CN110988854A - Robust self-adaptive beam forming algorithm based on alternative direction multiplier method - Google Patents
Robust self-adaptive beam forming algorithm based on alternative direction multiplier method Download PDFInfo
- Publication number
- CN110988854A CN110988854A CN201911347121.2A CN201911347121A CN110988854A CN 110988854 A CN110988854 A CN 110988854A CN 201911347121 A CN201911347121 A CN 201911347121A CN 110988854 A CN110988854 A CN 110988854A
- Authority
- CN
- China
- Prior art keywords
- interference
- vector
- estimated
- covariance matrix
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 62
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 48
- 230000003044 adaptive effect Effects 0.000 claims abstract description 26
- 239000011159 matrix material Substances 0.000 claims description 65
- 239000013598 vector Substances 0.000 claims description 55
- 238000005457 optimization Methods 0.000 claims description 39
- 230000003190 augmentative effect Effects 0.000 claims description 16
- 230000010354 integration Effects 0.000 claims description 8
- 230000000295 complement effect Effects 0.000 claims description 3
- 238000000354 decomposition reaction Methods 0.000 claims 1
- 238000012545 processing Methods 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 description 9
- 238000011068 loading method Methods 0.000 description 8
- 230000001427 coherent effect Effects 0.000 description 6
- 230000000694 effects Effects 0.000 description 5
- 238000004458 analytical method Methods 0.000 description 4
- 238000002474 experimental method Methods 0.000 description 4
- 238000012360 testing method Methods 0.000 description 4
- 238000009826 distribution Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000011946 reduction process Methods 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 238000009827 uniform distribution Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 238000007476 Maximum Likelihood Methods 0.000 description 1
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000003491 array Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000005562 fading Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000012887 quadratic function Methods 0.000 description 1
- 238000012163 sequencing technique Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- 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
- G01S13/006—Theoretical aspects
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radio Transmission System (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
The invention belongs to the field of radar signal processing, and discloses a robust adaptive beamforming algorithm based on an alternative direction multiplier method, which solves the problem of errors such as insufficient accuracy of an array or a signal of interest in the existing algorithm.
Description
Technical Field
The invention relates to the field of radar signal processing, in particular to a robust adaptive beamforming algorithm based on an alternating direction multiplier method.
Background
Adaptive beamforming has wide application in the fields of radar, sonar, wireless communication, and the like. Minimum variance distortion free response (MVDR) beamforming maximizes the beamformer output while maintaining the response in the signal direction. MVDR beamforming is optimal when the desired signal Steering Vector (SV) and the interference-plus-noise covariance matrix (INCM) are precisely known. However, in practical applications, Capon beamforming performance can be affected by inaccurate information such as directional mismatch, array calibration imperfections, and the like. To address these problems, many robust beamforming algorithms have been proposed in recent years. These beam forming methods can be roughly classified into the following categories: diagonal loading methods, feature space based methods, sparse reconstruction methods, and interference plus noise covariance matrix (INCM) reconstruction based methods.
The well-known diagonal loading method is to add a scaled identity matrix to the original INCM. To obtain the appropriate loading factor, different algorithms have been proposed based on the individual data uncertainty of the signal SV. However, the performance of these diagonal loading methods can be significantly degraded when the signal is contained in the sample snapshot; in some of the literature, INCM and signal SV are estimated by constructing a signal subspace and an interference subspace. However, in the general case, the feature space based approach is sensitive to the input signal-to-noise ratio (SNR) and the number of snapshots; in order to solve the problem of small number of snapshots, some documents have proposed a number of sparse reconstruction beamforming methods, such as IAA-based beamforming. However, these sparse reconstruction beamforming methods have the problem of SV model mismatch, and the estimation accuracy is also limited by the interval selection. The smaller the spacing, the greater the computational cost required. In an interference-plus-noise covariance matrix (INCM) reconstruction based method, the following two steps are required to estimate INCM and signal SV: first, to avoid performance degradation in high SNR situations, signal components need to be removed from the reconstructed INCM; the INCM can be reconstructed using Capon spectra to eliminate the desired signal component, and can also be reconstructed using a ring around the integration interval, even though the literature suggests a method to eliminate the effect of the desired signal using generalized angular low complexity INCM reconstruction. Second, the signal SV is constrained to maintain its robustness to SV mismatch. In some documents, a quadratic constraint quadratic optimization (QCQP) problem is constructed using components orthogonal to the assumed SV, and then the signal SV is solved by a MATLAB tool box CVX. Norm constraints for signal SV estimation are mentioned in some of the literature. The non-convex optimization problem can be converted into a convex optimization problem by using a semi-definite programming relaxation (SDR) method, and then a signal SV is obtained. But if the rank of the solution is not 1, an optimal solution may not be obtained in the rank reduction process.