A design method for sparsely distributed concentric circular array antenna based on gridless compressed sensing

Abstract

The invention discloses a design method for a sparse concentric circular ring array antenna based on gridless compressed sensing. The method comprises: taking minimizing the number of circular rings as an optimization target, taking the circular ring radius and the continuous current ring excitation as optimization variables, and establishing a sparse concentric circular ring array optimization model for minimizing the number of circular rings based on the Bessel approximation of the concentric circular ring array pattern; forming a vector expression of a desired pattern measurement column vector and the sparse concentric circular ring array pattern from K observation angles; performing regularization processing on the sparse concentric circular ring array optimization model based on the gridless compressed sensing technology and the vector expression of the sparse concentric circular ring array pattern; establishing a generalized compressed sensing optimization model according to the regularization; solving the generalized compressed sensing optimization model by adopting an alternating optimization strategy, and calculating the number of circular rings, the circular ring radius and the excitation value of the continuous current ring; and replacing the continuous current ring with the number of array elements evenly distributed on the circular ring to obtain the sparse concentric circular ring array.

Description

Technical Field

[0001] The invention relates to the field of wireless communications, and in particular to a design method for a sparsely distributed concentric circular array antenna based on gridless compressed sensing. Background Art

[0002] The array elements of concentric ring array antennas are distributed on multiple concentric rings, which can produce circularly symmetric radiation patterns and achieve 360° non-variable coverage in azimuth. They are widely used in satellite communications, radio astronomy, and wave arrival estimation. In recent years, the sparsely distributed concentric ring array with the minimum number of rings has received more and more attention. This array structure can not only reduce the sidelobe level while ensuring the circular symmetry of the radiation pattern, but also effectively save the number of array elements, which has important practical significance and engineering value. However, the corresponding comprehensive problem is a complex nonlinear non-convex optimization problem, which involves the optimization design of four parameters: the number of non-uniformly spaced rings, the ring radius, the number of array elements on the ring, and the excitation value. In order to solve it effectively, sparse reconstruction technology based on compressed sensing has been applied to the synthesis of sparse concentric ring arrays, see reference [1] ("A Hybrid Method for the Optimal Synthesis of 3-D Patterns of Sparse Concentric Ring Arrays," IEEE Trans. Antennas Propag., vol. 64, no. 2, pp. 515-524, Dec. 2016, X. Zhao, Q. Yang, and Y. Zhang,). However, this method restricts the positions of the concentric rings to a pre-divided discrete grid, and requires a sufficiently dense grid division to ensure the sparse effect of the synthesis result. This not only leads to a huge amount of calculation as the array aperture increases, but also easily produces infeasible solutions with too small array element spacing. In recent years, the requirements of the weighted l1 norm minimization algorithm on grid density have been reduced by introducing a smoothing vector. See reference [2] (“Efficient Large Sparse Arrays Synthesis by Means of Smooth Re-Weighted l1 Minimization,” Electronics, vol. 8, 2019, D. Pinchera, MD Migliore, M. Lucido, F. Schettino, G. Panariello). This method increases the grid spacing to the order of λ / 20, but this improvement is far from meeting the design requirements of large array antennas. In addition, the proposed algorithm only involves the optimization design of pencil beams and has not yet involved phase weighting. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of fixed grid division in the prior art, break the restriction of grid division on concentric rings, and propose a design method of sparsely distributed concentric ring array antenna based on gridless compressed sensing.

[0004] In order to achieve the above object, the present invention proposes a design method of a sparsely distributed concentric circular array antenna based on gridless compressed sensing, the method comprising:

[0005] Step 1) Taking minimizing the number of circular rings as the optimization goal, taking the circular ring radius and the continuous current ring excitation as the optimization variables, and based on the Bessel approximation of the concentric circular ring array pattern, an optimization model of the sparsely distributed concentric circular ring array that minimizes the number of circular rings is established;

[0006] Step 2) forming a vector expression of a desired pattern measurement column vector and a sparsely distributed concentric ring array pattern from K observation angles;

[0007] Step 3) Based on the gridless compressed sensing technology and combined with the vector expression of the sparse concentric circle array pattern, the sparse concentric circle array optimization model is regularized;

[0008] Step 4) establishing a generalized compressed sensing optimization model based on regularization;

[0009] Step 5) using an alternating optimization strategy to solve the generalized compressed sensing optimization model, and calculating the number of circular rings, the radius of the circular rings, and the excitation value of the continuous current loop;

[0010] Step 6) The continuous current ring is replaced by array elements evenly distributed on the ring to obtain a sparsely distributed concentric ring array.

[0011] As an improvement of the above method, the step 1) specifically includes:

[0012] The radius of the ring is r = [r1,…,r m …,r M ] and continuous current loop excitation w=[w1,…,w m ,…,w M ] T is the optimization variable, where r m represents the radius of the mth concentric ring, 1≤m≤M, M represents the number of concentric rings, w m represents the mth current loop excitation, and the superscript T represents the transposition operation.

[0013] Based on the Bessel function approximation of the concentric ring array pattern, the optimization model of the sparse concentric ring array that minimizes the number of rings is established as follows:

[0014]

[0015] Where θ is any angle within the entire observation range, Fd (θ) represents the expected radiation pattern at the observation angle θ, J0(·) represents the zero-order Bessel function, β is the wave number, and ε is the matching error.

[0016] As an improvement of the above method, the step 2) specifically includes:

[0017] For the kth observation angle θ k The desired radiation pattern is F d (θ k ), 1≤k≤K, the desired pattern measurement column vector F is formed d for:

[0018] F d =[F d (θ1),…,F d (θ k ),…,F d (θ K )] T

[0019] At the same time, the sparse concentric ring array pattern expression is vectorized, and the vector expression F of the sparse concentric ring array pattern corresponding to K observation angles is obtained as follows:

[0020] F=A(r)w (2)

[0021] Where w is the continuous current loop excitation vector, and A(r) is a matrix that satisfies the following equation:

[0022]

[0023] As an improvement of the above method, the step 3) specifically includes:

[0024] Based on gridless compressed sensing technology and combined with formula (2), the sparse concentric ring array optimization model in formula (1) is transformed into:

[0025]

[0026] Among them, ||·||0 represents the 0-norm of the vector, and ||·||2 represents the 2-norm of the vector.

[0027] The regularization parameter γ is introduced to regularize equation (4):

[0028]

[0029] As an improvement of the above method, the step 4) specifically includes:

[0030] The 2-norm is used to replace the 0-norm in the regularized optimization model, and the weighted 2-norm algorithm is used to enhance the sparsity of the solution. The corresponding generalized compressed sensing optimization model is established as follows:

[0031]

[0032] The superscript H represents the conjugate transpose operation, P (i) represents the diagonal matrix in the i-th iteration, satisfying the following formula:

[0033]

[0034] in, represents the excitation value on the mth ring of the ith iteration, represents the first current loop excitation of the i-th iteration, represents the Mth current loop excitation of the ith iteration, ξ (i) is the iteration parameter, and its initial value is ξ (0) =1,ξ (i) In the i-th iteration, the following formula is satisfied:

[0035]

[0036] Among them, w (i-1) and w (i-2) They represent the continuous current loop excitation vector of the i-1th iteration and the continuous current loop excitation vector of the i-2th iteration respectively.

[0037] As an improvement of the above method, the step 5) specifically includes:

[0038] An alternating optimization strategy is adopted to solve the generalized compressed sensing optimization model. The alternating optimization strategy of the steepest gradient descent method is used to iteratively solve the generalized compressed sensing optimization model, calculate the ring radius vector r, and use the least squares method to calculate the continuous current excitation vector w on the corresponding ring, and extract the number of rings M from it.

[0039] Compared with the prior art, the advantages of the present invention are:

[0040] The design method of the present invention overcomes the grid mismatch effect caused by fixed grid division in traditional optimization models. By minimizing the number of circular rings and designing non-uniform concentric circular rings, the number of required array elements is greatly reduced. The uniform distribution of array elements on the circular rings effectively ensures the circular symmetry of the radiation pattern, achieving the desired radiation characteristics at the lowest hardware cost, and has important application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the design method of the sparsely distributed concentric circular array antenna based on gridless compressed sensing of the present invention;

[0042] Figure 2 is a schematic diagram of a concentric ring array designed using the method of the present invention;

[0043] Figure 3 The array element distribution of the sparsely distributed concentric circular ring array designed on a circular surface with a radius of 4.98λ by the method of the present invention;

