CN108931758A - A method of low complex degree angle estimation is carried out using relatively prime linear array - Google Patents
A method of low complex degree angle estimation is carried out using relatively prime linear array Download PDFInfo
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- CN108931758A CN108931758A CN201810840884.XA CN201810840884A CN108931758A CN 108931758 A CN108931758 A CN 108931758A CN 201810840884 A CN201810840884 A CN 201810840884A CN 108931758 A CN108931758 A CN 108931758A
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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
Abstract
The invention discloses a kind of methods for carrying out low complex degree angle estimation using relatively prime linear array, first, vectorization processing is carried out to the covariance matrix of array received signal, redundant row is deleted and intercepts continuous array element part, obtains the reception signal for the virtual uniform linear array that array element spacing is λ/2；Then, to the virtual position for receiving signal and carrying out discrete Fourier transform (Discrete Fourier Transform, DFT) and finding out K peak-peak (K is information source number), it can thus be concluded that the initial estimation of direction of arrival；Finally, carrying out DFT transform to the virtual reception signal Jing Guo phase rotation, rotatable phase η is scanned in a small range, is found out respectively so that K peak contraction is to maximum rotatable phase, and thus obtains the accurate estimation of direction of arrival.The present invention combines DFT transform with the DOA estimation problem of relatively prime array, does not need to carry out decorrelation processing to the virtual signal that receives, can obtain relatively high spatial degrees of freedom, while having lower computation complexity and higher estimated accuracy.
Description
Technical field
The present invention relates to Estimation of Spatial Spectrum fields, are estimated more particularly to a kind of using relatively prime linear array progress low complex degree angle
The method of meter.
Background technique
Currently, a kind of array antenna being referred to as relatively prime battle array, which is laid out, is paid close attention to, which breaches traditional day
The limitation of linear array array element spacing half-wavelength can obtain mentioning for angle estimation performance so that antenna aperature is greatly extended
It rises.
There are two classes of ambiguity solution and virtualization using the method that relatively prime linear array carries out angle estimation.Wherein, ambiguity solution method energy
It is enough to obtain estimation performance more better than even linear array, but the method for using two submatrixs to carry out angle estimation respectively makes space certainly
It is substantially reduced by degree.And virtual method can then obtain spatial degrees of freedom more higher than practical array number, substantially increase
Detectable information source number.Since virtual signal equivalent after virtualization is the coherent signal of single snap, the angle based on virtualization
Algorithm for estimating usually requires to utilize spatial smoothing in a interface differential technique collection of letters number progress decorrelation processing, and this procedure reduces arrays
Spatial degrees of freedom.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of method for carrying out angle estimation using relatively prime linear array, the party
Method can obtain biggish spatial degrees of freedom, while have lower computation complexity and higher estimated accuracy.It can apply
In the fields such as wireless communication, sonar, positioning.
The present invention uses following technical scheme to solve above-mentioned technical problem: proposing a kind of combination virtualization and direct computation of DFT
The relatively prime linear array angle estimating method of leaf transformation (Discrete Fourier Transform, DFT), referred to as DFT algorithm, the party
Method specifically:
Firstly, the covariance matrix for receiving signal to relatively prime linear array carries out vectorization processing, then the vector of acquisition is pressed
Phase is ranked up and deletes redundant row, and the intermediate 2MN+2M-1 row element for intercepting vector at this time is received as Virtual array to be believed
Number.
Then, it to the virtual position for receiving signal and carrying out DFT transform and finding out K peak-peak (K is information source number), obtains
Direction of arrival initial estimation.
Finally, construction phase rotation matrix, carries out DFT transform to the virtual reception signal Jing Guo phase rotation, in small model
Enclose it is interior rotatable phase η is scanned for, found out respectively so that K peak contraction obtains direction of arrival to maximum rotatable phase
Accurate estimation.
The invention adopts the above technical scheme compared with prior art, has following technical effect that
1. taking full advantage of the relatively prime characteristic of array structure, and avoid space smoothing process, can obtain it is higher from
By spending；
2. having the characteristics that computation complexity is lower；
3. this method can obtain good angle estimation performance, such as relatively prime battle array compared to nested battle array, the battle array of relatively prime battle array
Member distribution is more sparse, and the mutual coupling effect between array element is weaker, therefore has preferably estimation performance under strong mutual coupling environment.
