CN109444807B - Single-snapshot off-grid signal direction-of-arrival estimation method suitable for any linear array - Google Patents
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Abstract
本发明公开了一种适用于任意线阵的单快拍离格信号波达方向估计方法，属于阵列信号处理技术领域。本发明对于单一离格信号波达方向估计，首先根据单快拍阵元数据获得位于候选网格上的信号波达方向初始估计值，并据此得到相应的阵列导向矢量；计算阵列导向矢量张成的子空间的正交子空间；对正交子空间做特征分解，得到对应于非零特征值的特征向量；将偏离网格的角度值作为估计参数对信号波达方向初始估计值进行校正，得到最终的波达方向。利用单一离格信号波达方向估计方法，得到多离格信号中第K个信号的波达方向估计值和估计幅度。本发明能够采用任意线阵，可以获得单一离格信号和多离格信号波达方向的精确估计。
The invention discloses a method for estimating the direction of arrival of a single-shot off-grid signal suitable for any linear array, and belongs to the technical field of array signal processing. For the estimation of the direction of arrival of a single off-grid signal, the invention first obtains the initial estimated value of the direction of arrival of the signal located on the candidate grid according to the single-shot array element data, and obtains the corresponding array steering vector accordingly; calculates the array steering vector Orthogonal subspace of the formed subspace; perform eigendecomposition on the orthogonal subspace to obtain eigenvectors corresponding to non-zero eigenvalues; use the angle value deviating from the grid as the estimation parameter to correct the initial estimated value of the direction of arrival of the signal , to get the final direction of arrival. Using the method of estimating the direction of arrival of a single out-of-cell signal, the estimated value of the direction of arrival and the estimated amplitude of the K-th signal in the multi-out-of-cell signal are obtained. The invention can adopt any linear array, and can obtain accurate estimation of the direction of arrival of single off-grid signal and multi-off grid signal.
Description
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a single-snapshot off-grid signal direction-of-arrival estimation method suitable for any linear array.
Background
The estimation of the direction of arrival is always the hot content of array signal processing, and has wide application in the fields of communication, radar, sonar and the like. The traditional multiple signal classification method and the rotation invariant subspace technology of signal parameter estimation have high estimation performance, but the algorithms are performed on the basis of eigenvalue decomposition operation, and a large number of fast beats are often needed to obtain good estimation performance, so that the method cannot be effectively applied to the single-snapshot condition, which is not practical in practical engineering application.
In an actual signal environment, a high-speed moving target has high real-time requirement on a system, received effective data only contains several times of snapshot data, and a direction-of-arrival estimation algorithm based on a large amount of snapshot data cannot meet actual requirements under the condition of the existing hardware system, so that the direction-of-arrival estimation by using single snapshot data becomes a solution. On the premise that the array has limited received data and the target moves at high speed, the real-time processing of the target can be realized, the estimation accuracy of the direction of arrival is high, and the technical support can be provided for positioning and tracking the high-speed moving target.
With the rise of the compressed sensing technology, the sparse representation theory is gradually applied to the direction of arrival estimation. Before applying sparse representation theory for direction of arrival estimation, equal-interval division needs to be performed in an angle domain to construct a fine overcomplete dictionary, so that these sparse representation-based direction of arrival estimation algorithms can only estimate signals located on an overcomplete dictionary atomic grid. The estimation accuracy of such algorithms will drop sharply when the direction of arrival of the signal is not on the grid (defined as an off-grid signal). Sparse reconstruction of off-grid signals is therefore of great interest.
The linear array has wide application in the array processing process. The uniform linear array has simple structure and is convenient for analysis and research. Under the condition that the array elements are equal, compared with a uniform linear array, the aperture of the array can be expanded as much as possible by the non-uniform linear array, and higher degree of freedom is obtained. Therefore, in practical applications, it is necessary to find a direction of arrival estimation method that is suitable for any linear array as much as possible.
