CN103207380B

CN103207380B - Broadband Target Direction Finding Method Based on Two-dimensional Frequency Domain Sparse Constraints

Info

Publication number: CN103207380B
Application number: CN201310078902.2A
Authority: CN
Inventors: 赵光辉; 刘自成; 王学磊; 石光明; 沈方芳
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2013-03-12
Filing date: 2013-03-12
Publication date: 2014-10-01
Anticipated expiration: 2033-03-12
Also published as: CN103207380A

Abstract

The invention discloses a broadband target direction finding method based on two-dimensional frequency domain sparse constraint. The method mainly solves the problems of a low angle resolution ratio, the poor coherent signal source estimation accuracy and a large calculation amount of common algorithms of prior methods. The technical scheme includes that the method comprises the steps of fully using target space sparseness and priori knowledge of array element receiving signals in a two-dimensional domain, and performing two-dimensional domain projection conversion on the array element receiving signals to obtain a two-dimensional projection spectrum; performing angle division on the angle measuring range, and designing a sparse base of the two-dimensional projection spectrum; solving an optimization problem through an optimization solving algorithm to obtain a high-resolution angle spectrum; and performing peak value detection on the angle spectrum through a threshold comparison method to obtain a target angle value. The broadband target direction finding method has the advantages of being small in calculation amount, high in measuring accuracy and angle resolution ratio and applicable to target angle estimation of radars and sonars.

Description

Broadband Target Direction Finding Method Based on Two-dimensional Frequency Domain Sparse Constraints

技术领域technical field

本发明属于通信技术领域，更进一步涉及阵列信号处理领域中一种基于二维频域稀疏约束的宽带目标测向方法，可用于雷达、声呐的目标角度估计。The invention belongs to the technical field of communication, and further relates to a wideband target direction finding method based on two-dimensional frequency domain sparse constraints in the field of array signal processing, which can be used for target angle estimation of radar and sonar.

背景技术Background technique

相控阵是利用电磁波的相干原理，通过计算机控制馈往各辐射阵元电流的相位，从而改变波束方向的阵列天线。传统的基于机械扫描结构来调整波束指向的方法,由于转动频率较低，数据更新缓慢而无法适应高机动目标的实时侦测任务。相控阵天线采用电子扫描方式，可实现回波数据的实时更新，因此获得了广泛的关注。其中利用相控阵测角是相控阵应用的一个主要方面。The phased array is an array antenna that uses the coherence principle of electromagnetic waves to control the phase of the current fed to each radiating array element through a computer, thereby changing the beam direction. The traditional method of adjusting the beam pointing based on the mechanical scanning structure cannot adapt to the real-time detection task of high maneuvering targets due to the low rotation frequency and slow data update. Phased array antenna adopts electronic scanning method, which can realize real-time update of echo data, so it has gained wide attention. Among them, the use of phased array angle measurement is a main aspect of phased array application.

目前，宽带相控阵测角技术主要有基于非相干信号的处理方法ISM和基于相干信号的处理方法CSM两种。At present, there are mainly two types of wideband phased array angle measurement technology: ISM based on incoherent signal processing and CSM based on coherent signal processing.

第一种，基于非相干信号处理方法ISM。该类方法是将宽带数据分解为不同的窄带数据，然后对每个窄带信号按照窄带信号处理方法进行处理，最终综合获得角度谱。例如，周宁，郭娜论文“基于奇异值分解的ISM算法”（《新乡学院学报》2009,26(6)）就是一种非相干信号处理方法，该方法的最大不足是计算量大、无法估计相干信号源。The first one is based on the incoherent signal processing method ISM. This type of method is to decompose the broadband data into different narrowband data, and then process each narrowband signal according to the narrowband signal processing method, and finally obtain the angle spectrum comprehensively. For example, Zhou Ning and Guo Na's paper "ISM Algorithm Based on Singular Value Decomposition" ("Journal of Xinxiang University" 2009, 26(6)) is an incoherent signal processing method. Estimate coherent signal sources.