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a robust adaptive beamforming algorithm based on an alternative direction multiplier (ADMM), which solves the problem of errors such as insufficient accuracy of an array or a signal of interest in the existing algorithm, solves the robust adaptive beamforming algorithm of a signal SV by reconstructing an interference and noise covariance matrix, improves the adaptability of constraint to real data on the basis of keeping mode constraint, and compared with the traditional RAB method, the algorithm provided by the invention has lower calculation complexity, better performance and improved robustness of the adaptive beamforming algorithm to unknown errors.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
The robust self-adaptive beam forming algorithm based on the alternative direction multiplier method comprises the following steps:
step 1, setting a uniform linear array with an array element number of M at an angle thetalAnd angle thetasRespectively receiving L interference signals and 1 expected signal to obtain received data x (k) at a kth snapshot, wherein L is 1,2, …, L; calculating by using the received data x (k) at the k-th snapshot to obtain an estimated ideal covariance matrix
Setting the steering vector of the desired signal to aeAccording to the steering vector a of the set desired signaleAnd estimated ideal covariance matrix
Establishing a signal optimization model:
s.t.||ae||2＝M
where C is the integration matrix in the interference region,
△0is a threshold value of the threshold value,
Θ is the angular region in which the desired signal is located,
is the complement of theta, d (theta) is the steering vector associated with the direction theta defined by the antenna array geometry;
step 2, constructing a projection matrix P of the interference subspaceIFrom the projection matrix P of the interference subspaceIAnd estimated ideal covariance matrix
Obtaining an estimated interference-plus-noise covariance matrix
Using estimated interference-plus-noise covariance matrix
Instead of the integration matrix C of the interference region, △ is used0' instead of the threshold value △0Introducing auxiliary variables to convert the signal optimization model into a real-value variable optimization model; converting the real-valued variable optimization model into an augmented Lagrange function by using a Lagrange multiplier method; wherein,
in the step 3, the step of,solving the augmented Lagrange function by using an alternative direction multiplier method to obtain a final estimated value of the guide vector
Final estimate of the sum weight vector
The technical scheme of the invention has the characteristics and further improvements that:
preferably, step 1 comprises the following substeps:
substep 1.1, the expression of the received data x (k) at the kth snapshot is:
x(k)＝s(k)+i(k)+n(k)
wherein s (k) represents a desired signal data vector, i (k) represents an interference signal data vector, and n (k) represents a noise vector;
substep 1.2, estimated ideal covariance matrix
The expression of (a) is:
wherein K is the total number of snapshots.
Preferably, step 2 comprises the following substeps:
the sub-step 2.1 of the method,
wherein, thetalIndicates the angular region in which the l-th interference is located, gammaiAnd eiC' and a feature vector, i ═ 1,2, …, L +1, …, M, γ, respectively1>＝γ2>＝...>＝γL＞＞γL+1...>＝γM；U＝UI+UN，UI＝[e1,e2...,eL]Representing an interference subspace, UN＝[eL+1,eL+2...,eM]Representing a noise subspace; according to the interference subspace UIConstructing a projection matrix P of an interference subspaceIThe expression is:
according to the projection matrix P of the interference subspaceIAnd estimated ideal covariance matrix
Obtaining an estimated interference-plus-noise covariance matrix
Comprises the following steps:
wherein,
represents the estimated noise power, n ═ L +2, L +3, …, M;
substep 2.2, using the estimated interference plus noise covariance matrix
Instead of the integration matrix C of the interference region, △ is used0' instead of the threshold value △0Wherein, △0' is:
order:
wherein,
and
respectively represent a real part and an imaginary part, and
order:
wherein,
the real-valued variable optimization model is:
||u||2≤△0′
||v||2＝M；
and (2.3) the expression of the augmented Lagrangian function is as follows:
wherein λ is1,
Are respectively Lagrange multiplier vectors, p>0 is the step size.
Preferably, step 3 comprises the following substeps:
if the number of iterations q is 1, λ1,λ 20, the final estimate of the steering vector
Wherein, thetapIs the direction of the desired signal; final estimate of weight vector
If the iteration number q is not equal to 1, the final estimated value of the guide vector
Final estimate of the sum weight vector
Solving by the following steps:
1) for u ═ uq,v＝vq,
The solution can be solved by minimizing the augmented lagrangian function:
wherein,
the solution of (a) is:
2) for the
The minimally augmented lagrangian function is decomposed into two optimization sub-problems:
s.t.||u||2≤△0′
and is
s.t.||v||2＝M
U from two optimization sub-problemsq+1，vq+1Comprises the following steps:
3) for the
u＝uq+1,v＝vq+1，λ1,λ2Can be solved by minimizing the augmented Lagrange function and updating the Lagrange multiplier
Comprises the following steps:
4)q≠1,u＝uq,v＝vq,
iteratively updating steps 1), 2), 3) until q>qmaxOr
Ending iteration to obtain the final estimated value of the guide vector as
The final estimate of the weight vector is
Wherein q ismaxε is the threshold for the maximum number of iterations.
Compared with the prior art, the invention has the beneficial effects that:
1) in the robust adaptive beam forming algorithm based on the alternative direction multiplier method, firstly, an estimated ideal covariance matrix is obtained by calculation according to the obtained received data x (k) at the kth snapshot
Ideal covariance matrix based on the obtained estimates
Establishing a signal optimization model of a secondary constraint secondary optimization (QCQP) RAB; estimated interference-plus-noise covariance matrix with re-reconstruction
And △0' and introducing auxiliary variables to convert the signal optimization model into a real-valued variable optimization model, and converting the constraint condition and the objective function into a real-valued condition to solve the problem of uncertainty of the sequencing process caused by the SDR method. And finally, converting the real-valued variable optimization model into an augmented Lagrange function by using a Lagrange multiplier method, and solving by using an Alternating Direction Multiplier Method (ADMM).
2) The invention estimates the interference-plus-noise covariance matrix by projection of the received snapshot onto the constructed interference subspace
Compared with Capon spectrum estimation, the method enhances the adaptivity to real data constraint containing potential information of SV mismatch.
3) Compared with the traditional RAB method, the robust adaptive beamforming algorithm based on the alternative direction multiplier method has lower computational complexity and better performance under different types of errors.
Drawings
The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 is a flow chart of a robust adaptive beamforming algorithm based on the alternative direction multiplier method according to the present invention;
FIG. 2 shows the relationship between the output SINR performance and the input SNR and the number of snapshots respectively under the condition that random aiming errors exist in different algorithms; wherein, the graph (a) is the variation of the output SINR performance with the input SNR; graph (b) is the variation of the output SINR performance with fast beat number;
FIG. 3 shows the relationship between the output SINR performance and the input SNR and the number of snapshots respectively under the condition that amplitude and phase errors exist in different algorithms; wherein, the graph (a) is the variation of the output SINR performance with the input SNR; graph (b) is the variation of the output SINR performance with fast beat number;
FIG. 4 shows the relationship between the output SINR performance and the input SNR and the number of snapshots respectively under the condition that array element position errors exist in different algorithms; wherein, the graph (a) is the variation of the output SINR performance with the input SNR; graph (b) is the variation of the output SINR performance with fast beat number;
FIG. 5 shows the relationship between the output SINR performance and the input SNR and the number of snapshots respectively under the condition that coherent local scattering exists in different algorithms; wherein, the graph (a) is the variation of the output SINR performance with the input SNR; graph (b) shows the variation of the output SINR performance with fast beat number.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
Example 1
Referring to the flowchart of fig. 1, the robust adaptive beamforming algorithm based on the alternative direction multiplier method includes the following steps:
step 1, setting a uniform linear array with an array element number of M at an angle thetai(i ═ 1,2, …, L) and angle θsRespectively receiving L interference signals and 1 expected signal to obtain received data x (k) at the kth snapshot; using the received data x (k) at the k-th snapshot to processDesired covariance matrix RxCalculating to obtain the estimated ideal covariance matrix
Setting the steering vector of the desired signal to aeAccording to the steering vector a of the set desired signaleAnd estimated ideal covariance matrix
And establishing a signal optimization model.
Specifically, step 1 comprises the following substeps:
substep 1.1, setting a uniform linear array with M array elements at an angle thetal(L ═ 1,2, …, L) and angle θsWhen L interference and 1 desired signal are received respectively, the received data x (k) of the uniform linear array at the kth snapshot is:
x(k)＝s(k)+i(k)+n(k) (1)
where s (k) represents a desired signal data vector, i (k) represents an interference signal data vector, and n (k) represents a noise vector.
According to the assumption that two of the expected signals, the interference signals and the noise are uncorrelated, an ideal covariance matrix R of the signal data received by the uniform linear arrayxComprises the following steps:
Rx＝Rs+RI+N(2)
wherein R issRepresenting an ideal desired signal covariance matrix; rI+NRepresenting an ideal expected interference plus noise covariance matrix, the ideal interference plus noise covariance matrix RI+NCan be expressed as:
wherein,
and
respectively representing the ideal interference power and noise power, a (theta)l) Is the steering vector of the ith interference, L is 1,2, …, L, I denotes the M-th order identity matrix. To maximize the output SINR, a well-known MVDR beamforming method can be obtained by solving the following optimization problem:
wherein, as＝a(θs) Representing a signal steering vector, w is a weight vector, a solution of equation (3)
Substep 1.2, the point signal source is an ideal case, with the rank of the covariance matrix of the desired signal being 1 (i.e. rank (R)s) 1). However, in practical applications, the actual target signal sources received by the array have more complex spatial distribution characteristics than the point signal sources, and therefore, the covariance matrix R of the maximum likelihood pair ideal is often used in practicexThe estimation is carried out, and the received data x (k) at the k-th snapshot is used for calculating an estimated ideal covariance matrix
The expression is as follows:
wherein K is the total number of snapshots;
substep 1.3, if the steering vector of the desired signal is assumed to be aeThe corresponding desired signal power estimate P is:
estimating a steering vector a of a desired signaleIs equivalent to solving the Robust Adaptive Beamforming (RAB) problem based on quadratic constraint quadratic optimization (QCQP), i.e. according to the set periodSteering vector a of the observation signaleAnd estimated ideal covariance matrix
Establishing a signal optimization model:
wherein,
c is an integral matrix in an interference area and a threshold value
Θ is the angular region in which the desired signal is located,
is the complement of theta and d (theta) is the steering vector associated with the direction theta defined by the antenna array geometry.
