CN106960083A - A kind of robust adaptive beamforming method optimized based on main lobe beam pattern - Google Patents
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Abstract
The invention belongs to array signal process technique field, it is related to a kind of robust adaptive beamforming method optimized based on main lobe beam pattern when being applied to model mismatch.Including：Arrayed data carries out sampling and obtains time domain snap model, and estimated data covariance matrix；Input observation steering vector, main lobe distortion factor, array number, build the metric function of main lobe beam pattern distortion；Pair and power output enter row constraint to correct steering vector, obtain a nonlinear optimization problem of non-convex；The optimization problem is converted into the convex quadratically constrained quadratic programming problem of equivalence；Using the efficient decomposition operation of interior point method associate(d) matrix order 1 solve the estimate of steering vector after QCQP problems are corrected；The Beam-former weight coefficient that this method is obtained in SCB weight coefficient formula will be updated to and array data is handled, the desired signal of height output Signal to Interference plus Noise Ratio is obtained.Output Signal to Interference plus Noise Ratio is higher when the present invention has basic matrix model mismatch.The anti-distortion ability of main lobe beam pattern is stronger.
Description
Technical Field
The invention belongs to the technical field of array signal processing, and relates to a robust self-adaptive beam forming method based on mainlobe beam pattern optimization and suitable for model mismatch.
Technical Field
Beamforming, also known as spatial filtering, is an important branch of array signal processing and is currently widely used in the fields of aviation, aerospace, radar, sonar, and communications. The essence of the method is a preprocessing structure in array signal processing, and the method is to perform spatial filtering by weighting each array element to protect the expected signal from the interested direction and inhibit noise and interference so as to achieve the purpose of improving the output signal-to-interference-and-noise ratio. Depending on the selection of the array weight vector, the beamformer can be divided into a data-independent type and a data-independent type, which is called adaptive beamformer (adaptive beamforming), and is characterized in that the weight vector can be adaptively adjusted according to the statistical information of the received signal. The Standard Capon Beamformer (SCB) is the most classical adaptive beamformer, which is obtained by minimizing the output power while keeping the beam response in the desired direction undistorted. SCBs can typically achieve near optimal output signal-to-interference-and-noise ratios (SINRs) when there is no array model mismatch or no desired signal component in the training data. In many application areas, however, the above conditions are often not met, which can lead to a drastic degradation of the SCB performance. To improve the robustness of SCBs, much work has been devoted over the past decades to the design of robust adaptive beamformers.
Since the weighting coefficients of a standard Capon beamformer can be expressed as a function of both the covariance matrix and the steering vector, many classical robust adaptive beamformers attempt to optimize both components to improve the robustness of SCB. In the aspect of covariance matrix optimization, typical algorithms include a Diagonal Loading (DL) algorithm and an Eigenspace (Eigenspace) algorithm. The former reduces the spread of noise eigenvalues by diagonally loading the sample covariance matrix, but the optimal diagonal loading factor of the algorithm is usually difficult to select; the latter designs an adaptive beamformer by using an eigen matrix formed by desired signals and interference components instead of a sample covariance matrix, but the algorithm needs to know the total signal source number in advance, which extremely limits the application and further popularization.
In terms of guided vector optimization, the most typical algorithm is a guided vector estimation algorithm based on uncertainty set constraints. Among the algorithms, the basic idea of the cyclic quadratic programming (SQP) algorithm (1 a. hassanien, s.a. vorobyovand k.m.wong, Robust adaptive beamforming using sequential quadratic programming: an iterative solution to the mismatch map, 2008) proposed by a.hassanien is to search for an optimal steering vector in a predefined observation sector in a cyclic iteration manner, so as to maximize the total output power; however, the SQP algorithm needs iterative search, the operation is complex and is not suitable for real-time implementation, and a blocking matrix in the algorithm is difficult to determine. The basic idea of the Power Maximization (PM) algorithm proposed by stoica ([2] p.stoica, z.s.wang, and j.li, Robust Caponbeamforming,2003.) is to estimate the true steering vector of the desired signal under the constraint of an uncertainty set, so as to maximize the output power; however, simulation research shows that the PM algorithm still has the phenomenon of signal self-cancellation when the observation direction has a deviation, and the main lobe beam pattern still has distortion. The robust beam former based on semi-definite programming and rank-1 decomposition (3) Wangbiang, Wuwenfeng, fangshan, Liangnational dragon, robust beam forming based on semi-definite programming and rank-1 decomposition, 2013.) proposed by Wangbiang et al jointly deduces constraint conditions which should be met by new guide vectors from two aspects of interference suppression and noise suppression, converts the corresponding optimization problem into semi-definite programming easy to solve, and finally solves the problem by combining rank-1 decomposition. The constraint starting point of the beam forming method is different from that of the beam forming method of the invention, but the mathematical support used in the process of solving the optimization problem is the same finally.