Detailed description of the invention
Fig. 1 is relatively prime linear array structure schematic diagram used in the present invention；
Fig. 2 is relatively prime linear array virtual array structural schematic diagram；
Fig. 3 is the angle estimation scatter plot that is obtained using DFT algorithm when 10 signals are incident on relatively prime linear array；
Fig. 4 is DFT algorithm initial estimation and the performance comparison accurately estimated；
Fig. 5 be under different number of snapshots DFT algorithm performance with the comparison of signal-to-noise ratio variation tendency；
Fig. 6 is that DFT algorithm performance compares under various information source number.
Specific embodiment
With reference to the accompanying drawing and specific embodiment is described in further detail technical solution of the present invention:
The present invention proposes a kind of method for carrying out angle estimation using relatively prime linear array, the array antenna structure that this method uses
It is made of the even linear array that two array numbers are respectively 2M and N, array element spacing is respectively λ/2 N and λ/2 M, and wherein M and N is relatively prime
Number and M < N, λ are carrier wavelength, and two submatrix at the origins have an array element to be overlapped.It is required that array number be 2M and N be because
The number and range of the continuously and virtually array element generated in this way have closed solutions, while available more continuous array elements.
One, data model
One as shown in Fig. 1 can be used relatively prime linear array example of the invention, wherein M=3, N=4.
Assuming that K come from θkThe narrow band signal of (k=1,2 ..., K) is incident in relatively prime linear array as shown in Figure 1, then battle array
Column receive signal and are represented by
X=AS+N
Wherein, S=[s1, s2..., sK]TFor signal matrix, sk=[sk(1), sk(2) ..., sk(L)], L is number of snapshots,
skIt (l) is the l times sampled result to k-th of signal, l=1,2 ..., L；N is the additive white Gaussian noise of array, and mean value is
Zero, variance isA=[a (θ1), a (θ2) ..., a (θK)] be array direction matrix, a (θk) it is θkSquare upwardly direction to
Amount.The direction vector of two submatrixs can be expressed as
Wherein, λ/2 d=.Therefore when entire array being used to carry out DOA estimation, direction vector is represented by
Wherein, a21(θk) it is a2(θk) remove the vector after the first row.
Two, angle estimating method
1, it virtualizes
Firstly, seeking the covariance matrix of relatively prime linear array reception signal X.In Practical Project, since signal sampling is all to have
Carried out under limit number of snapshots, receive the covariance matrix of signal byIt is calculated.It willVectorization is carried out to handle
It arrives
Wherein,A long void can be regarded as
The direction matrix of matroid column,For single snap signal vector,WithRespectively noise power and k-th
The signal power of signal,I is unit matrix, and vec () indicates vectorization operation, []HRepresenting matrix or to
The conjugate transposition of amount, []TRepresenting matrix or vector transposition, []*Represent the conjugate operation of matrix or vector.
It, can be with since the virtual array of relatively prime array is made of one section of continuous even linear array and some discontinuous array elements
It proves, the range of even linear array is [- (MN+M-1) d, (MN+M-1) d], i.e. -1 array element of intermediate 2M (N+1) of virtual array is
Continuously distributed.It is M=3 as shown in Figure 2, virtual array when N=4.Since DFT algorithm usually requires that array is uniform line
Battle array, so our puncture tablesIn duplicate row, and intercept continuous array element part, obtain by continuously and virtually array received to
Signal
Wherein,For the direction matrix of continuously and virtually array, T=2M (N+1) -1
For continuously and virtually array element sum, (l, k) a element of matrix B is
VectorOnly (T+1)/2 element is 1, remaining element is zero.Next our receptions to continuously and virtually array
Signal z uses DFT algorithm.
2, initial estimation
Normalized DFT matrix is constructed firstI.e.
Wherein, (p, q) a element of matrix F isTo b (θk) DFT transform is carried out, it obtains Q-th of element be
If can be seen that q from the formulak=Tsin θk/ 2 be integer, thenHave and only qkA element is not zero.This
When, θkValue can be byThe location estimation of nonzero element obtains.Work as qk=Tsin θk/ 2 be integer when,?
round{T sinθk/ 2 } a element and its neighbouring element are nonzero value (round { } is the operation that rounds up), but by
InIt is still that (nonzero element concentrates on round { T sin θ to sparse vectork/ 2 } near), soThe position of peak value
Setting still can be used for θkCarry out initial estimation.
In practical applications, although azimuth is unknown can not to calculate direction vector, we can be to virtual after virtualization
It receives signal z and carries out DFT transform.Enabling transformed signal is yini=Fz, yiniQ-th of element be
The position for remembering its K peak-peak isIt can thus be concluded that the initial estimation of signal direction of arrival
3, accurate estimation
As the above analysis, as Tsin θk/ 2 be integer when, the accuracy of angle estimation can not be promoted.In order into one
Step promotes the estimated accuracy of the algorithm, we introduce phase rotation to compensate to error.
Defining phase rotation matrix Φ (η) is
Wherein, offset phase η ∈ (- π/T, π/T).DFT transform is carried out to the direction vector Jing Guo phase rotation, is obtainedIts q-th of element be
Obviously, an offset phase η is certainly existedk∈ (- π/T, π/T), so that equationAt
It is vertical, at this timeHave and only one nonzero element, solving nonzero element in initial estimation does not lead to estimated accuracy uniquely
The problem of reduction.ηkValue can be by be obtained in the search of (- π/T, π/T) interior small range, i.e.,
Wherein,It is the of matrix FRow.Thus we can obtain the accurate estimation of signal direction of arrival
Three, performance evaluation
1, spatial degrees of freedom (Degree of freedom, DOF)
As the above analysis, DFT algorithm can utilize whole continuously and virtually array elements of relatively prime array, and obtained space is free
Degree is DOFdft=2MN+2M-1.In contrast, common space smoothing class algorithm needs for continuously and virtually array element to be divided into several
Submatrix, therefore spatial degrees of freedom is only DOFss=MN+M, the almost half of DFT algorithm.It can be seen that in same antenna number feelings
DFT algorithm can obtain higher spatial degrees of freedom under condition.
2, computation complexity
To multiply number again as complexity judgment criteria, then the computation complexity of DFT algorithm specifically includes that calculating receives letter
Number covariance matrix needs O { (2M+N-1)2L }, O { T is needed to the virtual signal progress DFT transform that receives2, accurate estimation procedure
O { GTK } is needed, wherein G indicates the phase search number in accurate estimation procedure.Total complexity of DFT algorithm is O { (2M+N-
1)2L+T2+GTK}.In contrast, DFT algorithm is a kind of algorithm of low complex degree.
Fig. 3 is when 10 signals are incident on relatively prime array, the angle estimation scatter plot that is obtained using DFT algorithm.At this time mutually
The array number of matter linear array is M=7, N=9, L=500, SNR=0dB.It can be seen from the figure that the algorithm can be effectively estimated out
Direction of arrival.
Fig. 4 is that DFT algorithm initial estimation and the performance accurately estimated compare, and the array number of relatively prime linear array is M=7, N at this time
=9, the azimuth of signal is (10 °, 20 °), goes up=500.The case where wherein case1 is G=10, case2 are the feelings of G=100
Condition.
Fig. 5 is that algorithm performance compares under different number of snapshots, at this time the array number of relatively prime linear array be M=7, N=9, signal
Azimuth is (10 °, 20 °).
Fig. 6 is that DFT algorithm performance compares under various information source number, and the array number of relatively prime linear array is M=7, N=9, L=at this time
500.As information source number K=2, azimuth is (10 °, 20 °)；When K=3, azimuth is (10 °, 20 °, 30 °)；When K=4,
(10 °, 20 °, 30 °, 40 °).
The above, the only specific embodiment in the present invention, but scope of protection of the present invention is not limited thereto, appoints
What is familiar with the people of the technology within the technical scope disclosed by the invention, it will be appreciated that expects transforms or replaces, and should all cover
Within scope of the invention, therefore, the scope of protection of the invention shall be subject to the scope of protection specified in the patent claim.
Claims (3)
1. a kind of method for carrying out low complex degree angle estimation using relatively prime linear array, which comprises the steps of:
Step 1: using the array antenna received signals of relatively prime linear array structure, obtaining array received signal matrix；
Step 2: calculating the covariance matrix for receiving signal；
Step 3: the covariance matrix vectorization is handled, the vector of acquisition is ranked up by phase and is deleted redundant row,
It obtains virtual array and receives signal；
Step 4: intercepting the continuous array element part that the virtual array receives signal, obtain continuously and virtually array received signal z；
Step 5: DFT operation being carried out to the continuously and virtually array received signal z, obtains received spectrum yini, received spectrum
yiniThe position of K peak-peak beK is number of sources；
Step 6: phase rotation being carried out to the continuously and virtually array received signal z, carries out DFT transform later, rotation is obtained and connects
Receive signal spectrum zro, Rotation of receiver signal spectrum z is searched in region (- π/T, π/T)roK peak value to obtain optimal phase shift ηk；T
For continuously and virtually array element sum；
Step 7: utilizing optimal phase shift ηkWithCalculate accurate DOA estimation.
2. a kind of method for carrying out low complex degree angle estimation using relatively prime linear array according to claim 1, feature exist
In in step 1, the relatively prime linear array is made of the even linear array that two array numbers are respectively 2M and N, and array element spacing is respectively N
λ/2 and λ/2 M, wherein M and N is mutual prime rwmber and M < N, λ are carrier wavelength；Only at the origin has a battle array to two even linear arrays
Member is overlapped, and array element sum is 2M+N-1.
3. a kind of method for carrying out low complex degree angle estimation using relatively prime linear array according to claim 2, feature exist
In virtual array reception signal be ranked up by phase and is deleted intercepting vector at this time after redundant row in step 4
Intermediate 2MN+2M-1 row element receives signal z as continuously and virtually array element.
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| CN109932680A (en) * | 2019-04-04 | 2019-06-25 | 哈尔滨工程大学 | A kind of non-circular method for estimating signal wave direction based on the relatively prime array of translation |
| CN110297214A (en) * | 2019-07-17 | 2019-10-01 | 南京航空航天大学 | Mostly relatively prime array cooperates with indoor radiation source positioning device and method |
| CN110297213A (en) * | 2019-07-17 | 2019-10-01 | 南京航空航天大学 | Radiation source positioning device and method based on the unmanned aerial vehicle platform for loading relatively prime linear array |
| CN111224246A (en) * | 2020-03-02 | 2020-06-02 | 山东大学 | Method for realizing uniform linear array broadband beam large-angle scanning |
| CN112698264A (en) * | 2020-12-10 | 2021-04-23 | 南京航空航天大学 | DOA estimation method of coherent information source under augmented co-prime array impulse noise environment |
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2018
- 2018-07-27 CN CN201810840884.XA patent/CN108931758A/en not_active Withdrawn
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- 2019-01-29 CN CN201910083523.XA patent/CN109597020A/en active Pending
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| CN109932680A (en) * | 2019-04-04 | 2019-06-25 | 哈尔滨工程大学 | A kind of non-circular method for estimating signal wave direction based on the relatively prime array of translation |
| CN109932680B (en) * | 2019-04-04 | 2022-05-20 | 哈尔滨工程大学 | Non-circular signal direction of arrival estimation method based on translational co-prime array |
| CN110297214A (en) * | 2019-07-17 | 2019-10-01 | 南京航空航天大学 | Mostly relatively prime array cooperates with indoor radiation source positioning device and method |
| CN110297213A (en) * | 2019-07-17 | 2019-10-01 | 南京航空航天大学 | Radiation source positioning device and method based on the unmanned aerial vehicle platform for loading relatively prime linear array |
| CN111224246A (en) * | 2020-03-02 | 2020-06-02 | 山东大学 | Method for realizing uniform linear array broadband beam large-angle scanning |
| CN111224246B (en) * | 2020-03-02 | 2021-03-30 | 山东大学 | Method for realizing uniform linear array broadband beam large-angle scanning |
| CN112698264A (en) * | 2020-12-10 | 2021-04-23 | 南京航空航天大学 | DOA estimation method of coherent information source under augmented co-prime array impulse noise environment |
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