CN103926555B - A kind of method that utilization not rounded signal measuring antenna array receiver machine width is mutually responded - Google Patents
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Abstract
There is width phase response error in the antenna array receiver signal model used for antenna array signals Processing Algorithm in practical application by the present invention, in the case of not rounded signal known to two or more directions and the unknown signal in direction are simultaneous, not rounded signal is used as calibration source, the width for estimating aerial array using the orthogonality relation between the noise subspace of sample autocorrelation matrix and the propagation direction vector of not rounded signal of the spread vector of the received signal vector of aerial array is mutually responded, so as to be embodied as Mutual coupling, the used antenna array receiver signal model of the antenna array signals such as Wave beam forming process provides the purpose that accurate receiver width mutually responds estimation.
Description
Technical Field
The invention belongs to a method for measuring the amplitude-phase response of an antenna array receiver in the technical field of electronic information, in particular to a method for measuring the amplitude-phase response of the antenna array receiver by using the non-circular characteristic of signals under the condition that two or more non-circular signals with known directions and signals with unknown directions exist simultaneously.
Background
The technology of receiving signals by using an antenna array to acquire and detect information is widely applied to the fields of modern electronic reconnaissance, radar, communication, sonar, earthquake, radio astronomy and the like. Antenna array signal processing algorithms generally assume that model parameters such as antenna positions, amplitude responses and phase responses (amplitude-phase responses for short) of receivers in an antenna array received signal model are accurately known. However, various errors are inevitable in the current processing technology level and practical engineering application, and array element position errors and receiver amplitude-phase response errors occur in an antenna array receiving signal model used by an antenna array signal processing algorithm due to the environmental temperature, humidity, vibration of an antenna array platform, aging of active devices and the like. If these error factors are not considered in the antenna array received signal model used by the antenna array signal processing algorithm, the antenna array signal processing algorithm will suffer from severe performance degradation and even failure. Because the error in the antenna array received signal model used by the antenna array signal processing algorithm is a bottleneck in the practical application of the antenna array signal processing technology with high precision and high resolution, estimating the error in the antenna array received signal model has important practical value and is one of the keys in the practical application of the antenna array signal processing technology engineering.
An error estimation technology in an antenna array received signal model is developed along with an antenna array signal processing technology, and a common error estimation method in the antenna array received signal model is realized by directly measuring an antenna array direction vector in a specific direction, and the direction of an auxiliary signal needs to be accurately known. Due to physical changes of an application environment or maintenance and replacement of each antenna and a receiver of the antenna array, and the like, the actual amplitude-phase response in the antenna array received signal model also changes correspondingly, and if re-estimation is not performed, an amplitude-phase response error always exists in the antenna array received signal model used by the antenna array signal processing algorithm, and the situation that the performance of the antenna array signal processing algorithm is seriously deteriorated or even fails cannot be avoided.
If the actual amplitude-phase response in the antenna array received signal model can be estimated in real time while the antenna array signal processing is carried out, the method can be used for eliminating the amplitude-phase response error in the antenna array received signal model used by the antenna array signal processing algorithm, and the antenna array signal processing algorithm is prevented from seriously deteriorating the performance and even failing.
Disclosure of Invention
In order to estimate the actual amplitude-phase response in an antenna array received signal model in real time while performing antenna array signal processing, the invention firstly establishes an extension vector and an extension direction vector of a received signal vector of an antenna array by using the non-circular characteristic of a signal, and then estimates the receiver amplitude-phase response of the antenna array by using the orthogonal relation between a noise subspace of a sample autocorrelation matrix of the extension vector of the antenna array received signal and the extension direction vector of the non-circular signal, thereby realizing the purpose of providing accurate receiver amplitude-phase response estimation for the antenna array received signal model used for antenna array signal processing such as direction-of-arrival estimation, beam forming and the like.
The received signal vector of the antenna array employed in the present invention is generally expressed as:
wherein x (t) is the receiving signal vector of the antenna array, the vector dimension is equal to the number M of the antennas of the antenna array, t is the sampling time, sk(t)、φk、θkAnd a (theta)k) A real transmission signal representing the k-th non-circular signal, a phase angle, a direction with respect to the antenna array and a direction thetakDirection vector, s, of corresponding antenna arrayk(t) is the non-circular nature of the signal that is to be used in the present invention, K is 1,2, …, K is the number of non-circular signals, v (t) is the receiver noise vector of the antenna array, ∑ represents the summation, G is a diagonal matrix whose mth diagonal element G (M, M) represents the amplitude-phase response of the mth array element receiver, and G is equal to the identity matrix of order M without error.
The extension vector of the receiving signal vector of the antenna array established by the method is
Wherein,representing the conjugate transpose of a vector or matrix,representing a transpose of a vector or matrix. Correspondingly, the method of the invention establishes an expanding direction vector of the non-circular signal as
Wherein phi isk、θkAnd a (theta)k) Respectively representing the phase angle, direction relative to the antenna array and direction theta of the k-th non-circular signalkThe direction vector of the corresponding antenna array, K is 1, 2.
The sample autocorrelation matrix of the spread vector of the received signal vector of the antenna array is
Where t is the sampling time, and t is 1,2, …, and P indicates the number of received signal vectors of the antenna array corresponding to the number of sampling times.
The method of the invention utilizes the eigenvalue decomposition of the sample autocorrelation matrix as:
where the matrix Λ is a diagonal matrix, the elements on the diagonal are sample autocorrelationsIn descending order, i.e. λ1≥λ2＞λ3≥…≥λ2MThe matrix U is formed by an autocorrelation matrixCharacteristic vector u of1,u2,u3,…,u2MFormed matrix, one-to-one correspondence with eigenvalues, UHRepresenting the conjugate transpose of the matrix U.
Sample-taking autocorrelation matrixThe noise subspace of (c) is:
Q＝[uK+1uK+2… u2M]
wherein K is the number of signals, the number K of non-circular signals can be determined by adopting a common large eigenvalue judgment method in the background technology, and M is the antenna arrayNumber of antennas in a column. If the receiver noise is not considered, the expansion direction vector b (theta) of the noise subspace and the non-circular signal of the sample autocorrelation matrix can be known from the formula (1)k) There is an orthogonal relationship between:
QHb(θk)＝0，k＝1,2,…,K
the above orthogonal relationship holds approximately even in the presence of noise. Assuming the 1 st and 2 nd signals are non-circular signals with known directions, there are:
wherein Q1And Q2Representing the matrix consisting of the top M row vectors and the bottom M row vectors of the matrix Q, respectively. Note that, here, the case of two non-circular signals is merely described as an example, and the method of the present invention can be similarly applied to the case where the number of non-circular signals is greater than 2.
Is obtained from the formulae (3) and (4)
WhereingIs an M-th order vector, the M-th element is equal to the amplitude-phase response of the M-th array element receiver,representing the operation of converting a vector into a diagonal matrix. Combining the two formulas together to obtain
Thus, the vector g is the eigenvector corresponding to eigenvalue of matrix D equal to 1. Therefore, the vector g can be determined by calculating the eigenvector corresponding to the eigenvalue of the matrix D equal to 1, and the estimation of the antenna array amplitude-phase response is obtained.
The invention firstly establishes the extension vector of the receiving signal vector of the antenna array by utilizing the non-circular characteristic of the signal, and then estimates the receiver amplitude-phase response of the antenna array by utilizing the orthogonal relation between the noise subspace of the sample autocorrelation matrix of the extension vector of the receiving signal of the antenna array and the extension direction vector of the non-circular signal, thereby realizing the purpose of providing accurate receiver amplitude-phase response estimation for an antenna array receiving signal model used for antenna array signal processing such as direction of arrival estimation, beam forming and the like. The method comprises the following steps:
step 1, initialization processing: initializing and storing the number (marked as M) of the antennas of the antenna array and the number (marked as P) of the received signal vectors of the antenna array into a memory;
step 2, determining a sample autocorrelation matrix of an expansion vector of a received signal vector of the antenna array: firstly, processing by a conventional method to determine a received signal vector of the antenna array, secondly, generating an expansion vector of the received signal vector of the antenna array by the received signal vector of the antenna array, and then determining a sample autocorrelation matrix of the expansion vector of the received signal vector of the antenna array;
step 3, determining a noise subspace of the sample autocorrelation matrix: performing eigenvalue decomposition on the sample autocorrelation matrix to determine a noise subspace of the sample autocorrelation matrix;
and 4, step 4: determining an estimate of the antenna array amplitude-phase response: and determining the amplitude-phase response estimation of the antenna array by utilizing the orthogonal relation between the noise subspace of the sample autocorrelation matrix and the expansion direction vector of the non-circular signal.
In step 2, the vector of the received signal of the antenna array is obtained through conventional processing, and the processing method is an I/Q dual-channel receiving method or a hilbert transform processing method.
