CN110109051B - Frequency control array-based cross coupling array DOA estimation method - Google Patents
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Abstract
The invention relates to the field of array signal processing, and aims to provide a super-resolution DOA estimation algorithm for a far-field narrowband signal source. Firstly, generating frequency control array signals with uniform frequency difference based on a uniform linear array, and then constructing a selection matrix by a symmetrical Toeplitz structure of a mutual coupling coefficient matrix MCM (Mutual Coupling Matrix) to intercept received data so that the rest data have cyclic mutual coupling coefficients; then, by including the unknown mutual coupling coefficients into the source part, a new steering vector of the truncated data is obtained; then, singular value SVD decomposition is carried out on the received signals; and finally, constructing a sparse complete dictionary and a convex optimization solving function by utilizing the parameterization and sparse reconstruction theory of the guide vector, and improving the precision of the estimation result. The invention is mainly applied to the design and manufacture of the frequency control array radar.
Description
Technical Field
The invention relates to the field of array signal processing, in particular to a frequency control array-based cross coupling array DOA estimation method.
Background
DOA estimation has wide application in the fields of radar, sonar, channel detection, wireless communication and the like [1] . The super-resolution problem of the arrival direction of two or more adjacent sources has been a research hot spot in the array signal processing, and how to overcome the mutual coupling effect between the antenna units of the array in practical situations is another hot spot for performing DOA estimation on the sources.
Aiming at the super-resolution estimation problem of the direction of arrival, along with the compressed sensing theory [2,3] Proposed sparse representation class parameter estimation method based on grid division [4,5] Breakthroughs in conventional DOA estimation algorithms such as MUSIC (Multiple Signal Classificaion, multiple signal classification) algorithm and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques, rotation space invariance signal parameter estimation) algorithm [1] Is a performance of the (c). In the sparse representation type parameter estimation method algorithm based on grid division, the estimated parameters are discretized into a series of grids, the grids form an overcomplete dictionary, and the estimation problem of the parameters to be estimated is converted into a sparse recovery model of the parameters under the assumption that the parameters to be estimated only exist on a few grids of the grids.
FDA (Frequency diverse array, frequency controlled array) and conventional phased array have similar transmitting structure, and each antenna of the frequency controlled array can transmit signals with different frequencies, different from the phased array transmitting signals with the same frequency [6,7] . The mutual coupling effect between array elements may affect the accuracy of DOA estimation, because the influence between antennas is consistent, the mutual coupling coefficients of antennas are equal, and the matrix established by the mutual coupling coefficients between antennas can be represented by Toeplitz matrix [8] 。
In the cross-coupling DOA estimation problem, the conventional MUSIC algorithm and ESPRIT algorithm may fail due to the influence of the cross-coupling. Document [12 ] taking into consideration structural characteristics of a mutual coupling coefficient matrix and development of a sparse representation class algorithm based on grid division]By cutting off the received signal and then adopting L1_SVD algorithm [4] Performing DOA estimation; document [13 ]]DOA estimation algorithm based on block sparsity is proposed.
In the mutual coupling one-dimensional uniform linear array, the L1_SVD algorithm and the guide vector parameterization method can solve the Toeplitz structure and the block sparseness method. The technical route of the cross coupling array DOA estimation based on the frequency control array comprises four steps: 1) Establishing a signal model of a frequency control array; 2) Multiplying the signal matrix by the cross-coupling matrix; 3) Converting the original problem into a corresponding solution L1_SVD problem; 4) And 3) finishing final parameter estimation according to the optimized result in the step 3). Because the angular distance dependence of the frequency-controlled array has higher resolution characteristics in parameter estimation than in the estimation of a phased array under the same conditions.
[1]H.Krim and M.Viberg,“Two decades of array signal processing research:The parametric approach,”IEEE Signal Process.Mag.,vol.13,no.4,pp.67-94,Jul.1996.
[2]D.Donoho,“Superresolution via sparsity constraints,”SIAM Journal on Mathematical Analysis,vol.23,pp.1309-1331,Sep.1992.
[3]E.Candes,“Compressive sampling,”in Proc.of the International Congress of Mathematicians:Madrid,August 22-30,2006:invited lectures,2006,pp.1433-1452.
[4]D.Malioutov,M.Cetin,and A.S.Willsky,“A sparse signal reconstruction perspective for source localization with sensor arrays,”IEEE Transactions on Signal Processing,vol.53,no.8,pp.3010-3022.
[5]M.M.Hyder and K.Mahata,“Direction-of-arrival estimation using a mixed l2,0norm approximation,”IEEE Transactions on Signal Processing,vol.58,no.9,pp.4646-4655,Sep.2010.
[6]P.Antonik,M.C.Wicks,H.D.Griffiths,and C.J.Baker,“Frequency diverse array radars,”in 2006IEEE Conference on Radar,April 2006,pp.3pp.215–217
[7]J.Xu,G.Liao,S.Zhu,L.Huang,and H.C.So,“Joint range and angle estimation using mimo radar with frequency diverse array,”IEEE Transactions on Signal Processing,vol.63,no.13,pp.3396–3410,July 2015
[8]T.Svantesson,“Modeling and estimation of mutual coupling in a uniform linear array of dipoles,”in 1999IEEE International Conference on Acoustics,Speech,and Signal Processing,vol.5,1999,pp.2961–2964
[9]J.Dai,D.Zhao,and X.Ji,“A sparse representation method for DOA estimation with unknown mutual coupling,”IEEE Antennas and Wireless Propagation Letters,vol.11,pp.1210-1213,2012.
[10]Q.Wang,T.Dou,H.Chen,W.Yan and W.Liu,“Effective Block Sparse Representation Algorithm for DOA Estimation With Unknown Mutual Coupling,”IEEE Communications Letters,vol.21,no.12,pp.2622-2625,Dec.2017.
[11]L.Hao and W.Ping,“DOA estimation in an antenna array with mutual coupling based on ESPRIT,”Proc.International Workshop on Microwave and Millimeter Wave Circuits and System Technology,pp.86-89,2013。
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a super-resolution DOA estimation algorithm for a far-field narrowband signal source when mutual coupling effect exists under the condition of uniform linear array transmitting radio frequency control array signals. Firstly, generating frequency control array signals with uniform frequency difference based on a uniform linear array, and then constructing a selection matrix by a symmetrical Toeplitz structure of a mutual coupling coefficient matrix MCM (Mutual Coupling Matrix) to intercept received data so that the rest data have cyclic mutual coupling coefficients; then, by including the unknown mutual coupling coefficients into the source part, a new steering vector of the truncated data is obtained; then, singular value SVD decomposition is carried out on the received signals; and finally, constructing a sparse complete dictionary and a convex optimization solving function by utilizing the parameterization and sparse reconstruction theory of the guide vector, and improving the precision of the estimation result.
The specific steps are refined as follows:
step 1: establishing a transmitting signal with mutual coupling under a frequency control array;
step 2: for received signals
Singular value decomposition is carried out;
step 3: signal subspace calculation of received data from unitary signal space
Step 4: sparse signal complete dictionary A based on guide vector parameterization J J Is a structure of (2);
step 5: constructing a convex programming function for reconstructing the sparse signal according to the l1 norm;
step 6: and solving the convex programming function and searching a spectrum peak.
Further:
step 1: there is a uniformly distributed linear array ULA consisting of M isotropic antennas, remotely consisting of N far-field narrowband signals s k (t) at an angle θ respectively 1 ,θ 2 ,…,θ N Incident on the array, n=1, 2, …, N, and the difference between the transmission frequencies of the array elements is denoted as Δf, i.e. the transmission frequency of the nth array element is denoted as f n ＝(n-1)*△f+f 0 ，f 0 As the initial parameterThe array element transmitting frequency is examined;
when the mutual coupling effect among array elements is not considered, the sampling result of one snapshot is that the received signal matrix is:
X(t)＝[x 1 (t),x 2 (t),…,x M (t)] T representing output signal matrixes of M array elements under the snapshot sampling at the time;
s (t) represents a signal matrix composed of the original N narrowband signals. t represents a snapshot.
A is an array manifold matrix composed of steering vectors a (theta),
wherein the method comprises the steps of
I.e. the angle theta representing the i-th signal i The n-th array element is reached by taking the first one as the phase difference of the reference phase, wherein d represents the distance between two adjacent array elements of the uniform array,/for>
c is the speed of light, and is the speed of light,
is a noise signal matrix, wherein each column represents a noise signal received by each array element, and under the condition of considering the mutual coupling factor, a single snapshot is that of sampling the received signal once:
each column of the matrix represents coupling coefficients between an array element and other array elements at other positions, 1 represents the compared array elements, then the whole matrix C represents a coupling coefficient matrix formed by the combination of the coefficients of mutual coupling between the array elements, and then the receiving signal models under L snapshots:
s denotes a matrix of narrowband signals at a plurality of shots,
a matrix representing a plurality of snap-down noise signals;
step 2: calculating covariance matrix of the received signal:
where L is the number of snapshots and X (t) is the matrix of received signals, where the nth signal has a transmit frequency f n ＝f 0 ++ (n-1) Δf, the total steering vector is divided into two matrices according to the distance-related parameters and the angle-related terms, expressed as: />
The symbol indicates the multiplication of the corresponding position, a Θ Is a matrix of angle-dependent terms, a r Representing a matrix of distance-dependent terms, θ represents the angle of incidence when the signal arrives at the element, the original θ because the signal is a far-field signal 1 ,θ 2 ,…,θ N Can be seen as the same angle of incidence; r represents the distance of the signal to the array element;
step 3: singular value decomposition r=uΛv is performed on the covariance matrix R, where U and V are unitary matrices of magnitudes m×m and n×n (the magnitude of which depends on the number of array elements M and the number of signals N), Λ is a diagonal matrix of singular values of magnitude m×n, and the corresponding signal and noise portions undergo singular value decomposition u= [ U ] S U N ]，U s U matrix representing signals, U N A U matrix representing noise; similar v= [ V S V N ] T ，V S V matrix representing signals, V N V matrix representing noise, T represents transposed matrix, and Λ=diag [ Λ ] S Λ N ]；
Step 4: for mutual coupling of the matrices, a selection matrix D is constructed K ＝[I K 0]Wherein I K The unit matrix is K multiplied by K, and K is the number of preselected sources. Calculating a signal subspace R S ＝RVD K ；
Step 5: in accordance with the parameterization of the steering vector,
constructing a sparse complete dictionary A J ＝[J(θ 1 ),J(θ 2 ),…,J(θ N )]；
Step 6: constraining the spatial domain sparse characteristic of the signal by using the l1 norm, wherein the constraint condition is the l 2-norm time domain sparse and the noise suppression, namely constructing a convex programming function
Step 7: using l1-SVD theory, restraining with 99% confidence interval to automatically select regularization parameter xi, solving noise subspace U according to orthogonality of signal subspace and noise subspace n The angle theta corresponding to the value of (0) is estimated by using a convex optimization tool kit (CVX), the sparse signal space spectrum is estimated, and finally one-dimensional spectrum peak search is carried out;
step 8: and 5, repeating the step 5 and the step 6 to improve the estimation accuracy.
The invention has the characteristics and beneficial effects that:
the invention has the advantages of higher angle measurement precision, and simultaneously, DOA estimation still maintains excellent performance when the array mutual coupling phenomenon is obvious. While having better estimation performance than a phased array of comparable conditions.
The conventional array mutual coupling self-correction algorithm mostly discards array elements at two ends of the whole array and only uses receiving information of intermediate array elements, which inevitably affects measurement accuracy. Different from other algorithms, the algorithm fully utilizes all array element receiving information of a uniform array, and utilizes parameterization operation of a steering vector to sort and reorganize a receiving data model under the condition of mutual coupling, so that a new complete dictionary for sparse reconstruction is constructed. In the solving process, singular value decomposition is adopted to carry out dimension reduction processing on the data, so that the calculation complexity is reduced, and the effect of noise reduction is achieved.
In the DOA estimation performance aspect, the method compares with algorithms in the reference document under different signal-to-noise ratios and different snapshot numbers, and uses Root Mean Square Error (RMSE) as a performance measurement index, wherein the signal number is set to be 2, and the result is shown in the following graph. Fig. 1: the method provided performs best with a signal-to-noise ratio of 5dB and a snapshot count of 400. Fig. 2 and 3 show that, in the case of a snapshot count of 400, the root mean square error of the algorithm is smaller than that of other algorithms in the reference with the increase of the signal-to-noise ratio, and in the case of a signal-to-noise ratio of 20dB, the algorithm performance is gradually improved and better than that of the other algorithms with the increase of the snapshot count.
Description of the drawings:
fig. 1 several methods DOA estimation accuracy.
Fig. 2 DOA estimation accuracy versus signal-to-noise ratio.
FIG. 3 DOA estimation accuracy versus snapshot count.
Fig. 4 array model with uniformly distributed array elements.
FIG. 5 is a flow chart of the method.
Detailed Description
The invention belongs to the array signal processing field, and completes DOA estimation of far-field narrow-band signals by analyzing and reconstructing output signals of a uniform linear array under the condition of considering mutual coupling according to the characteristic of angular distance correlation of a frequency control array, and applying a sparse reconstructed parameter estimation framework to the mutual coupling DOA (Direction of Arrival ) estimation.
Firstly, a uniform frequency difference frequency control array signal is generated based on a uniform linear array, and then a selection matrix is constructed by a symmetrical Toeplitz structure of a mutual coupling coefficient matrix (Mutual Coupling Matrix, MCM) to intercept received data, so that the rest data has cyclic mutual coupling coefficients. Then, by including the unknown cross-coupling coefficients into the source part, a new steering vector for the truncated data is obtained. Then, subjecting the received signal to singular value decomposition (SVD decomposition) reduces the calculation amount and denoising. And finally, constructing a sparse complete dictionary and a convex optimization solving function by utilizing the parameterization and sparse reconstruction theory of the guide vector, and improving the precision of the estimation result. The specific scheme is as follows:
the DOA estimation method of the cross coupling array based on the frequency control array comprises the following steps:
step 1: as shown in FIG. 1, there is a uniformly distributed linear array (ULA) of M isotropic antennas, remotely defined by N far-field narrowband signals s k (t), (k=1, 2, …, N) at an angle θ respectively 1 ,θ 2 ,…,θ N Incident on the array. The transmitting frequencies of the array elements differ by delta f, i.e. the transmitting frequency f of the nth array element n ＝(n-1)*△f+f 0 。f 0 The frequency is transmitted for the initial reference array element.
When the mutual coupling effect among array elements is not considered, the sampling result of one snapshot is that the received signal matrix is:
X(t)＝[x 1 (t),x 2 (t),…,x M (t)] T representing the output signal matrix of M array elements at this snapshot sampling.
s (t) represents a signal matrix composed of the original N narrowband signals. t represents a snapshot.
A is an array manifold matrix composed of steering vectors a (theta),
wherein the method comprises the steps of
I.e. the angle theta representing the i-th signal i The n-th array element is reached by taking the first one as the phase difference of the reference phase, wherein d represents the distance between two adjacent array elements of the uniform array,/for>
c is the speed of light.
