CN116866123B - Convolution blind separation method without orthogonal limitation - Google Patents
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Abstract
The invention discloses a convolution blind separation method without orthogonal limitation, which comprises the following steps: s1, receiving a mixed signal; s2, converting the time domain convolution problem into an IVA problem; s3, optimizing the signal to be optimized according to a matrix optimization method based on a cost function of the minimum mutual information; s4, separating the optimized signals. The method decomposes the matrix optimization problem into a series of row vector optimization problems. The method of the invention has better separation performance, and the separated signals have lower average interference-signal ratio. The IVA algorithm based on decoupling has the best separation performance, and the separation performance index is 15-20dB lower than that of the two comparison algorithms. The algorithm decomposes the matrix optimization problem into a series of row vector optimization problems. The algorithm does not require that the vectors in the separation matrix be orthogonal as in the orthogonal limited algorithm. In addition, compared with a matrix updating algorithm in a shrinkage mode, the algorithm provided by the invention does not have a separation error accumulation phenomenon.
Description
Technical Field
The present invention relates to wireless communication technology; the technical field of communication anti-interference, in particular to a convolution blind separation method without orthogonal limitation.
Background
In many practical applications, especially in wireless mobile communication systems, the source signals often experience delays and reflections during propagation, eventually mixing in the form of convolutions. At this time, the transient mixing model does not express the mixing state exactly, resulting in difficulty in obtaining the intended separation effect. In recent years, many algorithms have been proposed to solve the convolutional hybrid blind separation problem. These algorithms can be broadly divided into two categories: time domain algorithms and frequency domain algorithms. The time domain algorithm is mainly based on the research developed by the existing blind deconvolution method, but has higher operation complexity. And the frequency domain method can effectively reduce the complexity of algorithm implementation. And performing short-time Fourier transform on the convolutionally mixed observation signals, wherein in the transformed frequency domain signals, the data of the observation signals on each frequency point are instantaneous mixing of source signals in corresponding frequency point values in corresponding time periods. After the conversion, the time domain convolution mixed blind separation problem is converted into the frequency domain instantaneous mixed blind separation problem, and then the instantaneous mixed blind separation algorithm can be adopted to realize the separation of all source signals. At this time, since the mixing matrices on different frequency points may be different and there is a problem that the sequence of the separation signals is not determined in the blind source separation algorithm, a further post-processing is required after the separation of the source signals is completed on each frequency point, so as to achieve the correct splicing of the separation signals in each frequency point, and then the source signals in the time domain are recovered through the short-time inverse fourier transform. There have been some studies reporting on how to accomplish the problem of correctly splicing the frequency point separated signals. But the performance of these algorithms is not stable. Considering the correlation of the same source signal among different frequency points in the frequency domain, a learner proposes to realize blind source separation in the frequency domain by adopting a joint blind source separation method, and the signals separated by all the frequency points have the same sequence. Therefore, the correct splicing of the source signal components in different frequency points is directly completed without a post-processing process after frequency domain separation.
Among joint blind source separation algorithms, the most common method is an Independent Vector Analysis (IVA) based algorithm. It is an extension method of ICA. As assumed in ICA theory, IVA also requires that the source signals are statistically independent within each dataset. A data set here refers to a set of observation signals, and for any source signal contained in each set of observation signals (data set), at most one source signal contained in any other set of observation signals (data set) can be associated with the source signal, and the mixing matrices in different data sets may also be different.
The IVA algorithm extends the cost function in the ICA algorithm from univariate to component dependent multivariate. Many algorithms describe the correlation of source signal components between different data sets using different multi-parameter prior probability distribution models and give corresponding cost function expressions. However, most algorithms require orthogonality of the separate matrices for each data set. Since a whitening matrix estimation error generated in the whitening process of the observed signal cannot be compensated for in the subsequent signal processing, the orthogonality limitation of the separation matrix may degrade the separation performance. Among non-orthogonal limited blind source separation algorithms, one simple and very popular algorithm is one based on relative or natural gradient descent learning. But this algorithm has the disadvantage of slow convergence. To accelerate algorithm convergence, some students have sequentially proposed learning algorithms based on the Newton method. However, because the Newton algorithm needs to solve the inverse of the Hessian matrix, its complexity is often high, and its performance is not satisfactory in some cases.
