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 the assay method that the antenna array receiver machine width in electronic information technical field is mutually responded, particularly
Using signal in the case of not rounded signal known to two or more directions and the unknown signal in direction are simultaneous
The method that mutually responds of not rounded characteristic measurement antenna array receiver machine width.
Background technology
Using antenna array receiver signal carry out acquisition of information with detection technology be widely used to hyundai electronicses scout,
The numerous areas such as radar, communication, sonar, earthquake, radio astronomy.Antenna array signals Processing Algorithm is typically assumed that and to be used
Each aerial position, the amplitude of each receiver and the models such as phase response (abbreviation width is mutually responded) in antenna array receiver signal model
Parameter is that accurately oneself knows.However, various errors are inevitable in the engineer applied of current processing technique level and reality,
The temperature of environment, humidity, the vibrations of aerial array platform, aging etc. can all the causing of active device adjust at antenna array signals
Occur sensor position uncertainties, receiver width phase response error in the antenna array receiver signal model used by method.If in antenna
These error components, antenna array signals are not considered in the antenna array receiver signal model used by Array Signal Processing algorithm
Processing Algorithm will appear from the situation that performance severe exacerbation even fails.Due to the antenna used by antenna array signals Processing Algorithm
Error in array received signal model be high accuracy, high-resolution antenna array signals treatment technology move towards practical one
Individual bottleneck, therefore, estimates that the error in antenna array receiver signal model has important practical value, is antenna array signals
One of key for the treatment of technology practical application.
Error estimation technology in antenna array receiver signal model be accompanied by antenna array signals treatment technology while
Development, the error estimation in common antenna array receiver signal model is by the aerial array side to specific direction
Directly measure to realize to vector, need the direction of accurately known auxiliary signal.Physical change due to applied environment
Or the maintenance of aerial array each antenna, receiver such as changes at the reason, the actual web in antenna array receiver signal model is mutually rung
Also respective change should occurs, if not reevaluated, the aerial array used by antenna array signals Processing Algorithm connects
Receive in signal model and there is width phase response error all the time, being still unavoidable from antenna array signals Processing Algorithm, performance occur serious
Deteriorate the situation of even failure.
If carrying out to estimate the reality in antenna array receiver signal model while antenna array signals are processed in real time
Border width is mutually responded, then can be used for offseting presence in the antenna array receiver signal model used by antenna array signals Processing Algorithm
Width phase response error, it is to avoid there is the situation that performance severe exacerbation even fails in antenna array signals Processing Algorithm.
Content of the invention
In order to carry out to estimate in real time in antenna array receiver signal model while antenna array signals are processed
Actual web is mutually responded, and the not rounded characteristic first with signal of the invention sets up the spread vector of the received signal vector of aerial array
With propagation direction vector, recycle antenna array receiver signal spread vector sample autocorrelation matrix noise subspace with
Orthogonality relation between the propagation direction vector of not rounded signal estimates that the receiver width of aerial array is mutually responded, so as to be embodied as ripple
Used antenna array receiver signal model offer is processed up to antenna array signals such as direction estimation, Wave beam formings accurately to connect
Receipts machine width mutually responds the purpose of estimation.
The received signal vector of the aerial array that the present invention is adopted is typically expressed as：
Received signal vectors of the wherein x (t) for aerial array, vector dimension are equal to antenna number M of aerial array, and t is
Sampling instant, sk(t)、φk、θkWith a (θk) represent respectively the real number transmission signal of k-th not rounded signal, phase angle, relative to
The direction of aerial array and direction θkThe direction vector of corresponding aerial array, skT () is real number rather than plural number is exactly the present invention
The not rounded characteristic of signal to be utilized, the number of k=1,2 ..., K, K for not rounded signal, v (t) are made an uproar for the receiver of aerial array
Sound vector, ∑ represent summation, and G is a diagonal matrix, and its m-th diagonal element G (m, m) represents m-th array element receiver
Width is mutually responded, and in the case of free from error, G is equal to the unit matrix of M ranks.
The spread vector of received signal vector of the aerial array that the inventive method is set up is
Wherein,The conjugate transpose of vector or matrix is represented,Represent the transposition of vector or matrix.Accordingly, the present invention
The propagation direction vector of not rounded signal that method is set up is
Wherein, φk、θkWith a (θk) represent respectively the phase angle of k-th not rounded signal, the direction relative to aerial array and
Direction θkThe direction vector of corresponding aerial array, k=1,2 ..., K, K for not rounded signal number.