Is a matrix of noise signals, each column of which represents a noise signal. Under the condition of considering the mutual coupling factor, the signal is received by single snapshot:
each column of the matrix represents a coupling coefficient between an array element and an array element at other positions, and 1 represents the array element to be compared. The whole matrix C represents a coupling coefficient matrix formed by mutually coupling and combining the array elements, and the received signal model under L snapshots:
step 2: calculating covariance matrix of the received signal:
where L is the number of snapshots and X (t) is the received signal matrix. Wherein the transmission frequency of the nth signal is f n ＝f 0 The total steering vector can be divided into two matrices according to the distance-related parameter and the angle-related relation, expressed as + (n-1) Δf
The symbol indicates the corresponding position multiplication. a, a Θ Is a matrix of angle-dependent terms, a r Representing a matrix of distance-dependent terms. θ represents the angle of incidence when the signal arrives at the element, since the signal is far-field 1 ,θ 2 ,…,θ N Can be seen as the same angle of incidence; r represents the distance of the signal to the array elements, d is the uniform array element spacing, and c is the speed of light.
Step 3: singular value decomposition r=uΛv is performed on the covariance matrix R, where U and V are unitary matrices of size m×m and n×n, respectively, and Λ is a singular value diagonal matrix of size m×n. The corresponding signal and noise parts (the magnitude of which depends on the number M of array elements and the number N of signals) are subjected to singular value decomposition U= [ U ] S U N ]，U s U matrix representing signals, U N A U matrix representing noise; similar v= [ V S V N ] T (V matrix of signal and V matrix of noise, respectively, in brackets), T represents transposed matrix, and Λ=diag [ Λ ] S Λ N ]. (the singular value diagonal matrix is also divided into a signal and a noise singular value diagonal matrix, and the singular value minimum in the signal singular value matrix is larger than the largest singular value of the noise singular value matrix.)
Step 4: for mutual coupling of the matrices, a selection matrix D is constructed K ＝[I K 0]Wherein I K The unit matrix is K multiplied by K, and K is the number of the pre-selected information sources. Calculating a signal subspace R S ＝RVD K 。
Step 5: in accordance with the parameterization of the steering vector,
constructing a sparse complete dictionary A J ＝[J(θ 1 ),J(θ 2 ),…,J(θ N )]。
Step 6: constraining the spatial domain sparse characteristic of the signal by using l1 norm, wherein the constraint condition is the time domain of l2 normSparseness and noise suppression, i.e. construction of convex programming functions
Step 7: using the l1-SVD theory, regularization parameters ζ are automatically selected with 99% confidence interval suppression. And solving an angle theta corresponding to un=0 according to the orthogonality of the signal subspace and the noise subspace. And estimating a sparse signal space spectrum by using a convex optimization tool kit CVX, and finally searching for a one-dimensional spectrum peak.
Step 8: and 5, repeating the step 5 and the step 6 to improve the estimation accuracy.
The flow is as in fig. 5.
Claims (3)
1. A DOA estimation method based on a frequency control array is characterized in that firstly, a frequency control array signal with uniform frequency difference is generated based on a uniform linear array, and then a selection matrix is constructed to intercept received data by a symmetrical Toeplitz structure of a mutual coupling coefficient matrix MCM (Mutual Coupling Matrix), so that the rest data has cyclic mutual coupling coefficients; then, by including the unknown mutual coupling coefficients into the source part, a new steering vector of the truncated data is obtained; then, singular value SVD decomposition is carried out on the received signals; and finally, constructing a sparse complete dictionary and a convex optimization solving function by utilizing the parameterization and sparse reconstruction theory of the guide vector, and improving the precision of the estimation result.
2. The frequency control array-based cross-coupling array DOA estimation method of claim 1, wherein the method comprises the following specific steps of:
step 1: establishing a transmitting signal with mutual coupling under a frequency control array;
step 2: for received signals
Singular value decomposition is carried out;
step 3: signal subspace calculation of received data from unitary signal space
Step 4: sparse signal complete dictionary A based on guide vector parameterization J J Is a structure of (2);
step 5: constructing a convex programming function for reconstructing the sparse signal according to the l1 norm;
step 6: and solving the convex programming function and searching a spectrum peak.
