CN109932681A - A kind of drop redundancy nested array setting method based on Space-Time information - Google Patents
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Abstract
The drop redundancy nested array setting method based on Space-Time information that the present invention is to provide a kind of.Total array number N is given first, obtains original nested array and its two sub- battle array array number N1And N2；Then the cross-correlation function for asking different array elements to receive data using the Space-Time characteristic that original nested array receives data obtains dropping redundancy nested array to obtain equivalent data model to carry out drop redundancy analysis to original nested array；Indexed set is obtained then according to original nested array and drop redundancy nested array relationship；Virtual array is finally obtained for Mutual coupling according to indexed set.Present invention mainly solves the virtual arrays of original nested array only to be constructed by difference set, promotes limited problem so as to cause virtual array freedom degree.Drop redundancy nested array proposed by the present invention has the advantages that the increase of physical array aperture, virtual array freedom degree height and virtual array are continuous, it can be achieved that more preferably owing to determine Mutual coupling compared with original nested array.
Description
Technical field
The present invention relates to a kind of signal processing method, specifically a kind of drop redundancy nested array setting method.
Background technique
Direction of arrival (DOA) estimation is an important research branch of field of signal processing, is had in fields such as radar, communications
It plays an important role.Traditional DOA estimation technique, such as MUSIC and ESPRIT etc. can only use array element spacing to be not more than incoming signal
The receiving array of half-wavelength executes overdetermination DOA estimation, i.e. maximum can estimate information source number no more than array number.However in face of increasingly multiple
Miscellaneous electromagnetic environment generally requires to estimate the information source DOA more than array number, that is, owes to determine DOA estimation.For this purpose, there has been proposed one
Serial array element spacing is greater than the sparse array structure of incoming signal half-wavelength, such as minimum redundant array and minimum pores array,
They have optimal virtual array freedom degree (DOFs), and the letter more than array number can be effectively estimated using these thinned arrays
Source DOA.However since their array element coordinate does not have closed solutions, simulation can only be enumerated by computer when giving array number
To obtain desired array structure.People have also been proposed the sparse array structure of DOFs suboptimum thus, such as nested array and mutually
Matter array etc. gets more and more people's extensive concerning since they have the array element coordinate calculation formula of enclosed.For the embedding of N array element
Cover array, it is easy to obtain the array number N of its two submatrixs1And N2, and then its physical array structure can be obtained, based on this benefit
It can be to O (N with smooth MUSIC algorithm2) a information source DOA is effectively estimated.Equally, as given two relatively prime integers M and N,
It when middle M < N, is then also easy to get to relatively prime array structure, and its total element number of array is M+N-1, using when smooth MUSIC algorithm, it is most
It can estimate that information source number is O (MN) greatly.
Believe however it is to be noted that the DOFs of the above thinned array is obtained merely with the airspace of array received data
Breath, the utilization rate of array received data information are not enough.When carrying out owing to determine DOA estimation using smooth MUSIC algorithm, due to
The discontinuity of relatively prime array virtual array will will lead to its discontinuous part and can not be used, to reduce the utilization of DOFs
Rate, DOA estimate limited performance.Although the virtual array of nested array is continuously, to believe when using the Space-Time of array received data
When breath obtains virtual array, there is very big redundancy in virtual array, and DOFs is promoted also limited.Therefore, it is connect based on nested array
The Space-Time information of data is received, the redundancy of nested array virtual array is reduced, its DOFs will be dramatically increased, to make to owe fixed
DOA estimation maximum can estimate that information source number and estimation performance improve.
Summary of the invention
The purpose of the present invention is to provide one kind, and DOA estimation can be carried out to more multiple source, and estimates what performance was improved
Drop redundancy nested array setting method based on Space-Time information.