Step 2, constructing a projection matrix P of the interference subspaceIFrom the projection matrix P of the interference subspaceIAnd estimated ideal covariance matrix
Obtaining an estimated interference-plus-noise covariance matrix
Using estimated interference-plus-noise covariance matrix
Instead of the integration matrix C of the interference region, △ is used0' instead of the threshold value △0Introducing an auxiliary variable to convert the signal optimization model into a real-valued variable optimization model, and converting the real-valued variable optimization model into an augmented Lagrange function by using a Lagrange multiplier method; wherein,
specifically, step 2 comprises the following substeps:
substep 2.1, observing the signal optimization model (7), C is SV
And has a weak correlation with the array structure, gain and phase errors, noise components. Rewriting C to C' and decomposing characteristically
Wherein, thetalIndicates the angular region in which the l-th interference is located, gammai(γ1>＝γ2>＝...>＝γL＞＞γL+1...>＝γM) And eiRespectively are the eigenvalue and eigenvector of C'; u is equal to UI+UN，UI＝[e1,e2...,eL]Representing an interference subspace, UN＝[eL+1,eL+2...,eM]Representing a noise subspace. According to the interference subspace UIConstructing a projection matrix of an interference subspace
Estimated interference-plus-noise covariance matrix
Can be expressed as:
wherein,
to remove the estimated noise power of 1 desired signal and L interferers, n is L +2, L +3, …, M.
Substep 2.2, in order to improve the adaptability of the constraint conditions to real numbers, an estimated interference-plus-noise covariance matrix is used
Replace the integral matrix C of the interference region in the signal optimization model (7) and set the threshold value △0Rewritten as △0', setting the maximum iteration number qmaxAnd a threshold value ε, wherein △0' is:
therefore, the constraints of the signal optimization model (7) are replaced by:
constraining
To avoid convergence of the estimated steering vector to the interference region.
Two auxiliary variables u, v are introduced and let:
wherein,
and
respectively represent a real part and an imaginary part, and
order to
Wherein,
substituting equations (10), (11), and (12) into equation (7), converting the signal optimization model into a real-valued variable optimization model:
and substep 2.3, converting the real-valued variable optimization model into an augmented Lagrange function by using a Lagrange multiplier method:
wherein,
are respectively Lagrange multiplier vectors, p>0 is the step size.
And 3, solving the augmented Lagrange function by using an alternative direction multiplier method to obtain a final estimation value of the guide vector and a final estimation value of the weight vector.
Specifically, step 3 comprises the following substeps:
if the number of iterations q is 1, λ1,λ2＝0,ae＝a(θp) (ii) a Wherein, thetap,a(θp) A steering vector of the desired signal direction and the desired signal, respectively; u, v are obtained by the formula (10).
If the number of iterations q ≠ 1, for u ≠ uq,v＝vq,
This can be solved by minimizing equation (14), which can be expressed as:
formula (15) is
With respect to the quadratic function, of the formula (15)Solution:
for the
Equation (15) can be re-expressed as two optimization sub-problems
And is
Solutions of the formulae (17) and (18) are readily available
Similarly, for
u＝uq+1,v＝vq+1，λ1,λ2Can be solved by minimizing equation (14). And updating lagrange multipliers
Is composed of
If q ≠ 1, u ═ uq,v＝vq,
Iterating equations (16), (19) and (20) until q>qmaxOr
End upIteration is carried out; q is 1,2, …, qmax。
Finally, the final estimated value of the steering vector is obtained as
The final estimate of the weight vector is
The performance of the robust adaptive beamforming algorithm based on the alternative direction multiplier method of the present invention is further explained by simulation experiments.
The beam forming method provided by the invention is compared with an Optimal beam forming method (Optimal), a diagonal loading method (DL), a Worst performance optimization method (Worst-case), an IAA-based INCM reconstruction method (IAA), an RAB method (RAB), an RSTVE method and a subspace projection method (ANSM), and the performances of the wave number former under the conditions of random aiming error, amplitude and phase error, array element position error and coherent local scattering of different algorithms are respectively compared. Wherein the loading factor of the DL is set to be twice the noise power; setting the parameters in Worst-case to be 3; the angular grid used in IAA and other RABs is set to 1 °. The maximum number of iterations of the beamformer is set to 100 and the threshold is set to 10-3. When the input SNR is variable, the number of snapshots is K-50; the signal SNR is set to 10dB when the number of fast beats is variable.
Test 1
1) Simulation parameters
And setting the array element number M as 10 uniform linear arrays, wherein the array element interval is half wavelength lambda/2. Assuming two interferers, a dry-to-noise ratio of 20dB, the directions are randomly generated in the interval (-25 deg., -15 deg.) and the interval (30 deg., 40 deg.), respectively. The noise follows an N (0,1) Gaussian distribution. In the simulation, the actual desired signal SV is unknown, the assumed signal direction θpIs 0 °, interval theta ═ thetap-5°,θp+5°]. In all experiments in this specification, the snapshots contain signals, and the simulation results are based on the average values obtained from 100 monte carlo experiments, and the effects of mutual coupling and multipath fading are not considered.
