CN106227701B - A kind of automatic correcting method of the amplitude phase error of the receiving channel of array signal - Google Patents
A kind of automatic correcting method of the amplitude phase error of the receiving channel of array signal Download PDFInfo
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Abstract
The invention belongs to array signal processing field more particularly to a kind of automatic correcting methods of the amplitude phase error of the receiving channel of array signal.The method of the present invention does not use external auxiliary signal source, by in different sampling time sections, switch the corresponding relationship between the array element and array element signals receiving channel of array, the time-domain signal under different corresponding relationships can be received, the signal in two time adjacent segments is chosen, using the automatic correcting method in this paper, the amplitude and phase error in each channel is estimated, and substitute into the estimated value of error in the direction finding formula finally derived, obtain arrival bearing's estimation of signal.
Description
Technical field
The invention belongs to array signal processing field more particularly to a kind of amplitude phase errors of the receiving channel of array signal
Automatic correcting method.
Background technique
Array signal processing is an important branch in field of signal processing, is rapidly developed in the past 30 years,
Using being related to, radar, communication, sonar, earthquake, exploration, radio astronomy and biomedical engineering etc. be numerous military and national economy
Field.Compared with traditional single directional sensor, array signal processing have the control of flexible wave beam, high signal gain,
The advantages that stronger anti-interference ability and high space hyperresolution, thus very big concern is received, research related to this
Work continues to develop and deeply, application range also constantly expands.Simultaneously with microelectric technique, Digital Signal Processing,
The theory and actual application of the fast development of parallel processing technique, array signal processing is also rapidly developed.
Most important two research directions of array signal processing are adaptive spatial filtering (adaptive array processing) and sky
Between Power estimation.Estimation of Spatial Spectrum is the emerging airspace signal processing technology to grow up in the past 30 years, it is in wave beam
Grow up on the basis of formation technology and Time Domain Spectrum estimation technique, main target is that research improves the sky in processing bandwidth
Between the estimated accuracy of signal angle, angular resolution and the various algorithms for improving arithmetic speed.Traditional Mutual coupling side
Method, for the angular resolution of array by the constraint of Rayleigh limit, i.e. extraterrestrial target in Rayleigh limit is indistinguishable.Estimation of Spatial Spectrum
Technology is applied to super-resolution estimation technique in DOA estimation, can break through the constraint of Rayleigh limit, obtains very high angle-resolved
Rate, it has extremely wide application prospect in various fields such as radar, communication, sonars.
By the intensive research of many decades, Space ball algorithm is had been greatly developed, occur it is many compared with
For the innovatory algorithm of mature algorithm and these algorithms, therefore it is widely used in practice.
Under ideal conditions, Space ball algorithm can get very good Measure direction performance, but in practical application
In, the amplitude phase error in the channel as caused by the non-ideal factors such as each receiving channel mismatch of array signal is often difficult to avoid that,
Influence to Direction Finding Algorithm is in the design process the problem of must be taken into consideration, thus in systems in practice must width phase to channel
Error is corrected.
Summary of the invention
The purpose of the present invention is in array df method, there are width between the receiving channel of each array element signals in array
Phase inconsistency has different amplitude and phase deviations, this is channel when leading to array signal by different channels
Amplitude phase error.This patent proposes a kind of automatic correcting method to such error.This method does not use external auxiliary signal source, passes through
In different sampling time sections, switch the corresponding relationship between the array element of array and array element signals receiving channel, so that it may receive
Time-domain signal under different corresponding relationships chooses the signal in two time adjacent segments, right using the automatic correcting method in this paper
The amplitude and phase error in each channel is estimated, and the estimated value of error is substituted into the direction finding formula finally derived, obtains
Arrival bearing to signal estimates.
