CN106227701A - A kind of automatic correcting method of the amplitude phase error receiving passage of array signal - Google Patents

Abstract

The invention belongs to Array Signal Processing field, particularly relate to the automatic correcting method of the amplitude phase error receiving passage of a kind of array signal.The inventive method does not use external auxiliary signal source, by in different sampling time sections, array element and the array element signals of switching array receive the corresponding relation between passage, just can receive the time-domain signal under different corresponding relation, choosing the signal in two time adjacent segments, utilize the automatic correcting method in this paper, amplitude and phase error to each passage are estimated, and the estimated value of error is substituted in the last direction finding formula derived, the arrival bearing obtaining signal estimates.

Description

A kind of automatic correcting method of the amplitude phase error receiving passage of array signal

Technical field

The invention belongs to Array Signal Processing field, particularly relate to the amplitude phase error receiving passage of a kind of array signal Automatic correcting method.

Background technology

Array Signal Processing is an important branch in signal processing field, is being developed rapidly over nearly 30 years, its Application relates to numerous military affairs and the national economy such as radar, communication, sonar, earthquake, exploration, radio astronomy and biomedical engineering Field.Compared with traditional single directional sensor, Array Signal Processing have wave beam flexibly control, high signal gain, The advantages such as stronger capacity of resisting disturbance and high space hyperresolution, thus receive greatly concern, research related to this Work development is with deeply, and its range of application the most constantly expands.Simultaneously along with microelectric technique, Digital Signal Processing, The fast development of parallel processing technique, the theory and actual application of Array Signal Processing is also developed rapidly.

Topmost 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 spatial domain signal processing technology that grown up over nearly 30 years is emerging, and it is at wave beam Growing up on the basis of formation technology and Time Domain Spectrum estimation technique, its main target is that research improves sky in processing bandwidth Between the estimated accuracy of signal angle, angular resolution and the various algorithms of raising arithmetic speed.Traditional Mutual coupling side Method, the angular resolution of array is retrained by Rayleigh limit, i.e. extraterrestrial target in Rayleigh limit is indistinguishable.Estimation of Spatial Spectrum Technology is applied to super-resolution estimation technique during DOA estimates, can break through the constraint of Rayleigh limit, obtain the highest angle-resolved Rate, it has the most wide application prospect in various fields such as radar, communication, sonars.

Through the intensive research of many decades, Space ball algorithm has obtained the biggest development, occurs in that many is relatively For ripe algorithm and the innovatory algorithm of these algorithms, it is widely used the most in practice.

Under ideal conditions, Space ball algorithm can obtain the most excellent Measure direction performance, but applies in reality In, each amplitude phase error receiving the passage that the non-ideal factors such as Channel Mismatch cause of array signal often it is difficult to avoid that, its Impact on Direction Finding Algorithm is the problem that must take in the design process, thus in systems in practice must be to the width phase of passage Error is corrected.

Summary of the invention

It is an object of the invention to, in array df method, array exist width between the reception passage of each array element signals Phase discordance, when causing array signal to pass through different passages, has different amplitudes and phase deviation, and this is passage Amplitude phase error.This patent proposes a kind of automatic correcting method to this kind of error.The method does not use external auxiliary signal source, passes through In different sampling time sections, array element and the array element signals of switching array receive the corresponding relation between passage, so that it may receive Time-domain signal under different corresponding relations, chooses the signal in two time adjacent segments, utilizes the automatic correcting method in this paper, right Amplitude and the phase error of each passage are estimated, and the estimated value of error are substituted in the last direction finding formula derived, Arrival bearing to signal estimates.

Specifically comprising the following steps that of the automatic correcting method of the amplitude phase error receiving passage of a kind of array signal

S1, formed even linear array by M array element, as receiving array, in receiving array between any two adjacent array elements away from From for d, make corresponding one of each array element in receiving array receive passage, the array element in receiving array is numbered, array element Number consecutively is c₁,c₂,...,c_M, at t₀In the moment, the array element of receiving array becomes with the corresponding annexation receiving passage: compile Number it is c₁The reception passage that is connected to of array element be designated as d₁, numbered c₂The reception passage that is connected to of array element be designated as d₂, until Numbered c_MThe reception passage that is connected to of array element be designated as d_M, under this annexation, the output to each reception passage gathers L The signal of individual discrete instants, obtains one group of sampled signal Y₁=[y₁(t₁) y₁(t₂) … y₁(t_L)]=[y₁₁ y₁₂ … y_1L], Wherein, y_1iIt is the signal vector in the ith sample moment that array received arrives, y₁(t_n) it is that receiving array is at t_nThe sampling letter in moment Number,s(t_n) it is t_nThe incoming signal in moment to Amount, s (t_n)=[s₁(t_n),s₂(t_n),...,s_K(t_n)]^T, s_i(t_n) it is i-th incoming signal, K is incoming signal number, []^T Represent transposition operation,It is in this sampling instant, there is the direction matrix of signal during the amplitude phase error receiving passage,A is the direction matrix of signal ideally, A=[a (θ₁) a(θ₂) ... a(θ_K)], a (θ_i) it is preferable In the case of the direction vector of i-th incoming signal,θ_iEnter for i-th Penetrate the incident angle of signal, φ_iWhen i-th incoming signal being received for receiving array, wave path-difference any two caused Phase contrast between the reception signal of adjacent array element,λ_iFor the wavelength of i-th incoming signal, G₁Logical for receiving The amplitude phase error matrix in road, G₁It is diagonal matrix, G₁=diag (g₁,g₂,...g_M), diag () is diagonal matrix symbol, g₁, g₂,...g_MFor G₁Element on diagonal, remaining element is 0, g_iIt is numbered c_iArray element connect receive passage width miss mutually Difference parameter, g_i=α_iexp(jφ_i), i=1,2 ... M, α_iFor the range error of this reception passage, φ_iPhase for this reception passage Position error, v (t_n) it is t_nThe white noise vector in moment, its noise variance is σ², described ideal situation refers to there is not reception passage Amplitude phase error and other errors；

S2, at t₀In+Δ T the moment, switching the reception passage that each array element is corresponding, the array element of receiving array is right with reception passage Annexation is answered to become: numbered c₁The reception passage that is connected to of array element be designated as d'₁, numbered c₂Connecing of being connected to of array element Receive passage and be designated as d'₂, until numbered c_MThe reception passage that is connected to of array element be designated as d'_M, under this annexation, equally Each reception passage is exported the signal gathering L discrete instants, obtains another group sampled signal Y₂=[y₂(t₁+ΔT) y₂ (t₂+ΔT) … y₂(t_L+ Δ T)]=[y₂₁ y₂₂ … y_2L], wherein, y_2iIt it is the letter in the ith sample moment that array received arrives Number vector,

$y_2(t_n+\mathrm{\Δ}T)=A_g^{2}s(t_n+\mathrm{\Δ}T)+v(t_n+\mathrm{\Δ}T)=G_{2}As(t_n+\mathrm{\Δ}T)+v(t_n+\mathrm{\Δ}T),n=1,2,\mathrm{...},L,$

It is in this sampling instant, there is the direction matrix of signal during the amplitude phase error receiving passage,G₂=diag (g '₁,g′₂,g'₃,...,g'_M), G₂It is diagonal matrix, g '₁,g'₂,g'₃,...,g'_MFor G₂Diagonal angle Element on line, remaining element is 0, g '_iFor numbered c_iArray element connect receive passage amplitude phase error parameter, g '_i= α′_iexp(jφ′_i), i=1,2 ... M, α '_iFor the range error of this reception passage, φ '_iPhase place for this reception passage is missed Difference；

S3, by two groups of sampled signals Y obtained in S1 and S2₁=[y₁₁ y₁₂ … y_1L] and Y₂=[y₂₁ y₂₂ … y_2L], Calculating the estimated value of the autocorrelation matrix of two groups of signals respectively, computing formula is:With

S4, estimated value R to two autocorrelation matrixes₁And R₂Carry out Eigenvalues Decomposition respectively, R can be obtained₁M eigenvalue, It is arranged as in descending order: λ₁≥λ₂≥…≥λ_K＞ λ_K+1=...=λ_M=σ², normalization characteristic vector corresponding to each eigenvalue is successively For: u₁,u₂,…,u_M, in like manner, R can be obtained₂M eigenvalue, be arranged as in descending order: λ '₁≥λ′₂≥…≥λ′_K＞ λ '_K+1=... =λ '_M=σ², the normalization characteristic vector that each eigenvalue is corresponding is followed successively by: u '₁,u′₂,…,u′_M；

S5, construct the Y of two groups of sampled signals₁And Y₂Noise subspace E_N1And E_N2, wherein, E_N1It is by λ_K+1,…,λ_MRight The normalization characteristic vector u answered_K+1,…,u_MThe noise subspace opened, E_N1=span{u_K+1,…,u_M}。E_N2It is by λ '_K+1,…,λ'_MCorresponding normalization characteristic vector u'_K+1,…,u'_MThe noise subspace opened, E_N2=span{u'_K+1,…,u '_M}；

S6, make in S1a'₁(θ_i) it is at t₀In the moment, there is the width receiving passage During phase error, the direction vector of i-th incoming signal, In like manner, make in S2a'₂(θ_i) it is at t₀In+Δ T the moment, there is the width receiving passage During phase error, the direction vector of i-th incoming signal,Root According to MUSIC algorithm principle, noise subspace E described in S5_N1Normalization characteristic vector u_K+1,…,u_MWith when there is amplitude phase error Sense vector is orthogonal, i.e.Make U₁=[u_K+1,…, u_M], U₂=[u'_K+1,…,u'_M], can obtain orthogonality relation equation group:Its In, O is the full null matrix of M-K row 1 row；

S7, make G₁=F₁g G₂=F₂G, wherein g=[g₁,g₂,g₃,...,g_M]^T, F₁And F₂It is to characterize array element and receive passage Between the M rank non-singular matrix of annexation, it is 1 that each row of every a line all only have 1 element, and remaining element is 0, F₁Right On linea angulata, element is 1, and remaining element is 0, F₂In element, as a example by the element of the first row, at t₀+ Δ T the moment, if compiling Number it is c₁Array element connect reception passage be numbered c_kArray element at t₀The reception passage that moment connects, then receive passage Error g '₁=g_k, corresponding F₂In the kth column element of the first row be 1, remaining element of the first row is 0, F₂In remaining the 2nd The row number at element 1 place in M row element, after the same method by numbered c₂To c_MArray element connect reception passage true Fixed；

S8, relational expression G that will obtain in S7₁=F₁G, G₂=F₂G substitutes in the orthogonality relation equation group in S6, can be as The equivalence transformation of lower orthogonality relation equation group:Make first element g in g (1)=1, continuation rewrite equation:

OrderB=[O'1]^T, and Q is sequency spectrum matrix so that equation group Qg=b exists A young waiter in a wineshop or an inn takes advantage of solution g_LS, described least square solution's expression is:Wherein,Φ () represents By the operation of the diagonally matrix of the vector transformation in bracket, the element on the diagonal of diagonal matrix is the unit of vector in bracket Element, []^HFor conjugate transposition operation,Pseudo-inverse operation for matrix；

S9, according to the result in S8, can obtain MUSIC spectral function as follows: θ∈[-π,π]。

Further, the condition of switching channel described in S2 is: array element place matrix is sequency spectrum matrix.

The invention has the beneficial effects as follows:

The present invention does not use auxiliary source, so that it may complete the correction to Ro-vibrational population, obtains effective incoming wave side To estimating angle.Therefore can effectively reduce the input cost of equipment, promote that the popularization in Practical Project of the Estimation of Spatial Spectrum method should With.The inventive method can be widely applied to the fields such as communication, radar, sonar, remote measurement, radio monitoring and management.

Accompanying drawing explanation

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

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, describe technical scheme in detail.

Present embodiment uses 9 yuan of even linear arrays, and has 9 to receive passage, and each array element is the most numbered c₁,c₂,...,c₉, receiving passage from left to right number consecutively is d₁,d₂,...,d₉, array element distance is λ 4, there are 9 battle arrays simultaneously Unit receives passage, two far field incoming signals, and angle of incidence is respectively 4.3 ° and 14.4 °, signal to noise ratio snr=9dB, and array element receives letter Number noise be the white Gaussian noise of zero-mean, if noise power is σ²=1.

Two kinds of annexations, are respectively as follows:

The first annexation: array element numbering c₁,c₂,...,c₉It is connected respectively to passage d₁,d₂,...,d₉；

The second annexation: array element numbering c₁,c₂,...,c₉It is connected respectively to passage d₈,d₆,d₄,d₂,d₉,d₁,d₃,d₅, d₇

Every kind of annexation is sampled one group of sequence, and often group sequence contains 64 sampled points.The sampling of the first annexation Sequence is first group of sample sequence, and the sample sequence of the second annexation is second group of sampled signal.

This kind of switching meets switching condition described in S8, and the order of matrix Q is 9, for sequency spectrum matrix.

The idiographic flow of embodiments of the present invention is as follows:

Step 1. is respectively as follows: by above two annexation, obtainable two groups of sample sequences

First group: sampling instant n=1,2 ..., 64, the most front 3 moment and the sample sequence in rear 3 moment

Second group: sampling instant n=65,66 ..., 128, the most front 3 moment and the sample sequence in rear 3 moment

Step 2., by two groups of sample sequences in step 1, calculates the estimation of its autocorrelation matrix, first group of sampling sequence respectively The estimation R of the autocorrelation matrix of row₁For: matrix is that 9 row 9 arrange, and the most front 3 row and rear 3 are classified as:

Estimation R by the autocorrelation matrix of first group of sample sequence₁, try to achieve its noise subspace matrix U₁=[u_K+1,…, u_M] be: matrix is that 9 row 7 arrange, the most front 3 row and last be classified as:

Under the first annexation, when there is the amplitude phase error receiving passage, the direction matrix of signal For:

The estimation R of the autocorrelation matrix of second group of sample sequence₂For: matrix is that 9 row 9 arrange, and the most front 3 row and rear 3 are classified as:

Estimation R by the autocorrelation matrix of second group of sample sequence₂, try to achieve its noise subspace matrix U₂=[u'_K+1,…, u'_M] it being: matrix is that 9 row 7 arrange, and the most front 3 row and last 1 are classified as:

Under the second annexation, when there is the amplitude phase error receiving passage, the direction matrix of signal For:

Step 3. is according to the MUSIC Power estimation formula obtained in technical scheme S9:

${\hat{f}}_{MUSIC}\left(\mathrm{\θ}\right)=\frac{1}{{(b-{\mathrm{Qg}}_{LS})}^H(b-{\mathrm{Qg}}_{LS})},\mathrm{\θ}\∈\[-\mathrm{\π},\mathrm{\π}\]$

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 Ratio, error is respectively 0.2 degree and 0.4 degree, and simulation result is shown in Fig. 1, by analogous diagram it can be seen that the self-correcting that this patent proposes is calculated Method can realize the effective correction to amplitude phase error, obtains effective angle estimation value.

Step 4. changes signal to noise ratio, and remaining simulated conditions is constant, Contrast to noise ratio SNR self-correcting in the range of 5～50dB Normal operation method estimated result and angle estimation result ideally, simulation result is shown in Fig. 2.By analogous diagram it can be seen that with The increase of signal to noise ratio, the angle estimation result gradually convergence that Self-Tuning Algorithm obtains angle estimation result ideally.

Step 5. changes signal to noise ratio, and remaining simulated conditions is constant, Contrast to noise ratio SNR self-correcting in the range of 5～50dB The root-mean-square error of normal operation method estimated result and the root-mean-square error of angle estimation result ideally, simulation result is shown in Fig. 3.By analogous diagram it can be seen that along with the increase of signal to noise ratio, the root-mean-square error of the angle estimation result of Self-Tuning Algorithm by Gradually in 0, it was demonstrated that the effectiveness of the Self-Tuning Algorithm that this patent proposes.

When the reception passage of receiving array exists sensor gain and phase uncertainties, MUSIC Power estimation method cannot obtain effective angle Degree estimated result, it is necessary to the amplitude phase unbalance receiving passage is corrected.The automatic correcting method of the present invention is not by auxiliary letter Number source, both can guarantee that the correction of the amplitude phase error of passage was received in docking, and can also effectively reduce complexity and the cost of equipment, Promote the application in Practical Project of the Estimation of Spatial Spectrum method.

Claims (2)

1. the automatic correcting method of the amplitude phase error receiving passage of an array signal, it is characterised in that specifically comprise the following steps that

S1, being formed even linear array by M array element, as receiving array, in receiving array, the distance between any two adjacent array elements is D, makes corresponding one of each array element in receiving array receive passage, is numbered the array element in receiving array, and array element is successively Numbered c₁,c₂,...,c_M, at t₀In the moment, the array element of receiving array becomes with the corresponding annexation receiving passage: numbered c₁ The reception passage that is connected to of array element be designated as d₁, numbered c₂The reception passage that is connected to of array element be designated as d₂, until numbered c_MThe reception passage that is connected to of array element be designated as d_M, under this annexation, output collection L to each reception passage is discrete The signal in moment, obtains one group of sampled signal Y₁=[y₁(t₁) y₁(t₂) … y₁(t_L)]=[y₁₁ y₁₂ … y_1L], wherein, y_1iIt is the signal vector in the ith sample moment that array received arrives, y₁(t_n) it is that receiving array is at t_nThe sampled signal in moment,s(t_n) it is t_nThe incoming signal vector in moment, s (t_n)=[s₁(t_n),s₂(t_n),...,s_K(t_n)]^T, s_i(t_n) it is i-th incoming signal, K is incoming signal number, []^TRepresent Transposition operates,It is in this sampling instant, there is the direction matrix of signal during the amplitude phase error receiving passage, A is the direction matrix of signal ideally, A=[a (θ₁) a(θ₂) ... a(θ_K)], a (θ_i) it is ideally i-th The direction vector of individual incoming signal,θ_iFor i-th incoming signal Incident angle, φ_iWhen i-th incoming signal being received for receiving array, wave path-difference any two adjacent array elements caused Reception signal between phase contrast,λ_iFor the wavelength of i-th incoming signal, G₁For receiving the width phase of passage Error matrix, G₁It is diagonal matrix, G₁=diag (g₁,g₂,...g_M), diag () is diagonal matrix symbol, g₁,g₂,...g_MFor G₁Element on diagonal, remaining element is 0, g_iIt is numbered c_iArray element connect receive passage amplitude phase error parameter, g_i =α_iexp(jφ_i), i=1,2 ... M, α_iFor the range error of this reception passage, φ_iFor the phase error of this reception passage, v (t_n) it is t_nThe white noise vector in moment, its noise variance is σ², described ideal situation refers to there is not the amplitude phase error receiving passage And other errors；

S2, at t₀In+Δ T the moment, switching the reception passage that each array element is corresponding, the array element of receiving array is corresponding with reception passage even The relation of connecing becomes: numbered c₁The reception passage that is connected to of array element be designated as d'₁, numbered c₂The reception that is connected to of array element lead to Road is designated as d'₂, until numbered c_MThe reception passage that is connected to of array element be designated as d'_M, under this annexation, equally to often The output of individual reception passage gathers the signal of L discrete instants, obtains another group sampled signal Y₂=[y₂(t₁+ΔT) y₂(t₂+ ΔT) … y₂(t_L+ Δ T)]=[y₂₁ y₂₂ … y_2L], wherein, y_2iIt it is the signal in the ith sample moment that array received arrives Vector,

$y_2(t_n+\mathrm{\Δ}T)=A_g^{2}s(t_n+\mathrm{\Δ}T)+v(t_n+\mathrm{\Δ}T)=G_{2}As(t_n+\mathrm{\Δ}T)+v(t_n+\mathrm{\Δ}T),n=1,2,...,L,$

It is in this sampling instant, there is the direction matrix of signal during the amplitude phase error receiving passage,G₂=diag (g'₁,g'₂,g'₃,...,g'_M), G₂It is diagonal matrix, g'₁,g'2,g'3,...,g'_MFor G₂Diagonal angle Element on line, remaining element is 0, g'_iFor numbered c_iArray element connect receive passage amplitude phase error parameter, g'_i= α'_iexp(jφ'_i), i=1,2 ... M, α '_iFor the range error of this reception passage, φ '_iPhase place for this reception passage is missed Difference；

S3, by two groups of sampled signals Y obtained in S1 and S2₁=[y₁₁ y₁₂ … y_1L] and Y₂=[y₂₁ y₂₂ … y_2L], respectively Calculating the estimated value of the autocorrelation matrix of two groups of signals, computing formula is:With

S4, estimated value R to two autocorrelation matrixes₁And R₂Carry out Eigenvalues Decomposition respectively, R can be obtained₁M eigenvalue, by fall Sequence is arranged as: λ₁≥λ₂≥…≥λ_K＞ λ_K+1=...=λ_M=σ², the normalization characteristic vector that each eigenvalue is corresponding is followed successively by: u₁, u₂,…,u_M, in like manner, R can be obtained₂M eigenvalue, be arranged as in descending order: λ '₁≥λ'₂≥…≥λ'_K＞ λ '_K+1=...=λ '_M= σ², the normalization characteristic vector that each eigenvalue is corresponding is followed successively by: u '₁,u′₂,…,u′_M；

S5, construct the Y of two groups of sampled signals₁And Y₂Noise subspace E_N1And E_N2, wherein, E_N1It is by λ_K+1,…,λ_MCorresponding Normalization characteristic vector u_K+1,…,u_MThe noise subspace opened, E_N1=span{u_K+1,…,u_M}。E_N2It is by λ '_K+1,…,λ'_M Corresponding normalization characteristic vector u'_K+1,…,u'_MThe noise subspace opened, E_N2=span{u'_K+1,…,u'_M}；

S6, make in S1a'₁(θ_i) it is at t₀In the moment, there is the width receiving passage During phase error, the direction vector of i-th incoming signal,In like manner, Make in S2a'₂(θ_i) it is at t₀In+Δ T the moment, there is the width phase receiving passage During error, the direction vector of i-th incoming signal,Root According to MUSIC algorithm principle, noise subspace E described in S5_N1Normalization characteristic vector u_K+1,…,u_MWith when there is amplitude phase error Sense vector is orthogonal, i.e.Make U₁=[u_K+1,…,u_M], U₂=[u'_K+1,…,u'_M], can obtain orthogonality relation equation group:Wherein, O It it is the full null matrix of M-K row 1 row；

S7, make G₁=F₁g G₂=F₂G, wherein g=[g₁,g₂,g₃,...,g_M]^T, F₁And F₂It is to characterize array element and receive between passage The M rank non-singular matrix of annexation, it is 1 that each row of every a line all only have 1 element, and remaining element is 0, F₁Diagonal Upper element is 1, and remaining element is 0, F₂In element, as a example by the element of the first row, at t₀+ Δ T the moment, if numbered c₁Array element connect reception passage be numbered c_kArray element at t₀The reception passage that moment connects, then receive the error of passage g₁'=g_k, corresponding F₂In the kth column element of the first row be 1, remaining element of the first row is 0, F₂In remaining the 2nd to M The row number at element 1 place in row element, after the same method by numbered c₂To c_MArray element connect reception passage determine；

S8, relational expression G that will obtain in S7₁=F₁G, G₂=F₂G substitutes in the orthogonality relation equation group in S6, can obtain the most orthogonal The equivalence transformation of relation equation group:Make first element g (1)=1 in g, Continuation rewrite equation:OrderB=[O'1]^T, And Q is sequency spectrum matrix so that equation group Qg=b exists least square solution g_LS, described least square solution's expression is:Wherein,Φ () represents the operation of the diagonally matrix of the vector transformation in bracket, right Element on the diagonal of angular moment battle array is the element of vector, [] in bracket^HFor conjugate transposition operation,Pseudoinverse for matrix Operation；

S9, according to the result in S8, can obtain MUSIC spectral function as follows:

The automatic correcting method of the amplitude phase error receiving passage of a kind of array signal the most according to claim 1, its feature It is: the condition of switching channel described in S2 is: array element place matrix is sequency spectrum matrix.