2) Simulation data processing results and analysis
The analysis discusses the impact of the problem of random aiming mismatch on the proposed beamforming algorithm. The actual desired signal is evenly distributed in (-3 °,3 °). Fig. 2(a) and fig. 2(b) respectively depict graphs of output SINR performance in the presence of random aiming error in different algorithms, respectively, versus input SNR and number of snapshots.
As can be seen from fig. 2, the robust adaptive beamforming algorithm based on the alternative direction multiplier method provided by the present invention is robust to signal direction errors and performs best in all RAB methods; when the input SNR is high, the performance of diagonal loading methods (such as DL and WC) degrades; the performance of the IAA and ANSM methods is mainly affected by the angular spacing accuracy.
Test 2
The conditions for the simulation were the same as in experiment 1.
The effect of amplitude and phase errors on the proposed beamforming algorithm is discussed separately. The amplitude and phase error of each array element respectively obeys N (1, 0.1)2) Gaussian distribution and U (-5 °,5 °) uniform distribution. Fig. 3(a) and fig. 3(b) depict the output SINR performance versus the input SNR and the number of snapshots, respectively, in the presence of amplitude and phase errors for different algorithms.
As can be seen from fig. 3, when the input SNR is less than 5dB, the performance of the diagonal loading methods such as DL and WC is better than that of other beamforming methods; when the input SNR is increased, the robust adaptive beam forming algorithm based on the alternative direction multiplier method provided by the invention is superior to other beam forming algorithms; when the fast beat number is taken as a variable, the robust adaptive beamforming algorithm based on the alternating direction multiplier method provided by the invention is almost the best algorithm.
Test 3
The conditions for the simulation were the same as in experiment 1.
The analysis discusses the effect of the beamforming algorithm proposed by the mismatch due to array element position errors. It is assumed that each array element position follows a uniform distribution of U (-lambda/40, lambda/40). Fig. 4(a) and fig. 4(b) respectively describe the relationship between the output SINR performance and the input SNR and the number of snapshots in the presence of array element position errors in different algorithms.
As can be seen from fig. 4, the performance of DL and Worst-case is better than other beamforming methods at low input SNR. When the input SNR is more than 0dB, the performance of the robust adaptive beam forming algorithm based on the alternative direction multiplier method is superior to that of other beam forming algorithms, and the method has stronger robustness to array element position errors.
Test 4
The conditions for the simulation were the same as in experiment 1.
The analysis discusses the effect of coherent local scattering on the proposed beamforming algorithm. The actual steering vector a is
Wherein, thetat,θuRespectively representing the directions of the direct path and the coherent scatter path, a (theta)t) Is a guide vector of the direct path direction, au(θu) Is the steering vector of the coherent path direction. Phi is au(u＝1,2,3,4)，θu(u-1, 2,3,4) in [0,2 pi ] respectively]And [ theta ]t-2,θt+2]Wherein, j is an imaginary unit. Fig. 5(a) and 5(b) depict the output SINR performance versus input SNR and number of snapshots, respectively, for different algorithms in the presence of coherent local scattering. As can be seen from fig. 5, the robust adaptive beamforming algorithm based on the alternative direction multiplier method according to the present invention performs best in all beamformers.
In summary, the present invention provides a new robust adaptive beamforming method for solving a non-convex optimization problem, in which the robust adaptive beamforming algorithm based on the alternating direction multiplier method improves performance by preserving mode constraints, then converts a complex non-convex optimization problem into a real number problem (i.e., converts constraint conditions and objective functions into real-valued functions), and solves the problem by using ADMM. Compared with the traditional SDR non-convex problem solving method, the robust adaptive beamforming algorithm based on the alternative direction multiplier method avoids the rank reduction process, so that the robust adaptive beamforming algorithm may not meet the rank 1 constraint rule of the solution, but simulation results show that the robust adaptive beamforming algorithm based on the alternative direction multiplier method has superiority under different types of errors.
Although the present invention has been described in detail in this specification with reference to specific embodiments and illustrative embodiments, it will be apparent to those skilled in the art that modifications and improvements can be made thereto based on the present invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (5)
1. The robust self-adaptive beam forming algorithm based on the alternative direction multiplier method is characterized by comprising the following steps of:
step 1, setting a uniform linear array with an array element number of M at an angle thetalAnd angle thetasRespectively receiving L interference signals and 1 expected signal to obtain received data x (k) at a kth snapshot, wherein L is 1,2, …, L; calculating by using the received data x (k) at the k-th snapshot to obtain an estimated ideal covariance matrix
Setting the steering vector of the desired signal to aeAccording to the steering vector a of the set desired signaleAnd estimated ideal covariance matrix
Establishing a signal optimization model:
s.t.||ae||2＝M
where C is the integration matrix in the interference region,
△0is a threshold value of the threshold value,
Θ is the angular region in which the desired signal is located,
is the complement of theta, d (theta) is the steering vector associated with the direction theta defined by the antenna array geometry;
step 2, constructing a projection matrix P of the interference subspaceIFrom the projection matrix P of the interference subspaceIAnd estimated ideal covariance matrix
Obtaining an estimated interference-plus-noise covariance matrix
Using estimated interference-plus-noise covariance matrix
Instead of the integration matrix C of the interference region, △ is used0' instead of the threshold value △0Introducing auxiliary variables to convert the signal optimization model into a real-value variable optimization model; converting the real-valued variable optimization model into an augmented Lagrange function by using a Lagrange multiplier method; wherein,
step 3, solving the augmented Lagrange function by using an alternative direction multiplier method to obtain a final estimated value of the guide vector
Final estimate of the sum weight vector
2. The robust adaptive beamforming algorithm based on the alternative direction multiplier method according to claim 1, wherein in step 1, the expression of the received data x (k) at the kth snapshot is:
x(k)＝s(k)+i(k)+n(k)
where s (k) represents a desired signal data vector, i (k) represents an interference signal data vector, and n (k) represents a noise vector.
3. The robust adaptive beamforming algorithm based on the alternative direction multiplier method of claim 1, wherein the estimated ideal covariance matrix
The expression of (a) is:
wherein K is the total number of snapshots.
4. The robust adaptive beamforming algorithm based on the alternative direction multiplier method according to claim 1, wherein step 2 comprises the following sub-steps:
substep 2.1, rewriting C to C', and feature decomposition
Wherein, thetalIndicates the angular region in which the l-th interference is located, gammaiAnd eiC' and a feature vector, i ═ 1,2, …, L +1, …, M; u is equal to UI+UN，UI＝[e1,e2...,eL]Representing an interference subspace, UN＝[eL+1,eL+2...,eM]Representing a noise subspace；
According to the interference subspace UIConstructing a projection matrix P of an interference subspaceIThe expression is:
according to the projection matrix P of the interference subspaceIAnd estimated ideal covariance matrix
Obtaining an estimated interference-plus-noise covariance matrix
Comprises the following steps:
wherein,
represents the estimated noise power, n ═ L +2, L +3, …, M; i represents an M-order identity matrix;
substep 2.2, using the estimated interference plus noise covariance matrix
Instead of the integration matrix C of the interference region, △ is used0' instead of the threshold value △0Wherein, △0' is:
order:
wherein,
and
respectively represent a real part and an imaginary part, and
order:
wherein,
the real-valued variable optimization model is:
||u||2≤△0′
||v||2＝M；
and (2.3) the expression of the augmented Lagrangian function is as follows:
wherein λ is1,
Are respectively Lagrange multiplier vectors, p>0 is the step size.
5. The robust adaptive beamforming algorithm based on the alternative direction multiplier method according to claim 4, wherein step 3 comprises the following sub-steps:
if the number of iterations q is 1, λ1,λ20, the final estimate of the steering vector
Wherein, thetapIs the direction of the desired signal; final estimate of weight vector
If the iteration number q is not equal to 1, the final estimated value of the guide vector
Final estimate of the sum weight vector
Solving by the following steps:
1) for u ═ uq,v＝vq,λ1＝λ1 q,
The solution can be solved by minimizing the augmented lagrangian function:
wherein,
the solution of (a) is:
2) for lambda1＝λ1 q,
The minimally augmented lagrangian function is decomposed into two optimization sub-problems:
s.t.||u||2≤△0′
and is
s.t.||v||2＝M
U from two optimization sub-problemsq+1，vq+1Comprises the following steps:
3) for the
u＝uq+1,v＝vq+1，λ1,λ2Can be solved by minimizing the augmented Lagrangian function and updating the Lagrangian multiplier lambda1 q+1,
Comprises the following steps:
4)q≠1,u＝uq,v＝vq,λ1＝λ1 q,
iteratively updating steps 1), 2), 3) until q>qmaxOr
