CN112230226B - Adaptive beam former design method based on Bayes compressed sensing algorithm - Google Patents
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- 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
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Abstract
The invention discloses a design method of an adaptive beam former based on a Bayesian compressed sensing algorithm, which comprises the following steps: (1) The planar array elements receive sound wave incident signals, the sound wave incident signals comprise target signals and interference signals, an adaptive beam former is constructed on the basis of the sound wave incident signals, and the arrival direction of the sound wave incident signals is estimated by adopting a Bayesian compression sensing algorithm; (2) Obtaining an interference plus noise covariance matrix according to the direction of arrival of the interference signal and Capon space spectrum reconstruction of the incident sound wave signal; (3) And defining a maximum sidelobe level constraint value, constraining sidelobes of the target beam pattern according to the maximum sidelobe level constraint value, and calculating an array element weight coefficient of the self-adaptive beam former through a convex optimization method according to an interference and noise covariance matrix. With a greater output signal-to-dry ratio.
Description
Technical Field
The invention relates to the field of sonar array signal processing, in particular to a design method of an adaptive beam former based on a Bayesian compressed sensing algorithm (BCS).
Background
In recent years, phased array three-dimensional imaging sonar technology has been rapidly developed due to its application to underwater physics, biology, geology, and the like. The traditional phased array three-dimensional sonar has a fixed beam direction, cannot automatically track the incoming direction of a desired signal while cancelling interference, and cannot meet the working requirement in a complex underwater acoustic environment, for example, a patent application with application publication number CN109116334A discloses a sonar beam forming method and system based on super-beam weighting.
The adaptive beam forming algorithm is used as a new technical means, and on the premise of ensuring the large gain reception of the expected signal, the beam pattern null is adaptively aligned to the interference direction, so that the adaptive control on the beam pattern of the array is realized, and the interference is suppressed or the intensity of the interference signal is reduced. Therefore, it is of great significance to study adaptive beamforming algorithms. For example, patent application with publication number CN110736976A discloses a method for estimating the performance of sonar beam former in any array. Patent application publication No. CN110196421A discloses a dense-distributed MIMO sonar adaptive beam forming detection method.
Disclosure of Invention
The invention aims to provide a design method of an adaptive beam former based on a Bayes compressed sensing algorithm, which realizes more accurate reconstruction of an interference plus noise covariance matrix through the Bayes compressed sensing algorithm, has a larger output signal-to-noise ratio compared with other adaptive algorithms, and is also restricted to a lower level by sidelobe peaks of a beam pattern.
In order to realize the purpose of the invention, the technical scheme provided by the invention is as follows:
a design method of an adaptive beam former based on a Bayesian compressed sensing algorithm comprises the following steps:
(1) The planar array elements receive sound wave incident signals, the sound wave incident signals comprise target signals and interference signals, an adaptive beam former is constructed on the basis of the sound wave incident signals, and the arrival direction of the sound wave incident signals is estimated by adopting a Bayesian compression sensing algorithm;
(2) Obtaining an interference and noise covariance matrix according to the direction of arrival of the interference signal and Capon space spectrum reconstruction of the sound wave incident signal;
(3) Defining a maximum sidelobe level (PSLL) constraint value, constraining sidelobes of a target beam pattern according to the maximum sidelobe level constraint value, and calculating a weight coefficient value of the adaptive beam former through a convex optimization method according to an interference and noise covariance matrix.
In step (1), the received sound wave incident signal is expressed as:
wherein k represents the number of fast sampling beats, and X (k) represents the number of fast sampling beatsA received acoustic incident signal at k, n (k) representing a Gaussian noise vector, s (k) = [ s = [ k ] l (k)，l＝1，2，...，L] T An incident signal source indicating L +1 directions, L indicating an index of the incident direction, and (α) when L =0 l ，β l ) Represents the incident direction of the target signal, and when L =1,2 l ，β l ) Indicates the incident direction of the interference signal, a (α) l ，β l ) Indicates an incident direction of (alpha) l ，β l ) Of phi = [ a (alpha) ] l ，β l )，l＝1，2，...，L]And expressing the array manifold matrix, specifically as follows:
wherein λ is the wavelength, x n ，y n Denotes the position of the nth array element, N =1,2 l ＝sinα l ，v l ＝sinβ l ，u l ，u l ∈[-1，1]L =1,2,. Wherein L, L is a natural number;
constructing an adaptive beamformer based on acoustic incident signals is represented as:
Y(k)＝w H X(k) (3)
where Y (k) represents the output of the adaptive beamformer, w H ∈C N Representing array element weight coefficients, superscript H Representing the Hermite transpose, the output signal-to-interference-plus-noise ratio (SINR) of the adaptive beamformer can be calculated as follows:
wherein, E [. C]Denotes expectation, | 2 Denotes the square, X s (k)，X i (k) And X n (k) Representing the target signal component, the interference signal component and the noise component, σ, respectively s 2 Representing the energy of the signal, a s Array manifold vector, R, representing a target signal i+n ＝E[(X i (k)+X n (k)(X i (k)+X n (k) H ]∈C N×N Representing the interference plus noise covariance matrix, the design of the adaptive beamformer turns into the following problem:
min w w H R i+n w，subject to w H a s ＝1. (5)
when the Bayes compressed sensing algorithm is adopted to estimate the direction of arrival (DOA) of the sound wave incident signal, the number of candidate signal directions is set to be M, and then the candidate signal source can be expressed as
The sound wave incident signal received by the array element
The rewrite is:
wherein,
which represents the vector of the noise, is,
representing candidate signal source vectors, array manifold matrices
As follows:
the DOA estimation problem can be transformed as follows:
wherein Q = R, I,
and
respectively representing candidate signal sources
The real and imaginary parts of (a) and (b),
represents the posterior probability, then
Comprises the following steps:
wherein R (-) denotes taking the real part, I (-) denotes taking the imaginary part, ε (k) is a fidelity coefficient, and represents the accuracy of the DOA estimation of the signal,
posterior probability
Introduction of hyper-parameters
Conversion to:
wherein Q = R, I, R, I respectively represent a real part and an imaginary part, and a hyperparameter
The value of (d) is obtained by solving its maximum likelihood function, as follows:
wherein Q = R, I, a and b are user-defined proportion control parameters,
is shown in
For diagonal matrices of diagonal elements, superscript T Represents a transpose of a matrix; the DOA estimate of the incident acoustic signal can be obtained by:
due to the fact that
There are K samples and the derivation above uses only one of the samples. When DOA estimation is carried out through a multitask Bayes compressed sensing algorithm (MT-BCS), K sampling points can be associated by sharing the same hyper-parameter and observation matrix, so that the estimation precision is improved, and the DOA estimation in the formula (14) can be written as follows:
when the incident direction index l =0, the direction of arrival of the target signal is obtained according to equation (15), and when the incident direction index l ≠ 0, the direction of arrival of the interference signal is obtained according to equation (15).
In the step (2), the direction of arrival obtained in the step (1) can be divided into the incident direction of the target signal source as (u) according to the prior information of the target signal azimuth 0 ,v 0 ) The corresponding array manifold vector is
And the incident direction of the interfering signal source is (u) l ,v l ) (L =1,2, \8230;, L), corresponding to an array manifold vector of
The spatial spectrum function of the sound wave incident signal Capon is as follows:
wherein,
the sampling covariance matrix of the array element is represented, and the interference-plus-noise covariance matrix is reconstructed according to the arrival direction of the interference signal
The following:
in step (3), defining a maximum side lobe level (PSLL) constraint value as BP PSLL Let (u) j ,v j ) (J =1,2, \8230;, J) denotes the side lobe region of the target beam pattern, the side lobe constraints are as follows:
interference plus noise covariance matrix incorporating reconstruction
Then the array element coefficients of the adaptive beam former are solved by a convex optimization method to obtain the weight coefficient values of the adaptive beam former, and the solving process is as follows:
subject to
after obtaining the weight coefficient values of the adaptive beamformer, the values can be determined according to Y (k) = w H X (k) results in an adaptive beamformer.
The maximum side lobe level (PSLL) constraint value is related to the aperture of the array and the number of the array elements, and the maximum side lobe level (PSLL) constraint value is set according to the aperture of the array and the number of the array elements, and the more the array elements are, the smaller the side lobe is. For example, for a 20 x 20 array, the maximum side lobe level (PSLL) constraint value is-25 dB, and no solution is found when the constraint value is less than-25.
Compared with the prior art, the invention has the beneficial effects that:
according to the method, a Bayes compressed sensing algorithm carries out DOA estimation on sound wave incident signals received by an array element to obtain the directions of a target signal source and an interference signal source, and an interference plus noise covariance matrix can be accurately reconstructed according to the obtained directions of the target signal source and the interference signal source and combined with Capon space spectrum estimation of sampled data. Meanwhile, compared with other adaptive beam forming algorithms, the adaptive beam former provided by the invention restricts the sidelobe of a beam pattern and controls the sidelobe at a lower level. The method realizes more accurate reconstruction of the interference and noise covariance matrix, and has a larger output signal-to-noise ratio and a better side lobe control level.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic view of the azimuth definition of the adaptive beamformer design method based on the Bayesian compressive sensing algorithm according to the present invention;
FIG. 2 is a schematic diagram of the signal source and the direction and intensity of an interference source of the adaptive beamformer design method based on the Bayesian compressive sensing algorithm of the present invention;
fig. 3 is a beam diagram of the adaptive beamformer design method based on the bayesian compressive sensing algorithm according to the present invention.
FIG. 4 is a graph comparing the performance of the present invention with other methods at different input signal-to-noise ratios.
Fig. 5 is a graph comparing the performance of the present invention with other methods at different sampling times.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a design method of an adaptive beam former based on a Bayes compressed sensing algorithm, which realizes more accurate reconstruction of an interference and noise covariance matrix through the Bayes compressed sensing algorithm, has a larger output signal-to-noise ratio compared with other adaptive algorithms, and is also restricted at a lower level by a side lobe peak value of a beam pattern.
In this embodiment, the design is considered to be a 20 x 20 two-dimensional transducer array. Fig. 1 is a schematic azimuth angle definition diagram of the adaptive beamformer design method based on the bayesian compressed sensing algorithm of the present invention, wherein α and β represent the angles of the incident acoustic wave signals in the horizontal and vertical directions. Assuming that the signal incidence direction is (0 ° ), the two interference source incidence directions are (45 °,36 °) and (30 °,60 °) respectively, and the input interference-to-noise ratio (INR) is 30dB. The transducers are uniformly distributed in a rectangular plane according to the half-wavelength distance, the horizontal and vertical distances of the transducers are equal, the carrier frequency is f =300kHz, the sound velocity is 1500m/s, the value ranges of u and v are (-1, 1) and (-1, 1) respectively, and the beam number is 181 multiplied by 181.
The embodiment provides a design method of an adaptive beam former based on a Bayesian compressed sensing algorithm, which comprises the following specific steps:
wherein, the array manifold matrix is as follows:
the DOA estimation problem can be transformed as follows:
wherein,
and
respectively represent
The real and imaginary parts of (a) and (b),
the posterior probability is expressed. Then
Comprises the following steps:
where ε (k) is the fidelity coefficient representing the accuracy of the signal DOA estimate. Posterior probability
Introduction of hyper-parameters
Conversion to:
wherein R and I respectively represent real part and imaginary part, and hyperparameter
The value of (a) is obtained by solving its maximum likelihood function,as follows:
wherein a and b are user-defined proportional control parameters,
is shown in
A diagonal matrix being diagonal elements; the DOA of the incident signal can be found by:
the resulting orientations and normalized intensities of the signal source and the interference source are shown in fig. 2.
Step 2, according to the obtained direction of the incident signal source, the direction is (0 degree ), and the array manifold vector is
The interference sources are oriented at (45, 36) and (30, 60) degrees, and the array manifold vector is
Capon spatial spectrum function is:
wherein,
a sampled covariance matrix representing array elements. The interference plus noise covariance matrix can be reconstructed as follows:
and 3, setting the peak value of the side lobe to be-25 dB, and solving the array element coefficient of the adaptive beam former by a convex optimization method. The resulting beam pattern is shown in fig. 3, and compared with other adaptive beamforming algorithms, including the diagonal loading method (DL), the worst case method (WC), the direct inversion method (SMI), and the covariance matrix reconstruction method (CMR), is shown in fig. 4 and 5, where fig. 4 compares the output signal-to-interference ratio (SINR) at different input signal-to-noise ratios (SNR), and fig. 5 compares the output signal-to-interference ratio (SINR) at different sampling times. It can be seen that the performance of the present invention is always superior to other methods under different conditions.
The technical solutions and advantages of the present invention have been described in detail in the foregoing detailed description, and it should be understood that the above description is only the most preferred embodiment of the present invention, and is not intended to limit the present invention, and any modifications, additions, and equivalents made within the scope of the principles of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A design method of an adaptive beam former based on a Bayesian compressed sensing algorithm is characterized by comprising the following steps:
(1) The planar array element receives an acoustic wave incident signal, the acoustic wave incident signal comprises a target signal and an interference signal, and an adaptive beam former is constructed based on the acoustic wave incident signal, wherein the received acoustic wave incident signal is represented as:
where k denotes a sampling fast beat number, X (k) denotes an acoustic wave incident signal received when the sampling fast beat number is k, n (k) denotes a gaussian noise vector, and s (k) = [ s ] - [ s ] l (k)，l＝0，1，2，...，L] T An incident signal source indicating L +1 directions, L indicating an index of the incident direction, and (α) when L =0 l ，β l ) Indicating the direction of incidence of the target signal, when l =1,2.,when is equal to (alpha) l ，β l ) Indicates the incident direction of the interference signal, a (alpha) l ，β l ) Indicates an incident direction of (alpha) l ，β l ) Of phi = [ a (alpha) ] l ，β l )，l＝0，1，2，...，L]And expressing the array manifold matrix, specifically as follows:
wherein λ is the wavelength, x n ，y n Denotes the position of the nth array element, N =1,2 l ＝sinα l ，v l ＝sinβ l L =0,1,2, ·, L is a natural number;
constructing an adaptive beamformer based on acoustic incident signals is represented as:
Y(k)＝w H X(k) (3)
where Y (k) represents the output of the adaptive beamformer, w H ∈C N Representing array element weight coefficients, and superscript H representing a Hermite transpose;
estimating the direction of arrival of the incident sound wave signals by adopting a Bayesian compressed sensing algorithm, and when estimating the direction of arrival of the incident sound wave signals by adopting the Bayesian compressed sensing algorithm, making the number of candidate signal directions M, and then expressing the candidate signal sources as M
Then the acoustic incident signal received by the array element is rewritten as:
wherein,
representing the incident signal of the acoustic wave being overwritten,
the representation of the noise vector is carried out,
representing candidate signal source vectors, array manifold matrices
As follows:
the direction of arrival estimation problem translates to the following:
wherein,
and
respectively representing candidate signal sources
The real and imaginary parts of (a) and (b),
represents the posterior probability, then
Comprises the following steps:
wherein R (-) denotes taking the real part, I (-) denotes taking the imaginary part, ε (k) is a fidelity coefficient, and represents the accuracy of the DOA estimation of the signal,
posterior probability
Introducing a hyperparameter
Conversion to:
wherein Q = R, I, R, I respectively represent a real part and an imaginary part, and a hyperparameter
The value of (d) is obtained by solving its maximum likelihood function, as follows:
wherein Q = R, I, a and b are user-defined proportion control parameters,
is shown in
A superscript T represents the transpose of the matrix for a diagonal matrix of diagonal elements; the DOA estimate of the acoustic incident signal is then obtained by:
when the incident direction index l =0, obtaining the direction of arrival of the target signal according to a formula (13), and when the incident direction index l ≠ 0, obtaining the direction of arrival of the interference signal according to the formula (13);
(2) Obtaining an interference-plus-noise covariance matrix according to the direction of arrival of the interference signal and Capon space spectrum reconstruction of the incident signal of the acoustic wave
(3) Defining a maximum sidelobe level constraint value as BP PSLL Order (u) j ，v j ) Represents the sidelobe region of the target beam pattern, where J =1, 2.. And J, then the sidelobes of the target beam pattern are constrained according to a maximum sidelobe level constraint value, which is expressed as:
wherein the reconstructed interference-plus-noise covariance matrix is combined
Then the array element coefficients of the adaptive beam former are solved by a convex optimization method to obtain the weight coefficient values of the adaptive beam former, and the solving process is as follows:
after obtaining the weight coefficient values of the adaptive beamformer, i.e. according to Y (k) = w H X (k) results in an adaptive beamformer.
2. The adaptive beamformer design method based on the bayesian compressed sensing algorithm according to claim 1, wherein the output signal to interference plus noise ratio SINR of the adaptive beamformer is calculated as follows:
wherein, E [. C]Denotes expectation, | 2 Represents the square, X s (k)，X i (k) And X n (k) Respectively representing a target signal component, an interference signal component and a noise component, sigma s 2 Representing the energy of the signal, a s Array manifold vector, R, representing target signal i+n ＝E[(X i (k)+X n (k))(X i (k)+X n (k)) H ]∈C N×N Representing the interference plus noise covariance matrix, the design of the adaptive beamformer turns into the following problem:
min w w H R i+n w，subject to w H a s ＝1 (19)。
3. the adaptive beamformer design method based on Bayesian compressive sensing algorithm as claimed in claim 1, wherein in step (2), the sound wave incident signal Capon spatial spectrum function
Comprises the following steps:
wherein,
a sampling covariance matrix representing the array elements;
the interference-plus-noise covariance matrix reconstructed from the direction of arrival of the interfering signal
The following were used:
wherein,
indicating the direction of incidence (u) of the interfering signal source l ，v l ) A corresponding array manifold vector.
4. The adaptive beamformer design method based on the Bayesian compressed sensing algorithm as recited in claim 1, wherein a maximum sidelobe level constraint value is set according to an aperture of an array and the number of array elements, and sidelobes are smaller as array elements are larger.
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