The samples of the received signal vector of the antenna array in step 2 are typically expressed as:
x(t)＝[x1(t) x2(t) … xM(t)]T
where x (t) is the signal vector received by the antenna array, the vector dimension is equal to the number M of antennas of the antenna array, t is the sampling time, t is 1,2, …, P represents the number of the received signal vectors of the antenna array corresponding to the number of sampling times, x (t) is the number of the received signal vectors of the antenna array corresponding to the number of sampling times, andm(t) denotes the mth element of the received signal vector x (t) of the antenna array, M being 1,2, …, M,representing a transpose of a matrix or vector.
In step 2, the generating of the spread vector from the received signal vector of the antenna array is:
wherein, the vector x*(t) denotes the conjugate of the vector x (t).
In step 2, the sample autocorrelation matrix of the spreading vector of the received signal vector of the antenna array is determined as follows:
wherein,a sample autocorrelation matrix representing the spread vector, t being the sampling instants at which one received signal vector is sampled, t being 1,2, …, P representing the number of received signal vectors of the antenna array corresponding to the number of sampling instants,representing the conjugate transpose of a vector or matrix.
In step 3, the eigenvalue decomposition is performed on the sample autocorrelation matrix of the extended vector, and the eigenvalue decomposition of the sample autocorrelation matrix of the extended vector is as follows:
wherein the matrix Λ is a diagonal matrix, and the elements in the diagonal direction respectively correspond to the sample autocorrelation matrix of the spread vectorIn descending order, i.e. λ1≥λ2＞λ3≥…≥λ2MThe matrix U is a sample autocorrelation matrix of the spread vectorCharacteristic vector u of1,u2,u3,…,u2MThe formed matrix is in one-to-one correspondence with the characteristic values,represents a conjugate transpose of a vector or matrix; in step 3, determining a noise subspace of the sample autocorrelation matrix of the extended vector, where the noise subspace of the sample autocorrelation matrix of the extended vector is: q ═ u [ u ]K+1uK+2… u2M]The number K of the non-circular signals can be determined by a large eigenvalue determination method commonly used in the background art, and M is the number of antennas of the antenna array.
In step 4, the orthogonal relationship between the noise subspace of the sample autocorrelation matrix using the spread vector and the spread direction vector of the non-circular signal is:
wherein phik、θkAnd a (theta)k) Respectively representing the phase angle, direction relative to the antenna array and direction theta of the k-th non-circular signalkAnd the corresponding antenna array direction vector, K is 1,2, …, K is the number of non-circular signals, G is a diagonal matrix, and the mth diagonal element G (m, m) of the diagonal matrix represents the amplitude-phase response of the mth array element receiver.
In step 4, the determining of the estimation of the antenna array amplitude-phase response is to perform eigen decomposition on the matrix D, and then select an eigenvector corresponding to an eigenvalue closest to 1 in the eigenvalues of the matrix D as the estimation of the antenna array amplitude-phase response, where the matrix D is formed by the noise subspace Q of the sample autocorrelation matrix and the direction vector a (θ) of the known non-circular signal1) And a (theta)2) Determined from an orthogonal relationship, i.e.
D＝1/2(B1+B2)
Wherein
Q1And Q2Representing the matrix consisting of the top M row vectors and the bottom M row vectors of the matrix Q, respectively.
Aiming at the problem that amplitude-phase response errors always exist in an antenna array received signal model used by an antenna array signal processing algorithm in practical application, the invention uses a non-circular signal as a correction source, and estimates the amplitude-phase response of an antenna array by utilizing the orthogonal relation between the noise subspace of a sample autocorrelation matrix of an expansion vector of a received signal vector of the antenna array and the expansion direction vector of the non-circular signal, thereby realizing the purpose of providing accurate receiver amplitude-phase response estimation for the antenna array received signal model used for antenna array signal processing such as direction-of-arrival estimation, beam forming and the like. Through correlation test, the correlation coefficients between the measured antenna array amplitude-phase response and the actual antenna array amplitude-phase response are all larger than 0.99 under the condition that 2 non-circular signals and 1 direction unknown signal coexist by adopting the mode of the specific embodiment of the invention. Therefore, the method can effectively estimate the amplitude-phase response of the antenna array and is easy to implement.
