse reconstruction, comprising:

[0177] Memory: a computer program for storing the above-mentioned frequency-controlled array variable beam shape synthesis method based on sparse reconstruction, which is implemented in the MATLAB programming environment and is a computer-readable device;

[0178] Processor: used to implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction when executing the computer program.

[0179] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction.

Claims

1. A frequency-controlled array variable beam shape synthesis method based on sparse reconstruction, characterized in that: The following steps are involved: S1: Initialization parameters Initialization parameters include but are not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r); S2: Discretization of continuous intervals According to the initialization parameters in step S1, N points are uniformly sampled in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset, which are respectively expressed as: Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively; S3: Constructing discrete grid points According to the initialization parameters in step S1 and the discretization result D in step S2 i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as: Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset; S4: Construct a two-dimensional orthogonal basis matrix According to the initialization parameters in step S1, a two-dimensional orthogonal basis matrix is ​​constructed, and the element Φ in the kth row and the lth column is k,l It is expressed as: Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively; S5: Construct mapping matrix P and dic i,j The desired beam pattern p(θ,r) defined in step S1 is mapped to the transform domain through the two-dimensional orthogonal basis matrix constructed in step S4 to construct a mapping matrix Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r); The discrete grid points A constructed in step S3 are converted into the two-dimensional orthogonal basis matrix constructed in step S4. i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain and the mapping matrix is ​​constructed. Among them, dic i,j Represents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point; S6: Construct the beam optimization problem and solve it According to the mapping matrix P and dic constructed in step S5 i,j , construct the beam optimization problem: The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ; S7: Synthesized frequency-steering array beam patterns The discrete grid points A constructed in step S3 i,j (θ, r) and the weight matrix element s solved in step S6 i,j Substituting into the frequency controlled array factor AF(θ,r): Synthesize the final frequency-controlled array beam pattern.

2. A frequency-controlled array variable beam shape synthesis system based on sparse reconstruction based on the method of claim 1, characterized in that: include: A parameter initialization module is used to initialize parameters, including but not limited to: carrier center frequency f0, array number M, frequency offset Δf, array spacing d, number of sampling points N, total observation range (θ, r), and expected beam pattern p(θ, r); The continuous interval discretization module is used to uniformly sample N points in the interval (0, Md) of the array element spacing and the interval (0, MΔf) of the frequency offset according to the initialization parameters, which are respectively expressed as: Among them, D i and ΔF j They represent the i-th array element spacing sampling point and the j-th frequency offset sampling point respectively; Discrete grid point construction module is used to construct the discrete grid point according to the initialization parameters and the discretization result D i and ΔF j , construct discrete grid points A i,j (θ,r),i,j=1,2,…,N,defined as: Among them, A i,j (θ, r) represents an element of the corresponding steering vector at a specific array element spacing and frequency offset; The two-dimensional orthogonal basis matrix construction module is used to construct a two-dimensional orthogonal basis matrix according to the initialization parameters. The element Φ in the kth row and lth column k,l It is expressed as: Where K represents the number of orthogonal bases, Φ k,l represents the elements of a two-dimensional orthogonal basis matrix, k and l are the indices of the rows and columns of the orthogonal basis matrix respectively; Mapping matrix P and dic i,j The construction module is used to map the desired beam pattern p(θ,r) defined in the transform domain through a two-dimensional orthogonal basis matrix to construct a mapping matrix Wherein, P represents the mapping matrix in the transform domain corresponding to the desired beam pattern p(θ,r); Through the two-dimensional orthogonal basis matrix, the discrete grid point A i,j (θ, r), i, j = 1, 2, ..., N are mapped to the transform domain and the mapping matrix is ​​constructed. Among them, dic i,j Represents the mapping matrix in the transform domain corresponding to the i-th array element spacing sampling point and the j-th frequency offset sampling point; Beam optimization problem construction and solution module, used to construct the mapping matrix P and dic i,j , construct the beam optimization problem: The constructed beam optimization problem is defined in the convex optimization tool CVX to solve the optimal weight matrix element s i,j ; The frequency-controlled array beam pattern synthesis module is used to construct discrete grid points A i,j (θ, r) and the weight matrix element s solved i,j Substituting into the frequency controlled array factor AF(θ,r): Synthesize the final frequency-controlled array beam pattern.

3. A frequency-controlled array variable beam shape synthesis device based on sparse reconstruction, characterized in that: include: Memory: a computer program storing the method for synthesizing variable beam shapes of frequency-controlled arrays based on sparse reconstruction as described in claim 1, which is a computer-readable device; Processor: used to implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction as described in claim 1 when executing the computer program.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement the frequency-controlled array variable beam shape synthesis method based on sparse reconstruction as described in claim 1.

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