Disclosure of Invention
In view of the practical limitation of single snapshot data and the practical requirement of estimation of the direction of arrival of the off-grid signal, the invention adopts any linear array, provides a method for estimating the direction of arrival of the single snapshot off-grid signal suitable for any linear array, and provides a key technology for estimating the direction of arrival of the signal under the practical limited condition. The random linear arrays comprise uniform linear arrays and non-uniform linear arrays.
The invention provides a single-snapshot off-grid signal direction-of-arrival estimation method suitable for any linear array. For the estimation of the direction of arrival of the single off-grid signal, the method comprises the following steps:
the method comprises the following steps: receiving single snapshot array element data, and obtaining an initial estimation value of a signal direction of arrival on a candidate grid by using a beam forming method according to the single snapshot array element data;
step two: obtaining a corresponding array guide vector according to the initial estimation value of the signal wave arrival direction;
step three: calculating an orthogonal subspace of a subspace spanned by the array guide vectors;
step four: performing feature decomposition on the orthogonal subspace to obtain a feature vector corresponding to the non-zero feature value;
step five: combining the array steering vector and the characteristic vector corresponding to the initial estimated value of the signal direction of arrival to form a new matrix FaUsing a matrix FaAnd correcting the initial estimation value of the signal direction of arrival by using the angle value of the deviation grid as an estimation parameter to obtain the final direction of arrival.
For the estimation of the direction of arrival of the multi-lattice signal, the method comprises the following steps:
the first step is as follows: assuming that there are K signals, K is greater than 2. Obtaining initial estimation values of the direction of arrival of each signal on the candidate grid by using a beam forming method according to the single snapshot array metadata;
the second step is that: estimating the signal amplitude by adopting a beam forming method according to the initial estimation value of the wave arrival direction of each signal and the single snapshot array element data to obtain the estimated amplitude of each signal;
the third step: multiplying array steering vectors corresponding to the initial estimation values of the wave directions of the first K-1 signals by the estimation amplitudes of the signals to obtain array element data of the first K-1 signals;
the fourth step: and subtracting the array element data of the first K-1 signals from the received single-snapshot array element data to obtain the array element data of the Kth signal, and obtaining the estimated value of the direction of arrival of the Kth signal by using a single off-grid signal direction of arrival estimation method.
The fifth step: estimating the amplitude of the Kth signal by adopting a beam forming method according to the estimated value of the direction of arrival of the Kth signal and the array element data of the Kth signal to obtain the estimated amplitude of the Kth signal;
and by analogy, obtaining the estimated values and the estimated amplitudes of the direction of arrival of the K signals, and correcting the angles and the amplitudes of all the signals in a zigzag three-time round-trip circulation manner.
The invention has the advantages that:
1. the method is suitable for estimating the direction of arrival of the single-snapshot off-grid signal of any linear array, can accurately estimate the off-grid signal by adopting any linear array under the condition of single-snapshot data, and provides a key technology for estimating the direction of arrival of the signal under the actual limited condition.
2. The method is suitable for estimating the direction of arrival of the single-snapshot off-grid signal of any linear array, and not only can obtain the accurate estimation of the direction of arrival of the single off-grid signal, but also can accurately estimate the direction of arrival of the multi-off-grid signal.
Drawings
Fig. 1A is a flowchart of a single-snapshot single-off-grid signal direction-of-arrival estimation method applicable to any linear array of the present invention.
FIG. 1B is a flow chart of a single-snapshot multi-lattice signal direction-of-arrival estimation method applicable to any linear array according to the present invention.
Fig. 2 is a schematic diagram of an 8-antenna uniform linear array.
Fig. 3 is a graph of the mean square error of a single off-grid signal with the variation of the signal-to-noise ratio under an 8-antenna uniform linear array.
Fig. 4 is a schematic diagram of a 32-antenna uniform linear array.
Fig. 5 is a graph of mean square error of three off-grid signals with signal-to-noise ratio variation under a 32-antenna uniform linear array.
