A method for estimating arrival angle of correlation signals based on atomic norm in the presence of amplitude and phase errors

Abstract

The present invention discloses a method for estimating the angle of arrival of correlated signals based on the atomic norm when there are amplitude and phase errors, which belongs to the technical field of array signal processing. For the signals received by the array antenna, a receiving signal model in which the receiving antenna has amplitude and phase errors is constructed; by mining the spatial sparse characteristics of the correlated signals and using a sparse reconstruction algorithm, a solution expression for the unknown angle of arrival is theoretically derived. The method studies the dual problem of atomic norm minimization, uses semi-positive definite programming to solve the corresponding convex optimization problem, and realizes sparse estimation of the angle of arrival of correlated signals. The present invention constructs a sparse signal model in which the receiving antenna has amplitude and phase errors, and uses a sparse estimation algorithm based on the atomic norm to realize estimation of the angle of arrival of correlated signals.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, in particular to an arrival angle estimation method for related signals when amplitude and phase errors exist in an array antenna. Background Art

[0002] Signal arrival angle estimation technology plays a key role in the fields of radar, communication, and electronic countermeasures. By estimating the direction of electromagnetic waves, the radar system can improve the estimation and detection performance of targets and the channel capacity of wireless communication systems. Traditional signal arrival angle estimation technology is mainly based on the discrete Fourier transform method. This method has a fast estimation speed but low accuracy and cannot distinguish multiple signals in the same beam. Therefore, a subspace estimation technology based on MUSIC or ESPRIT is proposed. By taking multiple snapshots of the received signal, the covariance matrix of the signal is constructed to distinguish the signal subspace and the noise subspace, and the spatial spectrum and arrival angle of the signal are estimated in the subspace. The subspace-based arrival angle estimation technology can distinguish multiple signals in the same beam and is a super-resolution estimation method. In order to further improve the estimation accuracy of related signals, a multi-smoothing subspace estimation technology based on space, frequency, and time is proposed to obtain better estimation performance.

[0003] However, the arrival angle estimation technology based on subspace only makes full use of the subspace information of the signal and noise, but does not use more signal feature information. Since the received signal has sparse characteristics in the spatial domain, the arrival angle estimation of the signal can be realized by sparse reconstruction with the help of the idea of ​​compressed sensing (CS). However, in array signal processing, the inconsistency between antennas will reduce the estimation performance.

[0004] This will cause some troubles in the compressed sensing scenario: when the sparse basis divides the sparse domain into uniform discrete grids, the finer the grid, the smaller the spacing between adjacent grid points, and the smaller the error between the grid points and the true value of the parameter. However, the denser the grid, the stronger the correlation between adjacent sparse basis vectors, thereby reducing the compressed sensing reconstruction performance. Once the actual sparse parameter value of the signal does not fall on the segmented grid, the sparse basis obtained by discretizing the sparse domain cannot accurately represent the signal. In fact, no matter how finely the frequency domain grid is divided, the frequency value of the actual primary user signal may not fall on these limited grid points.

[0005] In addition, the correlation between signals will also lead to serious degradation of estimation performance. Taking into account the existing arrival angle estimation technology, it is necessary to solve the problem of not fully considering the impact of the error amplitude between antennas in the actual array on the estimation performance, and abandon the original discrete sparse basis and adopt the atomic norm, a continuous variable, to avoid the error caused by the discretization of the arrival angle, thereby effectively improving the arrival angle estimation accuracy for correlated signals. Summary of the invention

[0006] Purpose of the invention: In order to overcome the deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a method for estimating the angle of arrival of correlated signals based on the atomic norm when there are amplitude and phase errors, make full use of the spatial sparse characteristics of the signal, compensate for the influence of the amplitude and phase errors of the array antenna on the angle of arrival estimation, and adopt the orthogonal matching pursuit theory to effectively improve the signal's angle of arrival estimation performance.

[0007] Technical solution: To solve the above technical problems, the present invention provides an arrival angle estimation method based on atomic norm when there are amplitude and phase errors, comprising the following steps:

[0008] Step 1: Initialize unknown parameters, including the number of antennas and antenna spacing, antenna sampling number, and antenna signal-to-noise ratio;

[0009] Step 2, constructing a spatial domain sparse correlation signal model with phase and amplitude errors;

[0010] Step 3, give an expression for describing the optimization problem based on the atomic norm;

[0011] Step 4, using the dual norm of the atomic norm, construct the dual problem of the optimization problem;

[0012] Step 5, solve the dual problem and solve the root of the exponential polynomial to complete the estimation of the arrival angle of the relevant signal.

[0013] As a further preferred solution of the method for estimating the angle of arrival of a correlated signal based on the atomic norm when there are amplitude and phase errors in the present invention, in step 2, the sparse signal model when there are amplitude and phase errors in the antenna array is expressed as follows:

[0014] Y=ΓAS+W

[0015] Where Y = [y0,y1,…,y M-1 ] is the M sampling signals received by N antennas. s At sampling time, the received signal of N antennas is y m =[y 0,m ,y 1,m ,…,y N-1,m ] T , T sis the sampling interval, A=[a(f0),a(f1),…,a(f K-1 )] is the dictionary matrix composed of vector manifolds, S is a sparse matrix, Γ = diag (γ) is the diagonal matrix of the amplitude and phase errors of the array antenna, z n and φ n are the amplitude and phase errors of the nth receiving antenna, respectively, is the amplitude and phase error vector of the array antenna, and W is the additive white Gaussian noise.

[0016] As a further preferred solution of the method for estimating the arrival angle of the correlation signal based on the atomic norm when there are amplitude and phase errors in the present invention, in step 3, the optimization problem based on the atomic norm can be described as follows:

[0017]

[0018] Among them, τ (τ>0) is a regularization parameter, is the error weight of sparse and signal reconstruction, Z is a matrix of N rows and M columns, and other variables are the same as above.

[0019] As a further preferred solution of the method for estimating the arrival angle of the correlation signal based on the atomic norm when there is an amplitude and phase error in the present invention, in step 4, the Lagrangian variable U can be solved by solving the semi-positive definite programming problem, which is expressed as

[0020]

[0021] Q is Hermitan

[0022] Among them, Q is the Hermitan matrix with N rows and N columns, U is the Lagrangian variable matrix with N rows and M columns, and I is the identity matrix with M rows and M columns.

[0023] As a further preferred solution of the method for estimating the angle of arrival of a correlation signal based on the atomic norm when there is an amplitude and phase error in the present invention, [In step 5, the angle of arrival is obtained by obtaining the constraint polynomial of the dual problem of the atomic norm minimization problem, specifically:

[0024] The atomic norm can be described as

[0025]

[0026] The constraints of the dual problem are

[0027]

[0028] The constraint polynomial of the dual problem is

[0029]

[0030] Beneficial effects: The beneficial effects of the present invention are:

[0031] (1) The problem of deviation of the arrival angle estimation value when the array antenna has amplitude and phase errors is solved. The present invention solves the problem that the arrival angle estimation value has deviation when the general array antenna has amplitude and phase errors, which reduces the arrival angle estimation performance. The amplitude and phase error vector is introduced into the general model based on the sparse characteristics of the signal, and the semi-positive definite programming optimization problem is solved to obtain the constraint polynomial of the atomic norm dual problem, estimate the arrival angle value, improve the estimation performance of the algorithm, and compensate for the loss of arrival angle estimation performance caused by antenna inconsistency.

[0032] (2) The spatial sparse features of the received signal are fully exploited. By modeling the arrival angle estimation problem as a sparse reconstruction problem, the present invention can fully exploit the sparse features of the signal, thereby improving the arrival angle estimation performance;

[0033] (3) The computational complexity is reduced. The present invention uses a semi-positive programming algorithm, which greatly reduces the computational complexity of the algorithm while ensuring the performance of the algorithm.

[0034] (4) Through the arrival estimation process based on the atomic norm, the problem of poor estimation accuracy of correlated signals in traditional estimation algorithms is effectively solved, and the arrival angle estimation accuracy of correlated signals is effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a block diagram of the application system of the present invention for uniform linear antenna array;

[0036] Figure 2 It is a schematic diagram of the method flow of the present invention;

[0037] Figure 3 It is a schematic diagram of the arrival angle estimation performance of the present invention under different signal-to-noise ratio conditions;

[0038] Figure 4 It is a schematic diagram of the arrival angle estimation performance of the present invention under different sampling number conditions;

[0039] Figure 5 The figure is a schematic diagram of the arrival angle estimation performance under the conditions of different numbers of receiving antennas of the present invention. DETAILED DESCRIPTION

[0040] The present invention will be further described below in conjunction with the accompanying drawings.

[0041] In order to solve the problem of estimating the angle of arrival of related signals when there are amplitude and phase errors in the array antenna, the present invention needs to design a new angle of arrival estimation method, aiming to fully exploit the sparse characteristics of the signal, and construct an angle of arrival estimation method based on the atomic norm by reasonably modeling the amplitude and phase error parameters and the received signal, so as to effectively improve the angle of arrival estimation performance in the array antenna. The overall design concept of the present invention is:

[0042] 1) First, the amplitude and phase error vectors are used to construct a signal model based on the sparse characteristics of the signal in the spatial domain;

[0043] 2) Based on the amplitude and phase errors, the optimization problem of semi-positive definite programming is theoretically derived;

[0044] 3) The Lagrangian variables solved by semi-positive definite programming are used to obtain the constraint polynomial of the atomic norm dual problem, thereby obtaining an accurate estimation of the signal arrival angle.

[0045] Based on the above considerations, the present invention proposes a method for estimating the angle of arrival of correlated signals based on the atomic norm when there are amplitude and phase errors, which is used to solve the problem of high-precision estimation of the angle of arrival under the condition of unknown antenna amplitude and phase error parameters, and proposes a semi-positive definite programming solution algorithm; the algorithm can be applied to Figure 1 In the uniform linear antenna array shown in FIG. 1 , the logic flow chart of the method is as follows: Figure 2 As shown, its working process includes the following steps:

[0046] (1) Construct a spatial sparse correlation signal model when the antenna array has amplitude and phase errors, and proceed to step (2);

[0047] (2) Initialize unknown parameters, including the number and spacing of antennas, the number and minimum spacing of target signal sources, the number of samples, the signal-to-noise ratio, and the signal correlation coefficient, and proceed to step (3);

[0048] (3) According to the current unknown parameter values, simulate and generate the receiving signal, and enter step (4);

[0049] (4) According to the current unknown parameter values, the Lagrangian variables can be obtained by solving the semi-positive definite programming optimization problem, and then proceed to step (5);

[0050] (5) Based on the obtained Lagrangian variables, the constraint polynomial of the dual problem of the atomic norm minimization problem is obtained, and then the angle of arrival is obtained, and the spatial spectrum of the received signal and the corresponding angle of arrival are output.

[0051] The following is a detailed description of the contents of several main parts:

[0052] Part I: Modeling of Sparse Signals

[0053] First, for Figure 1The uniform linear array (ULA) shown in Figure 2 can model the received signal as

[0054] Y=ΓAS+N

[0055] Where Y = [y0,y1,…,y M-1 ] is the M sampling signals received by N antennas. s At sampling time, the received signal of N antennas is y m =[y 0,m ,y 1,m ,…,y N-1,m ] T , T s is the sampling interval, A=[a(f0),a(f1),…,a(f K-1 )] is the dictionary matrix composed of vector manifolds, S is a sparse matrix, Γ = diag (γ) is the diagonal matrix of the amplitude and phase errors of the array antenna, z n and φ n are the amplitude and phase errors of the nth receiving antenna, respectively, is the amplitude and phase error vector of the array antenna, and W is the additive white Gaussian noise.

[0056] A is the dictionary matrix composed of vector flows, which can be expressed as

[0057]

[0058] Part II: Angle of Arrival Estimation Based on the Atomic Norm

[0059] The atomic norm of multiple measurements can be described as

[0060]

[0061] The dual problem can eventually be simplified to

[0062]

[0063] Then the optimization problem can be described as the SDP problem

[0064]

[0065] Q is Hermitan

[0066] The angle is obtained by solving the SDP optimization problem.

[0067] The present invention is further described below with reference to examples.

[0068] Table 1

[0069]

[0070] For the ULA system, using the simulation parameters in Table 1, we compared the current main arrival angle estimation methods, including the SOMP algorithm, the OGSBI algorithm, the MUSIC algorithm, and the TAN algorithm based on the atomic norm and Toeplitz matrix constraints.

[0071] Figure 3 The arrival angle estimation performance under different signal-to-noise ratio conditions is given. It can be seen from the figure that for correlated signals, when the signal-to-noise ratio (SNR) is greater than 0dB, the arrival angle estimation algorithm proposed in the present invention is significantly better than the existing algorithm.

[0072] Figure 4 The arrival angle estimation performance under different sampling numbers of the correlated signal is given. It can be seen from the figure that the arrival angle estimation algorithm proposed in the present invention is significantly better than the existing algorithm.

[0073] Figure 5 The arrival angle estimation performance under different numbers of receiving antennas for the correlated signal is given. It can be seen from the figure that the arrival angle estimation algorithm proposed in the present invention is significantly better than the existing algorithm.

[0074] The arrival angle estimation method for correlated signals and amplitude-phase errors proposed in the present invention can also be applied to scenarios where there is no amplitude-phase error or uncorrelated signals.

Claims

1. A method for estimating the angle of arrival of a correlation signal based on an atomic norm in the presence of amplitude and phase errors, characterized in that: The steps include: Step 1: Initialize unknown parameters, including the number of antennas and antenna spacing, antenna sampling number, and antenna signal-to-noise ratio; Step 2, constructing a spatial domain sparse correlation signal model with phase and amplitude errors; Step 3, give an expression for describing the optimization problem based on the atomic norm; Step 4, using the dual norm of the atomic norm, construct the dual problem of the optimization problem; Step 5, solve the dual problem and solve the root of the exponential polynomial to complete the estimation of the arrival angle of the relevant signal; In step 2, the sparse signal model when there are amplitude and phase errors in the antenna array is expressed as Y=ΓAS+W Where Y = [y0,y1,…,y M-1 ] is the M sampling signals received by N antennas. s At sampling time, the received signal of N antennas is y m =[y 0,m ,y 1,m ,…,y N-1,m ] T , T s is the sampling interval, A=[a(f0),a(f1),…,a(f K-1 )] is the dictionary matrix composed of vector manifolds, S is a sparse matrix, Γ = diag (γ) is the diagonal matrix of the amplitude and phase errors of the array antenna, z n and φ n are the amplitude and phase errors of the nth receiving antenna, respectively, is the amplitude and phase error vector of the array antenna, W is the additive white Gaussian noise; In step 3, the optimization problem based on the atomic norm can be described as Among them, τ (τ>0) is a regularization parameter, is the error weight of sparse and signal reconstruction, and Z is a matrix with N rows and M columns; In step 4, the Lagrangian variable U can be solved by solving the semi-positive programming problem, which is expressed as: Among them, Q is the Hermitan matrix of N rows and N columns, U is the Lagrangian variable matrix of N rows and M columns, and I is the identity matrix of M rows and M columns; In step 5, the angle of arrival is obtained by obtaining the constraint polynomial of the dual problem of the atomic norm minimization problem, which is specifically: The atomic norm can be described as: The constraints of the dual problem are: The constraint polynomial of the dual problem is

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