CN109239648A - Spectrum correlation subspaces direction-finding method based on symmetrical cycle frequency - Google Patents
Spectrum correlation subspaces direction-finding method based on symmetrical cycle frequency Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses the spectrum correlation subspaces direction-finding methods based on symmetrical cycle frequency, Cyclic Autocorrelation Function is established according to the cyclostationarity for receiving signal, utilize the weak dependence between the Cyclic Autocorrelation Function of symmetrical cycle frequency, construction circulation cross-correlation matrix, make the precision of direction finding better than existing spectrum correlation subspaces direction-finding method, and there is higher direction finding correct probability.
Description
Technical field
The present invention relates to electronic information technical fields, it particularly relates to which the spectrum correlator based on symmetrical cycle frequency is empty
Between direction-finding method.
Background technique
Array signal process technique can be used for handling array received signal, so that the wave for measuring multiple signals reaches
Direction (abbreviation direction finding), has a wide range of applications in fields such as radar, sonar, communication system and smart antennas.
In existing various direction-finding methods, interferometer direction finding method has good Measure direction performance to individual signals, but
In common-frequency multi-signal, method fails, by biggish limitation in application.Conventional subspace class direction-finding method believes same frequency more
Number there is good Measure direction performance, but direction finding freedom degree is limited by bay number, the signal number antenna arrays needed more
First number is bigger, and radio receiver volume is big, is restricted in specific application；Spectrum based on signal cycle smooth performance is related
Subspace direction-finding method is because having selection characteristic to signal, and boosting algorithm is anti-interference while extended antenna direction finding freedom degree
Ability, to be widely applied.But existing spectrum correlation subspaces algorithm signal second-order cyclic count unanimous circumstances under,
Algorithm failure.
For the problems in the relevant technologies, currently no effective solution has been proposed.
Summary of the invention
For above-mentioned technical problem in the related technology, the present invention proposes the spectrum correlation subspaces based on symmetrical cycle frequency
Direction-finding method, comprising the following steps:
Step 1: initialization process: initialization technique parameter is simultaneously stored；
Wherein, the technical parameter includes spread speed c, the signal of the element number of array M of array, element position md, signal
Carrier frequency f, signal sampling frequencies fs, azimuth angle theta, azimuth angle theta division interval delta θ, sampling snap number T0, signal cycle
Frequency a, signal symmetry cycle frequency-a, the signal number K that cycle frequency is a, auto-correlation delay, τ0；
Step 2: the azimuthal discrete of signal is determined according to the division interval delta θ of azimuth angle theta, azimuth angle theta in step 1
Value set and the corresponding steering vector set of the discrete value set；
Step 3: determine the time-domain sampling vector of array received signal: all array elements of reception device sampling array it is received enter
Signal is penetrated, so that it is determined that the time-domain sampling vector of array received signal:
X (t)=[x1(t),x2(t),...,xM(t)]
Wherein: at the time of t is analog-to-digital conversion, that is, receiving the time-domain sampling moment of signal, t=1,2 ..., T0, M is array element
Number, T0It is snap number；
Step 4: determining that array element receives the circulation cross-correlation matrix of sample of signal data, comprising:
Step 4-1: it according to the signal cycle frequency alpha set in step 1, calculates each in time-domain sampling vector in step 3
A vector xi(t), i=1, the Cyclic Autocorrelation Function of 2 ..., M
Step 4-2: according to the auto-correlation delay, τ set in step 10Determine corresponding circulation autocorrelation valueWithWherein: i=1,2 ..., M；
Each array element is correspondingForm matrix
And it is each array element is correspondingForm matrix
Step 4-3: according in step 4-2Determine its corresponding circulation cross-correlation matrix X
(α), X (- α)；
Step 4-4: it constructs array received sample data according to the X (α) in step 4-3, X (- α) and recycles cross-correlation matrix Ψ
(α)；
Step 5: determining that the pseudo- of each steering vector and noise subspace in steering vector set is composed, comprising:
Step 5-1: Eigenvalues Decomposition is carried out to Ψ in step 4 (α) respectively and determines its noise subspace；
Step 5-2: each steering vector a (α, the θ in step 2 in steering vector set are determinedi) with step 5-1 in noise
Pseudo- spectrum P (α, the θ of subspacei)；
Step 6: determining signal direction of arrival: respectively in step 5 each pseudo- spectrum P (α, θi) in search for maximum value, each pseudo- spectrum
In the corresponding steering vector of maximum value, taking the corresponding azimuth of the steering vector is the signal direction of arrival of measurement.
Further, signal cycle frequency a and signal number K are determined by modulated parameter estimating method in step 1,
In: auto-correlation delay, τ0Value be τ0=[1 234567 8].
Further, in step 2: determining signal according to the division interval delta θ of azimuth angle theta, azimuth angle theta in step 1
Azimuthal discrete value set and the corresponding steering vector set of the discrete value set specifically include:
Step 2-1 divides interval delta θ according to azimuth angle theta in step 1, azimuth angle theta is evenly dividing into NθA discrete value
For θiSet；
Step 2-2, corresponding each discrete value θi, α determines array steering vector a (α, θi), in which: i=1,2 ...,
Nθ。
Further, in step 2: according to each discrete value θi, determine array steering vector a (α, θi) are as follows:
a(α,θi)=[a1(α,θi), a2(α,θi),L aM(α,θi)]
Wherein,τm(i)=dmsin(θi)/c is that signal reaches m-th of array element
Time difference, c are the spread speed of signal, i=1,2 ..., Nθ, m=1,2 ..., M, M are element number of array, and α is k-th of signal
Cycle frequency.
Further, array element described in step 4 receives the Cyclic Autocorrelation Function of sample of signal dataWithCalculation are as follows:
Wherein<>indicates seeking time average calculating operation.
Further, the calculation of cross-correlation matrix X (α) and X (- α) are recycled in step 4 are as follows:
Wherein: α is the cycle frequency of signal, and-α is symmetrical cycle frequency corresponding with α.
Further, the calculation of array received sample data circulation cross-correlation matrix Ψ (α) is constructed in step 4 are as follows:
Ψ (α)=X (α)+IX (- α) I
Wherein: I is M × M switching matrix.
Further, the mode of noise subspace is determined in step 5 are as follows: mutual by recycling to array received sample data
It closes matrix Ψ (α) progress Eigenvalues Decomposition and obtains corresponding characteristic value and feature vector, according toIt carries out special
Value indicative is decomposed,
Wherein: Uk=[uk1,uk2,...,ukM], uk1,uk2,...,ukMFor left eigenvector,
vk1,vk2,...,vkMFor right feature vector, Σ=diag { λk1,λk2,...λkM, λk1> λk2> ... > λkMFor corresponding feature
Value；
According to subspace theory, λk(K+1),λk(K+2),...,λkMThe space of corresponding feature vector is that noise is empty
Between Ukn=[uk(K+1),uk(K+2),...,ukM]。
Further, in step 5: determining each steering vector a (α, the θ in step 2 in steering vector seti) and step
Pseudo- spectrum P (α, the θ of noise subspace in 5-1i) calculation are as follows:
P(α,θi)=20glg (| | a (α, θi)||/||Ukna(α,θi)||)
Wherein | | | | indicate modulus.
Beneficial effects of the present invention: the spectrum correlation subspaces direction-finding method based on symmetrical cycle frequency, according to reception signal
Cyclostationarity establish Cyclic Autocorrelation Function, utilize the weak correlation between the Cyclic Autocorrelation Function of symmetrical cycle frequency
Property, construction circulation cross-correlation matrix makes the precision of direction finding better than existing spectrum correlation subspaces direction-finding method, and has higher survey
To correct probability.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the spectrum correlation subspaces direction-finding method working principle flow chart element based on symmetrical cycle frequency according to the present invention
Figure.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art's every other embodiment obtained belong to what the present invention protected
Range.
According to an embodiment of the invention, providing the spectrum correlation subspaces direction-finding method based on symmetrical cycle frequency, use
The even linear array of 16 array elements, adjacent array element spacing are d=37.5 meters, and the straight line where selecting array element is x-axis, from left side number first
A array element is that origin establishes reference frame.Two carrier frequencies are 40MHz, the BPSK modulated signal that bit rate is 4MHz/s from
1.43 °, even linear array is incident in 5.74 ° of directions, and reception device acquires all array elements and receives signal.
Detailed process the following steps are included:
Step 1: initialization process: initialization technique parameter is simultaneously stored；
Wherein, the technical parameter includes spread speed c, the signal of the element number of array M of array, element position md, signal
Carrier frequency f, signal sampling frequencies fs, azimuth angle theta, azimuth angle theta division interval delta θ, sampling snap number T0, signal cycle
Frequency a, signal symmetry cycle frequency-a, the signal number K that cycle frequency is a, auto-correlation delay, τ0；Specifically, passing through signal
Method for parameter estimation determines signal cycle frequency a and signal number K；
In the present embodiment: initializing the element number of array M=16 of array, the rectangular co-ordinate of element position is md, wherein d=
37.5, m=0,1 ..., 15, spread speed c=3 × 10 of signal8M/s, signal(-) carrier frequency f=40MHz, signal sampling frequency
Rate fs=320MHz, azimuth angle theta ∈ [- 90 °, 90 °] divide interval delta θ=0.1 °, divide number Nh=180 °/Δ θ+1=
1801, signal cycle frequency alpha=4e6, symmetrical cycle frequency-α=- 4e6, signal number K=2, switching matrix IM×M, from phase
Close delay, τ0=[1 234567 8], snap number T0=2000.
Step 2: the azimuthal discrete of signal is determined according to the division interval delta θ of azimuth angle theta, azimuth angle theta in step 1
Value set and the corresponding steering vector set of the discrete value set；
In the present embodiment: according to each discrete value θi, determine array steering vector a (α, θi) are as follows:
a(α,θi)=[a1(α,θi), a2(α,θi),L aM(α,θi)]
Wherein,τm(i)=dmsin(θi)/c is that signal reaches m-th of array element
Time difference, c are the spread speed of signal, i=1,2 ..., Nθ, m=1,2 ..., M, M are element number of array, and α is k-th of signal
Cycle frequency.
In the present embodiment: being evenly dividing into azimuth angle theta firstly, dividing 0.1 degree of interval according to azimuth angle theta in step 1
1801 discrete values are θi=(i-1) × 0.1 degree of set, i=1,2 ..., 1801；
Secondly, corresponding each discrete value θi,α, determine signal from direction of arrival direction θiArray steering vector when incident
a(α,θi), array steering vector a (α, θi) 16 elements respectively pass through following formula determine:
Wherein: m=0,1 ..., 15, i=1,2 ..., 1801, d are array element spacing, and c is the spread speed of signal, and α is
Signal cycle frequency；Corresponding 1.4 ° of direction of arrival, preceding 8 elements of steering vector are as follows:
1.0000+0.0000i,0.9969-0.0785i,0.9877-0.1564i,0.9724-0.2334i
0.9511-0.3090i,0.9239-0.3827i,0.8910-0.4540i,0.8526-0.5225i
Corresponding 5.7 ° of direction of arrival, preceding 8 elements of steering vector are as follows:
1.0000+0.0000i,0.9511-0.3090i,0.8090-0.5878i,0.5878-0.8090i
0.3090-0.9511i,0.0000-1.0000i,-0.3090-0.9511i,-0.5878-0.8090i
Step 3: determine the time-domain sampling vector of array received signal: all array elements of reception device sampling array it is received enter
Signal is penetrated, so that it is determined that the time-domain sampling vector of array received signal:
X (t)=[x1(t),x2(t),...,xM(t)]
Wherein: at the time of t is analog-to-digital conversion, that is, receiving the time-domain sampling moment of signal, t=1,2 ..., T0, M is array element
Number, T0It is snap number；
8 elements are respectively as follows: before the time-domain sampling of first array element reception signal
-0.3878+0.2340i,-0.3972+0.6042i,0.2163-0.1836i,-0.2488+0.1669i,
-0.2183+0.0431i,-0.3023-0.5051i,0.1275+0.1100i,-0.3059+0.0095i
8 elements are respectively as follows: before the time-domain sampling of the last one array element reception signal
-1.6073-0.4407i,1.9497-0.1891i,0.9620-0.3590i,-1.3549+0.0334i,
-1.9182+0.2205i,-1.4811-0.0252i,-0.9528-0.1640i,0.9736+0.3686i
Step 4: determining that array element receives the circulation cross-correlation matrix of sample of signal data, comprising:
Step 4-1: it according to the signal cycle frequency alpha set in step 1, calculates each in time-domain sampling vector in step 3
A vector xi(t), i=1, the Cyclic Autocorrelation Function of 2 ..., M
Step 4-2: according to the auto-correlation delay, τ set in step 10Determine corresponding circulation autocorrelation valueWithWherein: i=1,2 ..., M；
Each array element is correspondingForm matrix
And it is each array element is correspondingForm matrix
Step 4-3: according in step 4-2Determine its corresponding circulation cross-correlation matrix X
(α), X (- α)；
Step 4-4: it constructs array received sample data according to the X (α) in step 4-3, X (- α) and recycles cross-correlation matrix Ψ
(α)；
In the present embodiment: the Cyclic Autocorrelation Function of the reception sample of signal data of array element described in step 4WithCalculation are as follows:
Wherein<>indicates seeking time average calculating operation.
In the present embodiment: recycling the calculation of cross-correlation matrix X (α) and X (- α) in step 4 are as follows:
Wherein: α is the cycle frequency of signal, and-α is symmetrical cycle frequency corresponding with α.
In the present embodiment: constructing the calculation of array received sample data circulation cross-correlation matrix Ψ (α) in step 4
Are as follows:
Ψ (α)=X (α)+IX (- α) I
Wherein: I is M × M switching matrix.
Specifically, determining that array element receives the circulation cross-correlation matrix of sample of signal data in step 4: corresponding circulation is mutual
8 elements before the first row of pass matrix are as follows:
0.0750,0.0715-0.0124i,0.0653-0.0249i,0.0572-0.0332i,
0.0414-0.0389i,0.0343-0.0463i,0.0237-0.0450i,0.0092-0.0365i
8 elements before the last line of corresponding circulation cross-correlation matrix are as follows:
0.0283-0.0029i,0.0197-0.0062i,0.0086-0.0015i,0.0072-0.0011i
-0.0028+0.0092i,-0.0005+0.0130i,0.0024+0.0238i,0.0029+0.0350i
Step 5: determining that the pseudo- of each steering vector and noise subspace in steering vector set is composed, comprising:
Step 5-1: Eigenvalues Decomposition is carried out to Ψ in step 4 (α) respectively and determines its noise subspace；
Step 5-2: each steering vector a (α, the θ in step 2 in steering vector set are determinedi) with step 5-1 in noise
Pseudo- spectrum P (α, the θ of subspacei)；
In the present embodiment: determining the mode of noise subspace in step 5 are as follows: mutual by being recycled to array received sample data
Correlation matrix Ψ (α) carries out Eigenvalues Decomposition and obtains corresponding characteristic value and feature vector, according toIt carries out
Eigenvalues Decomposition,
Wherein: Uk=[uk1,uk2,...,ukM], uk1,uk2,...,ukMFor left eigenvector,
vk1,vk2,...,vkMFor right feature vector, Σ=diag { λk1,λk2,...λkM, λk1> λk2> ... > λkMFor corresponding feature
Value；
According to subspace theory, λk(K+1),λk(K+2),...,λkMThe space of corresponding feature vector is that noise is empty
Between Ukn=[uk(K+1),uk(K+2),...,ukM]。
In the present embodiment: in step 5: determining each steering vector a (α, the θ in step 2 in steering vector seti) and step
Pseudo- spectrum P (α, the θ of noise subspace in rapid 5-1i) calculation are as follows:
P(α,θi)=20glg (| | a (α, θi)||/||Ukna(α,θi)||)
Wherein | | | | indicate modulus.
Specific: determine that the pseudo- of each steering vector and noise subspace in steering vector set is composed in step 5: wave reaches
- 90 ° of direction, -89.9 °, -89.8 °, -89.7 ° of corresponding pseudo- spectrum are 0.009685,0.009685,0.009682,
0.009679,1801 pseudo- spectrum are determined in total.
Step 6: determining signal direction of arrival: respectively in step 5 each pseudo- spectrum P (α, θi) in search for maximum value, each pseudo- spectrum
In the corresponding steering vector of maximum value, taking the corresponding azimuth of the steering vector is the signal direction of arrival of measurement；
In the present embodiment: in pseudo- spectrum P (α, the θ that step 5 determinesi), K=2 maximum of search in i=1,2 ..., 1801
Peak value, peak-peak are equal to 1.865, and direction of arrival corresponding to the corresponding steering vector of peak-peak is 6.1 °, that is, is measured
The direction of arrival of signal；
Secondary peak-peak is equal to 1.836, and direction of arrival corresponding to the corresponding steering vector of secondary peak-peak is 1.5 °, i.e.,
The direction of arrival of the signal of measurement.
The root-mean-square error of the signal direction of arrival of the method for the present invention after measured is examined in the present embodiment, counts 500 times solely
The measurement result of vertical test, signal-to-noise ratio are -4dB~10dB, in the case where stepping 2dB, the method for the present invention and existing spectrum correlation
The root-mean-square error comparison of the signal direction of arrival of subspace method measurement is as shown in table 1 below；
Table 1: the error performance of Wave arrival direction estimating method compares
The correct probability of the signal direction of arrival of the method for the present invention after measured is examined, and the measurement of 500 independent experiments is counted
As a result, signal-to-noise ratio is -10dB~4dB, in the case where stepping 2dB, once correctly estimate when angle measurement error absolute value is less than 2 °
Meter.The correct probability comparison such as the following table 2 of the method for the present invention and the signal direction of arrival of existing spectrum correlation subspaces method measurement
It is shown；
Table 2: the correct probability performance of Wave arrival direction estimating method compares
As it can be seen that the method for the present invention can accurately measure signal direction of arrival；Compared to existing spectrum correlation subspaces method, survey
Root-mean-square error between fixed signal direction of arrival and actual signal direction of arrival is smaller, and the method for the present invention is in direction finding
In the case that Error Absolute Value is correct estimation less than 2 °, correct probability is higher than existing spectrum correlation subspaces method.
It can be seen that the spectrum correlation subspaces based on symmetrical cycle frequency are surveyed by means of above-mentioned technical proposal of the invention
To method, establish Cyclic Autocorrelation Function according to the cyclostationarity for receiving signal, using symmetrical cycle frequency circulation from
Weak dependence between correlation function, construction circulation cross-correlation matrix, surveys the precision of direction finding better than existing spectrum correlation subspaces
To method, and there is higher direction finding correct probability.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (9)
1. the spectrum correlation subspaces direction-finding method based on symmetrical cycle frequency, which comprises the following steps:
Step 1: initialization process: initialization technique parameter is simultaneously stored；
Wherein, the technical parameter includes spread speed c, the signal carrier of the element number of array M of array, element position md, signal
Frequency f, signal sampling frequencies fs, azimuth angle theta, azimuth angle theta division interval delta θ, sampling snap number T0, signal cycle frequency
A, signal symmetry cycle frequency-a, the signal number K that cycle frequency is a, auto-correlation delay, τ0；
Step 2: azimuthal discrete value of signal is determined according to the division interval delta θ of azimuth angle theta, azimuth angle theta in step 1
Set and the corresponding steering vector set of the discrete value set；
Step 3: determining the time-domain sampling vector of array received signal: the received incident letter of all array elements of reception device sampling array
Number, so that it is determined that the time-domain sampling vector of array received signal:
X (t)=[x1(t),x2(t),...,xM(t)]
Wherein: at the time of t is analog-to-digital conversion, that is, receiving the time-domain sampling moment of signal, t=1,2 ..., T0, M is element number of array,
T0It is snap number；
Step 4: determining that array element receives the circulation cross-correlation matrix of sample of signal data, comprising:
Step 4-1: according to the signal cycle frequency alpha set in step 1, each arrow in step 3 in time-domain sampling vector is calculated
Measure xi(t), i=1, the Cyclic Autocorrelation Function of 2 ..., M
Step 4-2: according to the auto-correlation delay, τ set in step 10Determine corresponding circulation autocorrelation valueWithWherein: i=1,2 ..., M；
Each array element is correspondingForm matrixAnd
Each array element is correspondingForm matrix
Step 4-3: according in step 4-2Determine its corresponding circulation cross-correlation matrix X (α), X (-
α)；
Step 4-4: array received sample data circulation cross-correlation matrix Ψ (α) is constructed according to the X (α) in step 4-3, X (- α)；
Step 5: determining that the pseudo- of each steering vector and noise subspace in steering vector set is composed, comprising:
Step 5-1: Eigenvalues Decomposition is carried out to Ψ in step 4 (α) respectively and determines its noise subspace；
Step 5-2: each steering vector a (α, the θ in step 2 in steering vector set are determinedi) empty with noise in step 5-1
Between pseudo- spectrum P (α, θi)；
Step 6: determining signal direction of arrival: respectively in step 5 each pseudo- spectrum P (α, θi) in search for maximum value, in each pseudo- spectrum most
Big to be worth a corresponding steering vector, taking the corresponding azimuth of the steering vector is the signal direction of arrival of measurement.
2. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
Signal cycle frequency a and signal number K are determined by modulated parameter estimating method in rapid 1, in which: auto-correlation delay, τ0Value
For τ0=[1 234567 8].
3. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
In rapid 2: determining azimuthal discrete value set of signal according to the division interval delta θ of azimuth angle theta, azimuth angle theta in step 1
And the corresponding steering vector set of the discrete value set specifically includes:
Step 2-1 divides interval delta θ according to azimuth angle theta in step 1, azimuth angle theta is evenly dividing into NθA discrete value is θi
Set；
Step 2-2, corresponding each discrete value θi, α determines array steering vector a (α, θi), in which: i=1,2 ..., Nθ。
4. the spectrum correlation subspaces direction-finding method according to claim 3 based on symmetrical cycle frequency, which is characterized in that step
In rapid 2: according to each discrete value θi, determine array steering vector a (α, θi) are as follows:
a(α,θi)=[a1(α,θi), a2(α,θi),L aM(α,θi)]
Wherein, am(θi)=exp (j2 π α τm(i)),τm(i)=dmsin(θi)/c is that signal reaches m-th of array element
Time difference, c are the spread speed of signal, i=1,2 ..., Nθ, m=1,2 ..., M, M are element number of array, and α is k-th of signal
Cycle frequency.
5. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
The Cyclic Autocorrelation Function of the reception sample of signal data of array element described in rapid 4WithCalculation are as follows:
Wherein<>indicates seeking time average calculating operation.
6. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
The calculation of cross-correlation matrix X (α) and X (- α) are recycled in rapid 4 are as follows:
Wherein: α is the cycle frequency of signal, and-α is symmetrical cycle frequency corresponding with α.
7. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
The calculation of array received sample data circulation cross-correlation matrix Ψ (α) is constructed in rapid 4 are as follows:
Ψ (α)=X (α)+IX (- α) I
Wherein: I is M × M switching matrix.
8. the spectrum correlation subspaces direction-finding method according to claim 1 based on symmetrical cycle frequency, which is characterized in that step
The mode of noise subspace is determined in rapid 5 are as follows: by carrying out feature to array received sample data circulation cross-correlation matrix Ψ (α)
Value decomposition obtains corresponding characteristic value and feature vector, according toEigenvalues Decomposition is carried out,
Wherein: Uk=[uk1,uk2,...,ukM], uk1,uk2,...,ukMFor left eigenvector,
vk1,vk2,...,vkMFor right feature vector, Σ=diag { λk1,λk2,...λkM, λk1> λk2> ... > λkMFor corresponding feature
Value；
According to subspace theory, λk(K+1),λk(K+2),...,λkMThe space of corresponding feature vector is noise subspace Ukn
=[uk(K+1),uk(K+2),...,ukM]。
9. the spectrum correlation subspaces direction-finding method according to claim 8 based on symmetrical cycle frequency, which is characterized in that step
In rapid 5: determining each steering vector a (α, the θ in step 2 in steering vector seti) with step 5-1 in noise subspace puppet
Compose P (α, θi) calculation are as follows:
P(α,θi)=20glg (| | a (α, θi)||/||Ukna(α,θi)||)
Wherein | | | | indicate modulus.
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| CN112882111A (en) * | 2021-01-18 | 2021-06-01 | 吉林大学 | Magnetic resonance response signal parameter extraction method and system based on cyclic correlation |
| CN117590322A (en) * | 2024-01-18 | 2024-02-23 | 金华信园科技有限公司 | Virtual array direction finding method for cyclostationary signal |
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| CN117590322A (en) * | 2024-01-18 | 2024-02-23 | 金华信园科技有限公司 | Virtual array direction finding method for cyclostationary signal |
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