CN109639333B - Beam forming method based on effective reconstruction covariance matrix - Google Patents

Beam forming method based on effective reconstruction covariance matrix Download PDF

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CN109639333B
CN109639333B CN201811480843.0A CN201811480843A CN109639333B CN 109639333 B CN109639333 B CN 109639333B CN 201811480843 A CN201811480843 A CN 201811480843A CN 109639333 B CN109639333 B CN 109639333B
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covariance matrix
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theta
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CN109639333A (en
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雷舒杰
张军星
王雪博
王帅
蒲彬
吴迎春
史方明
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Shanghai Shentian Industrial Co ltd
Shanghai Radio Equipment Research Institute
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Shanghai Radio Equipment Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming

Abstract

The invention discloses a robust adaptive beam forming method based on an effective reconstruction covariance matrix. The method comprises the steps of firstly estimating the angle direction of an expected signal by using a power spectrum estimation algorithm, and taking whether the angle of the expected signal can be estimated as the standard for reconstructing the covariance matrix by introducing a judgment factor as the standard for reconstructing the covariance matrix by the algorithm, then respectively constructing the covariance matrix under the condition of different signal-to-noise ratios, namely, the covariance matrix is not required to be reconstructed under the condition of low signal-to-noise ratio, and finally, an array weight vector is obtained by adopting a covariance matrix reconstruction method under the condition of high signal-to-noise ratio, so that the output performance of a beam former is ensured and the calculation complexity is reduced. The invention has better output performance under the condition of high signal-to-noise ratio. The invention adds a threshold judgment process, and can well balance the relation between the complexity and the output performance by using the expected signal which can be estimated as a critical condition.

Description

Beam forming method based on effective reconstruction covariance matrix
Technical Field
The invention relates to the technical field of beam forming and the field of signal processing, in particular to a beam forming method based on an effective reconstruction covariance matrix.
Background
The adaptive beam forming technology can adaptively change the weight vector size according to the external environment change characteristic and the received signal characteristic, so that undistorted reception of the expected signal is ensured, and the interference performance is maximally inhibited, therefore, the adaptive beam forming technology can be applied to more complex engineering application environments, and has wide application prospects.
The beam former achieves the purpose that the main lobe beam is aligned with the expected signal incoming direction and the null is aligned with the interference signal incoming direction through the array weight vector, and the optimal weight vector is based on the condition that the interference noise matrix and the expected signal steering vector are both accurate. An interference noise matrix in an actual application environment is difficult to obtain, and is generally replaced by a sampling covariance matrix, but a sampling data usually contains an expected signal, when the expected signal power is low, the difference between the obtained sampling covariance matrix and the interference noise covariance matrix is small, and the difference between a corresponding obtained array weight vector and an optimal weight vector is also small, so that the influence on the output performance of a beam former is small, but when the expected signal power is high, the beam former easily takes the expected signal as an interference signal to inhibit, and further the output performance of an algorithm is reduced.
Aiming at the problem, a series of robust beam forming algorithms are proposed, and the main representative algorithm is an interference noise matrix reconstruction algorithm.
A beam forming method for interference noise covariance matrix reconstruction based on subspace (patent application No. 201510680829.5, application date 2015.10.19, university of electronic technology of the applicant) introduces a beam forming method for interference noise covariance matrix reconstruction based on subspace, replaces a sample covariance matrix with a reconstructed interference noise covariance matrix, and simultaneously provides a new steering vector estimation algorithm to estimate a steering vector of a desired signal, so that the beam forming algorithm has good robustness to interference signal steering vector errors, but the method does not consider the complexity problem of algorithm engineering realization.
An adaptive beam forming method based on correlation calculation and covariance matrix reconstruction (patent application No. 201510548956.X, application date 2015.08.31, acoustic institute of the applicant's chinese academy of sciences) introduces an adaptive beam forming method based on correlation calculation and covariance matrix reconstruction, which solves the problems of main lobe deformation, side lobe increase, desired signal cancellation and serious output signal-to-interference-and-noise ratio reduction of an adaptive directional diagram of an SMI algorithm under the condition that a desired signal is contained in a sampling fast beat number, but the method only aims at the condition that the power of the desired signal in a received signal is large and weak, the method has no effect on the power of the desired signal, and the complexity is increased.
An adaptive beamforming method based on covariance matrix reconstruction (patent application No. 201611055429.6, 2016.11.25, university of electronic technology in line of the applicant) introduces an adaptive beamforming method based on covariance matrix reconstruction, which improves the performance of a beamformer by reconstructing an interference-plus-noise covariance matrix to eliminate a desired signal component in a sampling covariance matrix used for calculating weight vectors of the adaptive beamformer, but the method still aims at the situation that the desired signal power is large and does not consider the performance problem of an algorithm under a low-power desired signal.
The paper "Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and stereometric Vector Estimation" (author: Gu Y, et al, journal IEEE Transactions on Signal Processing, published 7 months 2012) proposes a method for reconstructing an Interference noise Covariance Matrix by using spatial spectrum Estimation, but this method requires cumulative calculation of the entire spatial domain except the angular region where the desired Signal is located, and the amount of calculation is large.
The interference noise matrix is reconstructed by a method of removing a desired signal component by using a sampling covariance matrix in a paper 'Robust MVDR beamforming based on covariance matrix recovery' (the author: Pengcheng M, journal Science China Information Sciences, 4 months 2013), but the method has a large error under the condition of mismatching of a guide vector angle.
The paper "Robust adaptive beamforming via a novel sub-method for interference covariance matrix reconstruction" (author: Yuan X, journal Signal Processing, published 2016 (7) month) proposes that only the angle region where the interference Signal is located needs to be calculated to reconstruct the covariance matrix, thereby greatly reducing the complexity of the algorithm.
In the paper, "Robust adaptive beamforming based on interference covariance matrix reconstruction" (author: Gu Y, journal Signal Processing, published in 2013, 9 months), sparse constraint is used to reconstruct interference noise covariance matrix reconstruction to improve the performance of the algorithm under the condition that the sample data contains the desired Signal and the condition that the model is mismatched, and the output performance is similar to the optimal performance, but the improvement of the performance of the algorithm under the low Signal-to-noise ratio is far less than the improvement of the complexity of the algorithm, and few documents relate to the problem of effective reconstruction of the covariance matrix, so that the method has important research significance for the problem of effective reconstruction of the covariance matrix.
Disclosure of Invention
The invention aims to provide a beam forming method based on an effective reconstruction covariance matrix, and solves the problems that the performance of the existing beam forming device reconstructed by an interference noise covariance matrix is improved higher under the condition of high input signal-to-noise ratio, but the performance is not improved greatly and the complexity is increased greatly under the condition of low input signal-to-noise ratio.
In order to achieve the above object, the present invention provides a beamforming method based on an effective reconstructed covariance matrix, which includes the following steps:
step 1: adopt the even linear array of M array elements constitution, there are J +1 far field narrowband signals to incide the array in the space, assume to regard array element number 1 as the reference point, and signal incidence direction angle is theta, and the time delay between other array elements and array element number 1 is taumAnd satisfy τm(m-1) dsin θ/c, then an array received signal model can be established;
step 2: obtaining the distribution condition of the eigenvalues of the covariance matrix by a characteristic decomposition method to obtain the number of large eigenvalues in the array received signals;
and step 3: estimating a signal corresponding to the large characteristic value by utilizing an MUSIC algorithm, and setting a power spectrum threshold value: the critical gate xi is used for estimating an angle corresponding to the high-power signal;
and 4, step 4: the angular region Θ of the desired signal is known and has θ ═ θmin,θmax]And assuming the incoming wave direction of the desired signal to be thetad，θdE.g. theta; setting the estimated angular direction to thetai(i is 1,2, …, P), where P is the estimated number of signal sources, by determining θi(i-1, 2, …, P) is present within the desired signal angle region Θ to determine the critical value of the reconstructed covariance matrix: judging a factor beta;
and 5: respectively solving the covariance matrixes corresponding to different judgment factors, specifically comprising:
step 5.1: under the condition of low signal-to-noise ratio, correcting the covariance matrix by adopting a noise averaging method so as to eliminate the influence of finite fast beat number on the sampling covariance matrix;
step 5.2: under the condition of high signal-to-noise ratio, a method of interference noise covariance matrix reconstruction is adopted to improve the performance of the algorithm;
step 6: and finally, solving the corresponding array weight vector under different conditions.
In the above beam forming method based on the effective reconstructed covariance matrix, in step 1, the step of establishing the uniform linear array received signal model includes:
step 1.1: the array received signal model is written as:
Figure GDA0003249701040000041
wherein J represents the number of interferers, s0(t) represents the desired signal, θ0Representing the desired signal direction of arrival, sj(t) (J is 1, …, J) represents the jth interference signal, θj(J-1, …, J) represents the interference signal direction of arrival, a (θ)0) Is the steering vector corresponding to the desired signal; a (theta)j) (J1, …, J) corresponds to interference signalIs Gaussian white noise, and defines
Figure GDA0003249701040000042
Step 1.2: assuming that the desired signal and the interfering signal are uncorrelated with each other, the array received data true covariance matrix is written as:
RX＝E[X(t)XH(t)]＝Rs+Rj+n
in the formula, Rs、Rj+nCovariance matrices for the desired signal, interference, and noise signals, respectively, (-)HRepresents a matrix transpose symbol;
step 1.3: the sampling covariance matrix is adopted to replace the real covariance matrix of array received data:
R＝X(t)XH(t)/K
in the formula, K is a sampling fast beat number.
In the above beam forming method based on the effective reconstructed covariance matrix, the method for obtaining the large eigenvalue in step 2 may be described as:
Figure GDA0003249701040000043
in the formula, λi(i ═ 1,2, …, M) is a covariance matrix eigenvalue, and λ is satisfied1≥λ2≥…≥λM，Λ＝diag{λ1,…,λM}，ei(i-1, 2, …, M) is a feature vector corresponding to the feature value, U-e1,e2,…,eM]。
In the above beam forming method based on the effective reconstructed covariance matrix, in step 3, the MUSIC algorithm is implemented based on the minimized output power, and is expressed as:
Figure GDA0003249701040000044
in the formula, θ represents a spatial domain angle, UN(theta) is a subspace corresponding to the noise signal, a (theta) is a guide vector corresponding to the spatial angle region, PMUSICI.e. the output power corresponding to the weight vector.
In the above beam forming method based on the effective reconstructed covariance matrix, in step 4, the desired signal angle region Θ is known, and θ ═ is determinedmin,θmax]And assuming the incoming wave direction of the desired signal to be thetad，θdE.g. theta; setting the estimated angular direction to thetai(i is 1,2, …, P), where P is the estimated number of signal sources, by determining θi(i-1, 2, …, P) contains a desired signal to determine a decision factor β, expressed as:
|θi-θd|≤δ
wherein, delta is a critical factor and satisfies the condition that 0 is more than or equal to delta and less than or equal to thetamax-θminIf i (i ═ 1,2, …, P) satisfies the above equation, it indicates that the desired signal can be estimated, i.e. the input SNR is large, and then the interference noise covariance matrix needs to be reconstructed; when the above equation does not hold for any i (i ═ 1,2, …, P), it means that the desired signal is not estimated, and at this time, the effect of the desired signal on the sampling covariance matrix is small and negligible, so that it is not necessary to reconstruct the interference noise matrix.
The judgment factor β can be expressed as:
Figure GDA0003249701040000051
when the judgment factor β is 1, it indicates that the covariance matrix needs to be reconstructed, and when the judgment factor β is 0, it indicates that the input SNR is small, the desired signal cannot be estimated, the influence on the algorithm performance is small, and the covariance matrix does not need to be reconstructed.
In the above beam forming method based on the effective reconstructed covariance matrix, in step 5,
when the judgment factor β is equal to 0, averaging the characteristic values corresponding to the noise signals to obtain a noise average power, which is recorded as:
Figure GDA0003249701040000052
wherein the content of the first and second substances,
Figure GDA0003249701040000053
is the noise average power. The covariance matrix at this time becomes
Figure GDA0003249701040000054
When the judgment factor β is equal to 1, all possible directions of the spatial spectrum distribution are estimated by using a spatial spectrum estimation algorithm, which is expressed as:
Figure GDA0003249701040000055
where P (θ) is a spatial spectrum value of the spatial angle.
The interference noise matrix can be estimated using the above equation, and is noted as:
Figure GDA0003249701040000056
in the formula (I), the compound is shown in the specification,
Figure GDA0003249701040000061
are all angles in space except the desired angular field Θ, and
Figure GDA0003249701040000062
including all angular directions in the whole space, and
Figure GDA0003249701040000063
the intersection of the two is empty, and a (theta) is a guide vector corresponding to the spatial angle area.
To reduce the complexity of the algorithm, the form of integration in the above equation is converted into a form of cumulative summation, which is expressed as:
Figure GDA0003249701040000064
wherein, a (theta)l) Is at an angle thetal(L1, 2, …, L) corresponding steering vector, angular region
Figure GDA0003249701040000065
Divided equally into L portions.
In the above beam forming method based on the effective reconstructed covariance matrix, in step 6, the corresponding array weight vectors under different conditions are respectively solved:
when the judgment factor β is equal to 0, it indicates that the covariance matrix does not need to be reconstructed, the covariance matrix at this time is obtained in step 6.1, and the corresponding weight vector is expressed as:
Figure GDA0003249701040000066
wherein a is a desired signal steering vector;
when the judgment factor β is equal to 1, it indicates that the covariance matrix needs to be reconstructed, the covariance matrix at this time is obtained in step 6.2, and the corresponding weight vector is expressed as:
Figure GDA0003249701040000067
compared with the prior art, the invention has the following beneficial effects:
(1) compared with the traditional beam forming algorithm, the invention still has better output performance under the condition of high signal-to-noise ratio.
(2) Compared with other covariance matrix reconstruction methods, the method adds a threshold judgment process, can be estimated by utilizing the expected signal as a critical condition, and can well balance the relation between the complexity and the output performance.
(3) The method adopts a noise averaging method to correct the covariance matrix under the condition of low input signal-to-noise ratio, improves the output performance of the algorithm under the limited snapshot number, and avoids the complexity increase caused by the covariance matrix reconstruction; and the output performance of the algorithm is greatly improved by adopting a covariance matrix reconstruction method under the condition of high input signal-to-noise ratio.
Drawings
FIG. 1 is a schematic diagram of a uniform linear array structure employed in the present invention;
FIG. 2 is a diagram of a-15 dB downsampling covariance matrix eigenvalue distribution;
FIG. 3 is a diagram of a 15dB SNR-based distribution of eigenvalues of a covariance matrix;
fig. 4 is a diagram of the corresponding angle estimation case at-15 dB SNR;
fig. 5 is a diagram of the corresponding angle estimation case at SNR of 15 dB;
FIG. 6 is a graph showing the relationship between the decision factor β and the input SNR;
fig. 7 is a graph of output SINR versus snapshot number for-20 dB SNR;
fig. 8 is a graph of the output SINR of the present invention as a function of snapshot number at SNR of 20 dB;
fig. 9 is a graph of the output SINR versus input SNR of the present invention.
Detailed Description
The invention will be further described by the following specific examples in conjunction with the drawings, which are provided for illustration only and are not intended to limit the scope of the invention.
The invention provides a robust adaptive beam forming method based on an effective reconstruction covariance matrix by deeply analyzing the influence of an input signal-to-interference-and-noise ratio (SNR) on the output performance of a beam former. The method comprises the steps of introducing a judgment factor to serve as a standard for whether an algorithm reconstructs a covariance matrix, firstly estimating the angle direction of an expected signal by using a power spectrum estimation algorithm, estimating whether the angle of the expected signal can be estimated to serve as the standard for reconstructing the covariance matrix, then respectively constructing covariance matrices under the conditions of different signal-to-noise ratios (SNRs), namely reconstructing the covariance matrix under the condition of low signal-to-noise ratio (SNR), adopting a covariance matrix reconstruction method under the condition of high SNR, finally obtaining an array weight vector, and finally achieving the purposes of ensuring the output performance of a beam former and reducing the calculation complexity.
The method for effectively reconstructing the covariance matrix mainly comprises the following aspects:
1. deducing array antenna received signal model
As shown in fig. 1, a Uniform Linear Array (ULA) composed of M array elements is used, and the array element spacing is d, where d is 1/2 λ and λ is the wavelength of the desired signal. When J +1 far-field narrow-band signals are incident in the space, the No. 1 array element is assumed to be used as a reference point, the angle of the incident direction of the signals is theta, and the time delay between other array elements and the No. 1 array element is taumAnd satisfy τm(m-1) dsin θ/c, the arrayable receive model can be written as:
Figure GDA0003249701040000081
wherein J represents the number of interferers, s0(t) represents the desired signal, θ0Representing the desired signal direction of arrival, sj(t) (J is 1, …, J) represents the jth interference signal, θj(J-1, …, J) represents the interference signal direction of arrival, a (θ)0) Is the steering vector, a (theta), corresponding to the desired signalj) (J-1, …, J) is a steering vector corresponding to the interference signal, and n (t) is white gaussian noise and is defined
Figure GDA0003249701040000082
Assuming that the desired signal and the interfering signal are uncorrelated with each other, the true covariance matrix of the received data of the array is given as:
RX＝E[X(t)XH(t)]＝Rs+Rj+n (2)
in the formula, Rs、Rj+nCovariance matrices for the desired signal, interference, and noise signals, respectively, (-)HRepresenting the matrix transpose symbol.
Usually, the real covariance matrix characteristic of the array received data is difficult to obtain, and a sampling covariance matrix is generally adopted to replace the characteristic, and is expressed as:
R＝X(t)XH(t)/K (3)
where K is the number of sampled fast beats.
2. Obtaining the distribution condition of the eigenvalue of the covariance matrix through a characteristic decomposition method, and when the expected signal power is greater than the noise power, corresponding to the large eigenvalue, obtaining the interference and the expected signal power; and when the desired power is lower than the noise power, then the large eigenvalue corresponds only to the interference power. Described as follows by the formula:
Figure GDA0003249701040000091
in the above formula, λi(i ═ 1,2, …, M) is a covariance matrix eigenvalue, and λ is satisfied1≥λ2≥…≥λM，Λ＝diag{λ1,…,λM}，ei(i ═ 1,2, …, M) is the characteristic value λiCorresponding feature vector, U is feature vector eiCombined characteristic space, U ═ e1,e2,…,eM]The distribution of R characteristic values can be clearly seen by plotting characteristic value curves, as shown in fig. 2 and 3.
3. The number of large eigenvalues in the array received signals can be obtained by analyzing the eigenvalue distribution condition of the sampling covariance matrix R. Then, on the basis, angle estimation is performed on the signal corresponding to the large eigenvalue by using the MUSIC algorithm, and as shown in fig. 4 and 5, the angle corresponding to the signal is estimated by setting a power spectrum threshold value, namely a critical threshold ξ. The MUSIC algorithm is implemented based on minimizing the output noise power, and is expressed as:
Figure GDA0003249701040000092
wherein θ represents a spatial domain angle, UN(theta) is a subspace corresponding to the noise signal, a (theta) is a guide vector corresponding to the spatial angle region, PMUSICThat is, the output power corresponding to the weight vector, and the angle corresponding to the peak value of the power spectrum is requiredThe interference or desired signal angle is estimated.
4. The angle direction of the high-power signal can be estimated by using the formula. The angular region Θ, Θ ═ θ of the desired signal is knownmin,θmax]Assuming the incoming wave direction of the desired signal is θd，θdE.g. theta. Estimating the angular direction as θi(i is 1,2, …, P), where P represents the estimated number of signal sources, by determining θiWhether or not there is a region (i-1, 2, …, P) within the desired signal angle region Θ determines a critical value of the reconstructed covariance matrix, i.e., the decision factor β. Is formulated as:
|θi-θd|≤δ (6)
wherein delta is a critical factor and satisfies the condition that 0 is more than or equal to delta and less than or equal to thetamax-θminIf i (i ═ 1,2, …, P) satisfies the above equation, it indicates that the desired signal can be estimated, i.e. the desired power is large and the input SNR is large, and then the interference noise matrix needs to be reconstructed; when the above equation does not hold for any i (i ═ 1,2, …, P), it means that the desired signal is not estimated, and at this time, the effect of the desired signal on the sampling covariance matrix is small and negligible, so that it is not necessary to reconstruct the interference noise matrix.
The judgment factor can be written in the form:
Figure GDA0003249701040000101
when the judgment factor β is 1, it indicates that the covariance matrix needs to be reconstructed, and when the judgment factor β is 0, it indicates that the input SNR is small at this time, the desired signal cannot be estimated, the influence on the algorithm performance is small, and the covariance matrix does not need to be reconstructed.
5. The methods for solving the covariance matrix corresponding to the judgment factor beta under different conditions are different, and the corresponding solving methods are as follows:
(1) when the judgment factor β is 0, it indicates that the output SNR is small at this time, the expected signal cannot be estimated, the influence on the algorithm performance is small, and the covariance matrix does not need to be reconstructed. In order to eliminate the influence of finite fast-beat number on the sampling covariance matrix, averaging the eigenvalues corresponding to the noise signal as the noise average power, which is recorded as:
Figure GDA0003249701040000102
wherein the content of the first and second substances,
Figure GDA0003249701040000103
is the noise average power.
The covariance matrix at this time becomes:
Figure GDA0003249701040000104
(2) when the judgment factor β is 1, it indicates that the covariance matrix needs to be reconstructed, and the method is implemented by using a matrix reconstruction method based on spatial spectrum estimation, and the implementation method is as follows:
first, all possible directions of spatial spectral distribution are estimated by using a spatial spectrum estimation algorithm, which is expressed as:
Figure GDA0003249701040000105
wherein P (θ) is a spatial spectrum value. The interference noise matrix can be estimated using the above equation, and is noted as:
Figure GDA0003249701040000111
wherein the content of the first and second substances,
Figure GDA0003249701040000112
are all angles in space except the desired angular field Θ, and
Figure GDA0003249701040000113
including all angular directions in the whole space, and
Figure GDA0003249701040000114
the intersection of (a) is empty.
To reduce the complexity of the algorithm, the form of integration in the above equation is generally converted into a form of cumulative summation, which is expressed as:
Figure GDA0003249701040000115
wherein, a (theta)l) Is at an angle thetal(L1, 2, …, L) corresponding steering vector, angular region
Figure GDA0003249701040000118
Divided equally into L portions. Thetal(L ═ 1,2, …, L) is the angle value for each share.
6. Corresponding covariance matrixes under different conditions are different, and corresponding array weight vector calculation is also different.
(1) When the judgment factor β is 0, which indicates that the covariance matrix does not need to be reconstructed, the covariance matrix is obtained in step 5 (1), and the corresponding weight vector can be expressed as
Figure GDA0003249701040000116
Where a is the desired signal steering vector.
(2) When the determination factor β is 1, which indicates that the covariance matrix needs to be reconstructed, the covariance matrix at this time is obtained in step 5 (2), and the corresponding weight vector can be expressed as
Figure GDA0003249701040000117
The effects of the present invention can be illustrated by the following simulations:
simulation conditions and contents:
1. output performance of a beamformer based on an efficiently reconstructed covariance matrix
Setting simulation experiment conditions, namely setting a Uniform Linear Array (ULA) of 16 array elements, wherein the spacing of the array elements adopts half wavelength, assuming that the direction of an expected signal is set to be 0 degrees, the direction of an estimated expected signal is set to be 3 degrees, SNR is set to be 10dB, the incoming directions of two interference signals are 50 degrees and-40 degrees, the interference-to-noise ratio (INR) is set to be 30dB, and assuming that the direction of the expected signal estimated by the MUSIC algorithm is theta1The direction of the interfering signal is theta2And theta3Noise is zero mean Gaussian white noise, and the angle region of the expected signal is set to be theta1＝[θ1-5°,θ1+5°]The angle range of the interference signal is set to theta2＝[θ2-5°,θ2+5°]And Θ3＝[θ3-5°,θ3+5°]The simulation times were set to 100 Monte-Carlo times.
The problem of algorithm complexity is analyzed, under the condition of low input SNR, the performance of the algorithm is not greatly improved by adopting the method for reconstructing the covariance matrix, but the operation complexity of the algorithm is increased from the original O (M)3) Increase to O (M)2S), where S > M, where S denotes the angular region
Figure GDA0003249701040000121
The number of points is divided equally. The algorithm provided by the invention can well avoid the problem, whether the covariance matrix needs to be reconstructed is determined by judging the signal-to-noise ratio of the input signal, and the covariance matrix is corrected by adopting a noise averaging method under the condition of low input SNR, so that the output performance of the algorithm under the condition of limited snapshot number is improved, and the complexity is lower; under the condition of high input SNR, the performance of the algorithm is improved to a great extent by adopting a method for reconstructing the covariance matrix. Therefore, the method based on the effective reconstruction covariance matrix has certain advantages in balancing complexity and algorithm output performance.
Fig. 6 is a graph of input SNR versus decision factor. When the judgment factor beta is 1, the expected signal can be estimated, and an interference noise matrix needs to be reconstructed at the moment; when the decision factor β is 0, it indicates that the desired signal cannot be estimated, and the interference noise matrix does not need to be reconstructed. It can be seen from the figure that it is the critical point whether the covariance matrix is reconstructed or not when the SNR is-8 dB, and when the SNR is greater than-8 dB, the interference noise matrix needs to be reconstructed, otherwise the other way around.
Fig. 7 and 8 show the output SINR as a function of the number of snapshots at-20 dB SNR and 20dB SNR. Fig. 7 is a graph showing that the SINR of the algorithm varies with the number of snapshots when the SNR is-20 dB, and it can be seen from the graph that, under low SNR, the output performance of the method proposed by the present invention is about 1dB higher than that of the reconstructed covariance matrix, and the main reason is that, under low SNR, the performance of the reconstructed covariance matrix algorithm is not greatly improved, but because the present invention considers the influence of the finite number of snapshots on the output performance of the algorithm and corrects it by a noise averaging method, the algorithm performance of the present invention has certain advantages under the finite number of snapshots and the complexity is greatly reduced. Fig. 8 is a graph of the algorithm output performance varying with the number of snapshots when the SNR is 20dB, and it can be known from the graph that, under high SNR, the output performance of the method based on the effective reconstruction covariance matrix proposed by the present invention coincides with the spatial spectrum estimation algorithm, because the method for reconstructing the covariance matrix is consistent in use and is much higher than the output performance of the MVDR algorithm. Therefore, the algorithm provided by the invention has obvious advantages in balancing complexity and output performance.
Fig. 9 is a graph of input SNR versus output SINR variation for several algorithms. It can be seen from the figure that the performance of the algorithm proposed by the present invention is almost the same at high SNR compared with other reconstruction algorithms, and at low SNR, the performance is slightly lower than that of the reconstructed covariance matrix algorithm, but the complexity of the algorithm is greatly reduced.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (7)

1. A beam forming method based on an effective reconstruction covariance matrix is characterized by comprising the following steps:
step 1: adopting a uniform linear array consisting of M array elements, enabling J +1 far-field narrow-band signals to enter the array in space, and establishing an array receiving signal model;
step 2: obtaining the distribution condition of the eigenvalues of the covariance matrix by a characteristic decomposition method to obtain the number of large eigenvalues in the array received signals;
and step 3: estimating a signal corresponding to the large characteristic value by utilizing an MUSIC algorithm, and setting a power spectrum threshold value: the critical gate xi is used for estimating an angle corresponding to the high-power signal;
and 4, step 4: the angular region Θ of the desired signal is known and has θ ═ θmin,θmax]And assuming the incoming wave direction of the desired signal to be thetad，θdE.g. theta; setting the estimated angular direction to thetai(i is 1,2, …, P), where P is the estimated number of signal sources, by determining θi(i-1, 2, …, P) is present within the desired signal angle region Θ to determine the critical value of the reconstructed covariance matrix: judging a factor beta;
and 5: respectively solving the covariance matrixes corresponding to different judgment factors, specifically comprising: step 5.1: under the condition of low signal-to-noise ratio, correcting the covariance matrix by adopting a noise averaging method so as to eliminate the influence of finite fast beat number on the sampling covariance matrix;
step 5.2: under the condition of high signal-to-noise ratio, a method of interference noise covariance matrix reconstruction is adopted to improve the performance of the algorithm;
step 6: and finally, solving the corresponding array weight vector under different conditions.
2. The beamforming method based on effective reconstructed covariance matrix as claimed in claim 1, wherein in step 1, the step of establishing the uniform linear array received signal model comprises:
step 1.1: the array received signal model is written as:
Figure FDA0003249701030000011
wherein J represents the number of interferers, s0(t) represents the desired signal, θ0Representing the desired signal direction of arrival, sj(t) (J is 1, …, J) represents the jth interference signal, θj(J-1, …, J) represents the interference signal direction of arrival, a (θ)0) Is the steering vector, a (theta), corresponding to the desired signalj) (J-1, …, J) is a steering vector corresponding to the interference signal, and n (t) is white gaussian noise and is defined
Figure FDA0003249701030000021
Step 1.2: assuming that the desired signal and the interfering signal are uncorrelated with each other, the array received data true covariance matrix is written as:
RX＝E[X(t)XH(t)]＝Rs+Rj+n
in the formula, Rs、Rj+nCovariance matrices for the desired signal, interference, and noise signals, respectively, (-)HRepresents a matrix transpose symbol;
step 1.3: the sampling covariance matrix is adopted to replace the real covariance matrix of array received data:
R＝X(t)XH(t)/K
in the formula, K is a sampling fast beat number.
3. The effective reconstructed covariance matrix-based beamforming method of claim 1, wherein in step 2, the method of finding the large eigenvalue can be described as:
Figure FDA0003249701030000022
in the formula, λi(i ═ 1,2, …, M) is a covariance matrix eigenvalue, and λ is satisfied1≥λ2≥…≥λM，Λ＝diag{λ1,…,λM},ei(i-1, 2, …, M) is a feature vector corresponding to the feature value, U-e1,e2,…,eM]。
4. The effective reconstructed covariance matrix-based beamforming method of claim 1, wherein in step 3, the MUSIC algorithm is implemented based on minimizing output power, and is expressed as:
Figure FDA0003249701030000023
in the formula, θ represents a spatial domain angle, UN(theta) is a subspace corresponding to the noise signal, a (theta) is a guide vector corresponding to the spatial angle region, PMUSICI.e. the output power corresponding to the weight vector.
5. The method as claimed in claim 1, wherein in step 4, the determination factor β is defined according to whether the source estimated in step 3 contains the desired signal, and is expressed as:
Figure FDA0003249701030000024
in the formula, the desired signal angle region Θ, Θ ═ θmin,θmax]Assuming the incoming wave direction of the desired signal is θd，θdE is as high as theta, and the estimated angular direction is thetai(i-1, 2, …, P), where P is the estimated number of sources, δ is the critical factor, and δ ≦ θ ≦ 0max-θmin|。
6. The effective reconstructed covariance matrix-based beamforming method of claim 1, wherein in step 5,
when the judgment factor β is equal to 0, averaging the characteristic values corresponding to the noise signals to obtain a noise average power, which is recorded as:
Figure FDA0003249701030000031
wherein the content of the first and second substances,
Figure FDA0003249701030000032
for noise mean power, the covariance matrix at this time becomes
Figure FDA0003249701030000033
Wherein λ isP+1Denotes the P +1 th characteristic value, λMRepresenting the Mth eigenvalue, and U representing an eigenvector matrix of the covariance matrix;
when the judgment factor β is equal to 1, all possible directions of the spatial spectrum distribution are estimated by using a spatial spectrum estimation algorithm, which is expressed as:
Figure FDA0003249701030000034
wherein P (theta) is a spatial spectrum value; a (theta) is a guide vector corresponding to the space angle area;
the interference noise matrix can be estimated using the above equation, and is noted as:
Figure FDA0003249701030000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003249701030000036
are all angles in space except the desired angular field Θ, and
Figure FDA0003249701030000037
including all angular directions in the whole space, and
Figure FDA0003249701030000038
the intersection of the two is empty, and a (theta) is a guide vector corresponding to the space angle area;
to reduce the complexity of the algorithm, the form of integration in the above equation is converted into a form of cumulative summation, which is expressed as:
Figure FDA0003249701030000039
wherein, a (theta)l) Is at an angle thetal(L1, 2, …, L) corresponding steering vector, angular region
Figure FDA0003249701030000041
Divided equally into L portions.
7. The method as claimed in claim 1, wherein in step 6, the corresponding array weight vectors under different conditions are respectively obtained:
when the judgment factor β is equal to 0, it indicates that the covariance matrix does not need to be reconstructed, the covariance matrix at this time is obtained in step 6.1, and the corresponding weight vector is expressed as:
Figure FDA0003249701030000042
wherein a is a desired signal steering vector;
when the judgment factor β is equal to 1, it indicates that the covariance matrix needs to be reconstructed, the covariance matrix at this time is obtained in step 6.2, and the corresponding weight vector is expressed as:
Figure FDA0003249701030000043
Figure FDA0003249701030000044
representing a covariance matrix, Rj+nRepresenting an interference noise matrix.
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