Specific step is as follows for a kind of automatic correcting method of the amplitude phase error of the receiving channel of array signal:
S1, even linear array is formed by M array element, as receiving array, in receiving array between any two adjacent array element away from
From the corresponding receiving channel of each array element for d, enabled in receiving array, the array element in receiving array is numbered, array element
Number consecutively is c1,c2,...,cM, in t0Moment, the array element of receiving array and the relationship that is correspondingly connected with of receiving channel become: compiling
Number be c1The receiving channel that is connected to of array element be denoted as d1, number c2The receiving channel that is connected to of array element be denoted as d2, until
Number is cMThe receiving channel that is connected to of array element be denoted as dM, under this connection relationship, L is acquired to the output of each receiving channel
The signal of a discrete instants obtains one group of sampled signal Y1=[y1(t1) y1(t2) … y1(tL)]=[y11 y12 … y1L],
Wherein, y1iIt is the signal vector at the ith sample moment that array received arrives, y1(tn) it is receiving array in tnThe sampling at moment is believed
Number,s(tn) it is tnThe incoming signal at moment to
Amount, s (tn)=[s1(tn),s2(tn),...,sK(tn)]T, si(tn) it is i-th of incoming signal, K is incoming signal number, []T
Indicate transposition operation,Be in the sampling instant, there are the direction matrix of the signal when amplitude phase error of receiving channel,A is the direction matrix of signal ideally, A=[a (θ1) a(θ2) ... a(θK)], a (θi) it is ideal
In the case of i-th of incoming signal direction vector,θiEnter for i-th
The incident angle of signal is penetrated,When being received for receiving array to i-th of incoming signal, any two-phase as caused by wave path-difference
Phase difference between the reception signal of adjacent array element,λiFor the wavelength of i-th of incoming signal, G1For receiving channel
Amplitude phase error matrix, G1It is diagonal matrix, G1=diag (g1,g2,...gM), diag () is diagonal matrix symbol, g1,
g2,...gMFor G1Element on diagonal line, remaining element are 0, giBe number be ciThe width of receiving channel of array element connection mutually miss
Poor parameter, gi=αiexp(jφi), i=1,2 ... M, αiFor the range error of the receiving channel, φiFor the phase of the receiving channel
Position error, v (tn) it is tnThe white noise vector at moment, noise variance σ2, the ideal situation refers to that there is no receiving channels
The case where amplitude phase error；
S2, in t0+ Δ T the moment switches the corresponding receiving channel of each array element, the array element of receiving array and pair of receiving channel
Connection relationship is answered to become: number c1The receiving channel that is connected to of array element be denoted as d'1, number c2Connecing of being connected to of array element
It receives channel and is denoted as d'2, until number is cMThe receiving channel that is connected to of array element be denoted as d'M, under this connection relationship, equally
To the signal of the output L discrete instants of acquisition of each receiving channel, another group of sampled signal Y is obtained2=[y2(t1+ΔT) y2
(t2+ΔT) … y2(tL+ Δ T)]=[y21 y22 … y2L], wherein y2iIt is the letter at the ith sample moment that array received arrives
Number vector, It is in the sampling instant, there are the direction matrix of the signal when amplitude phase error of receiving channel, G2=diag
(g′1,g'2,g'3,...,g'M), G2It is diagonal matrix, g '1,g'2,g'3,...,g'MFor G2Element on diagonal line, remaining member
Element is 0, g 'iIt is c for numberiArray element connection receiving channel amplitude phase error parameter, g 'i=α 'iexp(jφ′i), i=1,
2 ... M, α 'iFor the range error of the receiving channel, φ 'iFor the phase error of the receiving channel；
S3, two groups of sampled signal Y as obtained in S1 and S21=[y11 y12 … y1L] and Y2=[y21 y22 … y2L],
Calculate separately the estimated value of the autocorrelation matrix of two groups of signals, calculation formula are as follows:With
S4, to the estimated value R of two autocorrelation matrixes1And R2Eigenvalues Decomposition is carried out respectively, can obtain R1M characteristic value,
It arranges in descending order are as follows: λ1≥λ2≥…≥λK> λK+1=...=λM=σ2, the corresponding normalization characteristic vector of each characteristic value is successively
Are as follows: u1,u2,…,uM, similarly, R can be obtained2M characteristic value, arrange in descending order are as follows: λ '1≥λ′2≥…≥λ'K> λ 'K+1=...
=λ 'M=σ2, the corresponding normalization characteristic vector of each characteristic value is successively are as follows: u '1,u′2,…,u′M；
S5, the Y for constructing two groups of sampled signals1And Y2Noise subspace EN1And EN2, wherein EN1It is by λK+1,…,λMIt is right
The normalization characteristic vector u answeredK+1,…,uMThe noise subspace opened, EN1=span { uK+1,…,uM}。EN2It is by λ
'K+1,…,λ'MCorresponding normalization characteristic vector u'K+1,…,u'MThe noise subspace opened, EN2=span { u'K+1,…,u
'M}；
S6, it enables in S1a'1(θi) it is in t0At the moment, there are the width of receiving channel
When phase error, the direction vector of i-th of incoming signal,
Similarly, it enables in S2a'2(θi) it is in t0At+Δ T the moment, there are the width phases of receiving channel
When error, the direction vector of i-th of incoming signal,
According to MUSIC algorithm principle, noise subspace E described in S5N1Normalization characteristic vector uK+1,…,uMWith there are when amplitude phase error
Sense vector it is orthogonal, i.e.,Enable U1=
[uK+1,…,uM], U2=[u'K+1,…,u'M], orthogonality relation equation group can be obtained:
Wherein, O is the full null matrix that M-K row 1 arranges
S7, G is enabled1=F1g G2=F2G, wherein g=[g1,g2,g3,...,gM]T, F1And F2It is characterization array element and receiving channel
Between connection relationship M rank non-singular matrix, it is 1 that each column of every a line, which all only have 1 element, remaining element is 0, F1Pair
Element is 1 on linea angulata, remaining element is 0, F2In element, by taking the element of the first row as an example, in t0+ Δ T the moment, if compiling
Number be c1Array element connection receiving channel be number be ckArray element in t0The receiving channel of moment connection, then receiving channel
Error g '1=gk, corresponding F2In the kth column element of the first row be 1, remaining element of the first row is 0, F2In remaining the 2nd
Row number into M row element where element 1, is after the same method c by numbering2To cMArray element connection receiving channel it is true
It is fixed；
S8, by relational expression G obtained in S71=F1G, G2=F2G is substituted into the orthogonality relation equation group in S6, can be obtained such as
The equivalence transformation of lower orthogonality relation equation group:Enable first element g in g
(1)=1, continue rewrite equation:It enablesB=
[O' 1]T, and Q is sequency spectrum matrix, so that there are least square solution g by equation group Qg=bLS, the expression of the least square solution
Formula are as follows:Wherein,Φ () is indicated the behaviour of the diagonally matrix of the vector transformation in bracket
Make, the element on the diagonal line of diagonal matrix is the element of vector in bracket, []HFor conjugate transposition operation,For matrix
Pseudo- inverse operation；
S9, according in S8 as a result, MUSIC spectral function as follows can be obtained:
Further, the condition of switching channel described in S2 are as follows: matrix where array element is sequency spectrum matrix.
The beneficial effects of the present invention are:
The present invention does not use auxiliary source, so that it may complete the correction to Ro-vibrational population, obtain effective incoming wave side
To estimation angle.Therefore it can effectively reduce the input cost of equipment, the popularization of Estimation of Spatial Spectrum method in practical projects promoted to answer
With.The method of the present invention can be widely applied to the fields such as communication, radar, sonar, telemetering, radio monitoring and management.
Detailed description of the invention
The MUSIC Power estimation result figure of this bearing calibration of Fig. 1
The comparison diagram of the angle estimation result of this bearing calibration of Fig. 2
The comparison diagram of the root-mean-square error of the angle estimation result of this bearing calibration of Fig. 3
Specific embodiment
Below with reference to embodiment and attached drawing, the technical solution that the present invention will be described in detail.
Present embodiment uses 9 yuan of even linear arrays, and has 9 receiving channels, and successively from left to right number is each array element
c1,c2,...,c9, from left to right number consecutively is d to receiving channel1,d2,...,d9, array element spacing is λ 4, exists simultaneously 9 battle arrays
First receiving channel, two far field incoming signals, incidence angle are respectively 4.3 ° and 14.4 °, and Signal to Noise Ratio (SNR)=9dB, array element, which receives, to be believed
Number noise be zero-mean white Gaussian noise, if noise power be σ2=1.
Two kinds of connection relationships, are respectively as follows:
The first connection relationship: array element number c1,c2,...,c9It is connected respectively to channel d1,d2,...,d9；
Second of connection relationship: array element number c1,c2,...,c9It is connected respectively to channel d8,d6,d4,d2,d9,d1,d3,d5,
d7
Every kind of connection relationship samples one group of sequence, and every group of sequence contains 64 sampled points.The sampling of the first connection relationship
Sequence is first group of sample sequence, and the sample sequence of second of connection relationship is second group of sampled signal.
Such switching meets switching condition described in S8, and it is sequency spectrum matrix that the order of matrix Q, which is 9,.
The detailed process of embodiments of the present invention is as follows:
Step 1. is respectively as follows: by above two connection relationship, obtainable two groups of sample sequences
First group: sampling instant n=1,2 ..., 64, wherein the sample sequence at preceding 3 moment and rear 3 moment
Second group: sampling instant n=65,66 ..., 128, wherein the sample sequence at preceding 3 moment and rear 3 moment
Step 2. calculates separately the estimation of its autocorrelation matrix, first group of sampling sequence by two groups of sample sequences in step 1
The estimation R of the autocorrelation matrix of column1Are as follows: matrix is 9 rows 9 column, wherein preceding 3 arrange and rear 3 are classified as:
By the estimation R of the autocorrelation matrix of first group of sample sequence1, acquire its noise subspace matrix U1=[uK+1,…,
uM] are as follows: matrix be 9 rows 7 column, wherein it is preceding 3 arrange and last be classified as:
Under the first connection relationship, there are when the amplitude phase error of receiving channel, the direction matrix of signalAre as follows:
The estimation R of the autocorrelation matrix of second group of sample sequence2Are as follows: matrix is 9 rows 9 column, wherein preceding 3 arrange and rear 3 are classified as:
By the estimation R of the autocorrelation matrix of second group of sample sequence2, acquire its noise subspace matrix U2=[u'K+1,…,
u'M] are as follows: matrix is 9 rows 7 column, wherein preceding 3 arrange and last 1 are classified as:
Under second of connection relationship, there are when the amplitude phase error of receiving channel, the direction matrix of signalAre as follows:
Step 3. MUSIC Power estimation formula according to obtained in technical solution S9:
Last angle estimation result is 4.5000 degree and 14.000 degree, with 4.3 degree and 14.4 degree phases of true incident angle
Than error is respectively 0.2 degree and 0.4 degree, and simulation result is shown in Fig. 1, and the self-correcting that this patent proposes it can be seen from analogous diagram is calculated
Method can realize effective correction to amplitude phase error, obtain effective angle estimation value.
Step 4. changes signal-to-noise ratio, remaining simulated conditions is constant, self-correcting of the Contrast to noise ratio SNR within the scope of 5~50dB
Normal operation method estimated result and angle estimation ideally are as a result, simulation result is shown in Fig. 2.It can be seen from analogous diagram with
The increase of signal-to-noise ratio, the angle estimation result that Self-Tuning Algorithm obtains gradually approach angle estimation result ideally.
Step 5. changes signal-to-noise ratio, remaining simulated conditions is constant, self-correcting of the Contrast to noise ratio SNR within the scope of 5~50dB
The root-mean-square error of the root-mean-square error of normal operation method estimated result and angle estimation result ideally, simulation result are shown in
Fig. 3.With the increase of signal-to-noise ratio it can be seen from analogous diagram, the root-mean-square error of the angle estimation result of Self-Tuning Algorithm by
Gradually in 0, it was demonstrated that the validity for the Self-Tuning Algorithm that this patent proposes.
When the receiving channel of receiving array is there are when sensor gain and phase uncertainties, MUSIC Power estimation method is unable to get effective angle
Spend estimated result, it is necessary to be corrected to the amplitude phase unbalance of receiving channel.Automatic correcting method of the invention is not believed by auxiliary
Number source both can guarantee that the correction of the amplitude phase error in channel is received in docking, and the complexity and cost of equipment can also be effectively reduced,
Promote the application of Estimation of Spatial Spectrum method in practical projects.
Claims (2)
1. a kind of automatic correcting method of the amplitude phase error of the receiving channel of array signal, which is characterized in that specific step is as follows:
S1, even linear array is formed by M array element, as receiving array, the distance in receiving array between any two adjacent array element is
D enables the corresponding receiving channel of each array element in receiving array, the array element in receiving array is numbered, array element is successively
Number is c1,c2,...,cM, in t0Moment, the array element of receiving array and the relationship that is correspondingly connected with of receiving channel become: number c1
The receiving channel that is connected to of array element be denoted as d1, number c2The receiving channel that is connected to of array element be denoted as d2, until number is
cMThe receiving channel that is connected to of array element be denoted as dM, discrete to output acquisition L of each receiving channel under this connection relationship
The signal at moment obtains one group of sampled signal Y1=[y1(t1) y1(t2) … y1(tL)]=[y11 y12 … y1L], wherein
y1iIt is the signal vector at the ith sample moment that array received arrives, y1(tn) it is receiving array in tnThe sampled signal at moment,s(tn) it is tnThe incoming signal vector at moment, s
(tn)=[s1(tn),s2(tn),...,sK(tn)]T, si(tn) it is i-th of incoming signal, K is incoming signal number, []TIt indicates
Transposition operation,Be in the sampling instant, there are the direction matrix of the signal when amplitude phase error of receiving channel,
A is the direction matrix of signal ideally, A=[a (θ1) a(θ2) ... a(θK)], a (θi) it is ideally i-th
The direction vector of a incoming signal,θiFor i-th incoming signal
Incident angle,When being received for receiving array to i-th of incoming signal, any two adjacent array element as caused by wave path-difference
Phase difference between signal is received,λiFor the wavelength of i-th of incoming signal, G1It is mutually missed for the width of receiving channel
Poor matrix, G1It is diagonal matrix, G1=diag (g1,g2,...gM), diag () is diagonal matrix symbol, g1,g2,...gMFor G1
Element on diagonal line, remaining element are 0, giBe number be ciArray element connection receiving channel amplitude phase error parameter, gi=
αiexp(jφi), i=1,2 ... M, αiFor the range error of the receiving channel, φiFor the phase error of the receiving channel, v
(tn) it is tnThe white noise vector at moment, noise variance σ2, the ideal situation refers to the amplitude phase error there is no receiving channel
The case where；
S2, in t0+ Δ T the moment switches the corresponding receiving channel of each array element, and the array element of receiving array is corresponding with receiving channel to be connected
The relationship of connecing becomes: number c1The receiving channel that is connected to of array element be denoted as d'1, number c2The reception that is connected to of array element it is logical
Road is denoted as d'2, until number is cMThe receiving channel that is connected to of array element be denoted as d'M, under this connection relationship, equally to every
The signal of the output L discrete instants of acquisition of a receiving channel, obtains another group of sampled signal Y2=[y2(t1+ΔT) y2(t2+
ΔT) … y2(tL+ Δ T)]=[y21 y22 … y2L], wherein y2iIt is the signal at the ith sample moment that array received arrives
Vector,
Be in the sampling instant, there are the direction matrix of the signal when amplitude phase error of receiving channel,G2=diag (g '1,g'2,g'3,...,g'M), G2It is diagonal matrix, g '1,g'2,g'3,...,g'MFor G2Diagonally
Element on line, remaining element are 0, g 'iIt is c for numberiArray element connection receiving channel amplitude phase error parameter, g 'i=
α′iexp(jφ′i), i=1,2 ... M, α 'iFor the range error of the receiving channel, φ 'iIt is missed for the phase of the receiving channel
Difference；
S3, two groups of sampled signal Y as obtained in S1 and S21=[y11 y12 … y1L] and Y2=[y21 y22 … y2L], respectively
Calculate the estimated value of the autocorrelation matrix of two groups of signals, calculation formula are as follows:With
S4, to the estimated value R of two autocorrelation matrixes1And R2Eigenvalues Decomposition is carried out respectively, can obtain R1M characteristic value, by drop
Sequence arrangement are as follows: λ1≥λ2≥…≥λK> λK+1=...=λM=σ2, the corresponding normalization characteristic vector of each characteristic value is successively are as follows: u1,
u2,…,uM, similarly, R can be obtained2M characteristic value, arrange in descending order are as follows: λ '1≥λ′2≥…≥λ'K> λ 'K+1=...=λ 'M=
σ2, the corresponding normalization characteristic vector of each characteristic value is successively are as follows: u '1,u′2,…,u′M；
S5, the Y for constructing two groups of sampled signals1And Y2Noise subspace EN1And EN2, wherein EN1It is by λK+1,…,λMIt is corresponding
Normalization characteristic vector uK+1,…,uMThe noise subspace opened, EN1=span { uK+1,…,uM}；EN2It is by λ 'K+1,…,λ'M
Corresponding normalization characteristic vector u'K+1,…,u'MThe noise subspace opened, EN2=span { u'K+1,…,u'M}；
S6, it enables in S1a'1(θi) it is in t0At the moment, there are the width phases of receiving channel
When error, the direction vector of i-th of incoming signal,
Similarly, it enables in S2a'2(θi) it is in t0At+Δ T the moment, there are the width of receiving channel
When phase error, the direction vector of i-th of incoming signal,
According to MUSIC algorithm principle, noise subspace E described in S5N1Normalization characteristic vector uK+1,…,uMWith there are when amplitude phase error
Sense vector it is orthogonal, i.e.,Enable U1=
[uK+1,…,uM], U2=[u'K+1,…,u'M], orthogonality relation equation group can be obtained:Wherein, O is the full null matrix that M-K row 1 arranges；
S7, G is enabled1=F1g G2=F2G, wherein g=[g1,g2,g3,...,gM]T, F1And F2It is between characterization array element and receiving channel
Connection relationship M rank non-singular matrix, it is 1 that each column of every a line, which all only have 1 element, remaining element is 0, F1Diagonal line
Upper element is 1, remaining element is 0, F2In element, by taking the element of the first row as an example, in t0+ Δ T the moment, if number is
c1Array element connection receiving channel be number be ckArray element in t0The receiving channel of moment connection, the then error of receiving channel
g′1=gk, corresponding F2In the kth column element of the first row be 1, remaining element of the first row is 0, F2In remaining the 2nd arrive M
Row number in row element where element 1, is after the same method c by numbering2To cMArray element connection receiving channel determine；
S8, by relational expression G obtained in S71=F1G, G2=F2G is substituted into the orthogonality relation equation group in S6, can be obtained orthogonal as follows
The equivalence transformation of relation equation group:First element g (1)=1 in g is enabled,
Continue rewrite equation:It enablesB=[O'1]T,
And Q is sequency spectrum matrix, so that there are least square solution g by equation group Qg=bLS, the least square solution's expression are as follows:Wherein,Φ () is indicated the operation of the diagonally matrix of the vector transformation in bracket, right
Element on the diagonal line of angular moment battle array is the element of vector in bracket, []HFor conjugate transposition operation,For the pseudoinverse of matrix
Operation；
S9, according in S8 as a result, MUSIC spectral function as follows can be obtained:
2. a kind of automatic correcting method of the amplitude phase error of the receiving channel of array signal according to claim 1, feature
It is: the condition of switching channel described in S2 are as follows: matrix where array element is sequency spectrum matrix.
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