第二种，基于相干信号处理方法。该类方法将宽带信号不同频率成分的信号空间聚焦到参考频率点，然后再采用窄带信号处理的方法进行高分辨角度估计。例如，于红旗，刘剑，黄知涛，周一宇论文“基于CSM的波束域宽带DOA估计方法”（《电子对抗》2007，No.5）就是一种相关信号处理方法。该方法存在的不足是需要构造聚焦矩阵和进行角度预估计，且估计精度容易受预估计误差的影响。The second is based on coherent signal processing methods. This type of method focuses the signal space of different frequency components of the broadband signal to the reference frequency point, and then uses the narrowband signal processing method for high-resolution angle estimation. For example, Yu Hongqi, Liu Jian, Huang Zhitao, and Zhou Yu's paper "CSM-Based Beam Domain Wideband DOA Estimation Method" ("Electronic Countermeasures" 2007, No.5) is a related signal processing method. The disadvantage of this method is that it needs to construct the focusing matrix and perform angle pre-estimation, and the estimation accuracy is easily affected by the pre-estimation error.

发明内容Contents of the invention

本发明目的在于针对上述已有技术的不足，提出一种基于二维频域稀疏约束的宽带目标测向方法，以减小非相干信号处理的计算量，避免相干信号处理中角度预估计对测角精度的影响。The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, and propose a wideband target direction finding method based on two-dimensional frequency domain sparse constraints, so as to reduce the calculation amount of non-coherent signal processing and avoid the impact of angle prediction in coherent signal processing. The influence of angular precision.

实现本发明目的的技术思路是通过建立稀疏重构模型，迭代求解优化问题获得高分辨角度谱，通过对角度谱进行峰值检测得到目标的角度信息。其具体步骤包括如下：The technical idea for realizing the object of the present invention is to obtain a high-resolution angle spectrum by establishing a sparse reconstruction model, iteratively solving an optimization problem, and obtaining the angle information of a target by performing peak detection on the angle spectrum. Its concrete steps include as follows:

(1)设雷达发射的宽带信号为s(t)，第i个目标和第m个阵元之间的距离引起的信号传播相对时间延迟为τ_mi，构建第m个阵元接收到的目标反射信号模型为：(1) Suppose the broadband signal transmitted by the radar is s(t), and the relative time delay of signal propagation caused by the distance between the i-th target and the m-th array element is τ _mi , construct the target received by the m-th array element The reflected signal model is:

${x x}_{m m} ((t t)) = = {Σ Σ}_{i i = = 11}^{N N} s the s ((t t - - {τ τ}_{mi mi})) + + {n no}_{m m} ((t t)),, m m = = 1,2 1,2,, \cdot &Center Dot; \cdot \cdot \cdot \cdot,, M m$

其中，x_m(t)为第m个阵元接收到的目标反射信号，t表示时间，N为目标总数，M为阵元数目，n_m(t)为第m个阵元接收到的噪声；Among them, x _m (t) is the target reflection signal received by the mth array element, t represents the time, N is the total number of targets, M is the number of array elements, and n _m (t) is the noise received by the mth array element ;

(2)对目标反射信号x_m(t)进行离散采样，得到离散数据x_m(n)，再以离散数据x_m(n)作为第m行，构造接收信号矩阵X(m,n)：(2) Perform discrete sampling on the target reflected signal x _m (t) to obtain discrete data x _m (n), and then use the discrete data x _m (n) as the mth row to construct the received signal matrix X(m,n):

$X x ((m m,, n no)) = = [\begin{matrix} {x x}_{11} ((n no)) \\ \cdot &Center Dot; \\ \cdot \cdot \\ \cdot \cdot \\ {x x}_{m m} ((n no)) \\ \cdot \cdot \\ \cdot \cdot \\ \cdot &Center Dot; \\ {x x}_{M m} ((n no)) \end{matrix}];;$

对接收信号矩阵X(m,n)进行预处理，即对接收信号矩阵X(m,n)第m行的数据乘以(-1)^m，得到预处理后的数据X'(m,n)；Preprocess the received signal matrix X(m,n), that is, multiply the data in the mth row of the received signal matrix X(m,n) by (-1) ^m to obtain the preprocessed data X'(m,n );

