CN108303671A - Space stretches five elementary dipole array Mutual couplings and polarization estimate - Google Patents
Space stretches five elementary dipole array Mutual couplings and polarization estimate Download PDFInfo
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- CN108303671A CN108303671A CN201711387017.7A CN201711387017A CN108303671A CN 108303671 A CN108303671 A CN 108303671A CN 201711387017 A CN201711387017 A CN 201711387017A CN 108303671 A CN108303671 A CN 108303671A
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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
- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
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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
- G01S3/146—Systems for determining direction or deviation from predetermined direction by comparing linear polarisation components
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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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Abstract
The invention discloses a kind of spaces to stretch five elementary dipole array Mutual couplings and polarization estimate, has following steps：S1, structure space stretch five elementary dipole arrays；S2, observation signal；S3, the steering vector that space stretches five elementary dipole arrays is obtained；S4, vector cross-products are sought；S5, array element spacing judge：When array element is smaller than the half equal to far field narrowband EM signal wavelengths, step S6 is executed；When array element spacing is more than the half of far field narrowband EM signal wavelengths, step S7 is executed；S6, direction of arrival and polarization parameter are asked；S7, deblurring processing；S8, direction of arrival and polarization parameter are asked.
Description
Technical field
The present invention relates to a kind of spaces to stretch five elementary dipole array Mutual couplings and polarization estimate.
Background technology
Electromagnetic Vector Sensor Array signal processing is that academic circles at present is ground as an important branch of signal processing
The hot issue studied carefully.Electromagnetic vector sensor (EMVS) is due to that can perceive polarization of electromagnetic wave characteristic, with scalar sensors phase
Than having advantage outstanding in terms of Mutual coupling (DOA) and polarization estimation.But traditional electromagnetic vector sensor
Each antenna concurrent is placed, and there are serious mutual couplings, and implement complex and expensive, constrain answering in Practical Project
With.In order to solve problem above, it proposes in recent years and stretches electromagnetic vector sensor (SS-EMVS), the sky of this non-concurrent point formula
Between structure each antenna is separated, lower coupling and the opposite antenna aperature improved are made it have, in recent years in wave
Up to direction estimation (DOA) and polarization estimate aspect by higher and higher concern.
Spatial electromagnetic propagation vector sensor (SS-EMVS) is orthogonal non-total by three orthogonal non-dipoles of position altogether and three
The ring composition [1]-[9] set.Dipole and loop are used, respectively, to measure the electric field and magnetic field of electromagnetism (EM) wave.Due to spatially
Sensor spacing, for SS-EMVS compared to EMVS [10]-[11], [14] reduce coupling effect, therefore greatly reduce EMVS's
Hardware cost.Initialization about SS-EMVS is concentrated mainly on its physics realization [1]-[3].There is the work of some early stages anti-
The SS-EMVS thoughts based on signal processing are reflected.For example, [4] propose a kind of variant of Root-MUSIC algorithms, in this feelings
Under condition, dipole and ring can arbitrary collocation or with L-type array it is evenly distributed.In addition to work mentioned above, nearest
Research work is directed generally to the design of SS-EMVS space structures, can carry out DOA estimations and the polarization estimate of low cost
[6]-[8].Particularly, [6] and [8] respectively estimate the DOA of the vector cross-products of two kinds of specific SS-EMVS structures estimations and polarization
Meter is proved.SS-EMVS has found so big effect in practice, and so for the research of SS-EMVS be mainly because
For：(1) mutual coupling effect is far smaller than the EMVS of space arrangement；(2) DOA estimation and polarization estimate can by it is low at
This mode obtains good result of calculation；(3) SS-EMVS is compared to EMVS, due to a half-wave of the ratio signal between sensor
It is long to want greatly more, there is better aperture.All it is to use SS-EMVS, and assume in SS-EMVS in the research being generally noted above
Dipole and ring be all identical for EM responses.However, this is difficult to realize in practice, because of natural conditions
The response of lower dipole has prodigious different [10] [11] [12] from the response of ring.In order to solve this problem, [12] are directed to
DOA estimates and polarization estimate proposes an a kind of array being made of five dipoles (or ring), referred to as SS-quint.
SS-quint is used for compensating the phase difference caused by spacing between sensor using two with reference to point sensor.Particularly,
[12] SS-quint proposed in needs to be evenly distributed L-type battle array.In [13], a kind of space of special only dipole
Distribution array, which is used, carries out DOA estimations and polarization estimate.However, its assume source signal azimuth be fixed pi/2 and
It is known that therefore the method in [13] is only limited to carry out one-dimensional DOA estimations.
Invention content
According to technical problem set forth above, stretches five elementary dipole array direction of arrival we have proposed a kind of space and estimate
Meter and polarization estimate.The space proposed stretches five elementary dipole arrays with the symmetrical geometric configuration of space center, therefore compared with
It is more more flexible than the SS-quint proposed in [12], it is not only restricted to any specific array configuration.Particularly, this center pair
The array structure of title makes the DOA estimations of the low cost based on vector cross-products and polarization estimate algorithm be achieved, and this method is
Through being widely used in EMVS and SS-EMVS, but be directed to not yet only be dipole or ring array case carry out it is real
It is existing.In addition, we will also study the case where sensor array element spacing is more than information source wavelength half, and propose a kind of estimation calculation
Method further improves the performance of SS-quint.
The symbol first used below to the present invention is done as described below：
Scalar variable and scalar constant are indicated with lower case and upper case letter respectively.Vector sum matrix uses the black matrix of small letter respectively
It is indicated with the bold-faced letter of capitalization.R of vectorial a are expressed as a (r) or ar.Similar, (r, u) item of matrix A is by table
It is shown as A (r, u) or ar,u.The unit matrix of one M × M is expressed as IM.Transposition, conjugation and norm are expressed as ()T,
(·)*With | | | |F.Symbol ' ∠ () ', ' Re () ', and ' Im () ' indicate phase angle, real and imaginary parts respectively.Letter
' i ' indicates imaginary unit.The estimated value that we define a variable a is
Symbol' * ' indicates Kronecker product and Hadamard product respectively, is defined as follows：
Symbol ' × ' indicates vector cross-products, is defined as follows：
Wherein
The technological means that the present invention uses is as follows：
A kind of space stretches five elementary dipole array Mutual couplings and polarization estimate, it is characterised in that has following step
Suddenly：
S1, structure space stretch five elementary dipole arrays：
The dipole that the array is placed in parallel along the x-axis direction by two, two dipoles being placed in parallel along the y-axis direction
The dipole triads being placed in parallel in the z-direction with one at；Set the dipole being placed in parallel in the z-direction to reference point, and will
It is placed in the origin of cartesian coordinate system, and two dipoles being placed in parallel along the x-axis direction are about origin central symmetry, two edges
For the dipole that y-axis direction is placed in parallel about origin central symmetry, that is, it is a pass to build space and stretch five elementary dipole arrays
In the centrosymmetric array configuration of z dipoles, useWith-k(1)Come indicate respectively two it is parallel along the x-axis direction
The space vector of the dipole of placement is usedWith-k(2)To indicate two idols being placed in parallel along the y-axis direction
Extremely sub space vector；
S2, observation signal：
Narrowband EM signals in one far field are incident on the array, obtain following formula：
There is the far field narrowband EM signals unit power, electric field component to be expressed as：
Wherein,It is direction of arrival and polarization parameter, θ ∈ [0,2 π],γ ∈ [0, pi/2], η ∈ [- π,
π], azimuth, pitch angle, auxiliary polarization angle and polarization phases angle are respectively represented,It is to close
In direction of arrival parameterDirection vector；
S3, the steering vector that space stretches five elementary dipole arrays is obtained by formula (1) and formula (2)：
Wherein,
S4, vector cross-products are sought：
It is as follows to define two subvectors：
It can be obtained by formula (3)：So as to a1 withVector cross-products：
S5, array element spacing judge：
When array element is smaller than the half equal to far field narrowband EM signal wavelengths, step S6 is executed；
When array element spacing is more than the half of far field narrowband EM signal wavelengths, step S7 is executed；
When multiple information sources carry out incident, we firstly the need of by array received to blended data be oriented to arrow to obtain
Amount.For example, we can estimate to lead by rotational invariance technology (ESPRIT) [14] or second-order blind identification (SOBI) [15]
To vector.Estimation about steering vector is not the research emphasis of the present invention.Here we assume that steering vector
It obtains, problem to be solved is how to pass through steering vectorCalculate DOA and polarization parameter.
S6, direction of arrival and polarization parameter are asked：
Following property is used in formula (5)：
And γ ≠ 0 sin η sin γ cos is enabled, it obtains：
Therefore, knownUnder conditions of, the problem of Mutual coupling, is converted into a following optimization problem：
A kind of low cost has been suggested about optimization problem as above in [8], therefore is no longer introduced here.This hair
The main distinction of algorithm and algorithm in [8] proposed in bright is, the DOA estimations in [8] are total to dependent on dipole and ring
With the vector cross-products of response, and algorithm of the invention only needs the vector cross-products of the output of dipole or ring.
It is acquired by formula (8)Obtain direction of arrival parameter
Construction vector
Polarization parameter (γ, η) can be obtained by following formula：
The method of vector cross-products as introduced above can obtain accurate DOA estimations and polarization estimate knot under normal circumstances
Fruit.It, can be by way of array extending aperture come further but when array element spacing is more than a half-wavelength of incoming signal
Improve estimated accuracy.Here a kind of optimization method is briefly introduced, principle and [12], the method in [19]-[21] are similar.It is convenient
For the sake of, we set array configuration to k(1)=[d, 0,0]T, k(2)=[0, d, 0]T.Two such is placed in parallel along the x-axis direction
Dipole be just located at compare reference point distance be d x-axis both direction on, two are placed in parallel along the y-axis direction
Dipole be just located at compare reference point distance be d y-axis both direction on.Following derivation can expand to this
A example, and k therein(1)And k(2)It can be arbitrary.
S7, deblurring processing
DefinitionIt obtainsWithPass through formula (3)
Following formula is obtained with several simple transformation：
It is noted that due to the increase of array aperture in this case, formula (11) can obtain two groups accurately but have
The estimated value of fuzzy u ' and v '.This obscure is about m1And m2, their value can arbitrarily choose.Here we use logical
It is this fuzzy to eliminate to cross the result of vector cross-products acquisition：
Use ucpAnd vcpTo indicate the estimated value to u and v, m1And m2Optimal value can be counted by following formula
It calculates：
S8, direction of arrival and polarization parameter are asked：
It willWithValue substitute into formula (11), can obtain accuratelyValue, and pass throughWithCalculate direction of arrival parameter；Polarization parameter is calculated by formula (10).
Several simple transformation refer to handle in step S7WithBand
Enter in formula (3), formula (11) is acquired by solving equations.
The present invention has the following advantages：
1, the space proposed, which stretches five elementary dipole arrays, has the symmetrical geometric configuration of space center, therefore compared with than existing
Array configuration it is more flexible, be not only restricted to any specific array configuration.
2, centrosymmetric array structure enables DOA estimations and the polarization estimate algorithm of the low cost based on vector cross-products
It realizes.This method has been widely used in EMVS and SS-EMVS, but it is dipole or ring to be directed to not yet only
Array case is realized.
3, when array element spacing is more than the case where information source wavelength half, it is proposed that a kind of method of effective deblurring carries
High space stretches the performance of five elementary dipole arrays.
The present invention can be widely popularized in fields such as methods of estimation based on the above reasons.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to do simply to introduce, it should be apparent that, the accompanying drawings in the following description is this hair
Some bright embodiments for those of ordinary skill in the art without having to pay creative labor, can be with
Obtain other attached drawings according to these attached drawings.
Fig. 1 be the present invention specific implementation mode in space stretch five elementary dipole array Mutual couplings and polarization estimate
The flow chart of meter.
Fig. 2 be the present invention specific implementation mode in space stretch five elementary dipole arrays schematic diagram.
Fig. 3 be the present invention specific implementation mode in pitch angle and azimuthal CRB with array element spacing change curve.
Fig. 4 be the present invention specific implementation mode in the curves that change with signal-to-noise ratio of MSE and CRB (array element spacing is d=
0.5 λ, number of snapshots are fixed value 5000), wherein the incident result figure of (a) information source 1, (b) the incident result figure of information source 2, (c) two
The average MSE of kind information source.
Fig. 5 be the present invention specific implementation mode in the curves that change with number of snapshots of MSE and CRB (array element spacing is d=
0.5 λ, signal-to-noise ratio are fixed as 10dB), wherein the incident result figure of (a) information source 1, (b) the incident result figure of information source 2, (c) two kinds
The average MSE of information source.
Fig. 6 be the present invention specific implementation mode in the curves that change with signal-to-noise ratio of MSE and CRB (array element spacing is d=
8 λ, number of snapshots are fixed value 5000), wherein the incident result figure of (a) information source 1, (b) the incident result figure of information source 2, (c) two kinds
The average MSE of information source.
Fig. 7 be the present invention specific implementation mode in the curves that change with number of snapshots of MSE and CRB (array element spacing is d=
8 λ, signal-to-noise ratio are fixed value 20dB), wherein the incident result figure of (a) information source 1, (b) the incident result figure of information source 2, (c) two kinds
The average MSE of information source.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
The every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
As shown in Fig. 1-Fig. 7, a kind of space stretches five elementary dipole array Mutual couplings and polarization estimate, has such as
Lower step：
S1, structure space stretch five elementary dipole arrays：
The dipole that the array is placed in parallel along the x-axis direction by two, two dipoles being placed in parallel along the y-axis direction
The dipole triads being placed in parallel in the z-direction with one at；Set the dipole being placed in parallel in the z-direction to reference point, and will
It is placed in the origin of cartesian coordinate system, and two dipoles being placed in parallel along the x-axis direction are about origin central symmetry, two edges
The dipole that y-axis direction is placed in parallel is about origin central symmetry；WithWith-k(1)To indicate two respectively
The space vector for the dipole being placed in parallel along the x-axis direction is usedWith-k(2)To indicate two along y-axis side
To the space vector for the dipole being placed in parallel；
S2, observation signal：
Narrowband EM signals in one far field are incident on the array, obtain following formula：
There is the far field narrowband EM signals unit power, electric field component to be expressed as：
Wherein,It is direction of arrival and polarization parameter, θ ∈ [0,2 π],γ ∈ [0, pi/2], η ∈ [-
π, π], azimuth, pitch angle, auxiliary polarization angle and polarization phases angle are respectively represented,It is
About direction of arrival parameterDirection vector；
S3, the steering vector that space stretches five elementary dipole arrays is obtained by formula (1) and formula (2)：
Wherein,
S4, vector cross-products are sought：
It is as follows to define two subvectors：
It can be obtained by formula (3)：So as to a1 withVector cross-products：
S5, array element spacing judge：
When array element is smaller than the half equal to far field narrowband EM signal wavelengths, step S6 is executed；
When array element spacing is more than the half of far field narrowband EM signal wavelengths, step S7 is executed；
S6, direction of arrival and polarization parameter are asked：
Following property is used in formula (5)：
And γ ≠ 0 sin η sin γ cos is enabled, it obtains：
Therefore, knownUnder conditions of, the problem of Mutual coupling, is converted into a following optimization problem：
It is acquired by formula (8)Obtain direction of arrival parameter
Construction vector
Polarization parameter (γ, η) can be obtained by following formula：
S7, deblurring processing
DefinitionIt obtainsWithPass through formula (3)
Following formula is obtained with several simple transformation：
Formula (11) can obtain two groups accurately but with the estimated value of fuzzy u ' and v '.This obscure is about m1
And m2, their value can arbitrarily choose.Here we are eliminated this fuzzy using the result obtained by vector cross-products.Make
Use ucpAnd vcpTo indicate the estimated value to u and v, m1And m2Optimal value can be calculated by the following formula：
S8, direction of arrival and polarization parameter are asked：
It willWithValue substitute into formula (11), can obtain accuratelyValue, and pass throughWithCalculate direction of arrival parameter；Polarization parameter is calculated by formula (10).
Several simple transformation refer to handle in step S7WithBand
Enter in formula (3), formula (11) is acquired by solving equations.
We will derive that proposed space stretches DOA estimations and the polarization estimate of five elementary dipole arrays below
Cramér-Rao lower bound (CRB).CRB is unbiased estimator [17], and [18] provide the lower limit of variance, to calculate SS-quint times
Row carry out the best performance values of DOA estimation and polarization estimate.In document [6], had been proposed about other kinds of in [12]
The CRB's as a result, in the present invention of SS-EMVS, we and [6], [12] follow a similar derivation thinking, come obtain about
Itd is proposed by dipole triads at space stretch five elementary dipole arrays CRB.For annulate SS-quint arrays
CRB derive can also be similar obtain.
We use s (t)=exp (i2 π f in a far field0t1+ α) it is used as incoming signal, wherein f0One is respectively represented with α
The frequency and initial phase of a known a priori.Source signal stretches five elementary dipole arrays by space and is received, and addition is one
The white Gaussian noise n (t) that a mean value is zero.We assume that the hybrid matrix of noise item meets following form：Γ '=σ2I5, wherein
σ2Indicate the noise variance of a known a priori, therefore, the output of array can be expressed as following form：
Assuming that time sampling point t1,...,tN, we can be defined as follows data vector：
WhereinNoise item ε in formula (14) contains covariance square
Battle arrayWithIt indicates unknown parameter and definesTherefore, Fei Sheer information matrixs
(FIM) J can be expressed as：
Wherein k, l=1,2,3,4.We are given in Table 1 the display expression formula of J.After known to J, parameter ψkCRB
It can be acquired by following formula：
CRB(ψk)=(J-1)k,k, k=1,2,3,4. (16)
Table 1：
Simulation result is we provided to prove that proposed space stretches the performance of five elementary dipole arrays and corresponding
DOA estimates and the accuracy of polarization estimate.The space vector of two dipoles being placed in parallel along the x-axis direction is k respectively(1)=
[d,0,0]TWith-k(1).The space vector of two dipoles being placed in parallel along the y-axis direction is k respectively(2)=[0, d, 0]TWith-k(2).The dipole being placed in parallel in the z-direction is located at the origin of cartesian coordinate system.The battle array of different value is used in different emulation
First spacing d.DOA and polarization parameter are respectively
Noise is the white Gaussian noise chosen.Signal-to-noise ratio, which uses, such as gives a definition：
Wherein PsAnd PnRespectively represent signal power and noise power.
In emulating B and C, we estimate steering vector using SOBI [15], then use formula (4)-formula (12)
Involved method calculates DOA and polarization parameter.The performance of assessment algorithm is used for using mean square error (MSE) ε, definition to be such as
Under：
Wherein N represents Monte Carlo Experiment number, its value is that 500, α represents one of need in the emulation of the present invention
Estimative parameter,Represent the estimated value of n-th Monte Carlo Experiment.
In emulating B and C, we also estimate with the DOA proposed in [12] and polarization estimate algorithm compares.It needs
It should be noted that the algorithm proposed in [12] uses L-type array, we use it for space and stretch five yuan of dipoles herein
Subarray.First, five elementary dipole arrays are stretched according to the space of proposition, we can obtain
WithIn known steering vectorEach component prior information, we can defineWithDOA and polarization information can be calculated according to the algorithm proposed in [12] later.We can note
It anticipates and arrives, the adaptability of the algorithm above substantially relies on the prior information to direction cosine signal, therefore proposed in [12]
Algorithm can not with space stretch five elementary dipole arrays be matched well.In fact, algorithm proposed by the present invention and
[12] algorithm proposed in can match corresponding array configuration well, therefore be difficult to carry out one to the performance of these algorithms
A sequence.Therefore, the purpose that we are compared with [12] in simulations be to proposition method provide a comparator algorithm, and
It is not meant to carry out stringent performance ranking.
It is as follows to emulate A, B, C：
DOA and polarization parameter are respectively
Information source 1 is exactly the signal incidence that parameter is footmark 1；
Information source 2 is exactly the signal incidence that parameter is footmark 2；
The emulation that A.CRB changes with array element spacing
We are by drawing the CRB at the azimuth and elevation estimate of two source signals, to prove that proposed space stretches
The characteristic that five elementary dipole arrays change with array element spacing d.Number of snapshots are fixed value 5000, and Signal to Noise Ratio (SNR) is selected as 10dB.I
The value of d/ λ is changed to 10000 from 1.Simulation result is as shown in Figure 3.Can clearly it find out from figure, with array element spacing
Increase, the CRB of azimuth and pitch angle reduces, and therefore, the space proposed stretches five elementary dipole arrays can be
The resolution ratio of expanded- angle in DOA estimations.
B. the space under small array element spacing stretches DOA estimations and the polarization estimate of five elementary dipole arrays
We stretch five elementary dipole arrays by space small-sized a d=0.5 λ and exist to demonstrate vector cross-products algorithm
DOA estimates and the performance of polarization estimate.Number of snapshots are set as 5000. by us allows signal-to-noise ratio to be changed from 0dB to 20dB.
Later, it is 10dB that we, which fix signal-to-noise ratio, and number of snapshots T is made to be changed from 1000 to 5000.Fig. 4 and Fig. 5 is drawn
The curve of four kinds of parameters of each information source under the conditions of above two.It was noticed that two kinds of methods for being used for comparing all provide
Good MSE is as a result, with signal-to-noise ratio or the effect for increasing curve and monotone decreasing being presented of number of snapshots, and with corresponding
CRB lower limits.In addition, as can be seen that proposed algorithm has compared with than the algorithm in [12] from Fig. 4 (c) and Fig. 5 (c)
More accurate result.
C. the space under big array element spacing stretches DOA estimations and the polarization estimate of five elementary dipole arrays
We stretch five elementary dipole arrays to prove proposed calculation by space sparse an array element spacing d=8 λ
The performance of method.We fix number of snapshots T=5000 and signal-to-noise ratio are made to change to 20dB from 0dB.We fix Signal to Noise Ratio (SNR) later
=20dB simultaneously makes number of snapshots T change to 5000 from 1000.Fig. 6 and Fig. 7 depicts four kinds of each information source under the conditions of above two
The curve of parameter.Image in Fig. 6 and Fig. 7 shows that two methods can obtain accurate result.MSE curves are with noise
The increase of ratio and monotone decreasing, and variation tendency is consistent with CRB curves.It was noticed that if SNR and T are sufficiently large, this two
The result of kind method is almost the same.This can be visible in detail from Fig. 6 and Fig. 7.Particularly, in sufficiently high signal-to-noise ratio and
In the case of number of snapshots T, two methods can be generated correctly in the first step as a result, therefore in the presence of Optimization Steps
Fuzzy problem can be deleted.However, in the case of for low signal-to-noise ratio and fewer snapshots T, the result of first step acquisition
Just there is uncertainty, just will appear inaccurate result sometimes.Therefore, it is optimized using these inaccurate results
It is fuzzy to this may result in final result there are large errors.In fact, we have observed that two methods in low signal-to-noise ratio or
The exceptional value of result under conditions of fewer snapshots, the reason of drastically decline this also explains MSE curves in Fig. 6 and Fig. 7.Such as figure
Shown in 6 (c) and 7 (c), it was noticed that in the case of low signal-to-noise ratio and fewer snapshots, process proposed herein usually compares
[12] method in is more acurrate.
Finally it should be noted that：The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, it will be understood by those of ordinary skill in the art that：Its according to
So can with technical scheme described in the above embodiments is modified, either to which part or all technical features into
Row equivalent replacement；And these modifications or replacements, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
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Claims (2)
1. a kind of space stretches five elementary dipole array Mutual couplings and polarization estimate, it is characterised in that have following step
Suddenly：
S1, structure space stretch five elementary dipole arrays：
The dipole that the array is placed in parallel along the x-axis direction by two, two dipoles being placed in parallel along the y-axis direction and one
A dipole triads being placed in parallel in the z-direction at；It sets the dipole being placed in parallel in the z-direction to reference point, and is set
In the origin of cartesian coordinate system, two dipoles being placed in parallel along the x-axis direction are about origin central symmetry, and two along y-axis
The dipole that direction is placed in parallel is about origin central symmetry；WithWith-k(1)To indicate two respectively along x
The space vector for the dipole that axis direction is placed in parallel is usedWith-k(2)To indicate that two are put down along the y-axis direction
The space vector for the dipole that row is placed；
S2, observation signal：
Narrowband EM signals in one far field are incident on the array, obtain following formula：
There is the far field narrowband EM signals unit power, electric field component to be expressed as：
Wherein,It is direction of arrival and polarization parameter, θ ∈ [0,2 π],γ ∈ [0, pi/2], η ∈ [- π, π],
Azimuth, pitch angle, auxiliary polarization angle and polarization phases angle are respectively represented,Be about
Direction of arrival parameterDirection vector；
S3, the steering vector that space stretches five elementary dipole arrays is obtained by formula (1) and formula (2)：
Wherein,
S4, vector cross-products are sought：
It is as follows to define two subvectors：
It can be obtained by formula (3)：So as to a1 with's
Vector cross-products：
S5, array element spacing judge：
When array element is smaller than the half equal to far field narrowband EM signal wavelengths, step S6 is executed；
When array element spacing is more than the half of far field narrowband EM signal wavelengths, step S7 is executed；
S6, direction of arrival and polarization parameter are asked：
Following property is used in formula (5)：
And γ ≠ 0 sin η sin γ cos is enabled, it obtains：
Therefore, knownUnder conditions of, the problem of Mutual coupling, is converted into a following optimization problem：
It is acquired by formula (8)Obtain direction of arrival parameter
Construction vector
Polarization parameter (γ, η) can be obtained by following formula：
S7, deblurring processing
DefinitionIt obtainsWithBy formula (3) and several
A simple transformation obtains following formula：
Two groups can be obtained accurately but with the estimated value of fuzzy u ' and v '.This obscure is about m1And m2, their value
It can arbitrarily choose.Here we are eliminated this fuzzy using the result obtained by vector cross-products.More precisely, it uses
ucpAnd vcpTo indicate the estimated value to u and v, m1And m2Optimal value can be calculated by the following formula：
S8, direction of arrival and polarization parameter are asked：
It willWithValue substitute into formula (11), can obtain accuratelyValue, and pass throughWith
Calculate direction of arrival parameterPolarization parameter is calculated by formula (10).
2. space according to claim 1 stretches five elementary dipole array Mutual couplings and polarization estimate, feature
It is：Several simple transformation refer to handle in step S7WithIt brings into
In formula (3), formula (11) is acquired by solving equations.
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