The sample autocorrelation matrix of the spread vector of the received signal vector of aerial array is
Wherein t is sampling instant, and t=1,2 ..., P, P represent the reception signal of aerial array corresponding with sampling instant number
The number of vector.
The Eigenvalues Decomposition of the sample autocorrelation matrix that the inventive method is utilized is：
Wherein matrix Λ is diagonal matrix, and the element on diagonal is sample auto-correlationEigenvalue, arrange in descending order
That is λ1≥λ2＞ λ3≥…≥λ2M, matrix U is by autocorrelation matrixCharacteristic vector u1,u2,u3,…,u2MThe matrix of composition, with
Eigenvalue is corresponded, UHThe conjugate transpose of representing matrix U.
Note sample autocorrelation matrixNoise subspace be：
Q=[uK+1uK+2… u2M]
Using the big eigenvalue decision method that commonly uses in background technology, numbers of the wherein K for signal, can determine that not rounded is believed
Number number K, M for aerial array antenna number.If not considering receiver noise, sample autocorrelation matrix is understood by formula (1)
Noise subspace and not rounded signal propagation direction vector b (θk) between there is orthogonality relation：
QHb(θk)=0, k=1,2 ..., K
Even if there is noise, above-mentioned orthogonality relation is also approximately set up.Assume that the 1st and the 2nd signal is non-known to direction
Circle signal, then have：
Wherein Q1And Q2The matrix that matrix Q above M row vector and following M row vector be made up of is represented respectively.Note, this
In simply illustrated in case of two not rounded signals, the inventive method can be equally used for not rounded signal number and be more than
2 situation.
By formula (3) and formula (4) Shi Ke get
WhereingIt is that M ranks are vectorial, m-th element is mutually responded equal to the width of m-th array element receiver,Represent one
Vector is converted to the operation of diagonal matrix.Above-mentioned two formula is united, is obtained
Therefore, characteristic vectors of the vectorial g corresponding to the eigenvalue equal to 1 of matrix D.Therefore, it can by calculating square
The mode of the characteristic vector corresponding to the eigenvalue equal to 1 of battle array D determines vectorial g, and then obtains what aerial array width was mutually responded
Estimate.
Not rounded characteristic first with signal of the invention sets up the spread vector of the received signal vector of aerial array, then profit
Propagation direction with the noise subspace and not rounded signal of the sample autocorrelation matrix of the spread vector of antenna array receiver signal
Orthogonality relation between vector estimates that the receiver width of aerial array is mutually responded, so as to be embodied as Mutual coupling, wave beam shape
Into etc. antenna array signals process used antenna array receiver signal model accurate receiver width be provided and mutually respond estimation
Purpose.The inventive method is comprised the following steps：
Step 1. initialization process：By the antenna number (being designated as M) of aerial array, the received signal vector of aerial array
Number (being designated as P) initialization is stored in internal memory；
Step 2. determines the sample autocorrelation matrix of the spread vector of the received signal vector of aerial array：Often first pass around
Secondly the process of rule method generates antenna array by the received signal vector of aerial array to determine the received signal vector of aerial array
The spread vector of the received signal vector of row, it is then determined that the sample of the spread vector of the received signal vector of aerial array is from phase
Close matrix；
Step 3. determines the noise subspace of sample autocorrelation matrix：Eigenvalues Decomposition is carried out to sample autocorrelation matrix,
Determine the noise subspace of sample autocorrelation matrix；
Step 4：Determine the estimation that aerial array width is mutually responded：Noise subspace and not rounded using sample autocorrelation matrix
Orthogonality relation between the propagation direction vector of signal, determines that aerial array width mutually responds estimation.
In step 2 described through conventional method process obtaining the received signal vector of aerial array, its processing method
For I/Q dual-channel connections receiving method or Hilbert transform processing method.
The sample of the received signal vector of the aerial array is typically expressed as in step 2：
X (t)=[x1(t) x2(t) … xM(t)]T
Signal vectors of the wherein x (t) for antenna array receiver, vector dimension are equal to antenna number M of aerial array, and t is
Sampling instant, t=1,2 ..., P, P represent the number of the received signal vector of aerial array corresponding with sampling instant number, xm
M-th element of received signal vector x (t) of (t) expression aerial array, m=1,2 ..., M,Representing matrix or vector
Transposition.
The received signal vector by aerial array generates spread vector and is in step 2：
Wherein, vector x*T () represents the conjugation of vector x (t).
The sample autocorrelation matrix of the spread vector of the received signal vector for determining aerial array is in step 2：
Wherein,The sample autocorrelation matrix of spread vector is represented, t is sampling instant, and each sampling instant is connect to one
Signal vector sampling is received, t=1,2 ..., P, P represent the individual of the received signal vector of aerial array corresponding with sampling instant number
Number,Represent the conjugate transpose of vector or matrix.
The sample autocorrelation matrix to spread vector carries out Eigenvalues Decomposition, the sample of spread vector in step 3
The Eigenvalues Decomposition of autocorrelation matrix is：
Wherein matrix Λ is diagonal matrix, and diagonally element upwards corresponds to the sample autocorrelation matrix of spread vector respectively
Eigenvalue, arrangement in descending order is λ1≥λ2＞ λ3≥…≥λ2M, matrix U is by the sample autocorrelation matrix of spread vector's
Characteristic vector u1,u2,u3,…,u2MThe matrix of composition, is corresponded with eigenvalue,Represent the conjugate transpose of vector or matrix；
In step 3 described determine spread vector sample autocorrelation matrix noise subspace, the sample auto-correlation square of spread vector
Battle array noise subspace be：Q=[uK+1uK+2… u2M], numbers of the wherein K for not rounded signal can be adopted in background technology
Conventional big eigenvalue decision method determines number K of not rounded signal, antenna numbers of the M for aerial array.
The extension of the noise subspace of the sample autocorrelation matrix of the utilization spread vector and not rounded signal in step 4
Orthogonality relation between direction vector, the orthogonality relation is：
Wherein φk、θkWith a (θk) represent respectively the phase angle of k-th not rounded signal, the direction relative to aerial array and
Direction θkCorresponding direction vector of antenna array, the number of k=1,2 ..., K, K for not rounded signal, G are a diagonal matrix, its
M-th diagonal element G (m, m) represents that the width of m-th array element receiver is mutually responded.
The estimation for determining that aerial array width is mutually responded, is exactly first to carry out feature decomposition to matrix D, so in step 4
Afterwards in the eigenvalue of selection matrix D closest to 1 eigenvalue corresponding to characteristic vector be the estimation that mutually responds of aerial array width,
Wherein, matrix D by sample autocorrelation matrix noise subspace Q and known not rounded signal direction vector a (θ1) and a (θ2) root
Determine according to orthogonality relation, i.e.,
D=1/2 (B1+B2)
Wherein
Q1And Q2The matrix that matrix Q above M row vector and following M row vector be made up of is represented respectively.
The antenna array receiver signal model used for antenna array signals Processing Algorithm in practical application by the present invention
In there is width phase response error all the time, use not rounded signal as calibration source, using aerial array reception signal to
Orthogonal pass between the noise subspace of the sample autocorrelation matrix of the spread vector of amount and the propagation direction vector of not rounded signal
System estimating that the width of aerial array is mutually responded, so as to realize so as to being embodied as the aerial arrays such as Mutual coupling, Wave beam forming
The antenna array receiver signal model used by signal processing provides the purpose that accurate receiver width mutually responds estimation.Through correlation
Property inspection, using instantiation mode of the present invention in the case of 2 not rounded signals and 1 unknown signal in direction are simultaneous
The aerial array width of measure is mutually responded and is both greater than 0.99 with the correlation coefficient between actual antennas array width is mutually responded.Thus this
Bright method can effectively estimate that the width of aerial array is mutually responded, and easy to implement.
Specific embodiment
Present embodiment by radius be 0.5 times of wavelength, as a example by the even linear array of 10 antennas composition, i.e. M=10；In this example
The arrival bearing for arranging 3 not rounded signals is respectively θ1=-18.1 degree, θ2=8.4 degree and θ3=20.5 degree, signal to noise ratio is all
9.0dB, the 1st, 2 signals are calibration source, and the angle of incidence of the 3rd signal needs to estimate；The received signal vector of aerial array
Fast umber of beats is equal to 64, i.e. P=64.Unknown.It is exactly in the case of known to correction signal incident direction to implement the purpose of the present invention
Estimate that the width of aerial array is mutually responded.The vectorial g that embodiment aerial array width is mutually responded is set to：
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 process of the specific embodiment of the present invention is as follows：
Step 1. initialization process：By the antenna number (10) of receiving antenna array, the received signal vector of aerial array
Number (64) initialization be stored in internal memory；
Step 2. sets up the sample autocorrelation matrix of the spread vector of the received signal vector of aerial array：Initially with this
The conventional I/Q dual-channel connection receiving methods in field determine received signal vector x (t) of aerial array, and t is sampling instant, each adopt
The sample moment samples to a received signal vector, in the present embodiment t=1, and 2 ..., 64；Then by the reception of aerial array
Signal vector generates spread vector Representing matrix or the conjugate transpose of vector；Thus antenna array is set up
The sample autocorrelation matrix of the received signal vector of row：WhereinRepresent sample autocorrelation matrix, Σ tables
Show summation, t is sampling instant,Represent the conjugate transpose of vector or matrix；
Step 3. carries out singular value decomposition to sample autocorrelation matrix, determines the noise subspace Q of sample autocorrelation matrix,
Above note Q, the matrix of M row vectors and following M row vectors composition is respectively Q1And Q2, matrix Q1Each column vector be respectively：
1st～5 column vector：
6th～10 column vector：
11st～15 column vector：
16th～17 column vector：
Matrix Q2Each column vector be respectively：
1st～5 column vector：
6th～10 column vector：
11st～15 column vector：
16th～17 column vector：
Step 4：Determine the estimation that aerial array width is mutually responded, according to orthogonality relation, using Q1、Q2Believe with known not rounded
Number direction vector a (θ1) and a (θ2) structural matrix D：
D=1/2 (B1+B2)
Wherein
Carry out Eigenvalues Decomposition to matrix D, in the eigenvalue of selection matrix D closest to 1 eigenvalue corresponding to feature
Estimation of the vector for 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 correlation coefficient is：WhereinThe conjugate transpose of vector or matrix is represented, | | represent and take definitely
Value；Correlation coefficient then illustrates the aerial array width phase response vector that estimates closer to 1Closer to actual vector g.
Simultaneous with 1 unknown signal in direction in 2 not rounded correction signals using instantiation mode of the present invention
In the case of estimate aerial array width phase response vectorWith the correlation coefficient between actual antennas array width phase response vector g it is
0.9909.
Claims (1)
1. a kind of method that utilization not rounded signal measuring antenna array receiver machine width is mutually responded, including：
Step 1. initialization process：The antenna number of aerial array, the number initialization of the received signal vector of aerial array are deposited
Enter internal memory；
Step 2. determines the sample autocorrelation matrix of the spread vector of the received signal vector of aerial array：First pass around conventional side
Secondly method process generates aerial array by the received signal vector of aerial array to determine the received signal vector of aerial array
The spread vector of received signal vector, it is then determined that the sample auto-correlation square of the spread vector of the received signal vector of aerial array
Battle array；
Through conventional method process to determine the received signal vector of aerial array, its processing method is I/Q dual-channel connection debits
Method or Hilbert transform processing method, the received signal vector of the aerial array of determination is：
X (t)=[x1(t) x2(t) … xM(t)]T
Received signal vectors of the wherein x (t) for aerial array, vector dimension are equal to antenna number M of aerial array, and t is sampling
Moment, t=1,2 ..., P, P represent the number of the received signal vector of aerial array corresponding with sampling instant number, x1(t),x2
(t),…,xMT () represents the 1st, 2 ..., M element of received signal vector x (t) of aerial array respectively,Representing matrix
Or the transposition of vector；
The spread vector of received signal vector that aerial array is generated by the received signal vector of aerial array is：
Wherein, vector x*T () represents the conjugation of vector x (t), received signal vectors of the x (t) for aerial array；
The sample autocorrelation matrix for determining the spread vector of the received signal vector of aerial array is：
Wherein,Represent that the sample autocorrelation matrix of spread vector, each sampling instant are sampled to a received signal vector,
Represent the conjugate transpose of vector or matrix；
Step 3. determines the noise subspace of the sample autocorrelation matrix of spread vector：Sample autocorrelation matrix to spread vectorEigenvalues Decomposition is carried out, the sample autocorrelation matrix of spread vector is determinedNoise subspace；
The sample autocorrelation matrix of spread vectorEigenvalues Decomposition be：
Wherein matrix Λ is diagonal matrix, and diagonally element upwards corresponds to the sample autocorrelation matrix of spread vector respectivelySpy
Value indicative, arrangement in descending order is λ1≥λ2＞ λ3≥…≥λ2M, matrix U is by the sample autocorrelation matrix of spread vectorFeature
Vectorial u1,u2,u3,…,u2MThe matrix of composition, is corresponded with eigenvalue,Represent the conjugate transpose of vector or matrix；
Determine the noise subspace of the sample autocorrelation matrix of spread vector, be：Q=[uK+1uK+2… u2M], wherein K is non-
The number of circle signal, number K that not rounded signal is determined using big eigenvalue decision method, antenna numbers of the M for aerial array；
Step 4. determines the estimation that aerial array width is mutually responded：Noise subspace using the sample autocorrelation matrix of spread vector
And the orthogonality relation between the propagation direction vector of not rounded signal, determines the estimation that aerial array width is mutually responded；
The propagation direction vector of not rounded signal is
Wherein, φk、θkWith a (θk) represent respectively k-th not rounded signal phase angle, relative to aerial array direction and direction
θkThe direction vector of corresponding aerial array, the number of k=1,2 ..., K, K for not rounded signal, G are a diagonal matrix, and which the
M diagonal element G (m, m) represents that the width of m-th array element receiver is mutually responded；
The sample autocorrelation matrix of spread vectorNoise subspace and not rounded signal propagation direction vector b (θk) between deposit
In orthogonality relation, the orthogonality relation is：
QHb(θk)=0,
Sample autocorrelation matrixs of the wherein Q for spread vectorNoise subspace, k=1,2 ..., K, K for not rounded signal
Number；
Assume that the 1st and the 2nd signal for not rounded signal known to direction, then has：
Wherein Q1And Q2The matrix that matrix Q above M row vector and following M row vector be made up of, φ are represented respectivelyk、θkWith a (θk)
Phase angle, direction relative to aerial array and the direction θ of k-th not rounded signal are represented respectivelykThe side of corresponding aerial array
To vector, k=1,2；
Determine the estimation that aerial array width is mutually responded：According to orthogonality relation, using Q1、Q2Direction vector a with known not rounded signal
(θ1) and a (θ2) structural matrix D：
D=1/2 (B1+B2)
Wherein
Carry out Eigenvalues Decomposition to matrix D, in the eigenvalue of selection matrix D closest to 1 eigenvalue corresponding to characteristic vector
Aerial array width phase response vector for the estimation of actual antennas array width phase response vector g
Defining correlation coefficient is：
| | represent and take absolute value；Correlation coefficient then illustrates the aerial array width phase response vector that estimates closer to 1Closer to reality
Border aerial array width 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 |
| CN107490780B (en) * | 2017-06-01 | 2020-07-10 | 同方电子科技有限公司 | Direction finding method capable of restraining uniformly distributed phase errors |
| 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 |
| CN112098926B (en) * | 2020-09-15 | 2023-06-09 | 中国民用航空飞行学院 | Intelligent angle measurement training sample generation method by using unmanned plane platform |
| CN114039679B (en) * | 2022-01-10 | 2022-04-01 | 中国人民解放军海军工程大学 | Low-frequency orthogonal antenna signal detection method and system |
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| JP4339801B2 (en) * | 2003-05-22 | 2009-10-07 | 富士通株式会社 | Direction-of-arrival estimation method and reception beam forming apparatus without using eigenvalue decomposition |
| US6992622B1 (en) * | 2004-10-15 | 2006-01-31 | Interdigital Technology Corporation | Wireless communication method and antenna system for determining direction of arrival information to form a three-dimensional beam used by a transceiver |
| CN101915909B (en) * | 2010-08-11 | 2013-05-08 | 四川九洲电器集团有限责任公司 | Implementing method for calibrating amplitude and phase of system receiving channel |
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| CN102426350B (en) * | 2011-08-31 | 2013-04-10 | 西安空间无线电技术研究所 | Method for determining amplitude phase errors of direction-finding channels of space-borne array antenna |
| CN103138845B (en) * | 2011-11-22 | 2015-03-25 | 中国科学院电子学研究所 | Amplitude phase characteristic test method for down-conversion reception channel of ultra-wide band synthetic aperture radar (SAR) receiver |
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