Fig. 6 is a schematic diagram of an 8-antenna non-uniform line array.
Fig. 7 is a graph of the mean square error of a single off-grid signal with the variation of the signal-to-noise ratio under the non-uniform linear array of 8 antennas.
Fig. 8 is a schematic diagram of an uneven line array of 32 antennas.
Fig. 9 is a graph of the mean square error of three off-grid signals with the change of signal-to-noise ratio under the 32-antenna non-uniform linear array.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a single-snapshot off-grid signal direction-of-arrival estimation method suitable for any linear array, as shown in FIG. 1A, for single off-grid signal direction-of-arrival estimation, the specific steps are as follows:
the method comprises the steps of firstly, receiving single-snapshot array element data, and obtaining an initial estimation value of a signal direction of arrival on a candidate grid by utilizing a beam forming method according to the single-snapshot array element data.
Let the single snapshot array metadata be y ═ a (θ) s1+ n, θ is the angle of incidence of the signal, and the array steering vector a (θ) is
Wherein, c1,c2,...,cNRepresenting the position of N antenna elements, s1For a real valued deterministic signal, n is white gaussian noise. Obtaining x as Fy, F as M x N dimensional matrix, and array element (p, q) as F
1, N, M, q 1. The pth array element data of the single snapshot array element data adopting the beam forming method is as follows:
the position in x where the peak occurs is denoted as piniAnd obtaining an initial estimated value of the signal wave direction according to the peak position:
step two: obtaining a corresponding array steering vector according to the initial estimation value of the signal arrival direction:
step three: the orthogonal subspace of the subspace spanned by the array steering vectors is calculated:
i is an N × N dimensional identity matrix.
Step four: performing feature decomposition on the orthogonal subspace to obtain a feature vector a corresponding to N-1 non-zero feature values2,…,aN。
Step five: combining the array steering vector and the characteristic vector corresponding to the initial estimated value of the signal direction of arrival to form a new matrix Fa＝[a1,a2,…aN]Using a matrix FaAnd correcting the initial estimation value of the signal direction of arrival by taking the angle value eta of the deviation grid as an estimation parameter through the orthogonality of the medium array guide vector and the feature vector.
Define vector z ═ 1,0]T. The correction process is as follows:
Φ(η)y＝Faz (4)
wherein the correction matrix is
Assuming that the amplitude of the real-valued deterministic signal is 1, i.e. s1＝1。
In the noise-free case, equation (4) is written in matrix form:
taking the angle value eta of the deviation grid as an estimation parameter to carry out initial estimation on the signal direction of arrival thetainiAnd correcting to obtain a signal direction of arrival estimation value:
for the estimation of the direction of arrival of the multi-lattice signal, the specific steps are as follows:
the first step is as follows: and supposing that K signals are provided, and obtaining initial estimation values of the directions of arrival of the signals on the candidate grids by using a beam forming method according to the single snapshot array metadata.
The single-snapshot array element data is y ═ As + n, and the array manifold matrix A is As follows: a ═ a (θ)1),...a(θK)]Wherein θ ═ θ1,...,θK]For the incident angle of K signals, the array of the K signal is oriented to vector a (theta)k) Is composed of
c1,c2,...,cNRepresenting the position of N antenna elements, K x 1 dimensional real value deterministic signal s ═ s1,s2,...sK]And n is white gaussian noise. Obtaining x as Fy, F as M x N dimensional matrix, and array element (p, q) as F
1, N, M, q 1. The data of the p-th array element of the single snapshot array element data by adopting a beam forming method is as follows:
wherein s iskIs the amplitude of the kth signal.
The position of the occurrence of K peaks in x is denoted as
Obtaining K initial estimation values of signal wave directions according to the peak position:
the second step is that: estimating the signal amplitude by adopting a beam forming method according to the initial estimation value of the signal direction of arrival and the array element data to obtain the estimated amplitude:
the third step: multiplying array steering vectors corresponding to the initial estimation values of the wave directions of the first K-1 signals by the estimation amplitudes to obtain array element data of the first K-1 signals:
the fourth step: subtracting the array element data of the first K-1 signals from the received original array element data to obtain the array element data y of the K signalK＝y-y(K-1)And obtaining the estimated value of the direction of arrival of the Kth signal by using a single off-grid signal direction of arrival estimation method:
obtaining a corresponding array steering vector according to the initial estimation value of the direction of arrival of the Kth signal:
the orthogonal subspace of the subspace spanned by the array steering vectors is calculated:
i is an N × N dimensional identity matrix.
Feature decomposition is carried out on the orthogonal subspace to obtain feature vectors corresponding to N-1 non-zero feature values
Combining the array steering vector and the eigenvector corresponding to the K-th signal direction of arrival initial estimation value to form a new matrix
Using matrices
And correcting the initial estimation value of the signal direction of arrival by taking the angle value eta of the deviation grid as an estimation parameter according to the orthogonality of the medium array guide vector and the feature vector:
wherein the vector z is [1,0,.. 0, 0 ]]Τ. The correction matrix is
yKIs the array element data of the kth signal,
the array steering vector and the eigenvector for the kth signal are combined to form a new matrix.
In the noise-free case, equation (11) is written in matrix form:
the angle value eta of the deviation grid is used as an estimation parameter to carry out initial estimation on the signal direction of arrival
Correcting to obtain estimated value of direction of arrival of the Kth signal
The fifth step: according to the estimated value of the direction of arrival of the Kth signal and the array element data of the Kth signal, obtaining the estimated amplitude of the Kth signal by adopting a beam forming method:
therefore, estimated values and estimated amplitudes of the direction of arrival of the K signals are obtained, and the direction of arrival and the amplitude of all the signals are corrected in a zigzag form in a three-round-trip cycle.
Example (b):
in order to verify the correctness of the invention, relevant simulation experiments are carried out. As shown in figure 2, the position of an array element is half of the wavelength of an information source
Is a unit. The signal incidence angle is 30.5 deg., and the signal amplitude is 1. The fast beat number is 1. Mean square error was used as a metric:
the curve of the mean square error with the change of the signal-to-noise ratio is shown in fig. 3, and the simulation result is the statistical result of 200 monte carlo experiments. The result shows that under the condition that the signal-to-noise ratio is greater than 5dB, the mean square error approaches to the Clamei Lao bound, and the estimation precision is higher. As shown in FIG. 4, the position of an array element is half of the wavelength of an information source
Is a unit. The incidence angles of 3 incoherent signals are 30.5 degrees, 60.5 degrees, 80.5 degrees, and the signal amplitudes are all 1. The fast beat number is 1. The mean square error versus signal to noise ratio curve is shown in fig. 5. The simulation result is the statistical result of 200 Monte Carlo experiments. The result shows that under the condition that the signal-to-noise ratio is greater than 0dB, the mean square errors of the three signals approach the Claus Law bound, and the estimation precision is higher.
An inhomogeneous linear array adopting 8 antennas in a simulation experiment for estimating the direction of arrival of a single off-grid signal is shown in FIG. 6, and the position of an array element is half of the wavelength of an information source
Is a unit. Angle of incidence of signalThe degree is 30.5 deg., and the signal amplitude is 1. The fast beat number is 1. The curve of the mean square error with the change of the signal-to-noise ratio is shown in fig. 7, and the simulation result is the statistical result of 200 monte carlo experiments. The result shows that under the condition that the signal-to-noise ratio is greater than 5dB, the mean square error approaches to the Clamei Lao bound, and the estimation precision is higher. An inhomogeneous linear array adopting 32 antennas in a simulation experiment for estimating the direction of arrival of a multi-lattice signal is shown in FIG. 8, and the position of an array element is half of the wavelength of an information source
Is a unit. The incidence angles of 3 incoherent signals are 30.5 degrees, 60.5 degrees, 80.5 degrees, and the signal amplitudes are all 1. The fast beat number is 1. The mean square error versus signal to noise ratio curve is shown in fig. 9. The simulation result is the statistical result of 200 Monte Carlo experiments. The result shows that under the condition that the signal-to-noise ratio is greater than 0dB, the mean square errors of the three signals approach the Claus Law bound, and the estimation precision is higher.
According to the simulation chart, the method is suitable for any linear array. Even under the condition of less antenna array elements, the mean square error of the method provided by the invention can still approach the Claimei Lao bound, and the algorithm still has higher estimation precision. Meanwhile, the method provided by the invention can accurately estimate a single lattice separation signal or a multi-lattice separation signal, and has ideal estimation performance.
Claims (2)
1. A single-snapshot off-grid signal direction-of-arrival estimation method suitable for any linear array is characterized by comprising the following steps: including direction-of-arrival estimates for single off-grid signals and direction-of-arrival estimates for multi-off-grid signals; for the estimation of the direction of arrival of the single off-grid signal, the method comprises the following steps:
the method comprises the following steps: receiving single snapshot array element data, and obtaining an initial estimation value of a signal direction of arrival on a candidate grid by using a beam forming method according to the single snapshot array element data;
step two: obtaining a corresponding array guide vector according to the initial estimation value of the signal wave arrival direction;
step three: calculating an orthogonal subspace of a subspace spanned by the array guide vectors;
step four: performing feature decomposition on the orthogonal subspace to obtain a feature vector corresponding to the non-zero feature value;
step five: combining the array steering vector and the characteristic vector corresponding to the initial estimated value of the signal direction of arrival to form a new matrix FaUsing a matrix FaCorrecting the initial estimation value of the signal direction of arrival by using the angle value deviating from the grid as an estimation parameter to obtain the final direction of arrival;
for the estimation of the direction of arrival of the multi-lattice signal, the method comprises the following steps:
the first step is as follows: assuming that there are K signals, K is greater than 2; obtaining initial estimation values of the direction of arrival of each signal on the candidate grid by using a beam forming method according to the single snapshot array metadata;
the second step is that: estimating the signal amplitude by adopting a beam forming method according to the initial estimation value of the wave arrival direction of each signal and the single snapshot array element data to obtain the estimated amplitude of each signal;
the third step: multiplying array steering vectors corresponding to the initial estimation values of the wave directions of the first K-1 signals by the estimation amplitudes of the signals to obtain array element data of the first K-1 signals;
the fourth step: subtracting the array element data of the first K-1 signals from the received single-snapshot array element data to obtain the array element data of the Kth signal, and obtaining the estimated value of the direction of arrival of the Kth signal by using the single off-grid signal direction of arrival estimation method;
the fifth step: estimating the amplitude of the Kth signal by adopting a beam forming method according to the estimated value of the direction of arrival of the Kth signal and the array element data of the Kth signal to obtain the estimated amplitude of the Kth signal;
therefore, estimated values and estimated amplitudes of the direction of arrival of the K signals are obtained, and the angles and amplitudes of all the signals are corrected in a zigzag form in a three-round-trip cycle.
2. The method according to claim 1, wherein the method for estimating the direction of arrival of the single snap off-grid signal applied to any linear array comprises: the correction in the fifth step is specifically carried out by,
define vector z ═ 1,0]T：
Φ(η)y＝Faz (4)
Wherein the correction matrix is
c1,c2,...,cNRepresenting the position of N antenna elements, assuming that the amplitude of the real-valued deterministic signal is 1, i.e. s11 is ═ 1; in the noise-free case, equation (4) is written in matrix form:
taking the angle value eta of the deviation grid as an estimation parameter to carry out initial estimation on the signal direction of arrival thetainiAnd correcting to obtain a signal direction of arrival estimation value:
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