(3)对预处理后的数据X'(m,n)做二维频域投影变换，得到二维投影频谱F(ω,u)，其中ω表示投影空频位置，u表示离散时频采样点；(3) Perform two-dimensional frequency-domain projection transformation on the preprocessed data X'(m,n) to obtain a two-dimensional projection spectrum F(ω,u), where ω represents the projected space-frequency position, and u represents discrete time-frequency sampling point;

(4)对二维投影频谱F(ω,u)沿行累加，得到投影谱线Y(ω)；(4) Accumulate the two-dimensional projection spectrum F(ω,u) along the row to obtain the projection spectrum line Y(ω);

(5)按下式将雷达测角范围θ_min～θ_max等角度划分为P个角度：(5) Divide the radar angle measurement range θ _min ~ θ _max into P angles according to the following formula:

${θ θ}_{i i} = = {θ θ}_{min min} + + \frac{i i - - 11}{P P - - 11} (({θ θ}_{max max} - - {θ θ}_{min min})),, i i = = 1,2 1,2,, . . . . . .,, P P,,$

其中，θ_min、θ_max分别为测角范围的最小值与最大值；Among them, θ _min and θ _max are the minimum and maximum values of the angle measurement range;

(6)分别计算无噪情况下，目标角度为θ₁,θ₂,...,θ_P时的对应投影谱线Y₁(ω),Y₂(ω),...,Y_P(ω)；(6) Calculate the corresponding projected spectral lines _Y ₁ (ω), Y ₂ ₍ ω),...,Y _P ₍ ω);

(7)由投影谱线Y₁(ω),Y₂(ω),...,Y_P(ω)构造稀疏基：(7) Construct a sparse basis from the projected spectral lines Y ₁ (ω), Y ₂ (ω),...,Y _P (ω):

W=[Y₁(ω),Y₂(ω),...,Y_P(ω)]；W=[Y ₁ (ω),Y ₂ (ω),...,Y _P (ω)];

(8)利用稀疏基W和投影谱线Y(ω)，通过求解下式，获得角度谱向量β：(8) Using the sparse basis W and the projected spectral line Y(ω), the angle spectrum vector β is obtained by solving the following formula:

$\underset{β β}{min min} {{{| | | | Y Y ((ω ω)) - - Wβ Wβ | | | |}_{22} + + λ λ {| | | | β β | | | |}_{11}}}$

其中，表示求最小值的运算符号，λ为由用户输入的正则化参数，|| ||₁、|| ||₂分别表示求向量的1范数和2范数；in, Indicates the operation symbol for finding the minimum value, λ is the regularization parameter input by the user, || || ₁ and || || ₂ represent the 1-norm and 2-norm of the vector respectively;

(9)采用阈值比较法，对角度谱向量β进行峰值检测，获得角度谱向量峰值元素索引值l；(9) Using the threshold value comparison method to perform peak detection on the angle spectrum vector β, and obtain the index value l of the peak element of the angle spectrum vector;

(10)由峰值索引值l按下式确定出目标的角度值θ为：(10) Determine the angle value θ of the target from the peak index value l according to the following formula:

$θ θ = = {θ θ}_{min min} + + \frac{l l - - 11}{P P - - 11} (({θ θ}_{max max} - - {θ θ}_{min min})) . .$

本发明与现有技术相比具有如下优点：Compared with the prior art, the present invention has the following advantages:

第一，由于本发明整个信号处理过程都是对宽带回波信号整体进行处理，充分利用了宽带信号的信息，可以达到更高的分辨率。First, since the whole signal processing process of the present invention is to process the broadband echo signal as a whole, the information of the broadband signal is fully utilized, and a higher resolution can be achieved.

第二，由于本发明通过基于发射信号建立稀疏基，对相干信号的角度检测效果更加突出。Second, since the present invention establishes a sparse basis based on the transmitted signal, the angle detection effect on the coherent signal is more prominent.

第三，由于本发明稀疏基的构造方式与目标角度值无关，避免了相干信号处理中角度预估计的步骤，因此对相干信号的角度检测更加精确、稳定。Thirdly, since the construction method of the sparse basis of the present invention has nothing to do with the target angle value, the step of angle pre-estimation in the coherent signal processing is avoided, so the angle detection of the coherent signal is more accurate and stable.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is a flow chart of the present invention;

图2为用现有非相干信号处理方法获得角度谱向量的仿真结果图；Fig. 2 is the simulation result figure that obtains angle spectrum vector with existing non-coherent signal processing method;

图3为用现有相干信号处理方法获得角度谱向量的仿真结果图；Fig. 3 is the simulation result figure that obtains angle spectrum vector with existing coherent signal processing method;

图4为用本发明方法获得角度谱向量的仿真结果图。Fig. 4 is a diagram of the simulation results obtained by using the method of the present invention to obtain the angle spectrum vector.

具体实施方式Detailed ways

下面结合附图对本发明做进一步的详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings.

参照图1，本发明的具体实施步骤如下：With reference to Fig. 1, concrete implementation steps of the present invention are as follows:

步骤1，获取第m个阵元接收到的目标反射信号。Step 1: Obtain the target reflection signal received by the mth array element.

设雷达发射的宽带信号为s(t)，第i个目标和第m个阵元之间的距离引起的信号传播相对时间延迟为τ_mi，得到第m个阵元接收到的目标反射信号为：Assuming that the broadband signal transmitted by the radar is s(t), the relative time delay of signal propagation caused by the distance between the i-th target and the m-th array element is τ _mi , and the target reflection signal received by the m-th array element is :

${x x}_{m m} ((t t)) = = {Σ Σ}_{i i = = 11}^{N N} s the s ((t t - - {τ τ}_{mi mi})) + + {n no}_{m m} ((t t)),, m m = = 1,2 1,2,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, M m$

其中，x_m(t)为第m个阵元接收到的目标反射信号，t表示时间，N为目标总数，M为阵元数目，n_m(t)为第m个阵元接收到的噪声。Among them, x _m (t) is the target reflection signal received by the mth array element, t represents the time, N is the total number of targets, M is the number of array elements, and n _m (t) is the noise received by the mth array element .

步骤2，构造接收信号矩阵。Step 2, constructing the received signal matrix.

对目标反射信号x_m(t)进行离散采样，得到离散数据x_m(n)，再以该离散数据x_m(n)作为第m行，构造接收信号矩阵X(m,n)：Discretely sample the target reflection signal x _m (t) to obtain discrete data x _m (n), and then use the discrete data x _m (n) as the mth row to construct the received signal matrix X(m,n):

$X x ((m m,, n no)) = = [\begin{matrix} {x x}_{11} ((n no)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {x x}_{m m} ((n no)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {x x}_{M m} ((n no)) \end{matrix}];;$

对接收信号矩阵X(m,n)进行预处理，即对接收信号矩阵X(m,n)第m行的数据乘以(-1)^m，得到预处理后的数据X'(m,n)。Preprocess the received signal matrix X(m,n), that is, multiply the data in the mth row of the received signal matrix X(m,n) by (-1) ^m to obtain the preprocessed data X'(m,n ).

步骤3，对预处理后的数据X'(m,n)进行二维频域投影变换，获得二维投影频谱。Step 3, performing two-dimensional frequency-domain projection transformation on the preprocessed data X'(m,n) to obtain a two-dimensional projection spectrum.

(3.a)将预处理后的数据X'(m,n)按如下式进行二维傅里叶变换，得到二维频谱H(v,u)：(3.a) Perform two-dimensional Fourier transform on the preprocessed data X'(m,n) according to the following formula to obtain the two-dimensional spectrum H(v,u):

$H h ((v v,, u u)) = = {Σ Σ}_{m m = = 00}^{M m - - 11} {Σ Σ}_{n no = = 00}^{T T - - 11} {X x}^{' '} ((m m,, n no)) {e e}^{- - j j \frac{22 π π}{{M m}^{' '}} mv mv} {e e}^{- - j j \frac{22 π π}{{T T}^{' '}} nu nu}$

其中，v表示离散空频采样点，u表示离散时频采样点，M'表示离散空频采样点数，T'表示离散时频采样点数；Among them, v represents discrete space-frequency sampling points, u represents discrete time-frequency sampling points, M' represents the number of discrete space-frequency sampling points, and T' represents the number of discrete time-frequency sampling points;

(3.b)对二维频谱H(v,u)中的数据按如下公式进行投影，得到二维投影频谱F(ω,u)：(3.b) Project the data in the two-dimensional spectrum H(v,u) according to the following formula to obtain the two-dimensional projected spectrum F(ω,u):

F(ω,u)=H(v,u)F(ω,u)=H(v,u)

其中ω表示投影位置，由下式得到where ω represents the projected position, obtained by the following formula

$ω ω = = round round ((\frac{v v - - \frac{{M m}^{' '}}{22}}{u u} {u u}_{p p} + + \frac{{M m}^{' '}}{22}))$

式中，u_p表示投影时频轴，round()表示取整运算；In the formula, u _p represents the projected time-frequency axis, and round() represents the rounding operation;

(3.c)将步骤(3.a)与步骤(3.b)综合为一步实现,得到二维投影频谱F(ω,u)为：(3.c) Combining step (3.a) and step (3.b) into a one-step implementation, the two-dimensional projection spectrum F(ω,u) is obtained as:

$F f ((ω ω,, u u)) = = {Σ Σ}_{m m = = 00}^{M m - - 11} {Σ Σ}_{n no = = 00}^{T T - - 11} {X x}^{' '} ((m m,, n no)) {e e}^{- - j j \frac{22 π π}{{T T}^{' '}} nu nu} {e e}^{- - j j \frac{22 π π}{{M m}^{' '}} m m [[\frac{u u}{{u u}_{p p}} ((ω ω - - \frac{{M m}^{' '}}{22})) + + \frac{{M m}^{' '}}{22}]]},,$

步骤4，相参累加。Step 4, coherent accumulation.

对二维投影频谱F(ω,u)沿行累加，得到投影谱线Y(ω)为：Accumulate the two-dimensional projection spectrum F(ω,u) along the row, and the projection spectrum line Y(ω) is obtained as:

$Y Y ((ω ω)) = = {Σ Σ}_{u u = = 11}^{{T T}^{' '}} F f ((ω ω,, u u))$

步骤5，构造稀疏基。Step 5, construct sparse base.

(5.a)按下式将雷达测角范围θ_min～θ_max等角度划分为P个角度：(5.a) Divide the radar angle measurement range θ _min ~ θ _max into P angles according to the following formula:

(5.b)分别计算无噪情况下，目标角度为θ₁,θ₂,...,θ_P时的对应投影谱线Y₁(ω),Y₂(ω),...,Y_P(ω)；(5.b) Calculate the corresponding projected spectral lines Y ₁ (ω), Y 2 (ω),...,Y when _the target angle is θ ₁ , θ ₂ ,...,θ _P in the case of noise-free _P (ω);

(5.c)由投影谱线Y₁(ω),Y₂(ω),...,Y_P(ω)构造稀疏基：(5.c) Construct a sparse basis from the projected spectral lines Y ₁ (ω), Y ₂ (ω),...,Y _P (ω):

W=[Y₁(ω),Y₂(ω),...,Y_P(ω)]。W=[Y ₁ (ω),Y ₂ (ω),...,Y _P (ω)].

步骤6，获得角度谱向量。Step 6, obtain the angle spectrum vector.

利用稀疏基W和投影谱线Y(ω)，可以通过牛顿法或共轭梯度法以及加权迭代最小二乘等优化算法求解下式，获得角度谱向量β为：Using the sparse basis W and the projected spectral line Y(ω), the following formula can be solved by Newton's method or conjugate gradient method and weighted iterative least squares optimization algorithm, and the angle spectrum vector β is obtained as:

其中，表示求最小值的运算符号，λ为由用户输入的正则化参数，|| ||₁、|| ||₂分别表示求向量的1范数和2范数。in, Indicates the operator symbol for finding the minimum value, λ is the regularization parameter input by the user, || || ₁ and || || ₂ represent the 1-norm and 2-norm of the vector, respectively.

步骤7，确定目标角度值。Step 7, determine the target angle value.

(7.a)对角度谱向量β进行归一化处理，得到归一化角度谱向量 (7.a) Normalize the angle spectrum vector β to obtain a normalized angle spectrum vector

(7.b)设置阈值ε=0.1，按下式获取峰值索引值l为：(7.b) Set the threshold ε=0.1, and obtain the peak index value l as follows:

$l l = = {{i i | | {\overset{&OverBar; &OverBar;}{β β}}_{i i} > > ϵ ϵ,, i i = = 1,2 1,2,, . . . . . .,, P P}}$

其中，为归一化角度谱向量的第i个元素；in, is the normalized angle spectrum vector The i-th element of ;

(7.d)由峰值索引值l按下式确定出目标的角度值θ为：(7.d) Determine the angle value θ of the target from the peak index value l according to the following formula:

本发明的效果可以通过下述仿真实验加以说明：Effect of the present invention can be illustrated by following simulation experiments:

1.仿真条件1. Simulation conditions

运行系统为Intel(R)Core(TM)Duo CPU E84003.00GHz，32位Windows操作系统，仿真软件采用MATLAB R(2011b)，仿真参数设置如下表所示。The operating system is Intel(R) Core(TM) Duo CPU E8400 3.00GHz, 32-bit Windows operating system, the simulation software uses MATLAB R(2011b), and the simulation parameter settings are shown in the table below.

参数parameter 参数值parameter value 系统载频System carrier frequency 1GHz1GHz 调频带宽FM bandwidth 400MHz400MHz 阵元个数Number of array elements 1616 系统阵元间距System element spacing 0.125m0.125m 阵列孔径array aperture 2m2m 时间采样点数time sampling points 3232 时间采样频率time sampling frequency 2.4GHz2.4GHz 信噪比SNR 10dB10dB 目标个数target number 22 目标角度target angle 0°,3.5°0°,3.5°

2.仿真内容与结果2. Simulation content and results

仿真1，用现有非相干信号处理方法获得角度谱向量，仿真结果如图2所示；Simulation 1, using the existing incoherent signal processing method to obtain the angle spectrum vector, the simulation results are shown in Figure 2;

仿真2，用现有相干信号处理方法获得角度谱向量，仿真结果如图3所示；Simulation 2, using the existing coherent signal processing method to obtain the angle spectrum vector, the simulation results are shown in Figure 3;

仿真3，用本发明方法获得角度谱向量，仿真结果如图4所示。Simulation 3, using the method of the present invention to obtain the angle spectrum vector, the simulation results are shown in Figure 4.

由图2和图3可知，现有非相干信号处理方法以及现有相干信号处理方法在阵列孔径有限的情况下，无法分辨角度间隔小且相干的两个目标；It can be seen from Figures 2 and 3 that the existing non-coherent signal processing methods and the existing coherent signal processing methods cannot distinguish two coherent targets with small angular intervals under the condition of limited array aperture;

由图4可知，本发明方法成功分辨出角度间隔小且相干的两个目标。两个目标所在的角度如表1：It can be seen from FIG. 4 that the method of the present invention successfully distinguishes two coherent targets with small angular intervals. The angles of the two targets are shown in Table 1:

表1目标角度值计算结果Table 1 Calculation results of the target angle value

空间目标space target 目标1target 1 目标2goal 2 角度angle 0.2°0.2° 3.5°3.5°

由表1可知，两个目标的角度值均得到了高精度的计算。It can be seen from Table 1 that the angle values of the two targets have been calculated with high precision.

Claims

1. A wideband target direction finding method based on two-dimensional frequency domain sparse constraints, comprising the steps of:

(1) Assuming that the broadband signal transmitted by the radar is s(t), the relative time delay of signal propagation caused by the distance between the i-th target and the m-th array element is τ _mi , and the target received by the m-th array element is obtained The reflected signal is:

{x x}_{m m} ((t t)) = = {Σ Σ}_{i i = = 11}^{N N} s the s ((t t - - {τ τ}_{mi mi})) + + {n no}_{m m} ((t t)),, m m = = 1,2 1,2,, . . . . . .,, M m

Among them, x _m (t) is the target reflection signal received by the mth array element, t represents the time, N is the total number of targets, M is the number of array elements, and n _m (t) is the noise received by the mth array element ;

(2) Perform discrete sampling on the target reflected signal x _m (t) to obtain discrete data x _m (n), and then use the discrete data x _m (n) as the mth row to construct the received signal matrix X(m,n):

X x ((m m,, n no)) = = [\begin{matrix} {x x}_{11} ((n no)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {x x}_{m m} ((n no)) \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot \cdot \\ {x x}_{M m} ((n no)) \end{matrix}];;

Preprocess the received signal matrix X(m,n), that is, multiply the data in the mth row of the received signal matrix X(m,n) by (-1) ^m to obtain the preprocessed data X'(m,n );

(3) Perform two-dimensional frequency-domain projection transformation on the preprocessed data X'(m,n) to obtain a two-dimensional projection spectrum F(ω,u), where ω represents the projected space-frequency position, and u represents discrete time-frequency sampling point;

(4) Accumulate the two-dimensional projection spectrum F(ω,u) along the row to obtain the projection spectrum line Y(ω);

(5) Divide the radar angle measurement range θ _min ~ θ _max into P angles according to the following formula:

{θ θ}_{i i} = = {θ θ}_{min min} + + \frac{i i - - 11}{P P - - 11} (({θ θ}_{max max} - - {θ θ}_{min min})),, i i = = 1,2 1,2,, . . . . . .,, P P,,

Among them, θ _min and θ _max are the minimum and maximum values of the angle measurement range;

(6) Calculate the corresponding projected spectral lines _Y ₁ (ω), Y ₂ ₍ ω),...,Y _P ₍ ω);

(7) Construct a sparse basis from the projected spectral lines Y ₁ (ω), Y ₂ (ω),...,Y _P (ω):

W＝[Y ₁ (ω),Y ₂ (ω),...,Y _P (ω)];

(8) Using the sparse basis W and the projected spectral line Y(ω), solve the following formula by Newton method or conjugate gradient method and weighted iterative least squares optimization algorithm to obtain the angle spectrum vector β:

\underset{β β}{min min} {{{| | | | Y Y ((ω ω)) - - Wβ Wβ | | | |}_{22} + + λ λ {| | | | β β | | | |}_{11}}}

in, Indicates the operation symbol for finding the minimum value, λ is the regularization parameter input by the user, || || ₁ and || || ₂ represent the 1-norm and 2-norm of the vector respectively;

(9) Using the threshold value comparison method to perform peak detection on the angle spectrum vector β, and obtain the index value l of the peak element of the angle spectrum vector;

(10) Determine the angle value θ of the target from the peak index value l according to the following formula:

θ θ = = {θ θ}_{min min} + + \frac{l l - - 11}{P P - - 11} (({θ θ}_{max max} - - {θ θ}_{min min})) . .

2. The broadband target direction-finding method based on two-dimensional frequency domain sparse constraints according to claim 1, wherein the two-dimensional frequency domain projection is done to the preprocessed data X' (m, n) described in step (3) The transformation is carried out according to the following formula:

F f ((ω ω,, u u)) = = {Σ Σ}_{m m = = 00}^{M m - - 11} {Σ Σ}_{m m = = 00}^{T T - - 11} {X x}^{' '} ((m m,, n no)) {e e}^{- - j j \frac{22 π π}{{T T}^{' '}} nu nu} {e e}^{- - j j \frac{22 π π}{{M m}^{' '}} m m [[\frac{11}{{u u}_{p p} - - \frac{{T T}^{' '}}{22}} ((u u - - \frac{{T T}^{' '}}{u u})) ((ω ω - - \frac{{M m}^{' '}}{22})) + + \frac{{M m}^{' '}}{22}]]}

Among them, F(ω, u) is the two-dimensional projected spectrum after two-dimensional frequency domain projection transformation, T represents the number of time sampling points, T' represents the number of discrete time-frequency sampling points, M' represents the number of discrete space-frequency sampling points, and u _p represents the projection time-frequency axis.

3. the broadband target direction-finding method based on two-dimensional frequency-domain sparse constraints according to claim 1, wherein the adopting threshold comparison method described in step (9), carries out peak detection to angle spectrum vector β, obtains angle spectrum vector peak value Element index value l, proceed as follows:

(9a) Normalize the angle spectrum vector β to obtain the normalized angle spectrum vector

(9b) Set the threshold ε=0.1, and obtain the peak index value l as follows:

l l = = {{i i | | {\overset{&OverBar; &OverBar;}{β β}}_{i i} > > ϵ ϵ,, i i = = 1,2 1,2,, . . . . . .,, P P}}

in, is the normalized angle spectrum vector The i-th element of .