3. The frequency control array-based cross-coupling array DOA estimation method of claim 1, further comprising:
step 1: there is a uniformly distributed linear array ULA consisting of M isotropic antennas, remotely consisting of N far-field narrowband signals s k (t) at an angle θ respectively 1 ,θ 2 ,…,θ N Incident on the array, n=1, 2, …, N, and the difference between the transmission frequencies of the array elements is denoted as Δf, i.e. the transmission frequency of the nth array element is denoted as f n ＝(n-1)*△f+f 0 ，f 0 Transmitting frequency for initial reference array element;
when the mutual coupling effect among array elements is not considered, the sampling result of one snapshot is that the received signal matrix is:
X(t)＝[x 1 (t),x 2 (t),…,x M (t)] T representing output signal matrixes of M array elements under the snapshot sampling at the time;
s (t) represents a signal matrix formed by the original N narrowband signals, and t represents a snapshot;
a is an array manifold matrix composed of steering vectors a (theta),
wherein the method comprises the steps of
I.e. the angle theta representing the i-th signal i To the nth array element by the firstIs the phase difference of the reference phase, where d represents the distance between two adjacent array elements of the uniform array,/->
c is the speed of light, and is the speed of light,
is a noise signal matrix, wherein each column represents a noise signal received by each array element, and under the condition of considering the mutual coupling factor, a single snapshot is that of sampling the received signal once:
each column of the matrix represents coupling coefficients between an array element and other array elements at other positions, 1 represents the compared array elements, then the whole matrix C represents a coupling coefficient matrix formed by the combination of the coefficients of mutual coupling between the array elements, and then the receiving signal models under L snapshots:
s denotes a matrix of narrowband signals at a plurality of shots,
a matrix representing a plurality of snap-down noise signals;
step 2: calculating covariance matrix of the received signal:
where L is the number of snapshots and X (t) is the matrix of received signals, where the nth signal has a transmit frequency f n ＝f 0 ++ (n-1) Δf, the total steering vector is calculated according to the sum of the distance-related parameters and the sumThe angular relationship is divided into two matrices, denoted:
the symbol indicates the multiplication of the corresponding position, a Θ Is a matrix of angle-dependent terms, a r Representing a matrix of distance-dependent terms, θ represents the angle of incidence when the signal arrives at the element, the original θ because the signal is a far-field signal 1 ,θ 2 ,…,θ N Can be seen as the same angle of incidence; r represents the distance of the signal to the array element;
step 3: singular value decomposition r=uΛv is performed on the covariance matrix R, where U and V are unitary matrices of magnitudes m×m and n×n (the magnitude of which depends on the number of array elements M and the number of signals N), Λ is a diagonal matrix of singular values of magnitude m×n, and the corresponding signal and noise portions undergo singular value decomposition u= [ U ] S U N ]，U s U matrix representing signals, U N A U matrix representing noise; similar v= [ V S V N ] T ，V S V matrix representing signals, V N V matrix representing noise, T represents transposed matrix, and Λ=diag [ Λ ] S Λ N ]；
Step 4: for mutual coupling of the matrices, a selection matrix D is constructed K ＝[I K 0]Wherein I K Calculating a signal subspace R for a unit matrix with the size of K multiplied by K, wherein K is the number of preselected information sources S ＝RVD K ；
Step 5: in accordance with the parameterization of the steering vector,
constructing a sparse complete dictionary A J ＝[J(θ 1 ),J(θ 2 ),…,J(θ N )]；
Step 6: constraining the spatial domain sparse characteristic of the signal by using l1 norm, wherein the constraint condition is time domain sparsity of l2 norm and pairNoise suppression, i.e. construction of convex programming functions
Step 7: using l1-SVD theory, restraining with 99% confidence interval to automatically select regularization parameter xi, solving noise subspace U according to orthogonality of signal subspace and noise subspace n The angle theta corresponding to the value of (0) is estimated by using a convex optimization tool kit (CVX), the sparse signal space spectrum is estimated, and finally one-dimensional spectrum peak search is carried out;
step 8: and 5, repeating the step 5 and the step 6 to improve the estimation accuracy.
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