CN105182293B - Based on relatively prime array MIMO radar DOA and DOD methods of estimation - Google Patents
Based on relatively prime array MIMO radar DOA and DOD methods of estimation Download PDFInfo
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- 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
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Abstract
The invention discloses one kind based on relatively prime array MIMO radar DOA and DOD methods of estimation, mainly solve the problems, such as that the low and recognizable number of source of MIMO radar system target reconnaissance accuracy is few in the prior art.The step of present invention is realized is as follows, and (1) sets up relatively prime Array Model；(2) array received data are obtained；(3) computing array receives vector；(4) estimate covariance matrix；(5) MUSIC power spectrum charts are drawn and estimates DOA and DOD values.The method that the present invention is combined using relatively prime array with MIMO radar system, hence it is evident that improve target reconnaissance accuracy and recognizable information source number.Can be used to realize carrying out target reconnaissance and passive location to aircraft, Ship Motion target by radar.
Description
Technical field
The invention belongs to communication technical field, a kind of in Radar Technology field is further related to based on relatively prime array
Multiple-input and multiple-output (Multiple-Input Multiple-Output, MIMO) radar system direction of arrival (Direction
Of Arrival, DOA) and objective emission angle (Direction of Departure, DOD) combined estimation method.The present invention is logical
Radar is crossed to realize carrying out target reconnaissance and passive location to aircraft, Ship Motion target.
Background technology
The estimation of the DOA and DOD of signal is an important branch in Array Signal Processing field, and it refers to utilize antenna array
Row carry out sensing reception to spatial-acoustic signal, electromagnetic signal, then are fast and accurately estimated with modern signal processing method
The direction of signal source, has significant application value in fields such as radar, sonar, radio communications.It is right with the continuous progress of science and technology
The accuracy of signal Mutual coupling and also there is higher and higher requirement with resolution ratio.
MIMO radar launches different waveform signals with multiple antennas, then receives echo-signal with multiple antennas again.
The DOA and DOD of MIMO radar estimate to have the following advantages that：Its virtual aperture is set to be expanded using matched filtering technique, so that
Improve the estimated accuracy of DOA and DOD；Virtual array after matched filtering estimates more targets than conventional phased array radar；Can
Increase the flexibility of more launching beam design using the waveform diversity of transmission signal, so as to improve the estimation essence of DOA and DOD
Degree.
The paper " Coprime Sampling and the MUSIC algorithm " that Piya Pal et al. are delivered at it
(《Digital signal processing workshop and IEEE signal processing education
workshop》, pp.289-294,2011.) in disclose a kind of DOA estimation method based on relatively prime array.The method structure first
A kind of relatively prime array heterogeneous is made, the array is divided into two uniform submatrixs, and the value at each submatrix array element interval is relatively prime.So
Afterwards, to the array received to the covariance matrix that is formed of signal enter the treatment such as rearrangement peace is sliding.Finally, then carry out
MUSIC algorithms are estimated, final to obtain DOA information.The method has the ability for estimating the signal number more than array element number, but,
The weak point that the method is still present is that the method is only capable of estimating the one-dimensional DOA values of generic array radar, it is impossible to for estimating
Two-dimensional angular angle value in MIMO array radar system.
Patent " a kind of estimation of bistatic MIMO radar angle that Harbin Institute of Technology Shenzhen Graduate School applies at it
A kind of bistatic MIMO thunders are disclosed in method " (number of patent application CN201410409417.3, publication number CN104215947A)
Up to the method for estimation of angle.The method carries out target and leaves angle DOD and direction of arrival angle DOA connection using least square SLS methods
Close and estimate.First, rotational invariance equation is solved using structure least square method, then iteration minimizes estimating for signal subspace
Meter error, so as to improve the estimated accuracy of signal subspace.But, the deficiency that the method is still present is that the method is used
Typical linear homogeneous array, causes the signal number estimated less than array element number, even None- identified when target number is a lot,
Target acquistion is caused to fail.
The content of the invention
The present invention for above-mentioned prior art exist deficiency, propose a kind of MIMO radar DOA based on relatively prime array with
DOD methods of estimation.The present invention propose it is a kind of estimate DOA and DOD values by the use of relatively prime array as the method for signal transmitting and receiving array,
Target reconnaissance accuracy and recognizable number of source are improve, to solve the recognizable information source of MIMO radar system in the prior art
The few problem of number.
Basic ideas of the invention are：Relatively prime Array Model is set up, array received data are obtained, computing array receives arrow
Amount, estimate covariance matrix draws MUSIC power spectrum charts and estimates DOA and DOD values.
(1) relatively prime Array Model is set up：
(1a) forms relatively prime array with 2P+Q-1 aerial receiver, and wherein P, Q represents two relatively prime numbers respectively, and it takes
Value scope is Q ＞ P >=2；
(1b) is using each aerial receiver an as array element；
Electromagnetic signal is incided relatively prime array by (1c)；
(2) array received data are obtained：
Using relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal,
Obtain relatively prime array output signal；
(3) computing array receives vector：
(3a) constructs a mutual stromal matrix to the array output signal obtained after the sampling of each snap and matched filtering operation
It is as follows：
Wherein, Y [l] represents the relatively prime square for carrying out being constructed by array output signal after snap sampling and matched filtering operation
Battle array, xz,m[l] represents the signal of the m-th array element transmitting of z-th array element reception, and the span of m is that 0,1 ..., M, M are represented
The number of relatively prime array emitter array element, the span of M is 2P+Q-1, and the span of z is that 0,1 ..., N, N represent relatively prime battle array
Row receive the number of array element, and the span of N is 2P+Q-1, and P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P
The span of >=2, l is 1,2 ..., and L, L represent fast umber of beats；
The length of (3b) by all array elements every interval d is split, and cut-point is judged with the presence or absence of array element, if so, then
The corresponding positional information of the array element is expressed as 1, otherwise, then the corresponding positional information of the array element 0 is expressed as, wherein, d's takes
Value scope is 0 ＜ d≤λ/2, and λ represents the electromagnetic signal wavelength for inciding relatively prime array；
(3c) constructs a vector for the dimension of [(2P-1) Q+1] × 1, wherein, P, Q represent two relatively prime numbers respectively, and it takes
Value scope is Q ＞ P >=2；
(3d) by the corresponding positional information of the array element of relatively prime array, according to suitable to last array element from first array element
, be put into positional information in [(2P-1) Q+1] × 1 n dimensional vector n successively by sequence, wherein, P, Q represent two relatively prime numbers respectively, and it takes
Value scope is Q ＞ P >=2, obtains array position vector；
(3e) according to the following formula, calculates element position vector：
ω (n)=(ν * v-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents battle array
Column position vector, * represents convolution operation, v-Represent carries out reversing the backward obtained after operation battle array to array position vector v
Column position vector；
It is the element that ζ and value are not zero that (3f) chooses element numbers in element position vector ω (n), constructs irredundant battle array
First position vectorWherein, ζ spans represent two relatively prime numbers for -1, -2 ...,-(2P-1) Q, P, Q respectively, its
Span is Q ＞ P >=2, and r represents irredundant element position vectorThe sequence number of middle element, the span of r is 1,
2 ... G, G represent irredundant element position vectorLength；
(3g) according to the following formula, calculates the data of each array element reception in irredundant element position vector：
yr=Yi(l)×Yj H(l)/L
Wherein, yrRepresent irredundant element position vectorIn r-th reception data of array element, r represents irredundant battle array
First position vectorThe sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vector
Length, YiL () represents the i-th row of mutual stromal matrix, YjL () represents the jth row of mutual stromal matrix, ()HRepresent conjugate transposition behaviour
Make, i, j represents satisfactionAny one group of integer pair of condition, the span of i is 0≤i≤2P-1, and j's takes
Value scope is 0≤j≤Q-1, and P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, and L represents fast umber of beats；
(3h) according to the following formula, constructs the corresponding array received vector of irredundant element position vector：
Y=[y1,y2,…,yr,…,yG]
Wherein, y represents irredundant element position vectorCorresponding array received vector, yrRepresent irredundant array element position
Put vectorIn r-th reception data of array element, the span of r is 1,2 ... G, G represent irredundant element position vectorLength；
(4) estimate covariance matrix：
According to the following formula, the covariance matrix of array received vector is estimated：
Wherein,The covariance matrix of array received vector is represented, the span of l is 1,2 ..., and L, L represent fast umber of beats,
∑ represents sum operation, and y represents irredundant element position vectorCorresponding array received vector, H represents that conjugate transposition is grasped
Make；
(5) multiple signal classification method MUSIC power spectrum charts are drawn and estimates direction of arrival angle DOA and objective emission angle DOD values：
The direction of arrival angular region of target electromagnetic signal is x-axis coordinate by (5a), by the objective emission of target electromagnetic signal
Angular region is y-axis coordinate, target electromagnetic signal power value is calculated using multiple signal classification method MUSIC, by target electromagnetic signal
Performance number is used as z-axis coordinate；With x-axis coordinate value, y-axis coordinate value, z-axis coordinate value draws performance number point, by each point of performance number
It is connected, obtains multiple signal classification method MUSIC power spectrum charts；
From big to small be ranked up the performance number of power spectrum chart by (5b), successively extract before K spectral peak, wherein, K represent into
It is mapped to the target electromagnetic signal number of relatively prime array；
(5c) incites somebody to action the x-axis coordinate value corresponding to the peak point of preceding K spectral peak as the direction of arrival angle DOA values of target
Y-axis coordinate value corresponding to the peak point of preceding K spectral peak as target objective emission angle DOD values.
The present invention has advantages below compared with prior art：
First, due to the method present invention employs being solved based on direction of arrival angle DOA and objective emission angle DOD simultaneously,
Overcome relatively prime array in the prior art and be simply possible to use in the estimation one-dimensional DOA values of generic array radar, it is impossible to for estimating MIMO gusts
The shortcoming of the two-dimensional angular angle value in row radar system so that the present invention has the advantages that target reconnaissance accuracy is higher.
Second, due to the method present invention employs relatively prime Array Model is combined with MIMO radar system, overcome
Typical linear homogeneous array is used in the prior art, causes shortcoming of the signal number less than array element number estimated so that this
Invention has under the conditions of array element number identical, the advantage more than the recognizable number of source of array.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is relatively prime array structure schematic diagram of the invention；
Fig. 3 is P=2, relatively prime array elements position vector figure during Q=3 in the present invention；
Fig. 4 is the MUSIC power spectrum charts of drafting in emulation experiment of the invention.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
It is of the invention to comprise the following steps that referring to the drawings 1.
Step 1, sets up relatively prime Array Model.
Relatively prime array is formed with 2P+Q-1 aerial receiver, wherein P, Q represents two relatively prime numbers, and its span is
Q ＞ P >=2.
Using each aerial receiver an as array element.
Electromagnetic signal is incided into relatively prime array.
Construct comprising the following steps that for relatively prime Array Model method：
The relatively prime Array Model reference picture 2 of construction in the embodiment of the present invention, forms array element spacing equal with Q aerial receiver
Even linear array 1, is formed between the uniform linear array 2 of array element spacing, the array element of linear array 1 with 2P-1 aerial receiver
Away from being Pd, the array element spacing of linear array 2 is Qd, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P
The span of >=2, d is 0 ＜ d≤λ/2, and λ represents the electromagnetic signal wavelength for inciding relatively prime array.
First array element of linear array 1 is set to the array element 0 of relatively prime array.
By 2P-1 array element in linear array 2, be sequentially placed in the spacing distance of array element 0 be Qd, 2Qd ..., (2P-1)
In the position of Qd, relatively prime array is obtained, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, d's
Span is 0 ＜ d≤λ/2, and λ represents the electromagnetic signal wavelength for inciding relatively prime array.
Since first array element of relatively prime array to last array element, each array element is named as array element 0 successively,
Array element 1 ... ..., array element 2P+Q-2, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2.
Because Q ＞ P >=2, first array element of linear array 2 are certain after the 2nd array element of linear array 1, linear array 2 is interspersed in line
Among battle array 1.In theory when array length is very big, linear array 1 and linear array 2 may be overlapped in the distance, and selected due to P, Q is
Relatively prime, the length that linear array 1 and linear array 2 are chosen is limited, so in the present invention, linear array 1 and linear array 2 are to overlap
, all array elements of linear array 2 are inserted in linear array 1 successively, and linear array 1 and linear array 2 are on the same line.
Step 2, obtains array received data.
Using relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal,
Obtain relatively prime array output signal.
Step 3, computing array receives vector.
To the array output signal obtained after the sampling of each snap and matched filtering operation, one mutual stromal matrix of construction is such as
Under：
Wherein, Y [l] represents the relatively prime square for carrying out being constructed by array output signal after snap sampling and matched filtering operation
Battle array, xz,m[l] represents the arbitrary element in the middle of Y [l], xz,m[l] is represented and is transmitted into up to z-th array element reception from m-th array element
Signal, the span of m is 0,1 ..., the span of M, z is that 0,1 ..., N, M represent the individual of relatively prime array emitter array element
Number, the value of M is 2P+Q-1, and N represents the number of relatively prime array received array element, and the value of N is 2P+Q-1, and P, Q represent two mutually
The number of matter, its span is Q ＞ P >=2, and the span of l is 1,2 ..., and L, L represent fast umber of beats.
Length by all array elements every interval d is split, and cut-point is judged with the presence or absence of array element, if so, then should
The corresponding positional information of array element is expressed as 1, otherwise, then the corresponding positional information of the array element is expressed as into 0, wherein, the value model of d
It is 0 ＜ d≤λ/2 to enclose, and λ represents the electromagnetic signal wavelength for inciding relatively prime array.
One vector of the dimension of [(2P-1) Q+1] × 1 of construction, wherein P, Q represent two relatively prime numbers, and its span is Q
＞ P >=2.
By the corresponding positional information of the array element of relatively prime array, according to from first array element to last array element sequentially, according to
It is secondary that positional information is put into [(2P-1) Q+1] × 1 n dimensional vector n, wherein, P, Q represent two relatively prime numbers respectively, its value model
It is Q ＞ P >=2 to enclose, and obtains array position vector.
According to the following formula, element position vector is calculated：
ω (n)=(ν * v-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents battle array
Column position vector, * represents convolution operation, v-Represent carries out reversing the backward obtained after operation battle array to array position vector v
Column position vector, in element position vector element numbers n to be possible to value as follows：
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
Wherein, P, Q represent two relatively prime numbers, and its span is Q ＞ P >=2.
Element position vector ω (n) value in the embodiment of the present invention as shown in figure 3, Fig. 3 is represented as relatively prime array P=2,
During Q=3, element position vector ω (n) for obtaining, the abscissa of Fig. 3 represents element position vector ω (n), and ordinate represents battle array
First position number of repetition.
It is the element that ζ and value are not zero that element numbers are chosen in element position vector ω (n), is configured to irredundant array element
Position vectorWherein, ζ spans are -1, -2 ...,-(2P-1) Q, and P, Q represent two relatively prime numbers, its value model
It is Q ＞ P >=2 to enclose, and r represents irredundant element position vectorThe sequence number of middle element, the span of r is 1,2 ... G, G table
ShowLength, this does not choose other elements in being in element position vector ω (n) because when ζ values are 0 reception letter
Number contain noise information, the reception signal and ζ spans when ζ spans are 1,2 ..., (2P-1) Q be -1, -2 ..., -
The reception signal of (2P-1) Q is conjugated each other, can not increase the estimated accuracy of angle, if it is Fig. 3 institutes that array element receives vector ω (n)
Show, as relatively prime array P=2, during Q=3, irredundant element position vector
According to the following formula, the data of each array element reception in irredundant element position vector are calculated：
yr=Yi(l)×Yj H(l)/L
Wherein, yrRepresent irredundant element position vectorIn r-th reception data of array element, r represents irredundant array element
Position vectorThe sequence number of middle element, the span of r is 1,2 ... G, G are representedLength, YiL () represents relatively prime
I-th row of matrix, YjL () represents the jth row of mutual stromal matrix, ()HConjugate transposition operation is represented, i, j represents satisfactionAny one group of integer pair of condition, the span of i is 0≤i≤2P-1, the span of j for 0≤j≤
Q-1, P, Q represent two relatively prime numbers, and its span is Q ＞ P >=2, and L represents fast umber of beats.
According to the following formula, the corresponding array received vector of irredundant element position vector is constructed：
Y=[y1,y2,…,yr,…,yG]
Wherein, y represents irredundant element position vectorCorresponding array received vector, yrRepresent irredundant array element position
Put vectorIn r-th reception data of array element, the span of r is 1,2 ..., and G, G are representedLength.
Step 4, estimate covariance matrix.
According to the following formula, the covariance matrix of array received vector is estimated：
Wherein,The covariance matrix of array received vector is represented, the span of l is 1,2 ..., and L, L represent fast umber of beats,
∑ represents sum operation, and y represents irredundant element position vectorCorresponding array received vector, H represents that conjugate transposition is grasped
Make.
Step 5, draws MUSIC power spectrum charts and estimates DOA and DOD values.
It is x-axis coordinate by the direction of arrival angular region of target electromagnetic signal, by the objective emission angle model of target electromagnetic signal
It is y-axis coordinate to enclose, and target electromagnetic signal power value is calculated using multiple signal classification method MUSIC, by target electromagnetic signal power
Value is used as z-axis coordinate；With x-axis coordinate value, y-axis coordinate value, z-axis coordinate value draws performance number point, and each point of performance number is connected,
Obtain multiple signal classification method MUSIC power spectrum charts, wherein, target electromagnetic signal wave up to direction angle range be -90 °~90 °, mesh
Mark electromagnetic signal objective emission angular region is -90 °~90 °.
The performance number for obtaining multiple signal classification method MUSIC spatial spectrums is comprised the following steps that：
First, relatively prime array manifold F is defined, relatively prime array manifold F is a vector for the dimension of (2PQ+1) × 1, and P, Q are represented
Two relatively prime numbers, its span is Q ＞ P >=2.
Secondly, according to the following formula, each element in relatively prime array manifold F is calculated：
Wherein, F (δ) represents the δ element in relatively prime array manifold F, and the span of δ is 1,2 ... ξ, ξ represent the length of F (δ)
Degree,RepresentIn i-th element,Represent that emission array is to objective emission angleSignal response vector,The objective emission angle of relatively prime array emitter signal is represented,Expression formula be
αk m-1Represent that m-th transmitting array element is to objective emission angleSignal response, the span of m is that 0,1 ..., M, M are represented
Launch element number of array, α in MIMO radar systemkCalculating formula isdtRepresent spacing, λ tables between emission array
It is shown into the electromagnetic signal wavelength for being mapped to relatively prime array, αrj(θk) represent αr(θk) in j-th element, αr(θk) represent reception battle array
Row are θ to direction of arrival anglekSignal response vector, θkRepresent the direction of arrival angle of relatively prime array received signal, αr(θk) table
It is α up to formular(θk)=[1, βk,…,βk n-1,…,βk N-1]T, βk n-1Represent that n-th reception array element is θ to direction of arrival anglekLetter
Number response, the span of n for 0,1 ..., N, N represent MIMO radar system in receive element number of array, βkCalculating formula isdrSpacing between receiving array is represented, λ represents the electromagnetic signal wavelength for inciding relatively prime array, i, j table
Show and meet conditionAny one group of integer pair, the span of i is 0≤i≤2P-1, and the span of j is 0
≤ j≤Q-1, P, Q represent two relatively prime numbers, and its span is Q ＞ P >=2.
Finally, according to the following formula, the performance number of multiple signal classification method MUSIC spatial spectrums is calculated：
Wherein, fco_musicThe performance number of multiple signal classification method MUSIC spatial spectrums is represented, F represents relatively prime array manifold, H
Representing matrix conjugate transposition operation, EnRepresent the covariance matrix of array received data vectorAfter carrying out singular value decomposition, by
The noise subspace that the corresponding characteristic vector of small characteristic value is constituted.
According to order from high to low from power spectrum chart, the larger preceding K spectral peak of power is found, wherein, K represents incident
To the target electromagnetic signal number of relatively prime array.
Using the x-axis coordinate value corresponding to the peak point of preceding K spectral peak as target direction of arrival angle DOA values, by preceding K
Y-axis coordinate value corresponding to the peak point of spectral peak as target objective emission angle DOD values.
Effect of the invention is further described with reference to analogous diagram.
1. simulated conditions：
Emulation of the invention is what is carried out under the software environment of MATLAB R2014a.
2. emulation content：
Emulation experiment of the present invention constitutes relatively prime array using 9 aerial receivers, wherein the array element of relatively prime array midline battle array 1
Spacing is 3d, and the array element spacing of linear array 2 is 4d, and d is the half of incoming electromagnetic signal wavelength, and fast umber of beats of sampling is 500, target electricity
The angular range in magnetic signal direction of arrival angle DOA observations spatial domain is [- 90 °, 90 °], and its space lattice is divided at intervals of 1 °, target
The angular range in electromagnetic signal objective emission angle DOD observations spatial domain is [- 90 °, 90 °], and its space lattice is divided at intervals of 1 °, many
It is all 9 to launch first number in input and output MIMO radar system and receive first number, incides the target electromagnetic of relatively prime array
Signal number is 12, and the angle of departure and acceptance angle of target electromagnetic signal are (- 60 °, -50 °), (- 50 °, -40 °), (- 40 °, -
30 °), (- 30 °, -20 °), (- 20 °, 0 °), (0 °, 10 °), (10 °, 20 °), (20 °, 30 °), (30 °, 40 °), (40 °, 50 °),
(50 °, 60 °), (60 °, 70 °), signal to noise ratio is 10db.
3. simulated effect analysis：
Fig. 4 is the multiple signal classification method MUSIC power spectrum charts of drafting in emulation experiment of the invention, wherein, in Fig. 4
X coordinate represents the direction of arrival angular region of target electromagnetic signal, the objective emission angular region of y coordinate representation target electromagnetic signal, z
The target electromagnetic signal power value that coordinate representation is calculated using multiple signal classification method MUSIC, Fig. 4 is represented using multiple signal point
The situation that the target electromagnetic signal power value that class method MUSIC is calculated changes with direction of arrival angular region and objective emission angular region.
As can be seen from Figure 4 the direction of arrival angle of target electromagnetic signal and objective emission angle are to using multiple signal classification
The target electromagnetic signal power value influence that method MUSIC is calculated is larger, and the x-axis corresponding to the peak point of the larger spectral peak of performance number is sat
Scale value as target direction of arrival angle DOA values, the y-axis coordinate value corresponding to the peak point of the larger spectral peak of performance number is used as mesh
Target objective emission angle DOD values.The relatively prime array number of array linear array 1 is being used to be 4, in the case that the array number of linear array 2 is 5,
The present invention can estimate most 12 signal sources, more than 8 signal sources that conventional uniform array can recognize that.Obviously, the present invention is carried
Target reconnaissance accuracy high and recognizable number of source higher than prior art MIMO radar object localization method, in many mesh
Identify on not and show prominent performance.
Claims (6)
1. it is a kind of to be based on relatively prime array MIMO radar DOA and DOD methods of estimation, comprise the following steps：
(1) relatively prime Array Model is set up：
(1a) forms relatively prime array with 2P+Q-1 aerial receiver, and wherein P, Q represents two relatively prime numbers respectively, its value model
It is Q ＞ P >=2 to enclose；
(1b) is using each aerial receiver an as array element；
Electromagnetic signal is incided relatively prime array by (1c)；
(2) array received data are obtained：
Using relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal, obtained
Relatively prime array output signal；
(3) computing array receives vector：
(3a) constructs a mutual stromal matrix such as to the array output signal obtained after the sampling of each snap and matched filtering operation
Under：
Wherein, Y [l] represents the mutual stromal matrix for carrying out being constructed by array output signal after snap sampling and matched filtering operation, xz,m
[l] represents the signal of the m-th array element transmitting of z-th array element reception, and the span of m is that 0,1 ..., M, M represent relatively prime battle array
The number of row transmitting array element, the span of M is 2P+Q-1, and the span of z is that 0,1 ..., N, N represent relatively prime array received
The number of array element, the span of N is 2P+Q-1, and P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, l
Span be 1,2 ... L, L represent fast umber of beats；
The length of (3b) by all array elements every interval d is split, and cut-point is judged with the presence or absence of array element, if so, then should
The corresponding positional information of array element is expressed as 1, otherwise, then the corresponding positional information of the array element is expressed as into 0, wherein, the value model of d
It is 0 ＜ d≤λ/2 to enclose, and λ represents the electromagnetic signal wavelength for inciding relatively prime array；
(3c) constructs a vector for the dimension of [(2P-1) Q+1] × 1, wherein, P, Q represent two relatively prime numbers respectively, its value model
It is Q ＞ P >=2 to enclose；
(3d) by the corresponding positional information of the array element of relatively prime array, according to from first array element to last array element sequentially, according to
It is secondary that positional information is put into [(2P-1) Q+1] × 1 n dimensional vector n, wherein, P, Q represent two relatively prime numbers respectively, its value model
It is Q ＞ P >=2 to enclose, and obtains array position vector；
(3e) according to the following formula, calculates element position vector：
ω (n)=(ν * v-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents array position
Vector is put, * represents convolution operation, v-Represent carries out reversing the backward array obtained after operation position to array position vector v
Put vector；
It is the element that ζ and value are not zero that (3f) chooses element numbers in element position vector ω (n), constructs irredundant array element position
Put vectorWherein, ζ spans represent two relatively prime numbers, its value for -1, -2 ...,-(2P-1) Q, P, Q respectively
Scope is Q ＞ P >=2, and r represents irredundant element position vectorThe sequence number of middle element, the span of r is 1,2 ... G, G
Represent irredundant element position vectorLength；
(3g) according to the following formula, calculates the data of each array element reception in irredundant element position vector：
yr=Yi(l)×Yj H(l)/L
Wherein, yrRepresent irredundant element position vectorIn r-th reception data of array element, r represents irredundant element position
VectorThe sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vectorLength,
YiL () represents the i-th row of mutual stromal matrix, YjL () represents the jth row of mutual stromal matrix, ()HRepresent conjugate transposition operation, i, j table
Show satisfactionAny one group of integer pair of condition, the span of i is 0≤i≤2P-1, and the span of j is 0
≤ j≤Q-1, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, and L represents fast umber of beats；
(3h) according to the following formula, constructs the corresponding array received vector of irredundant element position vector：
Y=[y1,y2,…,yr,…,yG]
Wherein, y represents irredundant element position vectorCorresponding array received vector, yrRepresent irredundant element position arrow
AmountIn r-th reception data of array element, the span of r is 1,2 ... G, G represent irredundant element position vector
Length；
(4) estimate covariance matrix：
According to the following formula, the covariance matrix of array received vector is estimated：
Wherein,The covariance matrix of array received vector is represented, the span of l is 1,2 ..., and L, L represent fast umber of beats, and Σ is represented
Sum operation, y represents irredundant element position vectorCorresponding array received vector, H represents conjugate transposition operation；
(5) multiple signal classification method MUSIC power spectrum charts are drawn and estimates direction of arrival angle DOA and objective emission angle DOD values：
The direction of arrival angular region of target electromagnetic signal is x-axis coordinate by (5a), by the objective emission angle model of target electromagnetic signal
It is y-axis coordinate to enclose, and target electromagnetic signal power value is calculated using multiple signal classification method MUSIC, by target electromagnetic signal power
Value is used as z-axis coordinate；With x-axis coordinate value, y-axis coordinate value, z-axis coordinate value draws performance number point, and each point of performance number is connected,
Obtain multiple signal classification method MUSIC power spectrum charts；
From big to small be ranked up the performance number of power spectrum chart by (5b), K spectral peak before extracting successively, wherein, K is represented and incided
The target electromagnetic signal number of relatively prime array；
(5c) using the x-axis coordinate value corresponding to the peak point of preceding K spectral peak as target direction of arrival angle DOA values, by preceding K
Y-axis coordinate value corresponding to the peak point of spectral peak as target objective emission angle DOD values.
2. according to claim 1 based on relatively prime array MIMO radar DOA and DOD methods of estimation, it is characterised in that：Step
(1) method of the relatively prime Array Model of construction described in is as follows：
The first step, the uniform linear array 1 of array element spacing is formed with Q aerial receiver, is formed with 2P-1 aerial receiver
The uniform linear array 2 of array element spacing, the array element spacing of linear array 1 is Pd, and the array element spacing of linear array 2 is Qd, wherein,
P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, and the span of d is 0 ＜ d≤λ/2, and λ represents incident
To the electromagnetic signal wavelength of relatively prime array；
Second step, the array element 0 of relatively prime array is set to by first array element of linear array 1；
3rd step, by 2P-1 array element of linear array 2 be sequentially placed in array element 0 at a distance of for Qd, 2Qd ..., (2P-1) Qd's
In position, relatively prime array is obtained, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2, the value of d
Scope is 0 ＜ d≤λ/2, and λ represents the electromagnetic signal wavelength for inciding relatively prime array；
4th step, since first array element of relatively prime array to last array element, is named as battle array by each array element successively
Unit 0, array element 1 ... ..., array element 2P+Q-2, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2.
3. according to claim 1 based on relatively prime array MIMO radar DOA and DOD methods of estimation, it is characterised in that：Step
The span of element numbers n is as follows in element position vector ω (n) described in (3e)：
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
Wherein, P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2.
4. according to claim 1 based on relatively prime array MIMO radar DOA and DOD methods of estimation, it is characterised in that：Step
The direction of arrival angular region of the target electromagnetic signal described in (5a) is
- 90 °~90 °.
5. according to claim 1 based on relatively prime array MIMO radar DOA and DOD methods of estimation, it is characterised in that：Step
The objective emission angular region of the target electromagnetic signal described in (5a) is -90 °~90 °.
6. according to claim 1 based on relatively prime array MIMO radar DOA and DOD methods of estimation, it is characterised in that：Step
Target electromagnetic signal power value described in (5a) is through the following steps that obtain：
The first step, defines relatively prime array manifold F, and relatively prime array manifold F is a vector for the dimension of (2PQ+1) × 1, wherein, P, Q point
Not Biao Shi two relatively prime numbers, its span be Q ＞ P >=2；
Second step, according to the following formula, calculates each element in relatively prime array manifold F：
Wherein, F (δ) represents the δ element in relatively prime array manifold F, and the span of δ is 1,2 ... ξ, ξ represent relatively prime array
The length of manifold F,RepresentIn i-th element,Represent that emission array is to objective emission angle
Signal response vector,Represent the objective emission angle of relatively prime array emitter signal, αrj(θk) represent αr(θk) in j-th yuan
Element, αr(θk) represent that receiving array is θ to direction of arrival anglekSignal response vector, θkRepresent the ripple of relatively prime array received signal
Up to deflection, i, j is represented and is met conditionAny one group of integer pair, the span of i is 0≤i≤2P-1,
The span of j is 0≤j≤Q-1, and P, Q represent two relatively prime numbers respectively, and its span is Q ＞ P >=2；
3rd step, according to the following formula, calculates the target electromagnetic signal power value of multiple signal classification method MUSIC spatial spectrums：
Wherein, fco_musicThe target electromagnetic signal power value of multiple signal classification method MUSIC spatial spectrums is represented, F represents relatively prime battle array
Row manifold, EnRepresent the covariance matrix of array received data vectorIt is special by small characteristic value correspondence after carrying out singular value decomposition
Levy the noise subspace of vector composition, H representing matrix conjugate transposition operations.
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| CN113219400B (en) * | 2020-08-05 | 2022-07-12 | 哈尔滨工业大学（威海） | Underdetermined direction-of-arrival estimation method based on void-free co-prime array structure |
| US11927664B2 (en) | 2021-02-25 | 2024-03-12 | Nxp B.V. | Radar-based detection using angle of arrival estimation based on sparse array processing |
| US11906651B2 (en) | 2021-02-25 | 2024-02-20 | Nxp B.V. | Radar-based detection using sparse array processing |
| CN114994651B (en) * | 2022-05-18 | 2024-02-06 | 电子科技大学 | Bistatic mutual MIMO radar target positioning method with channel amplitude-phase error |
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