Disclosure of Invention
The present invention aims to provide a convolution blind separation method without orthogonal limitation, thereby solving the aforementioned problems existing in the prior art. The invention extends the method to a complex domain to solve the problem of blind deconvolution in the frequency domain. The method decomposes the matrix optimization problem into a series of row vector optimization problems. The method does not require that the vectors in the separation matrix be orthogonal as in the orthogonal limited algorithm. In addition, compared with the matrix updating algorithm in a shrinkage mode, the algorithm in the invention does not have the phenomenon of separating error accumulation.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a convolution blind separation method without orthogonal limitation, comprising the steps of:
s1, receiving a mixed signal, wherein the mixed signal is obtained by convoluting and mixing a source signal;
s2, converting the time domain convolution problem into an IVA problem: performing short-time Fourier transform on sample values of a time domain source signal in the mixed signal to obtain a frequency domain signal of the time domain source signal; the convolution mixing problem of the time domain shows a form of instantaneous mixing in the frequency domain;
s3, optimizing the signal to be optimized according to a matrix optimization method based on a cost function of the minimum mutual information;
S4, separating the optimized signals.
Preferably, the process of receiving the mixed signal includes:
the mixed signal received by the nth sensor after the source signals are convolutionally mixed is
Wherein the method comprises the steps ofIs the sample value of the jth time domain source signal at time m, a nj (P) is the impulse response tap coefficient of the jth source signal to the nth sensor transmission channel, and P is the tap order of the channel impulse response.
Preferably, the process of converting the time domain convolution problem into the IVA problem includes:
For a perception signal Performing short-time Fourier transform to obtain frequency domain signal
Where ω k =2pi (K-1)/K, k=1, 2, …, K, J is the number of sample points for which two adjacent time periods are offset,Is a window function of the short-time fourier transform; if window function/>The convolution mixing problem of the time domain will show instantaneous mixing form in the frequency domain as shown in the formula, compared with the order of the channel impulse response a nj (p)
Wherein the method comprises the steps ofIs the value of the channel impulse response a nj (p) at frequency point k,/>Is the source signal/>The kth frequency point value in the tth short-time Fourier transform window, K is the number of short-time Fourier transform data points, L is the number of short-time Fourier transform windows, and K, L corresponds to the number of data sets in the model and the sample length in each data set respectively; at this point, the time domain convolution problem is converted into the IVA problem given by the equation.
Preferably, the optimizing the signal to be optimized according to the matrix optimizing method based on the cost function of the minimum mutual information, and further realizing the signal separation process includes:
the cost function based on the minimum mutual information is given by the formula, and the nonlinear function for approximating the probability density function of the source signal is G: In the concrete expression form of
According to the matrix optimization method given by the formula, the updating mode of the nth row element of the separation matrix W [k] of the kth frequency point is written as
Where Deltav is the small perturbation of the vector v to be optimized at point 0; the variation of the estimated value of the frequency point k of the nth source signal corresponding to the estimated value of the frequency point k of the nth source signal in the nth time window is that
Due toThe change in the cost function is written as
At this time use is made ofAnd the second order Taylor series expansion of log|1+Deltav Hen | gives a variance of the cost function that can be approximated as
Wherein the method comprises the steps of And/>G (||y n,t||2) is related to/>, respectivelyFirst and second partial derivatives of (a);
designing an updating algorithm based on Newton method for the parameter Deltav to be optimized; the quadratic term coefficient matrix in the algorithm requirement Must be positive, but in the separation signal/>Without convergence to the source signal/>Previously, the matrix may not meet the positive requirements; therefore, the parameter calculation in the algorithm needs to be corrected to ensure that the requirement of the Newton method on the parameter is met; when separating signals/>Convergence to the source signal/>When the algorithm is updated, the matrices D 0 and D 1 are diagonal matrices, and the algorithm is updated by approximating the matrices D 0 and D 1 respectively as follows
Wherein diag { d } represents a matrix of diagonal element vectors d; at this time, the Hessian matrix for the i-th element of the vector Deltav isWherein d 0,i and d 1,i are each matrix/>And/>Is the i-th diagonal element of (a); to ensure that the Hessian matrix is positive, the elements in the matrix are modified as follows
d0,i＝max[d0,i,(1+α)|d1,i|] (14)
Where α is a small positive constant, typically taken as α=10 -6; the update rule of the ith element of the vector Deltav is
Preferably, the matrix optimization method is a matrix optimization method based on Householder transformation, and the main idea is to convert a matrix optimization problem into a series of vector optimization problems, specifically including:
by repeatedly multiplying a base matrix In which I is an N x N identity matrix, u and v are two vectors of size N x 1 to be optimized,/>, until they convergeRepresenting transposition operation, wherein when vector elements are real numbers, the vector elements are transposed by real numbers, and the equivalent is (-) T; when the vector element is complex, the vector element is complex conjugate transpose, and the equivalent is (-) H; when/>When v+.0, this transformation is a Householder reflection; /(I)The eigenvalues of the reflection transformation are 1 and/>Wherein 1 is an N-1 weight characteristic value; if/>This transformation is reversible; for matrix W [k], its rank-1 is updated to
One nonsingular matrix can be converted into another arbitrary nonsingular matrix through N times of elementary reflections.
The beneficial effects of the invention are as follows:
The convolution blind separation method without orthogonal limitation has better separation performance, and the separated signals have lower average interference-signal ratio. The IVA algorithm based on decoupling has the best separation performance, and the separation performance index is 15-20dB lower than that of the two comparison algorithms. The algorithm decomposes the matrix optimization problem into a series of row vector optimization problems. The algorithm does not require that the vectors in the separation matrix be orthogonal as in the orthogonal limited algorithm. In addition, compared with a matrix updating algorithm in a shrinkage mode, the algorithm provided by the invention does not have a separation error accumulation phenomenon.
Drawings
FIG. 1 is a convolved speech signal separation result using the method of the present invention;
Fig. 2 shows the performance convergence curves k=4, n=4, l=3000 for ISRAV after separation in the example of the invention;
Fig. 3 is a graph showing the effect of different data set numbers on algorithm separation performance ISRAV in an example of the present invention, n=4, 10, l=3000;
Fig. 4 is a graph showing the effect of different sample lengths in a dataset on algorithm separation performance ISRAV, n=4, k=4, 8,12 in an example of the invention;
fig. 5 is a flow chart of the convolution blind separation method without orthogonal limitation of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description is presented by way of example only and is not intended to limit the invention.
IVA problem description
Assuming K data sets, each data set has N observation signals, each signal has L sample points, and the instantaneous mixing model of the signals in each data set is that
Wherein,Is the T-th sample value of the zero-mean source signal vector s [k], the superscript T is defined as the transpose operation, and a [k] is a non-singular mixing matrix of unknown size n×n. The nth source signal component vector (Source Component Vector, SCV) is expressed as/>The SCV is independent of all other SCVs. At this time, the probability density function of all source signals in the dataset satisfies the relation/>
The objective of the IVA algorithm is to find K separation matrices and estimate the corresponding source signal vectors in each dataset. Defining a separation matrix corresponding to the kth dataset as W [k], and estimating a signal vector asThe t estimated sample of the nth source signal in the kth data set is/>Wherein/>Is the nth row of the split matrix W [k]. The expression of the estimated nth SCV is/>
For blind source separation of a single data set, the separated signals may have order uncertainty. Multiple data sets combine blind source separation to have the same properties, but the order in which the signals are separated for each data set must be the same. That is to say the inverse of the separation matrix estimated for the kth datasetEstimated source signal vector/>Where P is an arbitrary permutation matrix and all datasets have the same P, Λ [k] is a non-singular diagonal matrix.
The goal of IVA is to obtain SCVs that are independent of each other, which can be obtained by minimizing the mutual information between estimated SCVs. The mutual information expression between the SCVs is estimated as
Wherein,Representing mutual information between variable x and variable y,/>The entropy of y n,t is represented. In the above, a linear reversible transformation/>Entropy of/>Wherein C 1 is a constant termThe prior art generally limits the separation matrix W [k] for each dataset to be orthogonal, which, as described in the present invention above, may degrade separation performance, which is eliminated in a decoupling manner.
2. Matrix optimization method based on Householder transformation
Decomposing the matrix optimization problem into a series of small sub-problems to improve the efficiency of the optimization algorithm is one way, such as Jacobi (Givens) rotations. The principle of Jacobi-like algorithms is to translate a matrix optimization problem into a series of smaller sub-matrix optimization problems, typically a 2x 2 matrix.
The invention adopts a Householder class technique to solve the matrix optimization problem, and the main idea is to convert the matrix optimization problem into a series of vector optimization problems. In particular by repeatedly left-multiplying a basis matrixIn which I is an N x N identity matrix, u and v are two vectors of size N x 1 to be optimized,/>, until they convergeThe transpose operation (real vector transpose when the vector elements are real, equivalently (-) T; complex conjugate transpose when the vector elements are complex, equivalently (-) H) is represented. When/>When v.noteq.0, this transformation is a Householder reflection. /(I)The eigenvalues of the reflection transformation are 1 and/>Wherein 1 is an N-1 weight characteristic value. Thus, if/>This transformation is reversible. For matrix W [k], its rank-1 is updated to
Therefore, at most N elementary reflections are required to convert one nonsingular matrix to another arbitrary nonsingular matrix.
The equation is more flexible than gradient descent algorithms, especially in the second order derivative update process. When u=e n, the equation only updates the nth row of the matrix W [k], where e n is a unit vector of size n×1 nth element of 1. In this way, a row-by-row optimization matrix W [k] can be implemented by optimizing v. It should be noted that, even if it is not assumed that u=e n, the update solution of the separation matrix can still be implemented by means of the Householder transform, which leads to an increase in the calculation amount. Therefore, only the special case when u=e n is considered in the present invention.
3. Convolution blind separation algorithm without orthogonal limitation
3.1 Description of the problem
Assuming that N sensors and N mutually independent source signals are provided, the mixed signals received by the nth sensor after the source signals are convolutionally mixed are
Wherein the method comprises the steps ofIs the sample value of the jth time domain source signal at time m, a nj (P) is the impulse response tap coefficient of the jth source signal to the nth sensor transmission channel, and P is the tap order of the channel impulse response. For perceived signal/>Performing short-time Fourier transform to obtain frequency domain signal
Where ω k =2pi (K-1)/K, k=1, 2, …, K, J is the number of sample points for which two adjacent time periods are offset,Is a window function of the short-time fourier transform. If window function/>The convolution mixing problem of the time domain will show instantaneous mixing form in the frequency domain as shown in the formula, compared with the order of the channel impulse response a nj (p)
Wherein the method comprises the steps ofIs the value of the channel impulse response a nj (p) at frequency point k,/>Is the source signal/>The kth frequency point value in the tth short-time Fourier transform window, K is the number of short-time Fourier transform data points, and L is the number of short-time Fourier transform windows, wherein K, L corresponds to the number of data sets in the model and the sample length in each data set respectively. At this point, the time domain convolution problem is converted into the IVA problem given by the equation.
3.2 Algorithm description
The section uses a cost function based on minimum mutual information as given by the formula. The nonlinear function used to approximate the source signal probability density function is G: The concrete expression form is
According to the matrix optimization method given by the formula, the updating mode of the nth row element of the separation matrix W [k] of the kth frequency point can be written as follows
Where Deltav is the small perturbation of the vector v to be optimized at point 0. The variation of the estimated value of the frequency point k of the nth source signal corresponding to the estimated value of the frequency point k of the nth source signal in the nth time window is that
Due toThe change in cost function can be written as
At this time use is made ofAnd the second order Taylor series expansion of log|1+Deltav Hen | gives a variance of the cost function that can be approximated as
Wherein the method comprises the steps of And/>G (||y n,t||2) is related to/>, respectivelyFirst and second partial derivatives of (a).
The updating algorithm based on Newton method is designed for the parameter Deltav to be optimized. The quadratic term coefficient matrix in the algorithm requirementMust be positive, but in the separation signal/>Without convergence to the source signal/>Previously, the matrix may not meet the positive qualitative requirement. Thus, the parameter calculations in the algorithm need to be modified to ensure that the requirements of the Newton method for the parameters are met. When separating signals/>Convergence to the source signal/>When the algorithm is updated, the matrices D 0 and D 1 are diagonal matrices, and the algorithm is updated by approximating the matrices D 0 and D 1 respectively as follows
Wherein diag { d } represents a matrix of diagonal element vectors d. At this time, the Hessian matrix for the i-th element of the vector Deltav isWherein d 0,i and d 1,i are each matrix/>And/>Is the i-th diagonal element of (c). To ensure that the Hessian matrix is positive, the elements in the matrix are modified as follows
d0,i＝max[d0,i,(1+α)|d1,i|] (14)
Where α is a small positive constant, typically α=10 -6. The update rule of the ith element of the vector Deltav is
It can be seen from the derivation of the algorithm that the algorithm does not limit the orthogonality of the separation matrix, and that no separation error accumulation occurs because each row vector in the separation matrix is independently optimally updated.
3.3 Simulation analysis
First, simulation experiments show whether the method of the present invention can correctly separate convolutionally mixed signals. The simulation considers the situation of convolution mixing of two paths of voice signals, a convolution mixing model is shown as a formula, and the convolution channel order is set to be P=3. For each mixed signal, the sliding window function is set to a rectangular window, the window size is 1024, and the adjacent time window offset is 256 sample points. Fig. 1 shows the separation of two convolved speech signals processed using the algorithm proposed in the present invention. As can be seen from the figures, the algorithm proposed in the present invention successfully separates the speech convolution signals.
In order to quantitatively compare the performance of the decoupling IVA algorithm proposed in the present invention with other IVA algorithms, the following simulation analysis analyzes the separation effect of different IVA algorithms on the multi-data set complex-valued signal mixture. A mixed model of multi-data set complex value signals is shown in the specification, and complex value signals SCV are generated according to the model
Where M n,i is a complex matrix of size KxK, and z n,t-i is a vector that obeys uniform distribution and has a mean value of zero. β=3 is set in the following simulation.
The algorithm provided in the invention is compared with the simulation performance of the other two IVA algorithms based on vector gradient learning and Newton learning. The separation performance evaluation index is the average interference-to-signal Ratio (AVERAGE INTERFERENCE to Source Ratio, ISR AV) of the separation signals of each data set, and the expression is
Wherein,Is the (m, n) th element of the global matrix D [k]＝W[k]A[k], assuming no order uncertainty exists. As can be seen from the definition of the performance index, the smaller ISR AV is, the better the separation performance of the algorithm, and when ISR AV =0, the separation effect is very ideal, so that the source signals in each data set are successfully separated. In all simulations, each performance curve is the average of 100 Monte Carlo simulations.
FIG. 2 shows the convergence curves of the separation performance of the three algorithms ISR AV. As can be seen from fig. 2, there is a significant difference in the convergence performance of the three algorithms. The algorithm based on gradient learning has the slowest convergence speed; while the convergence speed of the algorithm based on the Newton method is improved compared with that of the algorithm based on gradient learning, the final convergence value tends to be the same; the IVA algorithm based on decoupling provided by the invention not only improves the convergence rate compared with two comparison algorithms, but also reduces the convergence value greatly, which means that the algorithm provided by the invention has better separation performance and the separated signals have lower average interference signal ratio.
FIG. 3 depicts the effect of different data set numbers on algorithm separation performance when the simulated signal model is in the form of a model. As can be seen from fig. 3, the decoupling IVA algorithm provided in the present invention has the best separation performance, and the separation performance index ISR AV is 15-20dB lower than that of the two comparison algorithms. In addition, similar to the separation result of the real number multiple data sets, the influence of the number of source signals in the data sets on the separation performance is not obvious.
Figure 4 shows the effect of different sample length sizes on the separation performance of the algorithm. As can be seen from fig. 4, the greater the sample length in the dataset, the lower the separation index ISR AV of the three algorithms, i.e. the better the separation effect. The gradient learning-based algorithm and the Newton method-based algorithm have similar separation performance, and the average interference signal ratio ISR AV of the separation signals is 15-20 dB higher than that of the decoupling IVA algorithm proposed in the invention. It can also be seen from fig. 4 that as the sample length in the dataset increases, the number of datasets has less and less impact on the performance of the split ISR AV.
By adopting the technical scheme disclosed by the invention, the following beneficial effects are obtained:
The convolution blind separation method without orthogonal limitation has better separation performance, and the separated signals have lower average interference-signal ratio. The IVA algorithm based on decoupling has the best separation performance, and the separation performance index is 15-20dB lower than that of the two comparison algorithms. The algorithm decomposes the matrix optimization problem into a series of row vector optimization problems. The algorithm does not require that the vectors in the separation matrix be orthogonal as in the orthogonal limited algorithm. In addition, compared with a matrix updating algorithm in a shrinkage mode, the algorithm provided by the invention does not have a separation error accumulation phenomenon.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which is also intended to be covered by the present invention.
Claims (3)
1. A convolution blind separation method without orthogonal limitation, comprising the steps of:
s1, receiving a mixed signal, wherein the mixed signal is obtained by convoluting and mixing a source signal;
s2, converting the time domain convolution problem into an IVA problem: performing short-time Fourier transform on sample values of a time domain source signal in the mixed signal to obtain a frequency domain signal of the time domain source signal; the convolution mixing problem of the time domain shows a form of instantaneous mixing in the frequency domain;
s3, optimizing the signal to be optimized according to a matrix optimization method based on a cost function of the minimum mutual information;
s4, separating the optimized signals;
the process of receiving the mixed signal includes:
the mixed signal received by the nth sensor after the source signals are convolutionally mixed is
Wherein the method comprises the steps ofIs the sample value of the jth time domain source signal at time m, a nj (P) is the tap coefficient of the impulse response of the jth source signal to the nth sensor transmission channel, and P is the tap order of the channel impulse response;
The process of converting the time domain convolution problem into the IVA problem comprises the following steps:
For mixed signals Performing short-time Fourier transform to obtain frequency domain signal
Where ω k =2pi (K-1)/K, k=1, 2, l, K is the number of short-time fourier transform frequency points, t is the short-time fourier transform window index, J is the number of sample points offset by two adjacent time periods,Is a window function of the short-time fourier transform; if window functionThe convolution mixing problem of the time domain will show instantaneous mixing form in the frequency domain as shown in the formula, compared with the order of the channel impulse response a nj (p)
Wherein the method comprises the steps ofIs the value of the channel impulse response a nj (p) at frequency point k,/>Is the source signal/>K frequency point values in the t-th short-time Fourier transform window, K is the number of short-time Fourier transform data points, L is the number of short-time Fourier transform windows, and K, L corresponds to the number of data sets in the model and the sample length in each data set respectively; at this point, the time domain convolution problem is converted into the IVA problem.
2. The convolution blind separation method without orthogonal limitation according to claim 1, wherein the optimizing the signal to be optimized according to the matrix optimizing method based on the cost function of the minimum mutual information, and further realizing the signal separation process comprises:
The cost function based on the minimum mutual information is used for approximating the nonlinear function of the probability density function of the source signal as The concrete expression form is
Wherein y n,t represents the signal value of the recovery signal y at the nth user at the nth time window;
According to the matrix optimization method, the updating mode of the nth row element of the separation matrix W [k] of the kth frequency point is written as
Wherein the method comprises the steps ofIs the result obtained by the last iteration loop processing of the nth row element of the separation matrix,/>Is the result obtained by the current iteration loop of the nth row element of the separation matrix,/>Is the difference value of the results of two adjacent iterative processes of the nth row element of the separation matrix,/>The separation matrix is obtained by the last iterative loop calculation, and Deltav is the tiny disturbance of the vector v to be optimized at the 0 point; the variation of the estimated value of the frequency point k of the nth source signal corresponding to the estimated value of the frequency point k of the nth source signal in the nth time window is that
Wherein the method comprises the steps ofA signal value representing the kth frequency point of the recovery signal y in the kth time window;
Due to E n is the unit vector with the value of 1 at the nth bit,/>Is the separation matrix obtained by the last iteration loop calculation, and the change of the cost function is written as
At this time use is made ofAnd the second order Taylor series expansion of log|1+Deltav Hen |, the variation of the cost function given by equation (10) can be approximated as
Wherein the method comprises the steps of And/>G (||y n,t||2) is related to/>, respectivelyFirst and second partial derivatives of (a);
Designing an updating algorithm based on Newton method for the parameter Deltav to be optimized; the algorithm requires a quadratic coefficient matrix in (11) Must be positive, but in the separation signal/>Without convergence to the source signal/>Previously, the matrix may not meet the positive requirements; therefore, the parameter calculation in the algorithm needs to be corrected to ensure that the requirement of the Newton method on the parameter is met; when separating signals/>Convergence to the source signal/>When the algorithm is updated, the matrices D 0 and D 1 are diagonal matrices, and the algorithm is updated by approximating the matrices D 0 and D 1 respectively as follows
Wherein diag { d } represents a matrix of diagonal element vectors d; at this time, the Hessian matrix for the i-th element of the vector Deltav isWherein d 0,i and d 1,i are matrix/>, respectivelyAnd/>Is the i-th diagonal element of (a); to ensure that the Hessian matrix is positive, the elements in the matrix are modified as follows
d0,i＝max[d0,i,(1+α)|d1,i|] (14)
Where α is a small positive constant, typically taken as α=10 -6; the update rule of the ith element of the vector Deltav is
3. The convolution blind separation method without orthogonal limitation according to claim 2, wherein the matrix optimization method is a matrix optimization method based on Householder transformation, and the main idea is to convert a matrix optimization problem into a series of vector optimization problems, specifically comprising:
by repeatedly multiplying a base matrix In which I is an N x N identity matrix, u and v are two vectors of size N x 1 to be optimized,/>, until they convergeRepresenting transposition operation, wherein when vector elements are real numbers, the vector elements are transposed by real numbers, and the equivalent is (-) T; when the vector element is complex, the vector element is complex conjugate transpose, and the equivalent is (-) H; when/>When v+.0, this transformation is a Householder reflection; /(I)The eigenvalues of the reflection transformation are 1 and/>Wherein 1 is an N-1 weight characteristic value; if/>This transformation is reversible; for matrix W [k], its rank-1 is updated to
One nonsingular matrix can be converted into another arbitrary nonsingular matrix through N times of elementary reflections.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20120133038A (en) * | 2011-05-30 | 2012-12-10 | 서강대학교산학협력단 | Blind source separation method and apparatus |
| CN106887238A (en) * | 2017-03-01 | 2017-06-23 | 中国科学院上海微系统与信息技术研究所 | A kind of acoustical signal blind separating method based on improvement Independent Vector Analysis algorithm |
| CN108364659A (en) * | 2018-02-05 | 2018-08-03 | 西安电子科技大学 | Frequency domain convolution Blind Signal Separation method based on multiple-objection optimization |
| CN112201274A (en) * | 2020-08-21 | 2021-01-08 | 西安交通大学 | Underdetermined blind source separation method, system and device based on minimization and maximization |
| CN113823316A (en) * | 2021-09-26 | 2021-12-21 | 南京大学 | Voice signal separation method for sound source close to position |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR100636368B1 (en) * | 2005-11-09 | 2006-10-19 | 한국전자통신연구원 | Convolutive blind source separation using relative optimization |
-
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20120133038A (en) * | 2011-05-30 | 2012-12-10 | 서강대학교산학협력단 | Blind source separation method and apparatus |
| CN106887238A (en) * | 2017-03-01 | 2017-06-23 | 中国科学院上海微系统与信息技术研究所 | A kind of acoustical signal blind separating method based on improvement Independent Vector Analysis algorithm |
| CN108364659A (en) * | 2018-02-05 | 2018-08-03 | 西安电子科技大学 | Frequency domain convolution Blind Signal Separation method based on multiple-objection optimization |
| CN112201274A (en) * | 2020-08-21 | 2021-01-08 | 西安交通大学 | Underdetermined blind source separation method, system and device based on minimization and maximization |
| CN113823316A (en) * | 2021-09-26 | 2021-12-21 | 南京大学 | Voice signal separation method for sound source close to position |
Non-Patent Citations (3)
| Title |
|---|
| 付卫红 ; 张琮 ; .基于步长自适应的独立向量分析卷积盲分离算法.电子与信息学报.2018,(第09期),见全文. * |
| 基于步长自适应的独立向量分析卷积盲分离算法;付卫红;张琮;;电子与信息学报(第09期);见全文 * |
| 基于非正交联合对角化的自干扰信号消除;丁文春等;通信技术;第50卷(第11期);见全文 * |
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