Ending iteration to obtain the final estimated value of the guide vector as
The final estimate of the weight vector is
Wherein q ismaxε is the threshold for the maximum number of iterations.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911347121.2A CN110988854B (en) | 2019-12-24 | 2019-12-24 | Robust self-adaptive beam forming algorithm based on alternative direction multiplier method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911347121.2A CN110988854B (en) | 2019-12-24 | 2019-12-24 | Robust self-adaptive beam forming algorithm based on alternative direction multiplier method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110988854A true CN110988854A (en) | 2020-04-10 |
| CN110988854B CN110988854B (en) | 2022-10-28 |
Family
ID=70076175
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911347121.2A Active CN110988854B (en) | 2019-12-24 | 2019-12-24 | Robust self-adaptive beam forming algorithm based on alternative direction multiplier method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110988854B (en) |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111934795A (en) * | 2020-08-18 | 2020-11-13 | 电子科技大学 | Method for estimating signal-to-noise ratio and interference power in interference environment |
| CN113411112A (en) * | 2021-06-09 | 2021-09-17 | 西安交通大学 | Method for constructing distributed robust multi-cell cooperative beam forming ADMM network |
| CN113466899A (en) * | 2021-08-13 | 2021-10-01 | 电子科技大学 | Navigation receiver beam forming method based on small fast beat number under high signal-to-noise ratio environment |
| CN113704998A (en) * | 2021-08-27 | 2021-11-26 | 电子科技大学 | Wave beam forming method based on alternative direction multiplier method |
| CN113780533A (en) * | 2021-09-13 | 2021-12-10 | 广东工业大学 | Adaptive beamforming method and system based on deep learning and ADMM |
| CN113820664A (en) * | 2021-09-18 | 2021-12-21 | 石家庄铁道大学 | Radar signal processing method based on compressed sensing |
| CN113873622A (en) * | 2021-09-01 | 2021-12-31 | 武汉大学 | Communication network energy-saving method based on reconfigurable intelligent surface |
| CN114154347A (en) * | 2021-12-09 | 2022-03-08 | 吉林大学 | Dual-function MIMO radar communication system waveform design method based on ADMM |
| CN116068500A (en) * | 2023-03-16 | 2023-05-05 | 东南大学 | Novel space-time interference suppression method for multichannel synthetic aperture radar |
Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102983896A (en) * | 2012-11-16 | 2013-03-20 | 哈尔滨工程大学 | Projection virtual antenna beam-forming method |
| CN103983948A (en) * | 2014-05-29 | 2014-08-13 | 西安电子科技大学 | Target angle and distance combined estimation method based on sparse representation |
| CN104123462A (en) * | 2014-07-22 | 2014-10-29 | 西安电子科技大学 | Spectrum MUSIC method for achieving uniform linear array by means of root computing of real polynomials |
| CN104199052A (en) * | 2014-09-22 | 2014-12-10 | 哈尔滨工程大学 | Beam sidelobe suppression method based on norm constraint |
| CN106501785A (en) * | 2016-09-13 | 2017-03-15 | 深圳大学 | A kind of sane sparse recovery STAP methods and its system based on alternating direction multiplier method |
| CN106682405A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Low-side-lobe beam pattern integrated design method based on convex optimization |
| CN106682293A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Sparse beam pattern comprehensive designing method |
| WO2018049595A1 (en) * | 2016-09-14 | 2018-03-22 | 深圳大学 | Admm-based robust sparse recovery stap method and system thereof |
| CN109639332A (en) * | 2019-02-28 | 2019-04-16 | 电子科技大学 | A kind of steady beam forming optimization method based on steering vector model |
| CN110048753A (en) * | 2018-12-26 | 2019-07-23 | 同济大学 | The maximized distributed beamforming optimization method of efficiency is weighted based on mimo system |
-
2019
- 2019-12-24 CN CN201911347121.2A patent/CN110988854B/en active Active
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102983896A (en) * | 2012-11-16 | 2013-03-20 | 哈尔滨工程大学 | Projection virtual antenna beam-forming method |
| CN103983948A (en) * | 2014-05-29 | 2014-08-13 | 西安电子科技大学 | Target angle and distance combined estimation method based on sparse representation |
| CN104123462A (en) * | 2014-07-22 | 2014-10-29 | 西安电子科技大学 | Spectrum MUSIC method for achieving uniform linear array by means of root computing of real polynomials |
| CN104199052A (en) * | 2014-09-22 | 2014-12-10 | 哈尔滨工程大学 | Beam sidelobe suppression method based on norm constraint |
| CN106501785A (en) * | 2016-09-13 | 2017-03-15 | 深圳大学 | A kind of sane sparse recovery STAP methods and its system based on alternating direction multiplier method |
| WO2018049595A1 (en) * | 2016-09-14 | 2018-03-22 | 深圳大学 | Admm-based robust sparse recovery stap method and system thereof |
| CN106682405A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Low-side-lobe beam pattern integrated design method based on convex optimization |
| CN106682293A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Sparse beam pattern comprehensive designing method |
| CN110048753A (en) * | 2018-12-26 | 2019-07-23 | 同济大学 | The maximized distributed beamforming optimization method of efficiency is weighted based on mimo system |
| CN109639332A (en) * | 2019-02-28 | 2019-04-16 | 电子科技大学 | A kind of steady beam forming optimization method based on steering vector model |
Non-Patent Citations (6)
| Title |
|---|