[0044] Figure 4 yes Figure 3 The azimuth section pattern of the given sparsely distributed concentric ring array;

[0045] Figure 5 yes Figure 3 The three-dimensional radiation pattern of the sparsely distributed concentric circular array is given. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0047] Example 1

[0048] like Figure 1 As shown, embodiment 1 of the present invention proposes a design method for sparse concentric circular ring array antennas with grid-free compressed sensing. According to the Bessel function approximation of the concentric circular ring array factor, the sparse optimization problem of the two-dimensional array antenna is directly reduced to a one-dimensional array antenna problem for solution, and the fixed grid division is replaced by a dynamic grid along the radial direction of the circular ring to establish a generalized sparse optimization model. At this time, the circular ring radius and the equivalent continuous current excitation on the ring are both optimization variables, and the alternating optimization strategy can be used to achieve simultaneous optimization of the two.

[0049] Design methods include:

[0050] Step S01) takes minimizing the number of circular rings as the optimization goal, takes the circular ring radius and the continuous current loop excitation as optimization variables, and establishes a corresponding generalized sparse reconstruction model based on the Bessel function approximation of the concentric circular ring array pattern. It is solved using an alternating optimization strategy to calculate the number of circular rings, the circular ring radius, and the excitation value of the continuous current loop.

[0051] Step S01-1) According to the desired radiation pattern F d , with the radius of the ring r = [r1,…,r M ] and continuous current loop excitation w=[w1,…,w M ] T In order to optimize the variables, the optimization model of the sparsely distributed concentric ring array with the minimum number of rings is established as follows:

[0052]

[0053] Where θ is any angle within the entire observation range, then for K observation angles θ k (k=1,…,K) to form the desired pattern measurement column vector F d =[F d (θ1),…,F d (θ K )] T , the vector expression of the sparse concentric ring array pattern is

[0054] F=A(r)w (2)

[0055] The matrix A(r) is:

[0056]

[0057] Based on this, the optimization model in formula (1) is transformed into:

[0058]

[0059] Where ||·||0 represents the 0-norm of the vector, and ||·||2 represents the 2-norm of the vector.

[0060] Step S01-2) introduces the regularization parameter γ, and the optimization model can be regularized as:

[0061]

[0062] Step S01-3) Use the 2-norm to replace the 0-norm in the optimization model, and use the weighted 2-norm algorithm to enhance the sparsity of the solution, and obtain the corresponding generalized compressed sensing optimization model:

[0063]

[0064] In the i-th iteration, the diagonal matrix P (i) for:

[0065]

[0066] in, represents the excitation value on the mth ring of the ith iteration, represents the first current loop excitation of the i-th iteration, represents the Mth current loop excitation of the ith iteration, ξ (i) is the iteration parameter, and its initial value is ξ (0) =1,ξ (i) In the i-th iteration, the following formula is satisfied:

[0067]

[0068] Among them, w(i-1) and w (i-2) They represent the continuous current loop excitation vector of the i-1th iteration and the continuous current loop excitation vector of the i-2th iteration respectively.

[0069] Step S01-4) Use the alternating optimization strategy to solve the generalized compressed sensing optimization model, that is, use the steepest gradient descent method to calculate the radius vector r of the current secondary ring, then use the least squares method to calculate the continuous current excitation vector w on the corresponding ring, and extract the number of rings from it.

[0070] Step S02) Using array elements evenly distributed on the ring to replace the continuous current ring, finally obtaining a sparsely distributed concentric ring array. Figure 2 shown.

[0071] The sparsely distributed concentric circular array antenna design method proposed by the present invention according to the above method can be further verified and explained through the following specific simulation examples.

[0072] In this example, an array of sparsely distributed concentric circular rings with equal amplitude excitation is designed on a circular aperture with a given radius R = 4.98λ to achieve a desired radiation pattern with a sidelobe level lower than -23.5dB. Existing studies have shown that if a uniform full array with an adjacent ring spacing of 0.5λ is used, the sidelobe level will be as high as -17.5dB under equal amplitude excitation; if a genetic algorithm is used to optimize the design of an array of sparsely distributed concentric circular rings with equal amplitude excitation, the sidelobe level can be reduced to -22.94dB, and the number of array elements required is 201. Using the sparsely distributed concentric circular ring array design method proposed in the present invention, only 185 array elements distributed on 6 circular rings with uneven spacing are required to achieve a sidelobe level of -24.6dB. The array layout is as follows: Figure 3 The comprehensive azimuth section direction diagram is shown as Figure 4 As shown, the three-dimensional direction diagram is Figure 5 As shown in the figure, the radiation pattern has good circular symmetry and achieves 360° azimuth coverage without changes. It can be seen from the comparison that this method not only saves the number of array elements, but also effectively reduces the sidelobe level and leaves a design margin.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A design method for a sparsely distributed concentric circular array antenna based on gridless compressed sensing, the method comprising: Step 1) Taking minimizing the number of circular rings as the optimization goal, taking the circular ring radius and the continuous current ring excitation as the optimization variables, and based on the Bessel approximation of the concentric circular ring array pattern, an optimization model of the sparsely distributed concentric circular ring array that minimizes the number of circular rings is established; Step 2) forming a vector expression of a desired pattern measurement column vector and a sparsely distributed concentric ring array pattern from K observation angles; Step 3) Based on the gridless compressed sensing technology and combined with the vector expression of the sparse concentric circle array pattern, the sparse concentric circle array optimization model is regularized; Step 4) establishing a generalized compressed sensing optimization model based on regularization; Step 5) using an alternating optimization strategy to solve the generalized compressed sensing optimization model, and calculating the number of circular rings, the radius of the circular rings, and the excitation value of the continuous current loop; Step 6) replacing the continuous current loop with array elements evenly distributed on the circular ring to obtain a sparsely distributed concentric circular ring array; The step 1) specifically includes: The radius of the ring is r = [r1,…,r m …,r M ] and continuous current loop excitation w=[w1,…,w m ,…,w M ] T is the optimization variable, where r m represents the radius of the mth concentric ring, 1≤m≤M, M represents the number of concentric rings, w m represents the mth current loop excitation, and the superscript T represents the transposition operation. Based on the Bessel function approximation of the concentric ring array pattern, the optimization model of the sparse concentric ring array that minimizes the number of rings is established as follows: Where θ is any angle within the entire observation range, F d (θ) represents the expected radiation pattern at the observation angle θ, J0(·) represents the zero-order Bessel function, β is the wave number, and ε is the matching error; The step 2) specifically includes: For the kth observation angle θ k The desired radiation pattern is F d (θ k ), 1≤k≤K, the desired pattern measurement column vector F is formed d for: F d =[F d (θ1),…,F d (i k ),…,F d (i K )] T At the same time, the sparse concentric ring array pattern expression is vectorized, and the vector expression F of the sparse concentric ring array pattern corresponding to K observation angles is obtained as follows: F=A(r)w (2) Where w is the continuous current loop excitation vector, and A(r) is a matrix that satisfies the following equation: The step 3) specifically includes: Based on gridless compressed sensing technology and combined with formula (2), the sparse concentric ring array optimization model in formula (1) is transformed into: Among them, ||·||0 represents the 0-norm of the vector, ||·||2 represents the 2-norm of the vector, The regularization parameter γ is introduced to regularize equation (4): The step 4) specifically includes: The 2-norm is used to replace the 0-norm in the regularized optimization model, and the weighted 2-norm algorithm is used to enhance the sparsity of the solution. The corresponding generalized compressed sensing optimization model is established as follows: The superscript H represents the conjugate transpose operation, P (i) represents the diagonal matrix in the i-th iteration, satisfying the following formula: in, represents the excitation value on the mth ring of the ith iteration, represents the first current loop excitation of the i-th iteration, represents the Mth current loop excitation of the ith iteration, ξ (i) is the iteration parameter, and its initial value is ξ (0) =1,ξ (i) In the i-th iteration, the following formula is satisfied: Among them, w (i-1) and w (i-2) They represent the continuous current loop excitation vector of the i-1th iteration and the continuous current loop excitation vector of the i-2th iteration respectively.

2. The design method of the sparsely distributed concentric circular array antenna based on gridless compressed sensing according to claim 1 is characterized in that: The step 5) specifically includes: An alternating optimization strategy is adopted to solve the generalized compressed sensing optimization model. The alternating optimization strategy of the steepest gradient descent method is used to iteratively solve the generalized compressed sensing optimization model, calculate the ring radius vector r, and use the least squares method to calculate the continuous current excitation vector w on the corresponding ring, and extract the number of rings M from it.

Images