CN111157968B - High-precision angle measurement method based on sparse MIMO array - Google Patents
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- G—PHYSICS
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- 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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- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/42—Simultaneous measurement of distance and other co-ordinates
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- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
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Abstract
The invention discloses a high-precision angle measurement method based on a sparse MIMO array, which comprises the following steps: (1) Arranging an M-transmit N-receive sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; (2) Performing matched filtering on the received signal to obtain extended array data; (3) Constructing a covariance matrix of the extended array data and estimating a signal subspace; (4) Obtaining a set of fuzzy angle estimation values by using the transmitting translation invariant factors in the signal subspace; (5) Obtaining another set of fuzzy angle estimation values by utilizing the receiving translation invariant factors in the signal subspace; (6) Constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value; (7) And (3) performing two-step de-blurring processing on the fuzzy angle estimation values obtained in the steps (4) and (5) by using the low-precision non-fuzzy angle estimation value to obtain high-precision non-fuzzy angle estimation.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a high-precision angle measurement method based on a sparse MIMO array.
Background
Angle is a basic parameter representing a target signal, angle estimation is always an active subject in the field of signal processing, and has wide application in the fields of radar, sonar, communication and the like.
The MIMO array can obtain waveform diversity by transmitting orthogonal signals and performing matching processing on a receiving end so as to improve the precision of parameter estimation. According to the spatial form of the Nyquist sampling theorem, the conventional MIMO array needs to ensure that the pitch of the transmitting or receiving array does not exceed half a wavelength at least, thereby ensuring a non-ambiguous parameter estimation value.
In the array processing, the accuracy of parameter estimation can be improved by expanding the array aperture. However, the aperture expansion by increasing the array pitch causes blurring of parameter estimation, and the implementation of aperture expansion by increasing the number of array elements increases the hardware burden and the additional calculation amount.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a high-precision angle measurement method based on a sparse MIMO array. The technical scheme of the invention is as follows:
a high-precision angle measurement method based on a sparse MIMO array is used for solving the problem of lower angle estimation precision of the existing MIMO array, and comprises the following steps:
(1) Arranging an M-transmit N-receive sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; wherein M and N are positive integers;
(2) Performing matched filtering on the received signal to obtain extended array data;
(3) Constructing a covariance matrix of the extended array data and estimating a signal subspace;
(4) Obtaining a set of fuzzy angle estimation values by using the transmitting translation invariant factors in the signal subspace;
(5) Obtaining another set of fuzzy angle estimation values by utilizing the receiving translation invariant factors in the signal subspace;
(6) Constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value;
(7) And (3) performing two-step de-blurring processing on the fuzzy angle estimation values obtained in the steps (4) and (5) by using the low-precision non-fuzzy angle estimation value to obtain high-precision non-fuzzy angle estimation.
Optionally, a total of K.gtoreq.1 targets are respectively located at an angle θ 1 ，…，θ K The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target refers to the detected object, the θ 1 ，…，θ K The angles of the K targets are respectively, and K represents the number of the targets.
Optionally, in step (1), the transmitting antenna element spacing is d t The space between the receiving antenna units is d r ＝Md t +0.5λ, λ is the carrier wavelength, and d t ＞＞0.5λ。
Alternatively, the matched filtered spread array data vector in step (2) may be expressed as:
wherein x (t) represents a received signal vector;
b(t)＝[b 1 (t)，…，b k (t)] T ，
n(t)＝[n1(t)，…，n MN (t)] T
parameters on the left of the four equation equals signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; of the four formulas described above,representing the Kronecker product, the function based on e represents an exponential function based on a natural constant e, b k (t) is the kth signal，f k For its Doppler frequency, t represents a time variable.
Alternatively, the angle θ 1 ，…，θ K Are different from each other, and f 1 ≠f 2 ≠…≠f K 。
Optionally, the covariance matrix in step (3) is estimated as follows
Wherein T is the number of pulses, T n Indicating the nth pulse, the superscript H indicating the conjugate transpose;
the signal subspace is estimated as follows: calculating the characteristic value decomposition of R to obtain
R＝U V U H
Wherein V is a characteristic value matrix of the covariance matrix R, and U is a characteristic vector matrix corresponding to the characteristic value; arranging the characteristic values from large to small, wherein a matrix formed by characteristic vectors corresponding to the first K large characteristic values is a signal subspace matrix E s The method comprises the steps of carrying out a first treatment on the surface of the The first K large eigenvalues refer to first K eigenvalues; here, "large eigenvalues" means that the eigenvalues belong to the signal subspace eigenvalues.
Optionally, obtaining a set of blurred angle estimates from the transmit translational invariant factor in step (4) is calculated as follows:
construction matrix
wherein ,Jt1 ＝[I M-1 ,0 (M-1)，1 ],J t2 ＝[0 (M-1)，1 ,I M-1 ]；I N Representing an identity matrix, 0 M,N A zero matrix representing M x N dimensions; j (J) t1 and Jt2 Representing selection momentAn array.The eigenvalue decomposition of (c) can be expressed as:
wherein the matrix T is a K-dimensional nonsingular matrix, which is marked with the superscriptRepresenting a matrix pseudo-inverse;
is a diagonal matrix of K dimension phi t,k Phase information representing the kth diagonal element. Due to d r ＞＞λ/2，φ t,k Can be expressed as a set of fuzzy estimates:
the numerical value is a group of fuzzy angle estimated values obtained by transmitting a translation invariant factor in the step (4);
wherein ,nt As a set of integers,is->Principal value of argument ++>Is->And calculating the kth characteristic value.
Optionally, obtaining a set of blurred angle estimates from the received translational invariant factor in step (5) is calculated as follows: construction matrix
wherein ,Jr1 ＝[I N-1 ,0 (N-1)，1 ],J r2 ＝[0 (N-1)，1 ,I N-1 ]Is a selection matrix;the eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d r ＞＞λ/2，Can be expressed as a set of fuzzy estimates
The numerical value is a group of fuzzy angle estimated values obtained by receiving the translation invariant factor in the step (5);
wherein ,nr As a set of integers,is->Principal value of argument ++>Is->And calculating the kth characteristic value.
Optionally, the obtaining of the blur-free angle estimation value from the half-wavelength shift invariant factor in the step (6) is calculated as follows: construction matrix E v1 and Ev2, wherein Ev1 Corresponding to the last transmitting antenna and 1 st to N-1 st receiving antennas, E v2 Corresponding to the 1 st transmitting antenna and the 2 nd to nth receiving antennas.The eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d v =0.5λ, can give Φ v,k ＝sinθ k 。
Optionally, the high-precision blur-free angle estimation in step (7) is calculated by: phi (phi) t,k Middle and phi v,k The nearest value is phi t,k Is expressed asφ r,k Middle and->The nearest value is phi r,k Is expressed asAccording to->Directly calculate and get theta k Estimate of +.>
Compared with the prior art, the invention has the following beneficial effects:
the method and the device effectively solve the problem of low angle estimation precision of the conventional MIMO array.
Drawings
Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of a high-precision angle measurement method based on a sparse MIMO array according to an embodiment of the present invention;
FIG. 2 is a diagram of a MIMO array configuration in accordance with an embodiment of the present invention;
FIG. 3 is a simulation result of an embodiment of the present invention implementing an extended aperture;
fig. 4 is a comparison of simulation results of a conventional MIMO array with an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.
As shown in fig. 1 and fig. 2, the present embodiment discloses a high-precision angle measurement method based on a sparse MIMO array, which is used for solving the problem of lower precision of angle estimation of the existing MIMO array, and includes the following steps:
and (1) arranging an M-transmit-N-receive sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal. Wherein M and N are positive integers.
In this embodiment, a total of K.gtoreq.1 targets are located at an angle θ 1 ，…，θ K The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target refers to the detected object, the θ 1 ，…，θ K The angles of the K targets are respectively, and K represents the number of the targets.
The space between the transmitting antenna units is d t The space between the receiving antenna units is d r ＝Md t +0.5λ, λ is the carrier wavelength, and d t > 0.5λ. In fig. 2, R: T1-TM is transmit and R1-RM is receive. MF represents matched filtering.
Step (2), carrying out matched filtering on the received signals to obtain extended array data:
wherein x (t) represents a received signal vector;
b(t)＝[b 1 (t)，…，b K (t)] T ，
n(t)＝[n 1 (t)，…，n MN (t)] T
parameters on the left of the four equation equals signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; of the four formulas described above,representing the Kronecker product, the function based on e represents an exponential function based on a natural constant e, b k (t) is the kth signal, f k For its Doppler frequency, t represents a time variable. Where K represents 1, …, and K is actually a variable, and the value of K is one of 1, …, and K. Wherein the angle theta 1 ，…，θ K Are different from each other, and f 1 ≠f 2 ≠…≠f K 。
Step (3), constructing covariance matrix of the extended array data,
and decomposing the characteristic value to obtain a signal subspace E s Is a function of the estimate of (2).
Wherein T is the number of pulses, T n Indicating the nth pulse, the superscript H indicating the conjugate transpose;
the signal subspace is estimated as follows: calculating characteristic value decomposition of R to obtain:
R＝U V U H ；
wherein V is a characteristic value matrix of the covariance matrix R, and U is a characteristic vector matrix corresponding to the characteristic value; arranging the characteristic values from large to small, wherein a matrix formed by characteristic vectors corresponding to the first K large characteristic values (signal subspace characteristic values) is a signal subspace matrix E s The method comprises the steps of carrying out a first treatment on the surface of the The first K large eigenvalues refer to first K eigenvalues; here, "large eigenvalues" means that the eigenvalues belong to the signal subspace eigenvalues.
Step (4), obtaining a group of fuzzy angle estimation values by using the transmitting translation invariant factors in the signal subspace; the method comprises the following steps:
construction matrix
wherein ,Jt1 ＝[I M-1 ,0 (M-1)，1 ],J t2 ＝[0 (M-1)，1 ,I M-1 ]；I N Representing an identity matrix, 0 M,N A zero matrix representing M x N dimensions; j (J) t1 and Jt2 Representing the selection matrix.The eigenvalue decomposition of (c) can be expressed as:
wherein the matrix T is a K-dimensional nonsingular matrix, which is marked with the superscriptRepresenting a matrix pseudo-inverse;
is a diagonal matrix of K dimension phi t,k Phase information representing the kth diagonal element. Due to d t ＞＞λ/2，φ t,k Can be expressed as a set of fuzzy estimates:
the numerical value is a group of fuzzy angle estimated values obtained by transmitting a translation invariant factor in the step (4); wherein n is t As a set of integers,is->Of (a) amplitude angleMain value->Is->And calculating the kth characteristic value. Through phi t,k A set of high-precision ambiguous angle estimates is obtained.
Step (5), obtaining another group of fuzzy angle estimation values by utilizing the receiving translation invariant factors in the signal subspace; the method comprises the following steps: construction matrix
wherein ,Jr1 ＝[I N-1 ,0 (N-1)，1 ],J r2 ＝[0 (N-1)，1 ,I N-1 ]Is a selection matrix;the eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d r ＞＞λ/2，Can be expressed as a set of fuzzy estimates
The numerical value is a group of fuzzy angle estimated values obtained by receiving the translation invariant factor in the step (5);
wherein ,nr As a set of integers,is->Principal value of argument ++>Is->And calculating the kth characteristic value. Through phi r,k Another set of high-precision blurred angle estimates is obtained.
Step (6), constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value; the method comprises the following steps:
construction matrix E v1 and Ev2, wherein Ev1 Corresponding to the last transmitting antenna and 1 st to N-1 st receiving antennas, E v2 Corresponding to the 1 st transmitting antenna and the 2 nd to nth receiving antennas.The eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d v =0.5λ, can give Φ v,k ＝sinθ k . Through phi v,k And refining to a low-precision and non-fuzzy angle estimation value.
And (7) performing two-step de-blurring processing on the fuzzy angle estimation values obtained in the steps (4) and (5) by using the low-precision non-fuzzy angle estimation value to obtain high-precision non-fuzzy angle estimation. The method comprises the following steps:
calculating phi t,k Middle and phi v,k The nearest value is phi t,k Is expressed asφ r,k Middle and->The nearest value is phi r,k Is expressed as +.>According to->Directly calculate and get theta k Estimate of +.>
To further evaluate the performance of the present invention, we performed the following computer simulation experiments. Simulation conditions: the MIMO array formed by 2 transmitting and 6 receiving is adopted, and the space between the antenna units satisfies d r ＝2d t +0.5λ, two incoherent signals respectively located at an angle θ 1 ＝10°，θ 2 =20°, the number of samples taking t=200.
Fig. 3 shows the root mean square error (vertical axis) versus transmit antenna element spacing (horizontal axis) for a comparison angle 1 estimate. The angle estimation values corresponding to the four curves from top to bottom in the figure are respectively obtained by virtual invariant factors, transmitting invariant factors, receiving invariant factors through primary defuzzification processing and receiving invariant factors through twice defuzzification processing estimation. It can be seen from the figure that the virtual invariance causesThe cell pitch corresponding to the sub-is always half a wavelength, so the corresponding angle estimation error is almost unchanged. Since the receiving cell pitch is larger than the transmitting cell pitch, the angle estimation error obtained from the receiving invariant factor is smaller than the angle estimation error obtained from the transmitting invariant factor upon successful disambiguation, and the estimation error linearly decreases as the cell pitch increases. It is further observed that successful disambiguation can be achieved when the transmit element spacing is less than 100 lambda. When the distance between the transmitting units is larger than 100 lambda, the deblurring fails, and the estimation error is equivalent to the angle estimation error obtained by the virtual invariant factor. Thus, the method of the present invention can realize d t Aperture expansion of =100λ.
Fig. 4 shows a graph comparing the variation of the estimated error (vertical axis) with the signal-to-noise ratio (horizontal axis) for a conventional MIMO array (the virtual array of which is a uniform linear array). The upper one of the two curves corresponds to a conventional MIMO array and the lower one corresponds to a MIMO array of the present invention. It can be seen that the angle estimation error of the method of the present invention is smaller than that of a conventional MIMO array. That is, the performance of the method of the present invention on angle estimation is greatly improved.
The foregoing describes specific embodiments of the present invention. It is to be understood that the invention is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily without conflict.
Claims (10)
1. The high-precision angle measurement method based on the sparse MIMO array is used for solving the problem of lower angle estimation precision of the existing MIMO array, and is characterized by comprising the following steps of:
(1) Arranging an M-transmit N-receive sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; wherein M and N are positive integers;
(2) Performing matched filtering on the received signal to obtain extended array data;
(3) Constructing a covariance matrix of the extended array data and estimating a signal subspace;
(4) Obtaining a set of fuzzy angle estimation values by using the transmitting translation invariant factors in the signal subspace;
(5) Obtaining another set of fuzzy angle estimation values by utilizing the receiving translation invariant factors in the signal subspace;
(6) Constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value;
(7) And (3) performing two-step de-blurring processing on the fuzzy angle estimation values obtained in the steps (4) and (5) by using the low-precision non-fuzzy angle estimation value to obtain high-precision non-fuzzy angle estimation.
2. The method according to claim 1, wherein a total of K.gtoreq.1 targets are located at an angle θ 1 ，…，θ K The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target refers to the detected object, the θ 1 ，…，θ K The angles of the K targets are respectively, and K represents the number of the targets.
3. The method of claim 2, wherein the transmit antenna element spacing in step (1) is d t The space between the receiving antenna units is d r ＝Md t +0.5λ, λ is the carrier wavelength, and d t >>0.5λ。
4. A method according to claim 3, wherein the matched filtered spread array data vector in step (2) is represented as:
wherein x (t) represents a received signal vector;
b(t)＝[b 1 (t)，…，b K (t)] T ，
n(t)＝[n 1 (t)，…，n MN (t)] T
parameters on the left of the four equation equals signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; of the four formulas described above,representing the Kronecker product, the function based on e represents an exponential function based on a natural constant e, b k (t) is the kth signal, f k For its Doppler frequency, t represents a time variable.
5. The method of claim 4, wherein the angle θ 1 ，…，θ K Are different from each other, and f 1 ≠f 2 ≠…≠f K 。
6. The method of claim 4, wherein the covariance matrix in step (3) is estimated as follows:
wherein T is the number of pulses, T n Indicating the nth pulse, the superscript H indicating the conjugate transpose;
the signal subspace is estimated as follows: calculating the characteristic value decomposition of R to obtain
R＝U V U H
Wherein V is the eigenvalue matrix of covariance matrix R, and U is the eigenvalue matrixIs a feature vector matrix of (a); arranging the characteristic values from large to small, wherein a matrix formed by characteristic vectors corresponding to the first K large characteristic values is a signal subspace matrix E s The method comprises the steps of carrying out a first treatment on the surface of the The first K large eigenvalues refer to first K eigenvalues; here, "large eigenvalues" means that the eigenvalues belong to the signal subspace eigenvalues.
7. The method of claim 6, wherein the obtaining of the set of ambiguous angle estimates from the transmit translational invariant factor in step (4) is calculated as follows: constructing a matrix:
wherein ,Jt1 ＝[I M-1 ,0 (M-1)，1 ],J t2 ＝[0 (M-1)，1 ,I M-1 ]；I N Representing an identity matrix, 0 M,N A zero matrix representing M x N dimensions; j (J) t1 and Jt2 The selection matrix is represented by a representation of the selection matrix,the eigenvalue decomposition of (c) can be expressed as:
wherein the matrix T is a K-dimensional nonsingular matrix, which is marked with the superscriptRepresenting a matrix pseudo-inverse;
diagonal to the K dimensionMatrix phi t,k Representing phase information of the kth diagonal element due to d t ＞＞λ/2，φ t,k Can be expressed as a set of fuzzy estimates:
the numerical value is a group of fuzzy angle estimated values obtained by transmitting a translation invariant factor in the step (4);
wherein ,nt As a set of integers,is->Principal value of argument ++>Is->And calculating the kth characteristic value.
8. The method of claim 7, wherein the step (5) of deriving a set of ambiguous angle estimates from the received translational invariance factors is calculated as follows: construction matrix
wherein ,Jr1 ＝[I N-1 ,0 (N-1)，1 ],J r2 ＝[0 (N-1)，1 ,I N-1 ]Is a selection matrix;the eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d r ＞＞λ/2，Can be expressed as a set of fuzzy estimates
The numerical value is a group of fuzzy angle estimated values obtained by receiving the translation invariant factor in the step (5);
wherein ,nr As a set of integers,is->Principal value of argument ++>Is->And calculating the kth characteristic value.
9. The method of claim 8, wherein the obtaining of the blur-free angle estimate from the half-wavelength shift invariant factor in step (6) is calculated as follows: construction matrix E v1 and Ev2, wherein Ev1 Corresponding to the last transmitting antenna and 1 st to N-1 st receiving antennas, E v2 Corresponding to the 1 st transmitting antenna and the 2 nd to nth receiving antennas,the eigenvalue decomposition of (c) can be expressed as
wherein ,
due to d v =0.5λ, can give Φ v,k ＝sinθ k 。
10. The method of claim 9, wherein the high-precision blur-free angle estimate in step (7) is calculated by: phi (phi) t,k Middle and phi v,k The nearest value is phi t,k Is expressed asφ r,k Middle and->The nearest value is phi r,k Is expressed as +.>According to->Directly calculate and get theta k Estimate of +.>
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| CN106054121A (en) * | 2016-04-24 | 2016-10-26 | 中国人民解放军空军工程大学 | Method and device of determining radar target angle |
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