A one-dimensional sparse antenna array layout optimization method

Abstract

The present invention relates to the technical field of phased array antennas, and in particular to a one-dimensional sparse antenna array layout optimization method, the method comprising: arranging candidate antenna units with a preset minimum unit spacing based on the array aperture size, and arranging candidate antenna units based on a binary vector z Select several antenna units from the candidate antenna units to form a one-dimensional sparse antenna array; calculate the excitation column vector corresponding to the antenna unit based on the arranged antenna units and the preset beam scanning angle threshold w c ; Then prepare the matrix G ,matrix P and matrix D ; and based on the matrix G ,matrix P ,matrix D , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and an array layout with optimal beam scanning performance is obtained based on the calculation. The present invention provides a one-dimensional sparse antenna array layout optimization method, which can obtain an optimal one-dimensional sparse antenna array layout with both optimal beam scanning performance and hardware feasibility.

Description

Technical Field

[0001] The present invention relates to the technical field of phased array antennas, and in particular to a one-dimensional sparse antenna array layout optimization method. Background Art

[0002] Millimeter-wave imaging radar has broad application prospects in autonomous driving, smart transportation, and future smart cities. Narrow beam is an important way for millimeter-wave imaging radar to achieve high resolution. In order to make the beam narrower, a large-scale phased array antenna is needed. Since large-scale phased arrays need to integrate a large number of components such as active power amplifiers and phase shifters, they often have high manufacturing costs and system complexity. In order to reduce the manufacturing cost and system complexity of the phased array and maintain the high-resolution performance of the millimeter-wave imaging radar, a phased array antenna with sparse antenna units can be used, because it achieves a narrow beam by placing fewer antenna units and components in a wide aperture. However, different sparse array layouts often have completely different beam scanning performance, resulting in significant differences in performance when used for millimeter-wave imaging. In order to make the sparse array layout have the best beam scanning performance to achieve the best imaging effect, it is necessary to optimize the sparse array layout. During optimization, it is necessary to pay attention to the directivity coefficient performance and sidelobe performance of the sparse array during beam scanning to improve its imaging distance and anti-interference ability when applied to millimeter-wave imaging radar. At the same time, it is also necessary to ensure that the sparse array has hardware feasibility. Therefore, it has a high optimization complexity, which leads to the current method often cannot be fully optimized and can only obtain suboptimal solutions through some approximation methods. Summary of the invention

[0003] The object of the present invention is to provide a one-dimensional sparse antenna array layout optimization method to improve the above technical problems.

[0004] In order to achieve the above objectives, the present application provides the following technical solutions:

[0005] The present application provides a one-dimensional sparse antenna array layout optimization method, the method comprising: arranging candidate antenna units with a preset minimum unit spacing based on the array aperture size, and arranging candidate antenna units based on a binary vector z Select several antenna units from the candidate antenna units to form a one-dimensional sparse antenna array; calculate the excitation column vector corresponding to the antenna unit based on the arranged antenna units and the preset beam scanning angle threshold w c ; Prepare the matrix for calculating the total radiated power G and the matrix of the radiation level values ​​of the side lobe area P ; Prepare a matrix to limit the spacing between antenna elements D ; Based on the matrix G ,matrix P ,matrixD , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and the array layout with optimal beam scanning performance is calculated based on the mixed integer programming model.

[0006] Optionally, the matrix prepared for calculating the total radiated power G ,include:

[0007] Based on the first calculation model, the matrix is ​​calculated g , and based on G = g H g Calculated G ,based on( w c ☉ z ) H G ( w c ☉ z ) Calculate the total radiated power of all antenna units, where H Used to represent the conjugate transpose, ☉ represents w c and z The first calculation model is: ; where Δ represents i and f The sampling interval in two dimensions, ( i m , f m ) indicates the m Sampling angles, x n Indicates n The location of the candidate antenna elements.

[0008] Optionally, a matrix is ​​prepared for calculating the sidelobe radiation level value P ,include:

[0009] The matrix is ​​calculated based on the second calculation model P , and based on | P ( w c ☉ z )| calculates the radiation level value of the one-dimensional sparse antenna array in the sidelobe area, where || represents the amplitude value. The second calculation model is:

[0010] ;

[0011] in, i l Indicates the number of samples in the sidelobe area on the pitch plane. l indivual i Angle, j 2 =-1, λ represents the wavelength.

[0012] Optionally, the matrix prepared for limiting the antenna unit spacing D ,include:

[0013] ;

[0014] in r , s is the serial number of the candidate antenna unit, x r , x s Indicates the position of its corresponding unit, C is a large constant and can be taken as a value greater than the total number of candidate cells. d represents the preset minimum cell spacing threshold.

[0015] Optionally, the matrix-based G ,matrix P ,matrix D , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and the array layout with optimal beam scanning performance is calculated based on the mixed integer programming model, including:

[0016] ;

[0017] in PSLL represents the threshold used to limit the peak sidelobe level, R is the number of elements in the one-dimensional sparse antenna array, S is the total number of candidate units, b S×1 The length is S A binary column vector of z (1) = 1 and z ( S )=1, which is used to ensure that the two most marginal candidate units are selected, ☉ indicates w c and z The operation of multiplying corresponding elements in , · represents matrix or vector multiplication.

[0018] The beneficial effects of the present invention are:

[0019] The present invention provides a one-dimensional sparse antenna array layout optimization method, which can obtain an optimal one-dimensional sparse antenna array layout, which has both optimal beam scanning performance and hardware feasibility.

[0020] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or be understood by implementing the embodiments of the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0022] Figure 1 It is a schematic flow chart of a one-dimensional sparse antenna array layout optimization method described in an embodiment of the present invention;

[0023] Figure 2 Schematic diagram of array aperture and candidate antenna units;

[0024] Figure 3 This is a schematic diagram of the optimal one-dimensional sparse antenna array layout;

[0025] Figure 4 It is a schematic diagram of the layout of a one-dimensional dense antenna array;

[0026] Figure 5 The power pattern of the optimal one-dimensional sparse antenna array and the one-dimensional dense antenna array when scanning to 0°;

[0027] Figure 6 The power pattern of the optimal one-dimensional sparse antenna array and the one-dimensional dense antenna array when scanning to 15°;

[0028] Figure 7 The power patterns of the optimal one-dimensional sparse antenna array and one-dimensional dense antenna array when scanning to 30°;

[0029] Figure 8 The power patterns of the optimal one-dimensional sparse antenna array and one-dimensional dense antenna array when scanned to 45°. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0031] It should be noted that similar reference numerals or letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0032] Embodiment 1:

[0033] like Figure 1 As shown, this embodiment provides a one-dimensional sparse antenna array layout optimization method, which includes step S100, step S200, step S300, step S400 and step S500.

[0034] Step S100: Based on the array aperture size, candidate antenna elements are arranged with a preset minimum unit spacing, and based on the binary vector z Selecting a number of antenna units from the candidate antenna units to form a one-dimensional sparse antenna array;

[0035] Step S200: Calculate the excitation column vector corresponding to the antenna unit based on the arranged antenna units and the preset beam scanning angle threshold. w c ;

[0036] Step S300: Prepare a matrix for calculating the total radiated power G and the matrix of the radiation level values ​​of the side lobe area P ;

[0037] The matrix prepared for calculating the total radiated power is G The specific implementation method is:

[0038] Based on the first calculation model, the matrix is ​​calculated g , and based on G = g H gCalculated G ,based on( w c ☉ z ) H G ( w c ☉ z ) Calculate the total radiated power of all antenna units, where H Used to represent the conjugate transpose, ☉ represents w c and z The first calculation model is:

[0039] ;

[0040] Among them, Δ represents i and f The sampling intervals in two dimensions, ( i m , f m ) indicates the m Sampling angles, x n Indicates n The location of the candidate antenna element, j 2 =-1, λ represents the wavelength.

[0041] Secondly, prepare the matrix for calculating the radiation level value of the sidelobe area P The specific implementation method is:

[0042] The matrix is ​​calculated based on the second calculation model P , and based on | P ( w c ☉ z )| calculates the radiation level value of the one-dimensional sparse antenna array in the sidelobe area, where || represents the amplitude value. The second calculation model is:

[0043] ;

[0044] in, i l Indicates the number of samples in the sidelobe area on the pitch plane. l indivual i angle.

[0045] Step S400: Prepare a matrix for limiting the spacing between antenna elements D ;

[0046] ;

[0047] inr , s is the serial number of the candidate antenna unit, x r , x s Indicates the position of its corresponding unit, C is a large constant and can be taken as a value greater than the total number of candidate cells. d represents the preset minimum cell spacing threshold.

[0048] Step S500: Based on the matrix G ,matrix P ,matrix D , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and the array layout with optimal beam scanning performance is calculated based on the mixed integer programming model; ;

[0049] in PSLL represents the threshold used to limit the peak sidelobe level, R is the number of elements in the one-dimensional sparse antenna array, S is the total number of candidate units, b S×1 The length is S A binary column vector of z (1) = 1 and z ( S )=1, which is used to ensure that the two most marginal candidate units are selected, ☉ indicates w c and z The operation of multiplying corresponding elements in , · represents matrix or vector multiplication.

[0050] The one-dimensional sparse antenna array layout optimization method provided in this embodiment can obtain the optimal one-dimensional sparse antenna array layout, which has both optimal beam scanning performance and hardware feasibility.

[0051] Embodiment 2:

[0052] This embodiment will illustrate the method in Embodiment 1 by taking a specific case.

[0053] Step 1: Determine candidate antenna units based on array aperture.

[0054] like Figure 2 As shown, this embodiment considers an array aperture of 16λ in length, and the spacing between candidate antenna units is 0.1λ, so there are 161 candidate antenna units in total.

[0055] The unit pattern considered in this embodiment is cos( i ) 0.5 In order to select 20 antenna elements from the candidate antenna elements to form a one-dimensional sparse antenna array, a 161 × 1 binary column vector is used. z Select the antenna element. When the binary column vector z No. i When the first element is equal to 1, it means i antenna units are selected, otherwise the antenna unit is not selected. 20 antenna units are selected by sum( z ) = 20 for limitation.

[0056] Step 2: Pre-calculate the excitation column vector of the candidate antenna unit during large-angle scanning w c .

[0057] This embodiment considers allowing a 20-element one-dimensional sparse antenna array to perform beam scanning within a range of ±45°. Since the radiation performance of a one-dimensional sparse antenna array deteriorates as the scanning angle increases, the present invention optimizes the beam scanning performance of the array by optimizing the radiation performance when the array scans to the maximum angle, i.e., 45°. The present invention sets the excitation amplitude of the candidate antenna units to be 1 when the array scans to the maximum angle, and the excitation phase is based on the position of the candidate antenna unit. x n By -2 π / l × x n × sin(45°). The excitation of all candidate antenna elements forms a column vector w c .

[0058] Step 3: Prepare the matrix for calculating the total radiated power G。

[0059] Given a binary vector z and the candidate antenna element excitation vector w c In the context of w = w c ☉ z The radiation performance during excitation is the same, where ☉ indicates w c and z The present invention is to multiply the corresponding elements in ( w c ☉ z ) H G ( w c ☉z ) calculates the total radiated power of all candidate antenna units at this time, with the superscript H represents the conjugate transpose. G Before the values ​​of the elements in i and f In both dimensions, the step value is 0.1° (0°< i <90°, 0°< f <360°). Due to the existence of the antenna floor, the array radiates very little power into the lower half of the radiation space, so it is ignored in this embodiment. G The value of each element in G = g H g Calculate, where the matrix g The number of rows is equal to the number of angles sampled in the upper half of the radiation space, and the number of columns is equal to the number of candidate antenna elements. g The value of each element in is calculated by the following formula:

[0060] ;

[0061] in,( i m , f m ) indicates the m Sampling angles, x n Indicates n The location of the candidate antenna elements.

[0062] Step 4: Prepare the matrix for calculating the sidelobe radiation level value P .

[0063] Given a binary vector z and the candidate antenna element excitation vector w c In the context of the present invention, the present invention is realized by | P ( w c ☉ z )| calculates the radiation level value of the one-dimensional sparse antenna array in the side lobe area, and || represents the amplitude value. Considering that the one-dimensional antenna array has the same radiation performance on different elevation planes, the present invention only considers the side lobe performance on one elevation plane. The elevation plane considered in this embodiment corresponds to i and f (-90°< i <90°, f =0°). In the calculation matrix P Before the values ​​of the elements in the present invention are set, the above-mentioned i The matrix P The number of rows is equal to the number of rows sampled in the sidelobe area on this pitch plane. i The number of angles and columns is equal to the number of candidate antenna elements. P The value of each element in is calculated by the following formula:

[0064] ;

[0065] in, i l Indicates the number of samples in the sidelobe area on the pitch plane. l indivual i angle.

[0066] Step 5: Prepare a matrix to limit the spacing between antenna elements D .

[0067] In order to ensure that the optimized array layout is hardware-feasible, the spacing between antenna units must be no less than a certain threshold. d The threshold value set in this embodiment is d 0.5 l The present invention restricts the matrix D and z The product of realizes the restriction on the antenna unit spacing, where the matrix D The number of rows and columns of the matrix is ​​equal to the number of candidate antenna elements. D The value of each element in is calculated by the following formula:

[0068] ;

[0069] in, r , s is the serial number of the candidate antenna unit, x r , x s Indicates the position of its corresponding unit. C is a large constant. C = 100.

[0070] Step 6: Set up and solve the mixed integer programming problem for layout optimization.

[0071] Based on the above matrices and vectors, the mixed integer programming problem for one-dimensional sparse antenna array layout optimization is established as follows:

[0072] ;

[0073] in, PSLLIt indicates the threshold used to limit the peak sidelobe level. When the array scans to 45°, the level on the main lobe is a fixed value of 20×cos(45°). 0.5 , thus the directivity coefficient can be maximized by minimizing the total radiated power of the array. In this embodiment, the peak sidelobe level is set to be no higher than -10 dB, so PSLL = 20×cos(45°) 0.5 ×10 －10 / 20 . z (1) = 1 and z (161) = 1 means that the two outermost candidate elements in the array aperture are forcibly selected so that the one-dimensional sparse antenna array can fully utilize the aperture width to achieve a narrow beam. The above problem can be solved by the branchand bound method in commercial software such as Gurobi to obtain an array layout with optimal beam scanning performance.

[0074] The one-dimensional sparse antenna array layout with optimal beam scanning performance obtained by the present invention is as follows: Figure 3 As shown in , the minimum unit spacing is 0.5 λ, which meets the hardware feasibility requirements. If the antenna units are arranged at a regular spacing of 0.5 λ in the array aperture of 16 λ to form a one-dimensional dense antenna array, 33 antenna units are required, as shown in Figure 4 As shown. This one-dimensional sparse antenna array uses only 20 antenna elements, which can effectively reduce the manufacturing cost and system complexity of the phased array. The power pattern of this one-dimensional sparse antenna array and the above one-dimensional dense antenna array when scanning at 0°, 15°, 30° and 45° is shown in Figure 5-Figure 8 It can be seen that the one-dimensional sparse antenna array designed by the present invention not only has a narrow beam performance similar to that of a one-dimensional dense antenna array, but also has a peak sidelobe level lower than -10 dB, which can support the millimeter wave imaging radar to achieve good imaging effects.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A one-dimensional sparse antenna array layout optimization method, characterized in that: The method comprises: Based on the array aperture size, candidate antenna elements are arranged with a preset minimum element spacing, and based on the binary vector z Selecting a number of antenna units from the candidate antenna units to form a one-dimensional sparse antenna array; The excitation column vector corresponding to the antenna unit is calculated based on the arranged antenna units and the preset beam scanning angle threshold w c ; Prepare the matrix for calculating the total radiated power G and the matrix of the radiation level values ​​of the side lobe area P ; Prepare a matrix to limit the spacing between antenna elements D ; Matrix-based G ,matrix P ,matrix D , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and the array layout with optimal beam scanning performance is calculated based on the mixed integer programming model; The matrix prepared for calculating the total radiated power is G ,include: Based on the first calculation model, the matrix is ​​calculated g , and based on G = g H g Calculated G ,based on( w c ☉ z ) H G ( w c ☉ z ) to calculate the total radiated power of all antenna units, where H Used to represent the conjugate transpose, ☉ represents w c and z The first calculation model is: ； Among them, Δ represents θ and φ The sampling intervals in two dimensions, ( θ m , φ m ) indicates the m Sampling angles, x n Indicates n The locations of candidate antenna elements; Among them, the matrix prepared for calculating the radiation level value of the sidelobe area is P ,include: The matrix is ​​calculated based on the second calculation model P , and based on | P ( w c ☉ z )| calculates the radiation level value of the one-dimensional sparse antenna array in the sidelobe area, where || represents the amplitude value. The second calculation model is: ； in, θ l Indicates the number of samples in the sidelobe area on the pitch plane. l indivual θ angle; The matrix prepared to limit the spacing between antenna elements is D ,include: ； in r , s is the serial number of the candidate antenna unit, x r , x s Indicates the position of its corresponding unit, C is a value greater than the total number of candidate units; Among them, the matrix-based G ,matrix P ,matrix D , binary vector z and the excitation column vector w c A mixed integer programming model for one-dimensional sparse antenna array layout optimization is established, and the array layout with optimal beam scanning performance is calculated based on the mixed integer programming model, including: ； in PSLL represents the threshold used to limit the peak sidelobe level, R is the number of elements in the one-dimensional sparse antenna array, S is the total number of candidate units, b S×1 The length is S A binary column vector of z (1) = 1 and z ( S )=1, which is used to ensure that the two most marginal candidate units are selected, ☉ indicates w c and z Multiply the corresponding elements in .

Images