Disclosure of Invention
The invention aims to provide a robust self-adaptive beam forming method which is used for resisting main lobe beam pattern distortion and has low sensitivity to model mismatch and is based on main lobe beam pattern optimization.
The purpose of the invention is realized as follows:
(1.1) sampling array data to obtain a time domain snapshot model, and estimating a data covariance matrix;
(1.2) inputting an observation guide vectorConstructing a main lobe beam pattern distortion measurement function f (w,) by using a main lobe distortion factor and an array element number M;
(1.3) constraining f (w) and output power to correct a steering vector to obtain a non-convex nonlinear optimization problem;
(1.4) converting the optimization problem into an equivalent convex quadratic constraint quadratic programming problem;
(1.5) solving the QCQP problem by adopting an efficient interior point method and combining matrix rank-1 decomposition operation to obtain an estimated value of the corrected steering vector
(1.6) mixingSubstituting the weight coefficient w into the weight coefficient formula of SCB to obtain the weight coefficient w of the beam former of the method, and processing array data to obtain an expected signal with high output signal-to-interference-and-noise ratio.
Constructing a measurement function of the distortion of the main lobe beam pattern and constraining the measurement function and the output power to obtain an optimization problem; converting the optimization problem into a convex quadratic constraint quadratic programming problem; and solving by adopting an interior point method and matrix rank-1 decomposition to obtain an estimated value of the corrected steering vector.
The metric function f (w) for constructing the distortion of the main lobe beam pattern,where w is the beamformer weight coefficient, the parameter is an input fixed value, and the signal true steering vector belongs to an indeterminate set
The constraint on f (w) and the output power is characterized in that: in the uncertain setTo minimize the ratio of the metric function of the main lobe beam pattern distortion to the output power, i.e. to estimate the true steering vector of the desired signal
WhereinAndthe method comprises the following steps that an ideal guide vector and a real guide vector of an expected signal are respectively obtained, R is a theoretical covariance matrix of a base matrix for receiving snapshot data, M is an array element number, and | is | · | | is Euclidean norm operation of the vector.
Converting the optimization problem into an equivalent convex quadratic constraint quadratic programming problem, and converting the grade of the optimization problem into an equivalent convex quadratic constraint quadratic programming problem
Wherein in the Chinese formulatr (-) is the trace operation of the matrix.
The QCQP problem is solved by adopting an efficient interior point method and combining matrix rank-1 decomposition operation, the optimization problem in the step (1.4) is solved, and the optimal solution of the optimization problem is obtainedThen to the matrixCarrying out rank detection; if matrixIs 1, hasIn this case, only need to be alignedPerforming eigenvalue decomposition operation to obtain the optimal solutionIf matrixIs greater than 1, by aligning the matricesRank-1 decomposition to estimate
The invention has the beneficial effects that: compared with some classical robust adaptive beamforming methods, the invention has better performance in the following aspects: (1) the output signal-to-interference-and-noise ratio (SINR) is higher when the matrix model mismatch exists; (2) the main lobe beam pattern has stronger distortion resistance. The method can be better suitable for actual complex scenes with array model mismatch caused by different factors, such as a communication system and a sonar system, and has certain actual guidance value.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a graph comparing the variation curve of the output SINR with the input SINR of each robust adaptive beamforming algorithm in the presence of random steering vector deviation. Wherein, "opt.sinr" represents the optimal output signal to interference plus noise ratio; "Eigenspace" represents a feature space algorithm; "DL" represents a diagonal loading algorithm; "SQP" stands for cyclic quadratic programming algorithm; "PM" represents a power maximization algorithm; "SCB" stands for standard Capon beamformer; "MBO" represents the algorithm of the present invention;
fig. 3 is a beam pattern of the MBO algorithm and the power maximization PM algorithm of the present invention in the presence of an observation direction deviation, wherein the observation direction deviation is 2 °.