The object of the present invention is achieved like this:
Step (1): according to given total array number N, the array number N of two submatrixs of original nested array is first obtained1And N2,
And corresponding array element coordinate setWherein D is the half-wavelength of incoming signal；
Step (2): receiving the Space-Time characteristic of data according to original nested array, and any two array element is asked to receive the mutual of data
Correlation functionWherein xm(t+ τ) and xnIt (t) is m-th and n-th of array element at the t+ τ moment
With the sampled data of t moment, τ ≠ 0 is time delay,It is xn(t) conjugation；
Step (3): the equivalent data model constructed according to any two array element cross-correlation function carries out original nested array
Redundancy Analysis obtains drop redundancy nested array；
Step (4): redundancy nested array structure is dropped according to obtained in step (3), obtains indexed setIt refers to dropping
Index number after the arrangement of redundancy nested array coordinate value ascending order,The every column element of the first row corresponds to the m in step (2),Second
The every column element of row corresponds to the n in step (2)；
Step (5): indexed set is used and seeks cross-correlation function in drop redundancy nested array reception data, obtains virtual array
Column.
The present invention may also include:
1. the value of total array number N are as follows: N >=3.
2. according to N1And N2Numerical value it is different, the array element coordinate expressions of the drop redundancy nested array indicate are as follows:
A), work as N1=2 and N2When=1,Total element number of array is N=3 after then dropping redundancy；
B), work as N1>=3 be odd number and N2When=1,Wherein
T=N1+ 1+a,It refers toTheIt is a to N1A element, then total element number of array is after dropping redundancy
C), work as N1>=4 be even number and N2When=1,Wherein
T=N1+ 1+a, then total element number of array is after dropping redundancy
D), work as N1=2 and N2>=2 be even number when,Wherein T=
3N2+ a, then total element number of array is after dropping redundancy
E), work as N1=2 and N2>=3 be odd number when,Wherein T
=3N2+ a, then total element number of array is after dropping redundancy
F), work as N1>=4 be even number and N2>=2 be even number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
G), work as N1>=4 be even number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
H), work as N1=1 and N2>=2 be even number when,Wherein T=
2N2+ a, then total element number of array is after dropping redundancy
I), work as N1=1 and N2>=3 be odd number when,Wherein T
=2N2+ a, then total element number of array is after dropping redundancy
J), work as N1>=3 be odd number and N2>=2 be even number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
K), work as N1>=3 be odd number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
3. obtaining different indexed sets to be combined into:
A), work as N1=2 and N2When=1,
B), work as N1>=3 be odd number and N2When=1,WhereinByA 2 composition,ByA 1 composition,
C), work as N1>=4 be even number and N2When=1,WhereinByA 2 composition,ByA 1
Composition,
D), work as N1=2 and N2>=2 be even number when,WhereinByA 1 composition, ByIt is aComposition,
E), work as N1=2 and N2>=3 be odd number when,WhereinByA 1 composition,ByIt is aGroup
At,
F), work as N1>=4 be even number and N2>=2 be even number when,WhereinByA 1 composition,ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
G), work as N1>=4 be even number and N2>=3 be odd number when,WhereinByA 1 group
At,ByA 2 composition,ByA 1 composition, ByIt is aComposition,
H), work as N1=1 and N2>=2 be even number when,WhereinByA 1 composition,ByIt is aComposition；
I), work as N1=1 and N2>=3 be odd number when,WhereinByA 1 composition,ByIt is aComposition；
J), work as N1>=3 be odd number and N2>=2 be even number when,WhereinByA 1 composition,ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
K), work as N1>=3 be odd number and N2>=3 be odd number when,WhereinByA 1 group
At,ByA 2 composition,ByA 1 composition, ByComposition,
4. the DOFs of virtual array is expressed as L=4 (N1+1)(N2+1)+4a-3。
The present invention receives that data information utilization rate is low and DOFs finiteness problem for original nested array, proposes a kind of base
In the drop redundancy nested array setting method of Space-Time information.It is original embedding according to known to array number first in the setting method
Set array received data obtain the equivalent received data model based on Space-Time information, thus to the virtual array of original nested array
Column redundancy is analyzed.Redundancy array element is rejected according to Redundancy Analysis result, to obtain drop redundancy nested array.Finally count
Calculation obtains indexed set, and final virtual array structure can be obtained according to indexed set.Compared with original nested array, in identical array element
Under said conditions, the drop redundancy nested array DOFs based on Space-Time information is greatly improved, so as to carry out to more multiple source
DOA estimation, and estimate that performance is improved.
The present invention has the advantage that compared with original nested array
1), the present invention receives data Space-Time information structuring equivalent received data model using original nested array, to reject
Redundancy array element in original nested array obtains drop redundancy nested array, and virtual array DOFs is greatly improved, and virtual array is still
Keep continuation property；
2), drop redundancy nested array proposed by the present invention increases physical array aperture by rejecting redundancy array element, thus
Make to owe to determine DOA estimation performance raising.
Detailed description of the invention
Fig. 1 is array setting implementation flow chart of the invention；
Fig. 2 a to Fig. 2 b is fixed total array number when being 7, and array of the present invention and original nested array geometry are illustrated
Figure, Fig. 2 a are original nested arrays, and Fig. 2 b is the present invention；
Fig. 3 be array of the present invention and original nested array respectively virtual array DOFs with total array number variation diagram；
Fig. 4 is that array of the present invention and original nested array are owed to determine DOA estimation normalization spectrogram.
Specific embodiment
In conjunction with Fig. 1, the key step of the drop redundancy nested array setting method of the invention based on Space-Time information are as follows:
Step (1): according to given total array number N, the array number N of original nested array and two submatrixs is obtained1And N2,
Original nested array can be expressed as with aggregate formWherein D is the half-wavelength of incoming signal.
Step (2): different array elements are calculated according to the Space-Time characteristic that original nested array receives data and receive the mutual of data
Function is closed to construct equivalent received data model, Redundancy Analysis is carried out to original nested array structure to obtain according to the model
To drop redundancy nested array structure.
Step (3): indexed set is obtained according to relationship between drop redundancy nested array and original nested array array element.
Step (4): seeking cross-correlation function according to indexed set, to obtain desired virtual array structure for owing fixed
DOA estimation.
It illustrates below and the present invention is described in more detail.
Step (1): according to given total array number N, wherein N >=3, first obtain the array element of original two submatrixs of nested array
Number N1And N2, and corresponding array element coordinate setWherein D is the half-wavelength of incoming signal.
Step (2): receiving the Space-Time characteristic of data according to original nested array, and any two array element is asked to receive the mutual of data
Correlation functionWherein xm(t+ τ) and xnIt (t) is m-th and n-th of array element at the t+ τ moment
With the sampled data of t moment, τ ≠ 0 is time delay,It is xn(t) conjugation.
Step (3): the equivalent data model constructed according to any two array element cross-correlation function carries out original nested array
Redundancy Analysis is to obtain drop redundancy nested array.According to N1And N2Numerical value it is different, which can indicate
Are as follows:
A), work as N1=2 and N2When=1,Total element number of array is N=3 after then dropping redundancy.
B), work as N1>=3 be odd number and N2When=1,Wherein
T=N1+ 1+a,It refers toTheIt is a to N1A element, then total element number of array is after dropping redundancy
C), work as N1>=4 be even number and N2When=1,Wherein
T=N1+ 1+a, then total element number of array is after dropping redundancy
D), work as N1=2 and N2>=2 be even number when,Wherein T=
3N2+ a, then total element number of array is after dropping redundancy
E), work as N1=2 and N2>=3 be odd number when,Wherein T
=3N2+ a, then total element number of array is after dropping redundancy
F), work as N1>=4 be even number and N2>=2 be even number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
G), work as N1>=4 be even number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
H), work as N1=1 and N2>=2 be even number when,Wherein T=
2N2+ a, then total element number of array is after dropping redundancy
I), work as N1=1 and N2>=3 be odd number when,Wherein T
=2N2+ a, then total element number of array is after dropping redundancy
J), work as N1>=3 be odd number and N2>=2 be even number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
K), work as N1>=3 be odd number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
In above 11 in situation,
Step (4): redundancy nested array structure is dropped according to obtained in step (3), indexed set can be obtainedIt is referred to
Index number after dropping the arrangement of redundancy nested array coordinate value ascending order,The every column element of the first row corresponds to the m in step (2),The
The every column element of two rows corresponds to the n in step (2).Different indexed sets can be obtained according to different situations in step (3) to be combined into:
A), work as N1=2 and N2When=1,
B), work as N1>=3 be odd number and N2When=1,WhereinByA 2 composition,ByA 1 composition,
C), work as N1>=4 be even number and N2When=1,WhereinByA 2 composition,ByA 1
Composition,
D), work as N1=2 and N2>=2 be even number when,WhereinByA 1 composition,ByIt is aComposition,
E), work as N1=2 and N2>=3 be odd number when,WhereinByA 1 composition,ByGroup
At,
F), work as N1>=4 be even number and N2>=2 be even number when,WhereinByA 1 composition,ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
G), work as N1>=4 be even number and N2>=3 be odd number when,WhereinByA 1 group
At,ByA 2 composition,ByA 1 composition, ByIt is aComposition,
H), work as N1=1 and N2>=2 be even number when,WhereinByA 1 composition,ByIt is aComposition.
I), work as N1=1 and N2>=3 be odd number when,WhereinByA 1 composition,ByIt is aComposition.
J), work as N1>=3 be odd number and N2>=2 be even number when,WhereinByA 1 composition,ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
K), work as N1>=3 be odd number and N2>=3 be odd number when,WhereinByA 1 group
At,ByA 2 composition,ByA 1 composition, ByIt is aComposition,
Step (5): indexed set is used and seeks cross-correlation function in drop redundancy nested array reception data, and then is obtained virtual
Array, and the DOFs of virtual array is expressed as L=4 (N1+1)(N2+ 1)+4a-3, wherein
Referring to Fig. 2 a to Fig. 2 b, when to be fixed total element number of array be 7, the corresponding drop redundancy nested array of the present invention and original
Beginning nested array schematic diagram.It can be seen from the figure that remaining array element is arranged more after drop redundancy nested array rejects redundancy array element
Rationally, increase physical array aperture.
It is drop redundancy nested array and the respective virtual array DOFs of original nested array with total array number referring to Fig. 3
Variation diagram, wherein total element number of array increases to 30 from 3.As can be seen from the figure drop redundancy nested array of the present invention is virtual
For array DOFs obviously than the DOFs high of original nested array virtual array, this illustrates that the present invention can be used for estimating more information sources
DOA, and estimate that performance is more preferable than original nested array.
It is that drop redundancy nested array of the present invention and the deficient of original nested array determine DOA estimation normalization referring to Fig. 4
Spectral peak figure contrast simulation is as a result, wherein total array number is 7, and 15 information sources are evenly distributed on -60 °~60 ° ranges, and signal-to-noise ratio is
0dB, number of snapshots and frame length are 100.From the graph, it is apparent that array of the present invention is owed to determine DOA estimation normalization
Spectrogram is more sharp compared with original nested array corresponds to spectrogram, thus owes determine DOA to estimate that performance is more preferable.
To sum up, array of the present invention setting have that physical array aperture increases, virtual array DOFs is higher and virtual array still
Keep continuous feature because can realize to more multiple target carry out owe determine DOA estimation, and owe determine DOA estimate performance it is more preferable.
Claims (5)
1. a kind of drop redundancy nested array setting method based on Space-Time information, it is characterized in that:
Step (1): according to given total array number N, the array number N of two submatrixs of original nested array is first obtained1And N2, and
Corresponding array element coordinate setWherein D is the half-wavelength of incoming signal；
Step (2): receiving the Space-Time characteristic of data according to original nested array, and any two array element is asked to receive the cross-correlation of data
FunctionWherein xm(t+ τ) and xnIt (t) is m-th and n-th of array element at t+ τ moment and t
The sampled data at quarter, τ ≠ 0 are time delay,It is xn(t) conjugation；
Step (3): the equivalent data model constructed according to any two array element cross-correlation function carries out redundancy to original nested array
Degree analysis obtains drop redundancy nested array；
Step (4): redundancy nested array structure is dropped according to obtained in step (3), obtains indexed setIt refers to drop redundancy
Index number after the arrangement of nested array coordinate value ascending order,The every column element of the first row corresponds to the m in step (2),Second row is every
Column element corresponds to the n in step (2)；
Step (5): indexed set is used and seeks cross-correlation function in drop redundancy nested array reception data, obtains virtual array.
2. the drop redundancy nested array setting method according to claim 1 based on Space-Time information, it is characterized in that total array element
The value of number N are as follows: N >=3.
3. the drop redundancy nested array setting method according to claim 2 based on Space-Time information, it is characterized in that according to N1
And N2Numerical value it is different, the array element coordinate expressions of the drop redundancy nested array indicate are as follows:
A), work as N1=2 and N2When=1,Total element number of array is N=3 after then dropping redundancy；
B), work as N1>=3 be odd number and N2When=1,Wherein T=N1
+ 1+a,It refers toTheIt is a to N1A element, then total element number of array is after dropping redundancy
C), work as N1>=4 be even number and N2When=1,Wherein T=N1
+ 1+a, then total element number of array is after dropping redundancy
D), work as N1=2 and N2>=2 be even number when,Wherein T=3N2+
A, then total element number of array is after dropping redundancy
E), work as N1=2 and N2>=3 be odd number when,Wherein T=3N2
+ a, then total element number of array is after dropping redundancy
F), work as N1>=4 be even number and N2>=2 be even number when,
Wherein T=(N1+1)N2+ a, then total element number of array is after dropping redundancy
G), work as N1>=4 be even number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
H), work as N1=1 and N2>=2 be even number when,Wherein T=2N2+
A, then total element number of array is after dropping redundancy
I), work as N1=1 and N2>=3 be odd number when,Wherein T=2N2
+ a, then total element number of array is after dropping redundancy
J), work as N1>=3 be odd number and N2>=2 be even number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
K), work as N1>=3 be odd number and N2>=3 be odd number when,Wherein T=(N1+1)N2Total array element after redundancy then drops in+a
Number is
4. the drop redundancy nested array setting method according to claim 3 based on Space-Time information, it is characterized in that obtaining not
Same indexed set is combined into:
A), work as N1=2 and N2When=1,
B), work as N1>=3 be odd number and N2When=1,WhereinByA 2 composition,ByA 1
Composition,
C), work as N1>=4 be even number and N2When=1,WhereinByA 2 composition,ByA 1 composition,
D), work as N1=2 and N2>=2 be even number when,WhereinByA 1 composition, ByIt is aComposition,
E), work as N1=2 and N2>=3 be odd number when,WhereinByA 1 composition, ByIt is aGroup
At,
F), work as N1>=4 be even number and N2>=2 be even number when,WhereinByA 1 composition, ByA 2 composition,ByA 1 composition, ByIt is aComposition,
G), work as N1>=4 be even number and N2>=3 be odd number when,WhereinByA 1 composition, ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
H), work as N1=1 and N2>=2 be even number when,WhereinByA 1 composition, ByIt is aComposition；
I), work as N1=1 and N2>=3 be odd number when,WhereinByA 1 composition, ByIt is aComposition；
J), work as N1>=3 be odd number and N2>=2 be even number when,WhereinByA 1 composition, ByA 2 composition,ByA 1 composition, ByIt is aComposition,
K), work as N1>=3 be odd number and N2>=3 be odd number when,WhereinByA 1 composition, ByA 2 composition,ByA 1 composition,
ByIt is aComposition,
5. the drop redundancy nested array setting method according to claim 4 based on Space-Time information, it is characterized in that: virtually
The DOFs of array is expressed as L=4 (N1+1)(N2+1)+4a-3。
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112287517A (en) * | 2020-09-23 | 2021-01-29 | 清华大学 | Design method and design device of one-dimensional multiple redundant sensor array structure |
| CN112287517B (en) * | 2020-09-23 | 2022-08-09 | 清华大学 | Design method and design device of one-dimensional multiple redundant sensor array structure |
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