CN116866123A - Convolution blind separation method without orthogonal limitation - Google Patents
Convolution blind separation method without orthogonal limitation Download PDFInfo
- Publication number
- CN116866123A CN116866123A CN202310862717.6A CN202310862717A CN116866123A CN 116866123 A CN116866123 A CN 116866123A CN 202310862717 A CN202310862717 A CN 202310862717A CN 116866123 A CN116866123 A CN 116866123A
- Authority
- CN
- China
- Prior art keywords
- matrix
- signal
- algorithm
- separation
- convolution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000926 separation method Methods 0.000 title claims abstract description 88
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 90
- 239000011159 matrix material Substances 0.000 claims abstract description 87
- 238000000034 method Methods 0.000 claims abstract description 63
- 239000013598 vector Substances 0.000 claims abstract description 45
- 238000005457 optimization Methods 0.000 claims abstract description 33
- 230000006870 function Effects 0.000 claims description 27
- 230000009466 transformation Effects 0.000 claims description 14
- 230000004044 response Effects 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 9
- 230000014509 gene expression Effects 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000002441 reversible effect Effects 0.000 claims description 4
- 102000002274 Matrix Metalloproteinases Human genes 0.000 claims description 3
- 108010000684 Matrix Metalloproteinases Proteins 0.000 claims description 3
- 238000003491 array Methods 0.000 claims description 3
- 230000005540 biological transmission Effects 0.000 claims description 3
- 230000008447 perception Effects 0.000 claims description 3
- 238000009825 accumulation Methods 0.000 abstract description 5
- 241000947772 Strawberry crinkle virus Species 0.000 description 8
- 230000000694 effects Effects 0.000 description 8
- 238000004088 simulation Methods 0.000 description 7
- 239000004973 liquid crystal related substance Substances 0.000 description 6
- 238000004458 analytical method Methods 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000004891 communication Methods 0.000 description 2
- 238000012805 post-processing Methods 0.000 description 2
- 230000002087 whitening effect Effects 0.000 description 2
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 230000006978 adaptation Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000001934 delay Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000010295 mobile communication Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
- 238000009827 uniform distribution Methods 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
- H04L25/03019—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception
- H04L25/03057—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception with a recursive structure
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0212—Channel estimation of impulse response
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
- H04L25/03019—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception
- H04L25/03082—Theoretical aspects of adaptive time domain methods
- H04L25/03089—Theory of blind algorithms, recursive or not
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03178—Arrangements involving sequence estimation techniques
- H04L25/03305—Joint sequence estimation and interference removal
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L2025/03592—Adaptation methods
- H04L2025/03598—Algorithms
- H04L2025/03675—Blind algorithms using gradient methods
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Landscapes
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Complex Calculations (AREA)
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 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 signalPerforming short-time Fourier transform to obtain the final productFrequency domain signal
Wherein omega k =2pi (K-1)/K, k=1, 2, …, K, 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 function->Length of (a) compared to channel impulse response a nj (p) the order of (c) is large enough that the convolution mixing problem in the time domain will exhibit instantaneous mixing in the frequency domain, as shown in the formula
Wherein the method comprises the steps ofIs the channel impulse response a nj (p) value at frequency bin k, ">Is the source signal->The kth frequency point value in the kth 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 method, the separation matrix W of the kth frequency point [k] The update mode of the nth row element 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 log|1+Deltav H e n The second order Taylor series expansion of the equation gives a change in the cost function that can be approximated as
Wherein the method comprises the steps of And->Respectively is G (|) y n,t || 2 ) About->First 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 requirementMust 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 signal->Converging to the source signal->Matrix D 0 And D 1 Are all diagonal arrays, respectively corresponding to D in the process of updating algorithm 0 And D 1 To make the following approximation
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 is 0,i And d 1,i Respectively is a 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
d 0,i ＝max[d 0,i ,(1+α)|d 1,i |] (14)
Where α is a very small positive constant, typically α=10 -6 The method comprises the steps of carrying out a first treatment on the surface of the 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 matrixIn which I is an N identity matrix, u and v are two vectors of size N1 to be optimized,/are updated until convergence>Representing a transpose operation, which is a real number when the vector elements are real numbers, equivalent to () T The method comprises the steps of carrying out a first treatment on the surface of the When the vector element is complex, it is complex conjugate transpose, equivalent to ( H The method comprises the steps of carrying out a first treatment on the surface of the When->When v+.0, this transformation is a Householder reflection; />The characteristic values 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 as
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, n=4, 10, l=3000 in an example of the present invention;
fig. 4 is a graph showing the effect of different sample lengths in the dataset on the separation performance ISRAV of the algorithm in the example of the invention, n=4, k=4, 8,12;
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, the liquid crystal display device comprises a liquid crystal display device,is zero mean source signal vector s [k] The superscript T is defined as the transpose operation, A [k] Is an unknown non-singular mixing matrix of size N x 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 relationship +.>
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 data set as W [k] The estimated signal vector isThe t estimated sample of the nth source signal in the kth data set is +.>Wherein->Is a separation matrix W [k] Is the n-th row of (c). 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, the liquid crystal display device comprises a liquid crystal display device,representing mutual information between variable x and variable y, < ->Representing y n,t Is a function of the entropy of (a). In the above, a linearly reversible transformation is used>Entropy of->C in the formula 1 Is a constant termThe prior art generally uses a separate matrix W for each data set [k] The limitation is orthogonal, and as described in the present invention, this limitation may degrade the separation performance, and the present invention proposes a decoupling way to remove this limitation.
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) rotation. The principle of Jacobi-like algorithms is to translate a matrix optimization problem into a series of smaller sub-matrix optimization problems, typically a 2 x 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 identity matrix, u and v are two vectors of size N1 to be optimized,/are updated until convergence>Representing a transpose operation (the real vector transpose when the vector elements are real, equivalently () T The method comprises the steps of carrying out a first treatment on the surface of the When the vector element is complex, it is complex conjugate transpose, equivalent to ( H ). When->When v.noteq.0, this transformation is a Householder reflection. />The characteristic values 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 as
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 At this time, only the matrix W is updated [k] N-th row of (c), where e n Is a unit vector of size n×1nth element 1. In this way, a row-by-row optimization matrix W can be achieved by optimizing v [k] . Note that even if u=e is not assumed n The update solution of the separation matrix can still be realized by means of the Householder transformation, but this leads to an increase in the calculation amount. Therefore, only u=e is considered in the present invention n Special cases in this case.
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 nth sensor transmission channel, and P is the tap order of the channel impulse response. For perception signal->Performing short-time Fourier transform to obtain frequency domain signal
Wherein omega k =2pi (K-1)/K, k=1, 2, …, K, 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 function->Length of (a) compared to channel impulse response a nj (p) the order of (c) is large enough that the convolution mixing problem in the time domain will exhibit instantaneous mixing in the frequency domain, as shown in the formula
Wherein the method comprises the steps ofIs the channel impulse response a nj (p) value at frequency bin 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, where 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 method, the separation matrix W of the kth frequency point [k] The update mode of the nth row element of (a) can be 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 cost function can be written as
At this time use is made ofAnd log|1+Deltav H e n The second order Taylor series expansion of the equation gives a change in the cost function that can be approximated as
Wherein the method comprises the steps of And->Respectively is G (|) y n,t || 2 ) About->First 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 signal->Converging to the source signal->Matrix D 0 And D 1 Are all diagonal arrays, respectively corresponding to D in the process of updating algorithm 0 And D 1 To make the following approximation
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 is 0,i And d 1,i Respectively is a 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
d 0,i ＝max[d 0,i ,(1+α)|d 1,i |] (14)
Where α is a very small positive constant, typically α=10 -6 . Update rule of ith element of vector DeltavIs that
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
Wherein M is n,i Is a complex matrix with the size of K multiplied by K, 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 signal ratio (Average Interference to Source Ratio, ISR) of the separation signals of each data set AV ) The expression is
Wherein, the liquid crystal display device comprises a liquid crystal display device,is a global matrix D [k] ＝W [k] A [k] The (m, n) th element of (c), here assuming that no order uncertainty exists. From the definition of performance index, ISR AV Smaller algorithms have better separation performance when ISR AV When=0, the separation effect is very ideal, and 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 three algorithms ISR AV The separation performance converges. 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 by the invention has the best separation performance, and the separation performance index ISR AV 15-20dB lower than 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 data set, the separation index ISR of the three algorithms AV The lower the separation effect, i.e. the better. Gradient learning-basedHas similar separation performance as the algorithm based on Newton method, and the average interference signal ratio ISR of their separated signals AV 15-20dB higher than the decoupling IVA algorithm proposed in the present invention. It can also be seen from FIG. 4 that as the sample length in the dataset increases, the number of datasets versus the split ISR AV The performance impact is getting smaller and smaller.
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 (5)
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.
2. The non-orthogonal limited convolution blind separation method according to claim 1, wherein said process of receiving a mixed signal comprises:
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 nth sensor transmission channel, and P is the tap order of the channel impulse response.
3. The non-orthogonal limited convolution blind separation method according to claim 2, wherein said converting the time domain convolution problem to an IVA problem comprises:
for a perception signalPerforming short-time Fourier transform to obtain frequency domain signal
Wherein omega k =2pi (K-1)/K, k=1, 2, …, K, 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 function->Length of (a) compared to channel impulse response a nj (p) the order of (c) is large enough that the convolution mixing problem in the time domain will exhibit instantaneous mixing in the frequency domain, as shown in the formula
Wherein the method comprises the steps ofIs the channel impulse response a nj (p) value at frequency bin k, ">Is the source signal->The kth frequency point value in the kth 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.
4. The method for blind separation of convolution without orthogonal limitation according to claim 3, 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 given by the formula, and the nonlinear function for approximating the probability density function of the source signal is G:the concrete expression form is
According to the matrix optimization method given by the method, the separation matrix W of the kth frequency point [k] The update mode of the nth row element 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 log|1+Deltav H e n The second order Taylor series expansion of the equation gives a change in the cost function that can be approximated as
Wherein the method comprises the steps of And->Respectively is G (|) y n,t || 2 ) About->First 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 requirementMust 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 signal->Converging to the source signal->Matrix D 0 And D 1 Are all diagonal arrays, respectively corresponding to D in the process of updating algorithm 0 And D 1 To make the following approximation
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 is 0,i And d 1,i Respectively is a 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
d 0,i ＝max[d 0,i ,(1+α)|d 1,i ] (14)
Where α is a very small positive constant, typically α=10 -6 The method comprises the steps of carrying out a first treatment on the surface of the The update rule of the ith element of the vector Deltav is
5. The orthogonal-free convolution blind separation method according to claim 4, wherein the matrix optimization method is a Householder transformation-based matrix optimization method, 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 matrixIn which I is an N identity matrix, u and v are two vectors of size N1 to be optimized,/are updated until convergence>Representing a transpose operation, which is a real number when the vector elements are real numbers, equivalent to () T The method comprises the steps of carrying out a first treatment on the surface of the When the vector element is complex, it is complex conjugate transpose, equivalent to ( H The method comprises the steps of carrying out a first treatment on the surface of the When->When v+.0, this transformation is a Householder reflection; />The characteristic values 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 as
One nonsingular matrix can be converted into another arbitrary nonsingular matrix through N times of elementary reflections.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310862717.6A CN116866123B (en) | 2023-07-13 | 2023-07-13 | Convolution blind separation method without orthogonal limitation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310862717.6A CN116866123B (en) | 2023-07-13 | 2023-07-13 | Convolution blind separation method without orthogonal limitation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116866123A true CN116866123A (en) | 2023-10-10 |
| CN116866123B CN116866123B (en) | 2024-04-30 |
Family
ID=88223139
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310862717.6A Active CN116866123B (en) | 2023-07-13 | 2023-07-13 | Convolution blind separation method without orthogonal limitation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116866123B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070058737A1 (en) * | 2005-09-11 | 2007-03-15 | In-Seon Jang | Convolutive blind source separation using relative optimization |
| 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 |
-
2023
- 2023-07-13 CN CN202310862717.6A patent/CN116866123B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070058737A1 (en) * | 2005-09-11 | 2007-03-15 | In-Seon Jang | Convolutive blind source separation using relative optimization |
| 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 |
|---|
| 丁文春等: "基于非正交联合对角化的自干扰信号消除", 通信技术, vol. 50, no. 11 * |
| 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, no. 09 * |
| 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, no. 09, 20 June 2018 (2018-06-20) * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116866123B (en) | 2024-04-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wu et al. | Kernel recursive maximum correntropy | |
| Wiesel et al. | Time varying autoregressive moving average models for covariance estimation | |
| Buchner et al. | A generalization of a class of blind source separation algorithms for convolutive mixtures | |
| Ribeiro et al. | Identification of separable systems using trilinear filtering | |
| Lu et al. | Collaborative adaptive Volterra filters for nonlinear system identification in α-stable noise environments | |
| Faiz et al. | Analysis of the sign regressor least mean fourth adaptive algorithm | |
| CN116866123B (en) | Convolution blind separation method without orthogonal limitation | |
| Doukopoulos et al. | The fast data projection method for stable subspace tracking | |
| Mei et al. | Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices | |
| CN109474258B (en) | Nuclear parameter optimization method of random Fourier feature kernel LMS (least mean square) based on nuclear polarization strategy | |
| CN109217844A (en) | Hyperparameter optimization method based on the random Fourier's feature core LMS of pre-training | |
| CN102227096A (en) | Identification method for variable step-size least mean P-norm system in non-Gaussian environment | |
| Zhang et al. | Fast nonunitary joint block diagonalization with degenerate solution elimination for convolutive blind source separation | |
| Zhang et al. | Kernel estimation of truncated volterra filter model based on dfp technique and its application to chaotic time series prediction | |
| Waheed et al. | Blind source recovery: A framework in the state space | |
| Zheng‐hong et al. | Blind adaptive preprocessing to multichannel feedfoward active noise control system | |
| Li et al. | A convex combination LMS algorithm based on Krylov subspace transform | |
| Lawal et al. | Blind adaptive channel estimation using structure subspace tracking | |
| Al-Shabili et al. | Adaptive sparsity tradeoff for ℓ 1-constraint NLMS algorithm | |
| Rahman et al. | A unified analysis of proposed wavelet transform domain LMS-algorithm for ARMA process | |
| Abadi et al. | Family of affine projection adaptive filters with selective partial updates and selective regressors | |
| Turan et al. | A block LMS-type algorithm with a function controlled variable step-size for sparse system identification | |
| CN115841806A (en) | Transform domain robust adaptive filtering method for system identification | |
| Shao et al. | A study and comparison of different sparse Bayesian learning algorithms in DOA estimation | |
| Tang et al. | Noisy blind source separation based on adaptive noise removal |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |