CN108710102A - Wave arrival direction estimating method based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform - Google Patents
Wave arrival direction estimating method based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/78—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using electromagnetic waves other than radio waves
- G01S3/782—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Abstract
The invention discloses a kind of Wave arrival direction estimating method based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform, mainly solves the problems, such as that existing method computation complexity is higher and can not estimate simultaneously with signal power.Implementation step is：The relatively prime array of receiving terminal framework；Using relatively prime array received incoming signal and model；The second order equivalence virtual signal corresponding to the virtual uniform linear array of augmentation is derived according to relatively prime array received signal；It defines angle-spatial frequency and describes the second order equivalence virtual signal of virtual uniform linear array with it；Inverse discrete Fourier transform is carried out to the second order equivalence virtual signal using angle-spatial frequency description, builds space power spectrum；The Mutual coupling and power estimated information that spectrum peak search obtains signal are carried out according to constructed space power spectrum.The present invention reduces the computation complexity of Mutual coupling, and can obtain the power estimated information of signal simultaneously while improving Mutual coupling degree of freedom performance.
Description
Technical field
The invention belongs to signal processing technology fields, more particularly to the system of radar signal, acoustic signal and electromagnetic signal
Signal processing is counted, specifically a kind of direction of arrival based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform is estimated
Meter method, can be used for passive location and target acquisition.
Background technology
Direction of arrival (Direction-of-Arrival, DOA) estimation is that one of array signal processing field asks substantially
Topic, it refers to receiving signal using sensor array, and carry out Statistics Division by the docking collection of letters number of a series of signal processing method
Reason, to obtain direction of arrival information included in signal, has extensively in fields such as radar, sonar, voice, wireless communications
General application.
The degree of freedom of DOA estimation method refers to the incident signal source number that it can estimate.Traditional DOA estimation method is logical
The reception and modeling of signal, but the freedom of the DOA estimation method based on uniform linear array are carried out frequently with uniform linear array
Degree is limited to physics element number of array.When incident signal source number is more than physics element number of array in array, it is based on homogenous linear
The DOA estimation method of array will be unable to obtain effective estimated result.Relatively prime array is a kind of non-equal with systematization structure
Even thinned array can break through the limitation of conventional uniform linear array degree of freedom, realize in the case where physics array number is certain
The promotion of degree of freedom performance, therefore the extensive concern of academia is obtained in recent years.The original of DOA estimation method based on relatively prime array
Reason is built one and corresponds to the two of virtual uniform linear array to be derived relatively prime array to virtual Domain using the property of prime number
Rank equivalence virtual signal is estimated for DOA.Virtual array quantity is more than physics array element quantity in the virtual uniform linear array, because
This realizes the promotion of degree of freedom.
The existing DOA estimation method based on relatively prime array mostly on the basis of relatively prime array second order equivalence virtual signal into
The more complicated operation of row, including invert, the design of complicated matrix operation and convex optimization problem such as Eigenvalues Decomposition with ask
Processes, these calculating processes such as solution result in higher computation complexity, are faced under the higher application scenarios of requirement of real-time
Certain challenge, and hardware realization in systems in practice is more difficult.In addition, existing DOA estimation method mostly can not be
The power information of signal is obtained while obtaining Mutual coupling information.However, signal power is also describe signal one
Important Parameters, the detection for target and identification important in inhibiting.
Invention content
It is a kind of based on relatively prime array second order etc. it is an object of the invention in view of the deficiency of the prior art, propose
The Wave arrival direction estimating method of valence virtual signal inverse discrete Fourier transform, by using the mutual of angle-spatial frequency description
Matter array second order equivalence virtual signal carries out inverse discrete Fourier transform, realizes that DOA estimates degree of freedom performance boost, and obtain simultaneously
The Mutual coupling for the number of winning the confidence and corresponding signal power information.Institute's extracting method of the present invention has lower computation complexity,
It is easy to hardware realization in systems in practice.
The purpose of the present invention is achieved through the following technical solutions：One kind is based on relatively prime array second order virtual letter of equal value
The Wave arrival direction estimating method of number inverse discrete Fourier transform, comprises the steps of：
(1) receiving terminal uses 2M+N-1 array element, and carries out framework according to relatively prime array structure；Wherein M and N is relatively prime whole
Number；
(2) assume there are L to come from θ=s [θ1,θ2,…,θL]TThe far field narrowband incoherent signal source , [ in direction;·]TIt indicates to turn
Operation is set, incoming signal is received using the relatively prime array built in step (1), then in the relatively prime array received of t moment
Signal x (t) can be modeled as：
Wherein, x (t) is (2M+N-1) × 1 dimensional vector, sl(t) be first of incoming signal waveform, n (t) be and each letter
Number mutually independent noise component(s) in source, a (θl) it is corresponding to θlThe relatively prime array steering vector in direction signal source, is represented by
Wherein, μi, i=1,2,3 ..., 2M+N-1 indicate the physical location of i-th of physics array element in relatively prime array, and head
The position of a physics array element is μ1=0, λ are the wavelength of incident narrow band signal, and j is imaginary unit.
Covariance matrix is built according to relatively prime array received signal x (t)：The sampling association side obtained using T sampling snap
Poor matrixTo theoretical covariance matrix RxCarry out approximate substitution；
(3) the second order virtual letter of equal value corresponding to the virtual uniform linear array of augmentation is derived according to relatively prime array received signal
Number：Pass through vectorization sample covariance matrixObtain virtual array equivalence virtual signal y：
Wherein,For
(2M+N-1)2× L ties up guiding matrix,To include the vector of L incoming signal source power,
For noise power, i=vec (I2M+N-1), I2M+N-1Indicate (2M+N-1 × (2M+N-1 ties up unit matrix, and vec () indicates vector
Change operation, i.e., each row in matrix is stacked gradually to form a new vector, ()*Indicate conjugate operation,Expression gram
Kronecker product；
The corresponding non-homogeneous virtual array S of vectorial yDIt is expressed as：
SD={ ± (Mn-Nm) d, 0≤n≤N-1,0≤m≤2M-1 },
Wherein d is the half of incident narrow band signal wavelength, i.e.,
Choose non-homogeneous virtual array SDThe Virtual array of middle maximum continuous part, composition one include 2V+1 virtual array
The virtual uniform linear array S of memberV={-Vd ,-(V-1) d ..., 0 ..., (V-1) d, Vd }, V=MN+M-1；
Selection corresponds to S from vectorial yVIn each Virtual array position virtual signal of equal value, form virtual uniform linear array
Corresponding second order equivalence virtual signal zθ, it is represented by：
Wherein, B (θ)=s [b(θ1),b(θ2),…b(θL)], l row
It is right
It should be in θlThe virtual uniform linear array steering vector in direction signal source, e are by selecting to correspond to S from iVThe element of middle array element forms
Vector；
(4) it defines angle-spatial frequency and describes the second order equivalence virtual signal of virtual uniform linear array with it.Define angle
Degree-spatial frequency is propagated by the narrow band signal from direction θ in space within the scope of propagation distance difference between adjacent array element
Signal period number.The second order equivalence virtual signal z of virtual uniform linear array in step (3)θIt can be of equal value in angle-spatial frequency domain
It is expressed as：
Wherein, B (ξ)=s [b(ξ1),b(ξ2),…b(ξL)], l row ξ=s [ξ1,ξ2,…,ξL]TIt is right
Angle-spatial frequency of L angle included in θ；
(5) inverse discrete Fourier transform, and structure are carried out to the second order equivalence virtual signal using angle-spatial frequency description
Build space power spectrum：The second order equivalence virtual signal z that will be indicated by angle-spatial frequency by inverse discrete Fourier transformξ
Conversion obtains the dimension spaces of its K × 1 response ψ to spatial domain；
A space power spectrum is built, the horizontal axis of the spectrum indicates angle, θ, the pass with vectorial k-th of the element of roomage response
System is represented by：
Wherein, k=0,1 ..., K-1, arccos () are inverse cosine function, and h is to ensureMeet anticosine letter
The coefficient of several domains, whenWhen, h=-1, whenWhen, h=0；The longitudinal axis representation space of the spectrum
The mould P (k) of k-th of element in response vector；
(6) Mutual coupling is carried out according to gained space power spectrum and signal power is estimated.To space work(in step (5)
Rate spectrum carries out spectrum peak search operation, then the corresponding angle of the maximum preceding L peak value of amplitude is the direction of arrival of L incoming signal
Estimation, and its peak amplitude is the power estimation value to induction signal.
Further, the relatively prime array structure described in step (1) can be specifically described as：First, choose one group it is relatively prime whole
Number M, N, a pair of sparse homogenous linear subarray of construction.First subarray includes the array element that 2M spacing is Nd, and position is
0,Nd,…,(2M-1)Nd；Second subarray includes the array element that N number of spacing is Md, position 0, Md ..., (N-1) Md.It
Two subarrays are combined in such a way that first array element overlaps afterwards, are obtained non-homogeneous comprising 2M+N-1 physics array element
Relatively prime array.
Further, in step (3), if there are multiple and different elements and S in yVIn same Virtual array position it is corresponding
Situation then selects any one in these elements as composition of vector zθElement.
Further, angle-spatial frequency in step (4) is a kind of frequency related with signal incident angle, specifically
It defines in the following way：The narrow band signal arrival intervals from direction θ are that the adjacent array element of d will produce one section in space
Propagation distance difference u, is represented by：
U=dcos θ.
Fixed in array element spacing, propagation distance difference u only changes with incoming signal angle, θ, therefore obtains
The definition of angle-spatial frequency in step (4).Angle-spatial frequency ξ and the relationship of incoming signal angle, θ are represented by：
Further, the second order equivalence virtual signal z obtained by inverse discrete Fourier transform in the step (5)ξK
× 1 dimension space responds ψ, is represented by：
Wherein,Indicate inverse discrete Fourier transform operation, FKIt, can table for leaf inverse-transform matrix in K point discrete Fouriers
It is shown as：
The roomage response ψ of gained is the dimensional vectors of K × 1.
Further, in the step (5), constructed spatial spectrum reflects the response amplitude in each angle in space,
Wherein there is the L peak value corresponding to L incoming signal.
Further, there is the L peak value corresponding to L incoming signal, the knot in the step (5) in space power spectrum
By obtaining in the following way：Relationship P (k) for building space power spectrum is specifically represented by：
Wherein,For the power of first of signal, δ () indicates impulse function, is integer, for indicating the impulse function
For periodical impulse string sequence.According to the property of impulse function it is found that only when When, P (k) is peak
Value.Since L incoming signal has different angle-spatial frequencys, each angle-spatial frequency energy and it is only capable of in spatial power
Cause a peak value in spectrum, therefore there is the L peak value corresponding to L incoming signal in space power spectrum.
Compared with the prior art, the present invention has the following advantages：
(1) institute's extracting method of the present invention to the relatively prime array second order equivalence virtual signal using the description of angle-spatial frequency into
The mode of row inverse discrete Fourier transform obtains roomage response and based on this structure space power spectrum, by constructed space work(
The spectrum peak search process of rate spectrum obtains Mutual coupling as a result, avoiding common convex excellent in traditional Wave arrival direction estimating method
The design of change problem solves and the complicated calculations processes such as matrix inversion, Eigenvalue Decomposition, is ensureing DOA estimation degree of freedom
On the basis of capable of being promoted, the power estimation of signal can be obtained simultaneously.
(2) institute's extracting method of the present invention carries out Mutual coupling using inverse discrete Fourier transform, significantly reduces meter
Complexity is calculated, preferably meets the higher application demand of requirement of real-time, while being easy to hardware realization in systems in practice.
Description of the drawings
Fig. 1 is the method overall procedure block diagram of the present invention；
Fig. 2 is the sparse uniform subarray structural schematic diagram of a pair that relatively prime array is formed in the present invention；
Fig. 3 is the structural schematic diagram of relatively prime array in the present invention；
Fig. 4 is the schematic diagram for embodying institute's extracting method signal power accuracy of estimation under different signal-to-noise ratio of the present invention；
Fig. 5 is the signal for embodying institute's extracting method of the present invention signal power accuracy of estimation under different sampling number of snapshots
Figure；
Fig. 6 is the space power spectrum schematic diagram for embodying institute's extracting method degree of freedom performance of the present invention.
Specific implementation mode
Referring to the drawings, technical solutions and effects of the present invention is described in further detail.
Relatively prime array is realized due to that can carry out statistical disposition to its second order equivalence virtual array signal in physics array number
The promotion of degree of freedom performance, obtains the extensive concern of academia in recent years in the case of certain.It is existing in real system application
DOA estimation method computation complexity it is higher, it is difficult to meet the higher application scenarios of requirement of real-time, and complicated calculating process
There are certain difficulties for hardware realization in systems in practice.In addition, existing DOA estimation method can not obtain wave up to side mostly
To the power for estimating each signal source while estimation.In view of the above problems, the present invention provides one kind being based on relatively prime array second order
The Wave arrival direction estimating method of virtual signal inverse discrete Fourier transform of equal value, referring to Fig.1, steps are as follows for realization of the invention：
Step 1：In receiving terminal relatively prime array is built using 2M+N-1 practical array element.First, choose one group it is relatively prime whole
Number M, N, a pair of sparse homogenous linear subarray of construction.First subarray includes the array element that 2M spacing is Nd, and position is
0,Nd,…,(2M-1)Nd；Second subarray includes the array element that N number of spacing is Md, position 0, Md ..., (N-1) Md,
Middle unit spacing d is half-wavelength, that is, λ/2 d=of incident narrow band signal.Two subarrays are overlapped according to first array element later
Mode is combined, and obtains the non-homogeneous relatively prime array for including 2M+N-1 practical array element.
Step 2：Using relatively prime array received signal and to signal modeling.Assuming that there is L to come from θ=s [θ1,θ2,…,θL]T
The far field narrowband incoherent signal source , [ in direction;·]TTransposition operation is indicated, using the relatively prime array built in step 1 to incidence
Signal is received, then can be modeled as in the relatively prime array received signal x (t) of t moment：
Wherein, x (t) is (2M+N-1) × 1 dimensional vector, sl(t) be first of incoming signal waveform, n (t) be and each letter
Number mutually independent noise component(s) in source, a (θl) it is corresponding to θlThe relatively prime array steering vector in direction signal source, is represented by
Wherein, μi, i=1,2,3,2M+N-1 indicates the physical location of i-th of physics array element in relatively prime array, and first
The position of physics array element is μ1=0, λ are the wavelength of incident narrow band signal, and j is imaginary unit.In practice, fast using T sampling
Clap obtained sample covariance matrixTo theoretical covariance matrix RxApproximate substitution is carried out,And RxIt can be expressed as
Rx=E[x(t)xH(t)],
Wherein, ()HIndicate conjugate transposition, E[·]Indicate mathematic expectaion.
Step 3：The second order void of equal value corresponding to the virtual uniform linear array of augmentation is derived according to relatively prime array received signal
Quasi- signal.Virtual array equivalence virtual signal y can pass through the sample covariance matrix in vectorization step 2It obtains：
Wherein,For
(2M+N-1)2× L ties up guiding matrix,To include the vector of L incoming signal source power,
For noise power, i=vec (I2M+N-1), I2M+N-1Indicate (2M+N-1) × (2M+N-1) tie up unit matrix, vec () indicate to
Quantization operation is stacked gradually each row in matrix to form a new vector, ()*Indicate conjugate operation,It indicates
Kronecker product.The corresponding non-homogeneous virtual array S of vectorial yDIt is represented by：
SD={ ± (Mn-Nm) d, 0≤n≤N-1,0≤m≤2M-1 },
Wherein d is the half of incident narrow band signal wavelength, i.e.,Choose non-homogeneous virtual array SDIt is middle maximum continuous
Partial Virtual array forms a virtual uniform linear array S for including 2V+1 Virtual arrayV=-Vd ,-(V-1) d ...,
0 ..., (V-1) d, Vd }, wherein V=MN+M-1.Selection corresponds to S from vectorial yVIn each Virtual array position equivalence it is virtual
Signal, the corresponding second order equivalence virtual signal z of composition virtual uniform linear arrayθ, it is represented by：
Wherein, B (θ)=s [b(θ1),b(θ2),…b(θL)], l rowIt is right
It should be in θlThe virtual uniform linear array steering vector in direction signal source, e are by selecting to correspond to S from iVThe element composition of array element
Vector.If there are multiple and different elements and S in yVIn situation corresponding to same Virtual array position, then select in these elements
Any one is as composition of vector zθElement.
Step 4：It defines angle-spatial frequency and describes the second order equivalence virtual signal of virtual uniform linear array with it.Definition
Angle-spatial frequency is propagated by the narrow band signal from direction θ in space within the scope of propagation distance difference between adjacent array element
Signal period number.Specifically, the narrow band signal arrival intervals from direction θ are that the adjacent array element of d will produce one section in space
Propagation distance is poor, is represented by：
U=dcos θ,
In the case where array element spacing is certain, which changes with incident angle θ, and angle-spatial frequency is fixed
Justice is the periodicity that narrow band signal is propagated in the propagation distance difference, i.e.,：
Correspondingly, in step 3 virtual uniform linear array second order equivalence virtual signal zθIt can be in angle-spatial frequency domain
It is expressed equivalently as：
Wherein ξ=s [ξ1,ξ2,…,ξL]TCorresponding to angle-spatial frequency of L angle included in θ.
Step 5：Inverse discrete Fourier transform is carried out to the second order equivalence virtual signal using angle-spatial frequency description,
Obtain roomage response.It can be by the second order indicated by angle-spatial frequency virtual letter of equal value by inverse discrete Fourier transform
Number zξConversion obtains its roomage response ψ to spatial domain, is represented by：
Wherein,Indicate inverse discrete Fourier transform operation, FKIt, can table for leaf inverse-transform matrix in K point discrete Fouriers
It is shown as：
The roomage response ψ of gained is the dimensional vectors of K × 1.A space power spectrum is built, the horizontal axis of the spectrum indicates angle, θ,
It is represented by with the relationship of vectorial k-th of the element of roomage response：
Wherein, k=0,1 ..., K-1, arccos () are inverse cosine function, and h is to ensureMeet anticosine letter
The coefficient of several domains, whenWhen, h=-1, whenWhen, h=0；The spectrum
The mould P (k) of k-th of element, is represented by longitudinal axis representation space response vector：
P (k)=s |[ψ]k|,
Wherein , [·]kIndicate k-th of element , | in vector;·|Indicate the mould of plural number.Specifically, P (k) is represented by：
Wherein,For the power of first of signal, δ () indicates impulse function, is integer, for indicating the impulse function
For periodical impulse string sequence.According to the property of impulse function it is found that only whenWhen, P (k) is peak
Value.Since L incoming signal has different angle-spatial frequencys, each angle-spatial frequency energy and it is only capable of in spatial power
Cause a peak value in spectrum, therefore there is the L peak value corresponding to L incoming signal in space power spectrum.
Step 6：Mutual coupling and signal power estimation are carried out according to gained space power spectrum.It is hollow to step 5
Between power spectrum carry out spectrum peak search operation, by its peak value according to arranging from high to low, then it is a to correspond to L for maximum preceding L peak value
Incoming signal, while the peak value of this L spectral peak is respectively the power estimation value of corresponding signal.
The carried Wave arrival direction estimating method of the present invention passes through to the relatively prime array second order etc. using angle-spatial frequency description
Valence virtual signal carries out inverse discrete Fourier transform and obtains roomage response and build a space power spectrum based on this, by this
The spectrum peak search process of space power spectrum can obtain the power estimation letter of Mutual coupling information and corresponding signal simultaneously
Breath.Compared to traditional Wave arrival direction estimating method based on uniform linear array, institute's extracting method of the present invention ensure that wave reaches
While direction estimation degree of freedom performance boost, computation complexity is onlyPreferably meet to real-time have it is higher
It is required that practical application scene, be also easier to hardware realization in systems in practice.
The effect of the present invention is further described with reference to simulation example.
Simulation example 1：Using relatively prime array received incoming signal, parameter is chosen for M=9, N=10, i.e., framework is mutual
Matter array includes 2M+N-1=27 physics array element altogether.Fixed sample number of snapshots T=1000, tests different signal-to-noise ratio respectively
Under, institute's extracting method of the present invention passes through root-mean-square error to the power accuracy of estimation in individual signals source and 30 signal sources
(RMSE) it indicates, calculation formula is：
Wherein, Q is Monte Carlo experiment number,Indicate that the power of first of signal in the q times Monte Carlo experiment is estimated
Evaluation,For the actual power of first of signal.In this emulation, Q=1000.The case where for individual signals source, covers special every time
Signal source incident direction meets Gaussian Profile in the experiment of CarlowThe case where for 30 signal sources, signal
Source incident direction is distributed evenly within the scope of 45 ° to 135 ° this space angle domains.To individual signals source under different signal-to-noise ratio
It is as shown in Figure 4 with the power accuracy of estimation of 30 signal sources.As can be seen that in the two kinds of feelings in individual signals source and 30 signal sources
Under condition, institute's extracting method power estimation error of the present invention is respectively less than 1dB, can relatively accurately carry out the estimation of signal power.
Simulation example 2：Using relatively prime array received incoming signal identical with simulation example 1, signal-to-noise ratio is set as 10dB,
It is tested respectively in different sampling number of snapshots, power of the institute's extracting method of the present invention to individual signals source and 30 signal sources
Accuracy of estimation, other simulated conditions keep identical with simulation example 1.Individual signals source and 30 under the conditions of difference sampling number of snapshots
Power accuracy of estimation is as shown in Figure 5 in the case of a signal source.As can be seen that in the case of individual signals source, power estimation
Root-mean-square error be respectively less than 1dB；In the case of 30 signal sources, power estimation is square when sampling number of snapshots are more than 300
Root error is reduced to 1dB or less.Therefore, institute's extracting method of the present invention can relatively accurately carry out the estimation of signal power.
Simulation example 3：Using relatively prime array received incoming signal identical with simulation example 1, signal-to-noise ratio is set as 10dB,
Sampling number of snapshots are set as T=500.It is assumed that incident narrow band signal number is 30, incident direction be uniformly distributed in 45 ° to 135 ° this
Within the scope of one space angle domain.Space power spectrum that institute's extracting method of the present invention obtains as shown in fig. 6, wherein vertical dotted line represent into
Penetrate the true directions of signal source.As can be seen that institute's extracting method of the present invention can effectively differentiate this 30 incident signal sources.For passing
System can only at most differentiate 26 incident letters using the Wave arrival direction estimating method of uniform linear array using 27 physics array elements
Number, result above, which embodies institute's extracting method of the present invention, realizes the increase of degree of freedom.
In conclusion institute's extracting method of the present invention passes through the second order equivalence virtual signal to being described using angle-spatial frequency
It carries out inverse discrete Fourier transform to obtain its roomage response and build a space power spectrum based on this, by constructed space
The spectrum peak search process of power spectrum obtains DOA estimations, while ensureing that DOA estimates degree of freedom performance boost, obtains corresponding letter
Number power estimation value.The operation of inverse discrete Fourier transform significantly reduces computation complexity, preferably meets to reality
The practical application scene that when property has higher requirements, while being easy to hardware realization in systems in practice.
Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and
In scope of the claims, to any modifications and changes that the present invention makes, protection scope of the present invention is both fallen within.
Claims (7)
1. a kind of Wave arrival direction estimating method based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform, special
Sign is, comprises the steps of：
(1) receiving terminal uses 2M+N-1 array element, and carries out framework according to relatively prime array structure；Wherein M and N is relatively prime integer；
(2) assume there are L to come from θ=s [θ1,θ2,…,θL]TThe far field narrowband incoherent signal source , [ in direction;·]TIndicate transposition behaviour
Make, incoming signal is received using the relatively prime array built in step (1), then in the relatively prime array received signal x of t moment
(t) it can be modeled as：
Wherein, x (t) is (2M+N-1) × 1 dimensional vector, sl(t) be first of incoming signal waveform, n (t) be and each signal source phase
Mutual independent noise component(s), a (θl) it is corresponding to θlThe relatively prime array steering vector in direction signal source, is represented by
Wherein, μi, i=1,2,3 ..., 2M+N-1 indicate the physical location of i-th of physics array element in relatively prime array, and first physics
The position of array element is μ1=0, λ are the wavelength of incident narrow band signal, and j is imaginary unit.
Covariance matrix is built according to relatively prime array received signal x (t)：The sampling covariance square obtained using T sampling snap
Battle arrayTo theoretical covariance matrix RxCarry out approximate substitution；
(3) the second order equivalence virtual signal corresponding to the virtual uniform linear array of augmentation is derived according to relatively prime array received signal：
Pass through vectorization sample covariance matrixObtain virtual array equivalence virtual signal y：
Wherein,For (2M+N-
1)2× L ties up guiding matrix,To include the vector of L incoming signal source power,For noise
Power, i=vec (I2M+N-1), I2M+N-1Indicate that (2M+N-1) × (2M+N-1) ties up unit matrix, vec () indicates vectorization behaviour
Make, i.e., each row in matrix is stacked gradually to form a new vector, ()*Indicate conjugate operation,It indicates in Crow
Gram product；
The corresponding non-homogeneous virtual array S of vectorial yDIt is expressed as：
SD={ ± (Mn-Nm) d, 0≤n≤N-1,0≤m≤2M-1 },
Wherein d is the half of incident narrow band signal wavelength, i.e.,
Choose non-homogeneous virtual array SDThe Virtual array of middle maximum continuous part, composition one include 2V+1 Virtual array
Virtual uniform linear array SV={-Vd ,-(V-1) d ..., 0 ..., (V-1) d, Vd }, V=MN+M-1；
Selection corresponds to S from vectorial yVIn each Virtual array position virtual signal of equal value, composition virtual uniform linear array it is corresponding
Second order equivalence virtual signal zθ, it is represented by：
Wherein, B (θ)=s [b(θ1),b(θ2),…b(θL)], l row
To correspond to θlThe virtual uniform linear array steering vector in direction signal source, e are by selecting to correspond to S from iVThe element of middle array element
The vector of composition；
(4) it defines angle-spatial frequency and describes the second order equivalence virtual signal of virtual uniform linear array with it.Define angle-sky
Between signal week for being propagated within the scope of propagation distance difference between adjacent array element by the narrow band signal from direction θ in space of frequency
Issue.The second order equivalence virtual signal z of virtual uniform linear array in step (3)θCan in angle-spatial frequency domain equivalent representation
For：
Wherein, B (ξ)=s [b(ξ1),b(ξ2),…b(ξL)], l row ξ=s [ξ1,ξ2,…,ξL]TIt is right
Angle-spatial frequency of L angle included in θ；
(5) inverse discrete Fourier transform is carried out to the second order equivalence virtual signal using angle-spatial frequency description, and builds sky
Between power spectrum：The second order equivalence virtual signal z that will be indicated by angle-spatial frequency by inverse discrete Fourier transformξConversion
To spatial domain, and then obtain the dimension spaces of its K × 1 response ψ；
A space power spectrum is built, the horizontal axis of the spectrum indicates angle, θ, and the relationship with vectorial k-th of the element of roomage response can
It is expressed as：
Wherein, k=0,1 ..., K-1, arccos () are inverse cosine function, and h is to ensureMeet inverse cosine function
The coefficient of domain, whenWhen, h=-1, whenWhen, h=0；The longitudinal axis representation space of the spectrum is rung
Answer the mould P (k) of k-th of element in vector；
(6) Mutual coupling is carried out according to gained space power spectrum and signal power is estimated.To space power spectrum in step (5)
Spectrum peak search operation is carried out, then the corresponding angle of the maximum preceding L peak value of amplitude is that the direction of arrival of L incoming signal is estimated
Meter, and its peak amplitude is the power estimation value to induction signal.
2. the wave according to claim 1 based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform reaches side
To method of estimation, it is characterised in that：Relatively prime array structure described in step (1) can be specifically described as：First, one group of selection is relatively prime
Integer M, N, a pair of sparse homogenous linear subarray of construction.First subarray includes the array element that 2M spacing is Nd, position
It is set to 0, Nd ..., (2M-1) Nd；Second subarray includes the array element that N number of spacing is Md, position 0, Md ..., (N-1)
Md.Two subarrays are combined in such a way that first array element overlaps later, obtain including 2M+N-1 physics array element
Non-homogeneous relatively prime array.
3. the relatively prime array direction of arrival according to claim 1 based on angle-spatial frequency domain Fast Fourier Transform (FFT)
Method of estimation, it is characterised in that：In step (3), if there are multiple and different elements and S in yVIn same Virtual array position correspond to
The case where, then select any one in these elements as composition of vector zθElement.
4. the wave according to claim 1 based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform reaches side
To method of estimation, it is characterised in that：Angle-spatial frequency in step (4) is a kind of frequency related with signal incident angle,
Particular by being defined such as under type：The narrow band signal arrival intervals from direction θ are that the adjacent array element of d will produce in space
One section of propagation distance difference u, is represented by：
U=dcos θ.
Fixed in array element spacing, propagation distance difference u only changes with incoming signal angle, θ, therefore obtains step
(4) definition of angle-spatial frequency in.Angle-spatial frequency ξ and the relationship of incoming signal angle, θ are represented by：
5. the wave according to claim 1 based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform reaches side
To method of estimation, it is characterised in that：The second order equivalence virtual signal obtained by inverse discrete Fourier transform in the step (5)
zξThe dimension spaces of K × 1 respond ψ, be represented by：
Wherein,Indicate inverse discrete Fourier transform operation, FKFor leaf inverse-transform matrix in K point discrete Fouriers, it is represented by：
The roomage response ψ of gained is the dimensional vectors of K × 1.
6. the relatively prime array direction of arrival according to claim 1 based on angle-spatial frequency domain Fast Fourier Transform (FFT)
Method of estimation, it is characterised in that：In the step (5), constructed spatial spectrum reflects the response width in each angle in space
Degree, wherein there is the L peak value corresponding to L incoming signal.
7. the wave according to claim 6 based on relatively prime array second order equivalence virtual signal inverse discrete Fourier transform reaches side
To method of estimation, it is characterised in that：There is the L peak corresponding to L incoming signal in the step (5) in space power spectrum
Value, the conclusion obtain in the following way：Relationship P (k) for building space power spectrum is specifically represented by：
Wherein,For the power of first of signal, δ () indicates impulse function, and r is integer, for indicating that the impulse function is week
Phase property impulse string sequence.According to the property of impulse function it is found that only whenWhen, P (k) is peak value.By
There is different angle-spatial frequencys in L incoming signal, each angle-spatial frequency energy and be only capable of in space power spectrum
Cause a peak value, therefore there is the L peak value corresponding to L incoming signal in space power spectrum.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109471065A (en) * | 2018-09-28 | 2019-03-15 | 中国电子科技集团公司第三十六研究所 | A kind of direction-finding method of coherent signal |
| CN110133574A (en) * | 2019-07-02 | 2019-08-16 | 华南理工大学 | Utilize the one-dimensional DOA estimation method of the secondary virtual extended of multiple-frequency signal |
| CN111610486A (en) * | 2020-05-03 | 2020-09-01 | 浙江大学 | High-resolution accurate two-dimensional direction of arrival estimation method based on planar co-prime array virtual domain tensor space spectrum search |
| CN112162240A (en) * | 2020-09-25 | 2021-01-01 | 五邑大学 | Sparse frequency waveform generation method and device based on co-prime array and storage medium |
| WO2021068495A1 (en) * | 2020-05-03 | 2021-04-15 | 浙江大学 | Degree of freedom-enhanced spatial spectrum estimation method based on block sampled tensor signal construction using planar co-prime array |
| CN114167354A (en) * | 2021-11-25 | 2022-03-11 | 厦门大学 | Underwater DOA estimation method based on high degree of freedom |
| CN115407128A (en) * | 2022-07-29 | 2022-11-29 | 南京航空航天大学 | Power system harmonic and inter-harmonic frequency estimation method based on co-prime sampling |
| WO2023137812A1 (en) * | 2022-01-21 | 2023-07-27 | 浙江大学 | Coprime planar array two-dimensional direction-of-arrival estimation method based on virtual domain tensor filling |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107015190A (en) * | 2017-03-01 | 2017-08-04 | 浙江大学 | Relatively prime array Wave arrival direction estimating method based on the sparse reconstruction of virtual array covariance matrix |
| CN107422295A (en) * | 2017-08-30 | 2017-12-01 | 浙江大学 | The Wave arrival direction estimating method represented based on relatively prime array virtual Domain equivalent signal atom norm |
| CN108680892A (en) * | 2018-05-15 | 2018-10-19 | 浙江大学 | Relatively prime array Wave arrival direction estimating method based on angle-spatial frequency domain Fast Fourier Transform (FFT) |
-
2018
- 2018-05-15 CN CN201810460228.7A patent/CN108710102B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107015190A (en) * | 2017-03-01 | 2017-08-04 | 浙江大学 | Relatively prime array Wave arrival direction estimating method based on the sparse reconstruction of virtual array covariance matrix |
| CN107422295A (en) * | 2017-08-30 | 2017-12-01 | 浙江大学 | The Wave arrival direction estimating method represented based on relatively prime array virtual Domain equivalent signal atom norm |
| CN108680892A (en) * | 2018-05-15 | 2018-10-19 | 浙江大学 | Relatively prime array Wave arrival direction estimating method based on angle-spatial frequency domain Fast Fourier Transform (FFT) |
Non-Patent Citations (3)
| Title |
|---|
| CHENGWEI ZHOU等: "Doa estimation by covariance matrix sparse reconstruction of coprime array", 《 2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)》 * |
| YANG LIU等: "High-resolution Direction-of-Arrival estimation in SNR and snapshot challenged scenarios using multi-frequency coprime arrays", 《 2017 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)》 * |
| YIMIN D. ZHANG等: "Sparsity-based DOA estimation using co-prime arrays", 《 2013 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING》 * |
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| CN109471065B (en) * | 2018-09-28 | 2021-05-25 | 中国电子科技集团公司第三十六研究所 | Direction finding method for coherent signals |
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| US11422177B2 (en) | 2020-05-03 | 2022-08-23 | Zhejiang University | Spatial spectrum estimation method with enhanced degree-of-freedom based on block sampling tensor construction for coprime planar array |
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