Detailed Description
The following detailed description is made with reference to the accompanying drawings and specific examples:
the invention comprises the following steps:
(1.1) sampling array data to obtain a time domain snapshot model, and estimating a data covariance matrix;
(1.2) inputting an observation guide vectorConstructing a main lobe beam pattern distortion measurement function f (w,) by using a main lobe distortion factor and an array element number M;
(1.3) constraining f (w) and output power to correct a steering vector to obtain a non-convex nonlinear optimization problem;
(1.4) converting the optimization problem into an equivalent convex Quadratic Constraint Quadratic Programming (QCQP) problem;
(1.5) solving the QCQP problem by adopting an efficient interior point method and combining matrix rank-1 decomposition operation to obtain an estimated value of the corrected steering vector
(1.6) substituting the weight coefficient formula of the SCB to obtain the weight coefficient of the beam former of the method and processing array data to obtain an expected signal with high output signal-to-interference-and-noise ratio.
The core technical content of the invention is that the original non-convex nonlinear optimization problem of optimizing the main lobe beam distortion function and the output power is converted into an equivalent convex quadratic constraint quadratic programming problem, and an efficient inner point method is adopted to solve in combination with matrix rank-1 decomposition operation. According to the method, firstly, a main lobe beam pattern distortion function is constructed, and the ratio of the distortion function to the output power is minimized under the constraint of a real steering vector uncertainty set, so that the distortion of the main lobe beam pattern during model mismatch is reduced; and converting the obtained non-convex nonlinear optimization problem about the real steering vector into an equivalent QCPC problem, solving the estimated steering vector by using an inner point method and the rank-1 decomposition operation of the matrix, and simplifying the solving process of the optimization problem.
The main technical characteristics of the invention comprise:
1, constructing a main lobe beam pattern distortion function and deducing a closed form solution of the main lobe beam pattern distortion function; it can be known from the derivation that the main lobe distortion of the beamformer w is mainly proportional to its norm. This also exactly verifies the statement that the "weighting vector norm can usually evaluate the beamformer robustness parameter".
2 under the constraint of the real steering vector uncertain set, the ratio of the distortion function and the output power is minimized to obtain the optimization problem of the robust beam former based on the main lobe beam pattern optimization, thereby reducing the main points when the model is mismatchedDistortion of the lobe beam pattern. Wherein, in order to eliminate the scale ambiguity problem in the estimation of the desired signal power, the real guide vector is added to the optimization problemNorm constraint of, i.e.
And 3, converting the non-convex nonlinear optimization problem about the real steering vector into an equivalent QCPC problem, solving by using an inner point method and the rank-1 decomposition operation of the matrix, and simplifying the solving process of the optimization problem.
The method specifically comprises the following steps:
(1) sampling array data to obtain a time domain snapshot model, and estimating a data covariance matrix by using the formula (1)
Where R is the estimated data covariance matrix, N is the fast beat number,is snapshot data.
(2) Solving the optimization problem (2) by using an efficient interior point method to obtain an optimal solution
Wherein,tr (-) is the trace operation of the matrix.
(3) If it is notThen pairPerforming eigenvalue decomposition to obtain
Wherein, Λ ═ λ1,λ2,…λM]，U＝[u1,u2,…uM]；λiIs a matrixUi is the corresponding eigenvector; i is 1,2, … M.
The maximum characteristic value corresponding to the characteristic vector is taken and normalized to obtainAnd (6) estimating.
(4) If it is notThen pairPerforming rank-1 decomposition operation estimation
Theorem: order toAnd isIf r ≧ 3, we can always find a non-zero vector y ∈ Range (A) in polynomial time, so that
WhereinAnd is
According to the above theorem, whenAlways, a non-zero vector y ∈ Range (A) is obtained, through which
Decrease the rank of A by 1 untilFinally, the method in the step (3) is reused
Performing characteristic decomposition to obtain an estimated value of a guide vector
(5) Subjecting the product obtained in step (3)The MBO beamformer weight coefficients are calculated by substituting into the standard Capon beamformer weight coefficient equation (5).
(6) Finally, the received data x (k) is preprocessed as shown in formula (6) by using the obtained weight coefficient w of the beam former, so as to obtain a beam former output time domain signal y (k) with high SINR.
y(k)＝wHx(k) (6)
The performance design example of the invention:
considering a uniform linear array composed of 10-element isotropic array elements, the distance between the array elements is half wavelength of the signal, and additive noise received by each array element is a narrow-band Gaussian random signal which is independent in statistics. And assuming that two narrow-band far-field interferences are respectively incident to the array from the directions of-20 degrees and 30 degrees, the interference-to-noise power ratio is 20 dB. The desired signal is assumed to be a narrow-band far-field complex plane wave incident on the matrix at 10 ° from the assumed direction. The algorithms to be compared are a feature space algorithm (Eigenspace), a diagonal load algorithm (DL), a cyclic quadratic programming algorithm (SQP), a power maximization algorithm (PM), a Standard Capon Beamformer (SCB), and an algorithm of the present invention (MBO).
Design examples in the presence of random steering vector errors:
under the influence of random model mismatch factors, random deviation occurs between the true steering vector and the assumed steering vector of the expected signal, and the deviation vector is assumed to obey N (0, I) distribution, wherein the parameter reflects the model mismatch degree of the matrix. Assuming that the input snapshot number is fixed to 30, the model mismatch factor is set to 1.0. For both the present algorithm and the PM algorithm, the boundary of the indeterminate set is set to 1.0. For the Eigenspace algorithm, the source number is assumed to be known a priori. For the DL algorithm, the diagonal load is set toWhereinThe ambient noise power received for a single array element. For the SQP algorithm, 6 principal feature components are used to construct the feature space. And obtaining a curve of the output signal-to-interference-and-noise ratio of each algorithm along with the input signal-to-noise ratio when the random steering vector error exists, as shown in figure 2. From this figure, it is readily apparent that the SCB is calculatedThe method is most sensitive to model mismatch; the performance of the DL algorithm and the SQP algorithm is improved compared with the SCB algorithm, but the performance degradation is still serious at high SNR; the Eigenspace algorithm is very sensitive to subspace estimation errors, and particularly under the condition of low SNR, the signal subspace is easy to be aliased with the noise subspace, so that the signal subspace is invalid. Only the MBO algorithm of the present invention achieves the best performance over the entire SNR test range.
Design examples in the presence of observation direction errors:
assuming that the main factors causing the mismatch of the matrix model are the observation direction deviation, where the observation direction of the beamformer is set to 10 °, the true direction of the desired signal is set to 8 ° (which means that the observation direction deviation is 2 °), the input SNR is fixed to 5dB, and the other parameters are all consistent with the previous one. The comparison between the MBO algorithm and the PM algorithm of the present invention results in a comparative beam pattern of the two algorithms as shown in fig. 3. It can be seen that the main lobe beam pattern of the PM algorithm is distorted to some extent, and a signal self-cancellation phenomenon occurs in the direction of 8 °, which is a main cause of performance degradation; for the MBO algorithm of the invention, because the main lobe beam pattern is optimized, the distortion of the main lobe beam pattern is obviously reduced, and better performance is obtained.
Claims (6)
1. A robust adaptive beamforming method based on mainlobe beam pattern optimization is characterized by comprising the following steps:
(1.1) sampling array data to obtain a time domain snapshot model, and estimating a data covariance matrix;
(1.2) inputting an observation guide vectorConstructing a main lobe beam pattern distortion measurement function f (w,) by using a main lobe distortion factor and an array element number M;
(1.3) constraining f (w) and output power to correct a steering vector to obtain a non-convex nonlinear optimization problem;
(1.4) converting the optimization problem into an equivalent convex quadratic constraint quadratic programming problem;
(1.5) solving the QCQP problem by adopting an efficient interior point method and combining matrix rank-1 decomposition operation to obtain an estimated value of the corrected steering vector
(1.6) mixingSubstituting the weight coefficient w into the weight coefficient formula of SCB to obtain the weight coefficient w of the beam former of the method, and processing array data to obtain an expected signal with high output signal-to-interference-and-noise ratio.
2. The robust adaptive beamforming method based on mainlobe beam pattern optimization according to claim 1, wherein: constructing a measurement function of the distortion of the main lobe beam pattern and constraining the measurement function and the output power to obtain an optimization problem; converting the optimization problem into a convex quadratic constraint quadratic programming problem; and solving by adopting an interior point method and matrix rank-1 decomposition to obtain an estimated value of the corrected steering vector.
3. The robust adaptive beamforming method based on mainlobe beam pattern optimization according to claim 1, characterized in that: the metric function f (w) for constructing the distortion of the main lobe beam pattern,where w is the beamformer weight coefficient, the parameter is an input fixed value, and the signal true steering vector belongs to an indeterminate set
4. The robust adaptive beamforming method based on mainlobe beam pattern optimization according to claim 1, characterized in that: the constraint on f (w) and the output power is characterized in that: in the uncertain setTo minimize the ratio of the metric function of the main lobe beam pattern distortion to the output power, i.e. to estimate the true steering vector of the desired signal
WhereinAndthe method comprises the following steps that an ideal guide vector and a real guide vector of an expected signal are respectively obtained, R is a theoretical covariance matrix of a base matrix for receiving snapshot data, M is an array element number, and | is | · | | is Euclidean norm operation of the vector.
5. The robust adaptive beamforming method based on mainlobe beam pattern optimization according to claim 1, characterized in that: converting the optimization problem into an equivalent convex quadratic constraint quadratic programming problem, and converting the grade of the optimization problem into an equivalent convex quadratic constraint quadratic programming problem
Wherein in the Chinese formulatr (-) is the trace operation of the matrix.
6. According to the claimsSolving 1 a robust adaptive beam forming method based on mainlobe beam pattern optimization, which is characterized in that: the QCQP problem is solved by adopting an efficient interior point method and combining matrix rank-1 decomposition operation, the optimization problem in the step (1.4) is solved, and the optimal solution of the optimization problem is obtainedThen to the matrixCarrying out rank detection; if matrixIs 1, hasIn this case, only need to be alignedPerforming eigenvalue decomposition operation to obtain the optimal solutionIf matrixIs greater than 1, by aligning the matricesRank-1 decomposition to estimate
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| CN113189569A (en) * | 2021-04-06 | 2021-07-30 | 中国科学院声学研究所 | Robust self-adaptive beam forming method based on variable uncertain set constraint |
| CN114844543A (en) * | 2022-03-10 | 2022-08-02 | 电子科技大学 | Low-cross-polarization conformal array hybrid beam forming codebook design method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113189569A (en) * | 2021-04-06 | 2021-07-30 | 中国科学院声学研究所 | Robust self-adaptive beam forming method based on variable uncertain set constraint |
| CN113189569B (en) * | 2021-04-06 | 2021-12-28 | 中国科学院声学研究所 | Robust self-adaptive beam forming method based on variable uncertain set constraint |
| CN114844543A (en) * | 2022-03-10 | 2022-08-02 | 电子科技大学 | Low-cross-polarization conformal array hybrid beam forming codebook design method |
| CN114844543B (en) * | 2022-03-10 | 2023-10-03 | 电子科技大学 | Low cross polarization conformal array mixed beam forming codebook design method |
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