Array mutual coupling self-correction DOA method based on sparse off-network

Abstract

The invention discloses an array mutual coupling self-correction DOA method based on sparse off-network, and belongs to the field of array signal processing. The method comprises the following steps: constructing a sparse off-network DOA estimation system model considering an array mutual coupling effect; initializing a mutual coupling coefficient vector and an off-grid parameter vector, and reconstructing a signal sparse matrix by using a smooth norm according to a system model; estimating an off-network parameter vector according to the reconstructed signal sparse matrix and a known initialized (or after last iteration) mutual coupling matrix; estimating a mutual coupling matrix from a system model by using a method based on gradient descent by using the reconstructed signal sparse matrix and the estimated off-network parameter vector; and after iteration meets a stop condition, obtaining DOA estimation of the signal according to the signal sparse matrix, the mutual coupling coefficient matrix and the off-network parameter vector after iteration. According to the method, a better DOA estimation effect can be obtained on the premise that the array antenna has an unknown mutual coupling effect.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing, specifically relating to an array mutual coupling self-calibration DOA method based on sparse off-network. Background Technology

[0002] Direction of arrival (DOA) estimation is an important branch of array signal processing. Thanks to the continuous efforts of scholars at home and abroad over the past few decades, DOA estimation has been greatly developed and is widely used in radar, satellite communication, satellite navigation and indoor positioning.

[0003] The core idea of ​​DOA technology is to sample the incident signal by using spatially distributed array antennas, and extract the spatial information contained in the phase difference (also known as the delay difference) between different array elements of the interference signal to estimate the number and direction of the signal source.

[0004] Most current signal processing methods are based on the ideality of array manifolds. However, the mutual coupling effect between arrays can affect the ideality of the array manifold and seriously reduce the performance of the algorithm. Therefore, the research on array mutual coupling correction has theoretical significance and practical value. Summary of the Invention

[0005] This invention proposes a self-calibrating DOA (Directed Aspect of Analysis) method based on sparse off-network array mutual coupling, which can achieve better DOA estimation results even when there are unknown mutual coupling effects in uniform linear arrays. To achieve the above technical objectives, this invention employs the following technical solution:

[0006] A method for array cross-coupling self-calibration DOA based on sparse off-network includes the following steps:

[0007] Step 1: Construct a sparse off-network DOA estimation system model that considers array mutual coupling effects;

[0008] For one A uniform linear array utilizes the sparsity of the signal spatial domain to represent the range of possible signal origins in space. Divided into equal intervals From a grid, a complete array manifold matrix is ​​obtained. , To complete the column vectors of the array manifold matrix, an off-grid parameter vector is introduced. , representing the deviation between the actual angle and the corresponding grid, is used in conjunction with sparse representation theory to represent the received signal as:

[0009]

[0010] In the formula, Indicates time The observation matrix obtained above; Represents a complete array manifold matrix; To complete array manifold matrix The first derivative; This is the off-grid parameter vector; For the objective in a complete array manifold matrix The coefficients on the matrix are called the signal sparse matrix; It is Gaussian white noise; It is the mutual coupling matrix between antenna array elements and is also a Toeplitz matrix. The structure is simplified to the following symmetric banded Toeplitz matrix:

[0011]

[0012] In the formula, Indicates the interval is The mutual coupling coefficient between two array elements with an element spacing of 1;

[0013] Define the mutual coupling coefficient vector ;

[0014] Step 2: Initialize the cross-coupling coefficient vector and off-grid parameter vector ;

[0015] make , Let represent the initialized cross-coupling coefficient vector and the off-grid parameter vector, respectively. Based on the symmetry property of the Toeplitz matrix, the cross-coupling coefficient vector... Supplemented as a mutual coupling matrix ;

[0016] Step 3: Utilize smoothing based on the system model Norm-reconstructed sparse matrix of signal ;

[0017] Constructing an array-based self-calibrating DOA model based on sparse off-networks

[0018]

[0019] For the preset noise level, use smoothing The norm is used to minimize the constraints of the above equation, and the sparse matrix of the signal is estimated. ;

[0020] Step 4: Estimate the off-grid parameter vector ;

[0021]

[0022] in, , , This represents the matrix inversion operation. This represents the pseudo-inverse operation of a matrix;

[0023] Step 5: Utilize the reconstructed sparse signal matrix The estimated off-grid parameter vector The mutual coupling matrix is ​​estimated from the system model using a gradient descent-based method. ;

[0024] The sparse off-network DOA estimation system model considering array mutual coupling effect is expressed as follows:

[0025]

[0026] In the formula, , For matrix The first derivative, This represents the Kronecker product operation on a matrix. express 3D identity matrix;

[0027] The mutual coupling matrix is ​​then estimated using gradient descent. ;

[0028] Step 6: If the mutual coupling matrix in two adjacent iterations If convergence is achieved, the iteration stops, and the result is determined based on the sparse matrix of the signal after iteration. and the mutual coupling coefficient matrix and off-grid parameter vector Obtain the DOA estimate of the signal; otherwise, return to step 3.

[0029] The beneficial effects achieved by this invention compared with the prior art are as follows:

[0030] This invention proposes a sparse off-grid array mutual coupling self-correction DOA method. This method, even with unknown mutual coupling errors in the array, fully utilizes the strip-symmetric structure of the mutual coupling matrix and estimates the mutual coupling coefficients of a uniform linear array using gradient descent. Experimental results show that, compared with other known off-grid algorithms and mutual coupling self-correction algorithms, this algorithm achieves better DOA estimation performance even with mutual coupling effects and coarse grid partitioning. Attached Figure Description

[0031] Figure 1 This is a flowchart of an array mutual coupling self-calibration DOA method based on sparse off-network according to the present invention;

[0032] Figure 2 This is a schematic diagram of the uniform linear array described in this invention;

[0033] Figure 3 This is a schematic diagram of the spatial grid division described in this invention. Detailed Implementation

[0034] The present invention will be further described below with reference to the accompanying drawings;

[0035] A method for array mutual coupling self-calibration DOA based on sparse off-network, such as... Figure 1 As shown, it includes the following steps:

[0036] Step 1: Construct a sparse off-network DOA estimation system model that considers array mutual coupling effects;

[0037] like Figure 2 As shown, consider a A uniform linear array, utilizing the sparsity properties of the signal spatial domain, such as... Figure 3 As shown, the possible directions of the signal in space are... Divided into equal intervals A complete array manifold matrix can be obtained from a grid. , This is the column vector for a complete array manifold matrix. Considering the reality that the actual direction of arrival is not on the sampling grid, an off-grid parameter vector is introduced. , representing the deviation between the actual angle and the corresponding grid. Using sparse representation correlation theory, the received signal can be represented as...

[0038]

[0039] In the formula, This indicates the operation of taking a diagonal matrix. Indicates time The observation matrix obtained above; Represents a complete array manifold matrix; To complete array manifold matrix The first derivative; This is the off-grid parameter vector; For the objective in a complete array manifold matrix The coefficients on the matrix are called the signal sparse matrix; It is Gaussian white noise; Let be the mutual coupling matrix between antenna elements and a Toeplitz matrix. As the element spacing increases, the antenna mutual coupling effect decreases rapidly. When the element spacing exceeds 10 ... When the spacing between array elements is 1, the coupling coefficient is approximately zero, therefore The structure is simplified to the following symmetric banded Toeplitz matrix:

[0040]

[0041] In the formula, Indicates the first Each array element and the first The mutual coupling coefficients of each array element.

[0042] Define the mutual coupling coefficient vector A sparse off-network-based array mutual coupling self-calibration DOA model can be established.

[0043]

[0044] In the formula, These represent the weighting coefficients, used to balance the sparseness of the signal matrix. and off-grid coefficient energy ; Indicates the preset noise level; Represents finding a matrix Norm; Represents finding a matrix Norm; Represents finding a matrix Norm.

[0045] Step 2: Initialize the cross-coupling coefficient vector and off-grid parameter vector ;

[0046] make , Let represent the initialized cross-coupling coefficient vector and the off-grid parameter vector, respectively. Based on the symmetry property of the Toeplitz matrix, the cross-coupling coefficient vector can be... Supplemented as a mutual coupling matrix ;

[0047] Step 3: Utilize smoothing based on the system model Norm-reconstructed sparse matrix of signal ;

[0048] Since the mutual coupling matrix and the off-network parameter vector are now confirmed to be constants, the simplified array mutual coupling self-calibration DOA model of the uniform linear array based on sparse off-network is as follows:

[0049]

[0050] Using smoothing The norm is used to minimize the constraints of the above equation, and the sparse matrix of the signal is estimated. .

[0051] Step 4: Estimate the off-grid parameter vector ;

[0052] Using the obtained signal sparse matrix and the known initialization (or the mutual coupling matrix obtained from the previous iteration) Substitute into the sparse off-network DOA estimation system model Multiply both sides of the equation by a mutual coupling matrix. The inverse matrix can be rewritten as:

[0053]

[0054] In the formula , , The matrix inversion operation, in the case of multiple snapshots (time sampling), can be written as follows:

[0055]

[0056] According to the properties of diagonal matrix, we know that And thus obtain

[0057]

[0058] By merging all columns into a matrix, we get

[0059]

[0060] The estimated off-grid parameter vector is obtained by solving the problem. The expression is

[0061]

[0062] In the formula This represents the pseudo-inverse operation of a matrix.

[0063] Step 5: Utilize the reconstructed sparse signal matrix The estimated off-grid parameter vector The mutual coupling matrix is ​​estimated from the system model using a gradient descent-based method. ;

[0064] Lemma 1: For a complex symmetric Toeplitz matrix and a complex vector You can get

[0065]

[0066] In the formula, , The number of non-zero elements in the first row; .

[0067] According to Lemma 1 above, the expression for the mutual coupling effect of a uniform linear array can be rewritten as follows:

[0068]

[0069] In the formula, , express 3D identity matrix; For matrix The first derivative, This represents the operation of calculating the Kronecker product of a matrix.

[0070] Based on the rewritten system expression, the mutual coupling matrix can be estimated using gradient descent. .

[0071] Step 6: Determine the convergence condition of the iteration If the condition is not met, continue iterating; if it is met, then determine the sparse matrix of the signal after iteration. and the mutual coupling coefficient matrix and off-grid parameter vector Obtain the DOA estimate of the signal. In the iterative convergence condition... This represents the remaining energy between two adjacent iterations of the mutual coupling matrix. This indicates the threshold for ending the iteration.

[0072] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and improvements without departing from the principles of the present invention, and these modifications and improvements should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for array mutual coupling self-calibration DOA based on sparse off-network, characterized in that, It includes the following steps: Step 1: Construct a sparse off-network DOA estimation system model that considers array mutual coupling effects; For one A uniform linear array utilizes the sparsity of the signal spatial domain to represent the range of possible signal origins in space. Divided into equal intervals From a grid, a complete array manifold matrix is ​​obtained. , To complete the column vectors of the array manifold matrix, an off-grid parameter vector is introduced. , representing the deviation between the actual angle and the corresponding grid, is used in conjunction with sparse representation theory to represent the received signal as: In the formula, Indicates time The observation matrix obtained above; Represents a complete array manifold matrix; To complete array manifold matrix The first derivative; This is the off-grid parameter vector; For the objective in a complete array manifold matrix The coefficients on the matrix are called the signal sparse matrix; It is Gaussian white noise; It is the mutual coupling matrix between antenna array elements and is also a Toeplitz matrix. The structure is simplified to the following symmetric banded Toeplitz matrix: In the formula, Indicates the interval is The mutual coupling coefficient between two array elements with an element spacing of 1; Define the mutual coupling coefficient vector ; Step 2: Initialize the cross-coupling coefficient vector and off-grid parameter vector ; make , Let represent the initialized cross-coupling coefficient vector and the off-grid parameter vector, respectively. Based on the symmetry property of the Toeplitz matrix, the cross-coupling coefficient vector... Supplemented as a mutual coupling matrix ; Step 3: Utilize smoothing based on the system model Norm-reconstructed sparse matrix of signal ; Constructing an array-based self-calibrating DOA model based on sparse off-networks For the preset noise level, use smoothing The norm is used to minimize the constraints of the above equation, and the sparse matrix of the signal is estimated. ; Step 4: Estimate the off-grid parameter vector ; in, , , This represents the matrix inversion operation. This represents the pseudo-inverse operation of a matrix; Step 5: Utilize the reconstructed sparse signal matrix The estimated off-grid parameter vector The mutual coupling matrix is ​​estimated from the system model using a gradient descent-based method. ; The sparse off-network DOA estimation system model considering array mutual coupling effect is expressed as follows: In the formula, , For matrix The first derivative, This represents the Kronecker product operation on a matrix. express 3D identity matrix; The mutual coupling matrix is ​​then estimated using gradient descent. ; Step 6: If the mutual coupling matrix in two adjacent iterations If convergence is achieved, the iteration stops, and the result is determined based on the sparse matrix of the signal after iteration. and the mutual coupling coefficient matrix and off-grid parameter vector Obtain the DOA estimate of the signal; otherwise, return to step 3.

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