CN113253195B - Self-correcting MIMO system direction finding method under array element cross coupling and direction correlation situation - Google Patents
Self-correcting MIMO system direction finding method under array element cross coupling and direction correlation situation Download PDFInfo
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Abstract
The invention discloses a direction finding method of a self-correcting MIMO system under the condition that array elements are mutually coupled and direction is related, firstly, data received by an array are subjected to matched filtering, and the data after matched filtering are stacked into a third-order tensor; then decomposing the obtained third-order tensor by utilizing a parallel factor decomposition technology to obtain an actual transmitting array flow pattern and an actual receiving array flow pattern; then, separating the mutual coupling coefficient and the angle variable in the obtained array flow pattern by using matrix transformation, thereby constructing a cost function of the angle parameter; solving the cost function and searching a one-dimensional spectrum peak with twice target number to obtain a departure angle and an arrival angle which can be automatically paired; and finally, solving the mutual coupling vector depending on the direction by using the angle estimation values of the departure angle and the arrival angle. The invention can obviously improve the performance and the success rate of direction estimation under the nonideal condition and realize the array self-calibration under the condition that the cross coupling of the array elements depends on the angle.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a self-correcting MIMO system direction finding method.
Background
The incoming wave direction estimation technology of the target plays an important role in civil and military application, and because the bistatic MIMO system has the characteristics of high parameter estimation precision, strong clutter suppression capability and the like, the MIMO system angle estimation has a vigorous development situation in the past decades, and algorithms such as subspace type algorithms, maximum likelihood algorithms, tensor algorithms, compressed sensing and the like are endless.
Most of the current algorithms for estimating angles based on the MIMO system are based on the fact that the popularity of the array is accurately known and show good estimation performance. However, in practice, due to mutual coupling influence among array elements, the actual array model is not matched with the ideal model, and the estimation accuracy of the target incoming wave direction is greatly influenced.
Algorithms related to the mutual coupling and the direction of the array elements are few, but the array element does not need to be referenced in the array self-correction method, the estimation performance of target parameters under the situation of the mutual coupling is greatly improved, and the method has profound research significance.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a self-correcting MIMO system direction finding method under the condition that array element mutual coupling and direction are related, firstly, data received by an array are subjected to matched filtering, and the data after matched filtering are stacked into a third-order tensor; then decomposing the obtained third-order tensor by utilizing a parallel factor decomposition technology to obtain an actual transmitting array flow pattern and an actual receiving array flow pattern; then, separating the mutual coupling coefficient and the angle variable in the obtained array flow pattern by using matrix transformation, thereby constructing a cost function of the angle parameter; solving the cost function and searching a one-dimensional spectrum peak with twice target number to obtain a departure angle and an arrival angle which can be automatically paired; and finally, solving a mutual coupling vector depending on the direction by using angle estimation values of the departure angle and the arrival angle. The invention can obviously improve the performance and the success rate of direction estimation under the nonideal condition and realize the array self-calibration under the condition that the cross coupling of the array elements depends on the angle.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: establishing a signal model received by the bistatic MIMO array under the influence of array element mutual coupling: the method comprises the steps that M array elements are arranged in a transmitting array of the bistatic MIMO system, R array elements are arranged in a receiving array, and K far-field targets are arranged in the space;
step 2: signals transmitted among array elements of the MIMO system transmitting array are mutually orthogonal;
step 2-1: when the mutual coupling influence of array elements is not considered, the received signals are subjected to matched filtering to obtain an X received data model 0 ＝[A r ⊙A t ]S T + N, ", indicates a Khatri-Rao product,
and
an array manifold matrix of a receive array and a transmit array respectively,
and
k =1, \ 8230, K is the steering vector of the receiving array and the transmitting array to different directions respectively,
and theta k Respectively the departure angle and the arrival angle of the kth far-field target,
for receiving Q pulses within a coherent interval and matched filtering
α kq And f k The system cross-section RCS amplitude of the target and the doppler shift of the target, Q =1, \8230;, Q, respectively;
step 2-2: when the array element mutual coupling influence is considered, the received data model after matching filtering is X = [ B ] r ⊙B t ]S T +N，B r ＝[C r1 a r (θ 1 ),C r2 a r (θ 2 ),…,C rK a r (θ K )]，
Wherein
And
respectively representing the mutual coupling matrixes of the receiving array and the transmitting array based on different directions, P represents the range of the mutual coupling of the array elements, c r (θ k ) Representing the mutual coupling vectors of the receiving array in different directions,
representing mutual coupling vectors of the transmitting array in different directions;
and step 3: by using
Carrying out three-dimensional space stacking operation on the received data model to obtain a three-dimensional array, namely a third-order tensor model of the received data, wherein the relation between the received data model and the third-order tensor model in the step 2-2 is
And 4, step 4: obtained by parallel factorization
Wherein
The product of the external force is the product of the external force,
indicating steering vectors of the transmitting array affected by mutual coupling, b r (θ k ) Steering vectors, s, representing the influence of mutual coupling on the receiving array t (f k ) Indicating the received data of the kth target at the time t;
and 5: introducing a matrix transformation theorem:
C(θ k )a(θ k )＝T(θ k )c(θ k )
T(θ k )＝[E 1 a(θ k ),…,E P a(θ k )]
wherein, a (θ) k ) A steering vector, C (θ), representing the array k ) A cross-coupling matrix representing an array, E p Is an M × M matrix, P =1, \8230;, P, satisfying the formula (2):
wherein, the corner marks i, j respectively represent the matrix C (theta) k ) Row i, column j;
step 6: for B obtained by parallel factorization in step 3 t And B r And 5, performing matrix transformation to separate the mutual coupling vectors to obtain:
wherein, T r (θ k ) Transformation matrix T (theta) of the receiving array in expression (1) k )，
Transformation matrix T (theta) of the transmit array in expression (1) k )；
And 7: fitting the results obtained in the step 4 and the step 6 to obtain:
wherein the content of the first and second substances,
a steering vector estimate representing the transmit array affected by mutual coupling,
representing estimates of the mutual coupling vectors of the transmit arrays in different directions,
a steering vector estimate representing the effect of mutual coupling on the receive array,
representing the estimated value of the mutual coupling vector of the receiving array in different directions;
the expression of the mutual coupling coefficient is further obtained as follows:
wherein, the first and the second end of the pipe are connected with each other,
the operator represents the Moore-Penrose pseudo-inverse;
the formula (5) is taken into the formula (4) to obtain the estimation formula of the target departure angle and the arrival angle as follows:
then only 2K times of one-dimensional search is carried out to obtain the angle estimation values of K targets in the space;
and step 8: after the angle estimation value of the target is obtained, the angle estimation value is substituted into the formula (5) to estimate the mutual coupling vectors in different directions.
The invention has the following beneficial effects:
the method considers the influence of array element mutual coupling on target parameter estimation in a bistatic MIMO system, considers the more general condition that mutual coupling and direction are related, realizes the online self-calibration of the array under the condition of mutual coupling by a solution method for deducing the target direction and the mutual coupling coefficient, and greatly improves the parameter estimation precision of the target and the stability of the algorithm.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic direction-finding diagram of the bistatic MIMO system of the present invention.
Fig. 3 is a target direction estimation result of the embodiment of the present invention.
Fig. 4 is a plot of direction estimation error for different signal-to-noise ratios according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
The invention provides a direction estimation method of a self-correcting bistatic MIMO system for overcoming the influence of mutual coupling among array elements on target parameter estimation.
As shown in fig. 1, a self-correcting MIMO system direction finding method under the situation of mutual coupling of array elements and direction correlation includes the following steps:
step 1: establishing a signal model received by the bistatic MIMO array under the influence of array element mutual coupling: the method comprises the steps that M array elements are arranged in a transmitting array of the bistatic MIMO system, N array elements are arranged in a receiving array, and K far-field targets are arranged in the space;
step 2: signals transmitted among array elements of the MIMO system transmitting array are mutually orthogonal;
step 2-1: when the mutual coupling influence of array elements is not considered, the received signals are subjected to matched filtering to obtain a received data model X 0 ＝[A r ⊙A t ]S T + N, ", indicates a Khatri-Rao product,
and
an array manifold matrix of a receive array and a transmit array respectively,
and
k =1, \8230, K is the steering vector of the receiving array and the transmitting array respectively to different directions,
and theta k Respectively the departure angle and the arrival angle of the kth far-field target,
for receiving Q pulses within a coherence interval and matched filtering
α kq And f k The system cross-section RCS amplitude of the target and the doppler shift of the target, Q =1, \8230;, Q, respectively;
step 2-2: when the mutual coupling influence of array elements is considered, the received data model obtained after the matching filtering isX＝[B r ⊙B t ]S T +N，B r ＝[C r1 a r (θ 1 ),C r2 a r (θ 2 ),…,C rK a r (θ K )]，
Wherein
And
respectively representing the mutual coupling matrixes of the receiving array and the transmitting array based on different directions, P represents the range of the mutual coupling of the array elements, and if the range is exceeded, the mutual coupling does not exist between the two array elements, c r (θ k ) Representing the mutual coupling vectors of the receiving array in different directions,
representing mutual coupling vectors of the transmitting array in different directions;
and step 3: by using
Carrying out three-dimensional space stacking operation on the received data model to obtain a three-dimensional array, namely a third-order tensor model of the received data, wherein the relation between the received data model and the third-order tensor model in the step 2-2 is
And 4, step 4: obtained by parallel factorization
Wherein
The product of the external force is the product of the external force,
steering vectors representing the influence of mutual coupling on the transmitting array, b r (θ k ) Steering vectors, s, representing the influence of mutual coupling on the receiving array t (f k ) Indicating the received data of the kth target at the time t;
and 5: introducing a matrix transformation theorem:
C(θ k )a(θ k )＝T(θ k )c(θ k )
T(θ k )＝[E 1 a(θ k ),…,E P a(θ k )]
wherein, a (theta) k ) A steering vector, C (θ), representing the array k ) A cross-coupling matrix representing an array, E p Is an M × M matrix, P =1, \8230;, P, satisfying the formula (2):
wherein the indices i, j represent the matrix C (θ) respectively k ) Row i, column j;
step 6: for B obtained by parallel factorization in step 3 t And B r And 5, performing matrix transformation to separate the mutual coupling vectors to obtain:
wherein, T r (θ k ) Transformation matrix T (theta) of the receiving array in expression (1) k )，
Transformation matrix T (theta) of the transmit array in expression (1) k )；
And 7: fitting the results obtained in step 4 and step 6 to obtain:
wherein the content of the first and second substances,
a steering vector estimate representing the transmit array affected by mutual coupling,
representing estimates of mutual coupling vectors of the transmit arrays in different directions,
a steering vector estimate representing the receive array affected by mutual coupling,
representing the estimated values of the mutual coupling vectors of the receiving array in different directions;
the expression for further obtaining the mutual coupling coefficient is:
wherein the content of the first and second substances,
the operator represents the Moore-Penrose pseudo-inverse;
the formula (5) is taken into the formula (4) to obtain the estimation formula of the target departure angle and the arrival angle as follows:
then only 2K times of one-dimensional search is carried out to obtain the angle estimation values of K targets in the space;
and 8: after the angle estimation value of the target is obtained, the angle estimation value is substituted into the formula (5) to estimate the mutual coupling vectors in different directions.
The specific embodiment is as follows:
1. setting initialization parameters
As shown in the schematic diagram of bistatic MIMO system direction finding in fig. 2, the number of transmitting array elements and the number of receiving array elements are M =8, n =6, and the spacing between the array elements
The transmission array element transmits completely orthogonal signals for half wavelength, and the amplitude of the system cross section (RCS) is selected as alpha = [1,1 = [1,1,1 ]] T The Doppler shift is selected to be f = [200,400,850 ]] T /2000, K =3 targets in space, with directions selected separately
The number of pulse samples is chosen to be Q =100.
2. Establishing a tensor signal model of the received data according to the step 3;
3. according to the step 4, carrying out parallel factorization on the third-order tensor to obtain an emission array manifold;
4. using the matrix transformation C (theta) k )a(θ k )＝T(θ k )c(θ k ) Separating out the mutual coupling vector corresponding to each direction;
5. carrying out 2K =6 times of one-dimensional search through an estimation formula (4) of the target direction to obtain the departure angle and the arrival angle of each target;
6. after the direction estimation of the target is obtained, the angle information can be substituted into the formula (5) to obtain the mutual coupling vectors corresponding to different directions.
As shown in fig. 3, the signal-to-noise ratio SNR =5dB; the number of sampling pulses Q =100, and the amplitude of the cross-section (RCS) of the system is chosen to be α = [1,1 = [1,1,1 ]] T The Doppler shift is chosen to be f = [200,400,850 ]] T The number of transmitting array elements is =12, the number of receiving array elements is =10, and the mutual coupling vectors of the transmitting and receiving arrays in three different directions are ct = [1,0.22+ j 0.59,0.41-j 0.33;1,0.38+ j 0.48,0.23+ j 0.16;1,0.47+ j 0.39,0.34+ j 0.23]；cr＝[1,0.40+j*0.19,0.21+j*0.36；1,0.12+j*0.79,0.21+j*0.27；1,0.42-j*0.14,0.13-j*0.37](ii) a Target direction selection
And (4) a schematic diagram of the estimation result of the target direction.
It can be seen that the direction estimate obtained by the present method is more accurate than the uncorrected method.
The parameter settings of FIG. 4 are the same as those of FIG. 3, and the target directions are
And selecting Q =100 as the sampling pulse number, and obtaining a root mean square error change diagram of the uncorrected method and the method of the invention under different signal-to-noise ratios (SNR).
It can be seen that even at low signal-to-noise ratios, the method of the present invention still has higher accuracy, better than the uncorrected algorithm.
In conclusion, the self-correcting MIMO system direction finding method under the situation that the array elements are mutually coupled and the direction is related is far better than the uncorrected MIMO system direction finding method in the direction estimation precision, the direction estimation precision is greatly improved, and the algorithm robustness is improved.
Claims (1)
1. A self-correcting MIMO system direction finding method under the condition that array element mutual coupling and direction are related is characterized by comprising the following steps:
step 1: establishing a signal model received by the bistatic MIMO array under the influence of array element mutual coupling: supposing that a transmitting array of the bistatic MIMO system has M array elements, a receiving array has R array elements, and K far-field targets exist in the space;
step 2: signals transmitted among array elements of the MIMO system transmitting array are mutually orthogonal;
step 2-1: when the mutual coupling influence of array elements is not considered, the received signals are subjected to matched filtering to obtain an X received data model 0 ＝[A r ⊙A t ]S T + N, ", indicates a Khatri-Rao product,
and
an array manifold matrix for the receive array and the transmit array respectively,
and
respectively the steering vectors of the receiving array and the transmitting array to different directions,
and theta k Respectively the departure angle and arrival angle of the kth far-field target,
for receiving Q pulses within a coherent interval and matched filtering
And f k Q =1, \8230;, Q, respectively, the system cross-section RCS amplitude of the target and the doppler shift of the target;
step 2-2: when the mutual coupling influence of array elements is considered, the received data model obtained after the matching filtering is
B r ＝[C r1 a r (θ 1 ),C r2 a r (θ 2 ),…,C rK a r (θ K )]，
Wherein
And
respectively representing the mutual coupling matrixes of the receiving array and the transmitting array based on different directions, P represents the range of the mutual coupling of the array elements, c r (θ k ) Representing the mutual coupling vectors of the receiving array in different directions,
representing mutual coupling vectors of the transmitting array in different directions;
and step 3: by using
Carrying out three-dimensional space stacking operation on the received data model to obtain a three-dimensional array, namely a third-order tensor model of the received data, wherein the relation between the received data model and the third-order tensor model in the step 2-2 is
And 4, step 4: obtained by parallel factorization
Wherein
The product of the external force is the product of the external force,
indicating steering vectors of the transmitting array affected by mutual coupling, b r (θ k ) Steering vectors, s, representing the influence of mutual coupling on the receiving array t (f k ) Indicating the received data of the kth target at the time t;
and 5: introducing a matrix transformation theorem:
C(θ k )a(θ k )＝T(θ k )c(θ k )
T(θ k )＝[E 1 a(θ k ),…,E P a(θ k )]
wherein, a (θ) k ) A steering vector, C (θ), representing the array k ) A cross-coupling matrix representing an array, E p Is an M × M matrix, P =1, \8230;, P, satisfying the formula (2):
wherein, the corner marks i, j respectively represent the matrix C (theta) k ) Row i, column j;
and 6: for B obtained by parallel factorization in step 3 t And B r And 5, performing matrix transformation to separate the mutual coupling vectors to obtain:
wherein, T r (θ k ) Transformation matrix T (theta) of the receiving array in expression (1) k )，
Transformation matrix T (theta) of the transmit array in expression (1) k )；
And 7: fitting the results obtained in step 4 and step 6 to obtain:
wherein, the first and the second end of the pipe are connected with each other,
a steering vector estimate representing the transmit array affected by mutual coupling,
representing estimates of the mutual coupling vectors of the transmit arrays in different directions,
a steering vector estimate representing the effect of mutual coupling on the receive array,
representing the estimated values of the mutual coupling vectors of the receiving array in different directions;
the expression for further obtaining the mutual coupling coefficient is:
wherein the content of the first and second substances,
the operator represents the Moore-Penrose pseudo-inverse;
the formula (5) is taken into the formula (4) to obtain the estimation formula of the target departure angle and the arrival angle as follows:
then only 2K times of one-dimensional search is carried out to obtain the angle estimation values of K targets in the space;
and 8: after the angle estimation value of the target is obtained, the angle estimation value is substituted into the formula (5) to estimate the mutual coupling vectors in different directions.
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