Detailed Description
In the present embodiment, a uniform linear array with a radius of 0.5 times a wavelength and 10 antennas is taken as an example, that is, M is 10; in this example, 3 non-circular signals are set to have incoming wave directions of θ11 degree of ═ 18.1,. theta28.4 degrees and θ3The signal-to-noise ratio is 9.0dB at 20.5 degrees, the 1 st and 2 nd signals are correction sources, and the incidence angle of the 3 rd signal needs to be estimated; the snapshot number of the received signal vector of the antenna array is equal to 64, i.e., P is 64. Is unknown. The invention is implemented with the aim of estimating the amplitude-phase response of the antenna array with the direction of incidence of the correction signal known. The vector g embodying the amplitude-phase response of the antenna array is set as:
1.0000
0.3928-0.9402i
0.2626-0.8159i
-0.4790+0.9011i
-0.6008-0.7515i
0.8469-0.0840i
-0.0789+0.8851i
0.0482-0.9431i
-0.6829-0.7706i
0.3302-0.9769i
the flow of the specific embodiment of the invention is as follows:
step 1, initialization processing: initializing and storing the number (10) of antennas of the receiving antenna array and the number (64) of received signal vectors of the antenna array into a memory;
step 2, establishing a sample autocorrelation matrix of an expansion vector of a received signal vector of the antenna array: firstly, determining a received signal vector x (t) of an antenna array by using an I/Q dual-channel receiving method commonly used in the art, wherein t is a sampling time, and each sampling time samples one received signal vector, and in the embodiment, t is 1,2, …, and 64; then, an expansion vector is generated from the received signal vector of the antenna array Represents a conjugate transpose of a matrix or vector; thereby establishing a sample autocorrelation matrix of the received signal vector of the antenna array:whereinRepresenting a sample autocorrelation matrix, sigma representing a summation, t being a sampling instant,represents a conjugate transpose of a vector or matrix;
and 3, carrying out singular value decomposition on the sample autocorrelation matrix, determining a noise subspace Q of the sample autocorrelation matrix, wherein the matrixes formed by the upper M row vectors and the lower M row vectors of Q are respectively Q1And Q2The matrix Q1The respective column vectors of (a) are:
1 st to 5 th column vectors:
6 th to 10 th column vectors:
column 11-15 vectors:
16 th to 17 th column vectors:
matrix Q2The respective column vectors of (a) are:
1 st to 5 th column vectors:
6 th to 10 th column vectors:
column 11-15 vectors:
16 th to 17 th column vectors:
and 4, step 4: determining an estimate of the amplitude-phase response of the antenna array, and using Q according to the orthogonal relationship1、Q2And the direction vector a (theta) of the known non-circular signal1) And a (theta)2) Constructing a matrix D:
D＝1/2(B1+B2)
wherein
Decomposing the eigenvalues of the matrix D, and selecting the estimation that the eigenvector corresponding to the eigenvalue closest to 1 in the eigenvalues of the matrix D is g
1.0000
0.3271-0.8658i
0.1871-0.4952i
-0.5197+0.9280i
-0.6750-0.6636i
0.7929-0.0598i
-0.1125+0.7614i
-0.0602-0.8746i
-0.7960-0.7246i
0.3778-0.9628i
Defining the correlation coefficient as:whereinRepresenting the conjugate transpose of the vector or matrix, | | | represents the absolute value; the closer the correlation coefficient is to 1, the estimated antenna array amplitude-phase response vector is shownThe closer to the actual vector g.
Antenna array amplitude-phase response vector estimated by adopting specific embodiment mode of the invention under the condition that 2 non-circular correction signals and 1 direction unknown signal coexistThe correlation coefficient with the actual antenna array magnitude-phase response vector g is 0.9909.
Claims (1)
1. A method for determining an amplitude-phase response of an antenna array receiver using a non-circular signal, comprising:
step 1, initialization processing: initializing the number of antennas of the antenna array and the number of received signal vectors of the antenna array and storing the initialized number into a memory;
step 2, determining a sample autocorrelation matrix of an expansion vector of a received signal vector of the antenna array: firstly, processing by a conventional method to determine a received signal vector of the antenna array, secondly, generating an expansion vector of the received signal vector of the antenna array by the received signal vector of the antenna array, and then determining a sample autocorrelation matrix of the expansion vector of the received signal vector of the antenna array;
the received signal vector of the antenna array is determined by processing with a conventional method, wherein the processing method is an I/Q dual-channel receiving method or a Hilbert transform processing method, and the determined received signal vector of the antenna array is as follows:
x(t)＝[x1(t) x2(t) … xM(t)]T
where x (t) is the received signal vector of the antenna array, the vector dimension is equal to the number M of antennas of the antenna array, t is the sampling time, t is 1,2, …, P represents the number of received signal vectors of the antenna array corresponding to the number of sampling times, x (t) is the number of received signal vectors of the antenna array, and1(t),x2(t),…,xM(t) denotes the 1 st, 2 nd, M th elements of the received signal vector x (t) of the antenna array,represents a transpose of a matrix or vector;
generating an extension vector of the received signal vector of the antenna array from the received signal vector of the antenna array is:
wherein, the vector x*(t) denotes the conjugate of the vector x (t), x (t) being the received signal vector of the antenna array;
determining a sample autocorrelation matrix of an extension vector of a received signal vector of an antenna array as:
wherein,a sample autocorrelation matrix representing an expansion vector, one received signal vector sampled at each sampling instant,represents a conjugate transpose of a vector or matrix;
step 3, determining a noise subspace of a sample autocorrelation matrix of the expansion vector: sample autocorrelation matrix for extended vectorsPerforming eigenvalue decomposition to determine sample autocorrelation matrix of expansion vectorThe noise subspace of (1);
sample autocorrelation matrix of extended vectorThe eigenvalues of (d) are decomposed into:
wherein the matrix Λ is a diagonal matrix, and the elements in the diagonal direction respectively correspond to the sample autocorrelation matrix of the spread vectorIn descending order, i.e. λ1≥λ2＞λ3≥…≥λ2MThe matrix U is a sample autocorrelation matrix of the spread vectorCharacteristic vector u of1,u2,u3,…,u2MThe formed matrix is in one-to-one correspondence with the characteristic values,represents a conjugate transpose of a vector or matrix;
determining a noise subspace of a sample autocorrelation matrix of the spread vector as: q ═ u [ u ]K+1uK+2… u2M]Determining the number K of the non-circular signals by adopting a large characteristic value determination method, wherein K is the number of the non-circular signals, and M is the number of antennas of the antenna array;
and 4, determining the estimation of the antenna array amplitude-phase response: determining the estimation of the antenna array amplitude-phase response by utilizing the orthogonal relation between the noise subspace of the sample autocorrelation matrix of the expansion vector and the expansion direction vector of the non-circular signal;
the direction vector of the expansion of the non-circular signal is
Wherein phi isk、θkAnd a (theta)k) Respectively representing the phase angle, direction relative to the antenna array and direction theta of the k-th non-circular signalkA direction vector of a corresponding antenna array, wherein K is 1,2, …, K is the number of non-circular signals, G is a diagonal matrix, and the mth diagonal element G (m, m) of the diagonal matrix represents the amplitude-phase response of the mth array element receiver;
sample autocorrelation matrix of extended vectorIs the noise subspace and the expansion direction vector b (theta) of the non-circular signalk) There exists an orthogonal relationship between them, the orthogonal relationship is:
QHb(θk)＝0，
sample autocorrelation matrix where Q is an extended vectorK 1,2, …K, K is the number of non-circular signals;
assuming the 1 st and 2 nd signals are non-circular signals with known directions, there are:
wherein Q1And Q2Respectively representing the top M row vectors and the bottom M row vectors of the matrix QA composed matrix of phik、θkAnd a (theta)k) Respectively representing the phase angle, direction relative to the antenna array and direction theta of the k-th non-circular signalkThe direction vector of the corresponding antenna array, k is 1, 2;
determining an estimate of the antenna array amplitude-phase response: from the orthogonal relationship, using Q1、Q2And the direction vector a (theta) of the known non-circular signal1) And a (theta)2) Constructing a matrix D:
D＝1/2(B1+B2)
wherein
Decomposing the eigenvalue of the matrix D, and selecting the eigenvector corresponding to the eigenvalue closest to 1 in the eigenvalues of the matrix D as the estimated antenna array amplitude-phase response vector g of the actual antenna array amplitude-phase response vector g
Defining the correlation coefficient as:
| | represents taking an absolute value; the closer the correlation coefficient is to 1, the estimated antenna array amplitude-phase response vector is shownThe closer to the actual antenna array magnitude-phase response vector g.
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| CN106405485B (en) * | 2016-09-30 | 2019-01-01 | 电子科技大学 | A kind of aerial array amplitude and phase error correction method of calibration source Location-Unknown |
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| CN108490383A (en) * | 2018-03-07 | 2018-09-04 | 大连理工大学 | A kind of not rounded method for estimating signal wave direction based on bounded nonlinear cointegration variance |
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