| LU YAN ET AL.: "Robust adaptive beamforming based on interference covariance matrix reconstruction and mismatched steering vector compensation", 《PROCEEDINGS OF 2014 3RD ASIA-PACIFIC CONFERENCE ON ANTENNAS AND PROPAGATION》 * |
| YUYU SU ET AL.: "A knowledge aided SPICE space time adaptive processing method for", 《SIGNAL PROCESSING》 * |
| 李志保等: "回响环境下的最优波束形成器设计", 《中国科学：数学》 * |
| 李炳萨: "基于稀疏表示的稳健波达方向估计", 《中国优秀硕士论文电子期刊》 * |
| 林静然等: "基于ADMM的分布式功率分配和接入控制联合优化算法", 《电子科技大学学报》 * |
| 陈金铭等: "基于滤波器网格失配的分布式相参雷达", 《系统工程与电子技术》 * |
Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111934795A (en) * | 2020-08-18 | 2020-11-13 | 电子科技大学 | Method for estimating signal-to-noise ratio and interference power in interference environment |
| CN113411112B (en) * | 2021-06-09 | 2023-03-28 | 西安交通大学 | Method for constructing distributed robust multi-cell cooperative beam forming ADMM network |
| CN113411112A (en) * | 2021-06-09 | 2021-09-17 | 西安交通大学 | Method for constructing distributed robust multi-cell cooperative beam forming ADMM network |
| CN113466899A (en) * | 2021-08-13 | 2021-10-01 | 电子科技大学 | Navigation receiver beam forming method based on small fast beat number under high signal-to-noise ratio environment |
| CN113704998A (en) * | 2021-08-27 | 2021-11-26 | 电子科技大学 | Wave beam forming method based on alternative direction multiplier method |
| CN113704998B (en) * | 2021-08-27 | 2023-03-03 | 电子科技大学 | Wave beam forming method based on alternative direction multiplier method |
| CN113873622A (en) * | 2021-09-01 | 2021-12-31 | 武汉大学 | Communication network energy-saving method based on reconfigurable intelligent surface |
| CN113873622B (en) * | 2021-09-01 | 2023-10-27 | 武汉大学 | Communication network energy saving method based on reconfigurable intelligent surface |
| CN113780533A (en) * | 2021-09-13 | 2021-12-10 | 广东工业大学 | Adaptive beamforming method and system based on deep learning and ADMM |
| CN113820664A (en) * | 2021-09-18 | 2021-12-21 | 石家庄铁道大学 | Radar signal processing method based on compressed sensing |
| CN114154347A (en) * | 2021-12-09 | 2022-03-08 | 吉林大学 | Dual-function MIMO radar communication system waveform design method based on ADMM |
| CN114154347B (en) * | 2021-12-09 | 2024-05-14 | 吉林大学 | Waveform design method of dual-function MIMO radar communication system based on ADMM |
| CN116068500A (en) * | 2023-03-16 | 2023-05-05 | 东南大学 | Novel space-time interference suppression method for multichannel synthetic aperture radar |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110988854B (en) | 2022-10-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110988854B (en) | Robust self-adaptive beam forming algorithm based on alternative direction multiplier method | |
| CN111651719B (en) | Robust self-adaptive beam forming method based on shrinkage estimation covariance matrix reconstruction | |
| CN108809398B (en) | Robust adaptive beam forming method based on information source number constraint | |
| CN110045321B (en) | Robust DOA estimation method based on sparse and low-rank recovery | |
| CN107907852B (en) | Covariance matrix rank minimization DOA estimation method based on space smoothing | |
| CN110113085B (en) | Wave beam forming method and system based on covariance matrix reconstruction | |
| CN106569181A (en) | Algorithm for reconstructing robust Capon beamforming based on covariance matrix | |
| CN107167778A (en) | It is a kind of that the robust ada- ptive beamformer method estimated with steering vector is reconstructed based on covariance matrix | |
| CN109254261B (en) | Coherent signal null deepening method based on uniform circular array EPUMA | |
| CN108663668B (en) | IAA-based interference plus noise covariance matrix reconstruction robust beam forming method | |
| CN109639333B (en) | Beam forming method based on effective reconstruction covariance matrix | |
| US10764091B2 (en) | Robust adaptive method for suppressing interference in the presence of a signal of interest | |
| CN105699948A (en) | Beam forming method and system based on support vector machine and improving mean squared error performance | |
| Mu et al. | Robust MVDR beamforming based on covariance matrix reconstruction | |
| CN110727915B (en) | Robust self-adaptive beam forming method based on data correlation constraint | |
| CN109541552A (en) | The Adaptive beamformer method and system of radar antenna array | |
| CN111698011A (en) | Steady self-adaptive beam forming method for asymmetric signals in symmetric noise | |
| Mohammadzadeh et al. | Covariance matrix reconstruction based on power spectral estimation and uncertainty region for robust adaptive beamforming | |
| CN114236471A (en) | Robust adaptive beam forming method under relevant interference source | |
| CN110895327B (en) | Robustness self-adaptive beam forming method based on direct convex optimization modeling | |
| CN113051739A (en) | Robustness self-adaptive processing method based on sparse constraint | |
| Wang | Array signal processing algorithms for beamforming and direction finding | |
| CN107135026B (en) | Robust beam forming method based on matrix reconstruction in presence of unknown mutual coupling | |
| CN115808659A (en) | Robust beam forming method and system based on low-complexity uncertain set integration | |
| CN115270869A (en) | Two-dimensional space-time generalized sidelobe cancellation robust beamforming algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |