CN104332161B - It is a kind of that blind discrimination method is determined based on reception priori and the deficient of single source point detection - Google Patents
It is a kind of that blind discrimination method is determined based on reception priori and the deficient of single source point detection Download PDFInfo
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Abstract
Blind discrimination method is determined based on reception priori and the deficient of single source point detection the invention discloses a kind of, the prior information for combining signal mixed process carries out single source time frequency point detection, closer to practical object, has higher accuracy of detection；In actual calculating process, the mixed signal using first and second array elements is only needed once to be clustered computing, estimate the second row element in hybrid matrix, you can the reconstruct to whole hybrid matrix is realized according to prior information, computational efficiency is improved while estimated accuracy is improved.
Description
Technical Field
The invention relates to a blind separation problem of multi-signal mixing, in particular to an underdetermined blind identification method based on receiving prior and single-source point detection.
Background
In reality, the signal collected by us is not pure, and other interference signals and noise are mixed. The Blind Source Separation (BSS) technique can be described simply as: when the transmission channel is unknown, each unknown source signal is separated or estimated from the output signal of only one sensor array or transducer. "blind" has two layers meaning that the original signal to be estimated cannot be observed directly and it is unknown how the observed signal is mixed from the original signals. The blind source separation technology is a new research direction in the modern signal processing field, and has a solid theoretical basis, for example, independent Component Analysis (ICA) is a main method for solving the blind source separation problem. In reality, however, the number of signals to be separated is very likely to be larger than the number of observed mixed signals, and the Blind Source Separation at this time is called Underdetermined Blind Source Separation (UBSS). At present, a two-step method is mainly adopted for solving the underdetermined blind source separation problem, namely, a mixed matrix is firstly estimated, and then the separation of source signals is realized by the mixed signals and the estimated mixed matrix, and the corresponding difficulties are mainly reflected in two aspects: firstly, estimating a mixing matrix under an underdetermined condition; second, even if the mixing matrix has been estimated, the separation of signals under underdetermined conditions is still difficult to solve due to the model of the ill-conditioned condition, especially under conditions where the source signals are not sufficiently sparse.
The invention content is as follows:
the invention aims to solve the defects of the background technology, and provides an underdetermined blind identification method based on receiving prior and single-source point detection.
In order to solve the technical problems, the technical scheme of the invention is as follows:
an underdetermined blind identification method based on receiving prior and single source point detection is characterized by comprising the following steps: the method comprises the following steps that firstly, a uniform linear array antenna is used for receiving mixed signals and carrying out time-frequency transformation on the mixed signals to construct a time-frequency domain blind source separation model; step two, extracting prior information of the mixed matrix according to the time-frequency domain blind source separation model obtained in the step one; deducing a judgment standard of the single-source time frequency point according to the prior information; step four, detecting single-source time-frequency points of the time-frequency domain according to a judgment standard; step five, calculating data pairs corresponding to the detected single-source time-frequency points, automatically clustering the data pairs by adopting a coacervation hierarchical clustering method, and estimating a second row element value of the mixing matrix by utilizing a clustering center; and step six, according to the special structure of the mixed matrix shown by the prior information obtained in the step two and the second row element value of the mixed matrix obtained in the step four, realizing the reconstruction of all elements of the mixed matrix and finishing the underdetermined blind identification of the mixed matrix.
Preferably, the specific steps of step one include: 11 Receive N narrow-band signals s with a uniform linear array antenna of M elements n (t), the mixed signal received by the mth array element isWherein e represents a natural constant, j represents a complex number, M =1,2, \ 8230;, M, f n Is a signal s n Carrier frequency of (t), g m (t) is zero-mean additive white Gaussian noise, τ mn ＝(m-1)dcosφ n C is the time delay of the mth array element for receiving the nth source signal, d is the array element spacing, phi n Is the source signal angle of incidence; 12 Mixed signal received by mth array elementConversion into a matrix form x (t) = As (t) + g (t), x (t) = [ x = x 1 (t),…,x M (t)] T ，s(t)＝[s 1 (t),…,s N (t)] T And g (t) = [ g = 1 (t),…,g M (t)] T Respectively, the mix signal, the source signal and the noise.Is a complex-valued hybrid matrix with elements of13 Performing Fourier transform on two sides of X (t) = As (t) + G (t) simultaneously to construct a time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f), wherein X (t, f) = [ X = 1 (t,f),…,X M (t,f)] T ，S(t,f)＝[S 1 (t,f),…,S N (t,f)] T 。
Preferably, the second step is to receive the delay τ of the nth source signal by the mth array element according to the time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) obtained in the steps 11) to 13) mn ＝(m-1)dcosφ n C and elements of the mixing matrixWriting a mixing matrix intoThe prior information of the mixing matrix A can be summarized as
Preferably, step three includes the steps of: 31 Let a = [ b ]) ignoring noise terms in frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) 1 ,b 2 ,…,b N ]To obtain X (t, f) = AS (t, f) = b 1 S 1 (t,f)+b 2 S 2 (t,f)+…+b N S N (t, f); 32 Let X (t, f) be at a time-frequency point (t) 1 ,f 1 ) Is that only the signal s appears n (t) single-source time-frequency point to obtain X (t) 1 ,f 1 )＝b n S n (t 1 ,f 1 ) Wherein b is n ＝[1,A 2,n ,A 3,n ,…,A M,n ] T (ii) a 33 A priori information of the combined mixing matrix A) is obtainedLet A m,n ＝R m,n +jI m,n Separately calculate X m (t 1 ,f 1 )，S n (t 1 ,f 1 ) And A m,n To obtain complex calculated forms thereofAnd respectively and correspondingly equalizing the real part numerical value and the imaginary part numerical value on two sides of the equation to obtain an equation set:
34 Solving the system of equations obtained in step 33) based on the prior information of the mixing matrix A to obtainFurther written in the form of matrix operations35 Each single source time-frequency point detection standard formula isThe value range of the parameter epsilon is 0.0001-0.01.
Preferably, the fourth step includes: firstly, a time-frequency domain signal X in a time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) of a time-frequency domain representation matrix is extracted 1 (t, f) and X 2 (t, f), then calculating the time-frequency domain signal X by using the formula of the single-source time-frequency point detection standard 1 (t, f) and X 2 And (f) each point in (t, f) satisfies the single-source time frequency point detection standard formula, namely the single-source time frequency point.
Preferably, step five includes: using formulasCalculating data pairs corresponding to the single-source time frequency points; automatically clustering the data pairs by adopting a clustering method to obtain a clustering center; the second row of elements in the mixing matrix is estimated.
Preferably, the clustering method is an improved aggregation level clustering method, whether two classes are merged and clustering is completed is judged by setting a minimum Euclidean distance threshold d _ threshold between the classes, a threshold N _ threshold is set, and the class with the number of elements larger than the threshold N _ threshold in the classes is selected as a final class.
The invention has the beneficial effects that: the prior information in the signal mixing process is integrated to carry out single-source time frequency point detection, so that the method is closer to an actual object and has higher detection precision; in the actual calculation process, only one clustering operation needs to be performed by using the mixed signals of the first array element and the second array element to estimate the second row element in the mixed matrix, so that the reconstruction of the whole mixed matrix can be realized according to the prior information, and the calculation efficiency is improved while the estimation precision is improved.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention
FIG. 2 is a diagram illustrating the determination of inter-class distance threshold in the agglomerative hierarchical clustering algorithm in accordance with an embodiment of the present invention
FIG. 3 is a pre-clustering single-source point distribution diagram illustrating the effect of mixture matrix element estimation by agglomerative hierarchy clustering in accordance with an embodiment of the present invention,
FIG. 4 is a step-by-step plot of clustered single-source points for the effect of mixed matrix element estimation by agglomerative hierarchical clustering in accordance with an embodiment of the present invention,
FIG. 5 is a time domain waveform diagram of four source signals showing the effect of underdetermined blind separation on speech signals according to an embodiment of the present invention,
FIG. 6 is a time domain waveform diagram of three mixed signals showing the effect of underdetermined blind separation on speech signals according to an embodiment of the present invention,
FIG. 7 is a diagram of the time domain waveforms of signals obtained from the separation of the underdetermined blind separation effect of speech signals according to an embodiment of the present invention,
figure 8 is a comparison graph of the performance of the hybrid matrix estimation according to the embodiment of the present invention,
FIG. 9 is a graph comparing source signal separation performance according to an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The method comprises the following steps that firstly, a uniform linear array antenna is used for receiving mixed signals and carrying out time-frequency transformation on the mixed signals to construct a time-frequency domain blind source separation model;
blind source separation most studies separation under linear mixing conditions. Linear mixing can be further divided into linear instantaneous mixing, linear delay mixing and linear convolution mixing, depending on the delay or reflection of the source signal to the different receiving array elements. In this embodiment, a Linear delay hybrid model is considered, and a Uniform Linear array Antenna (ULA) with M elements is used to receive N narrowband signals s n (t) (if real, converted to analytic signal by Hilbert transform), N>, M, as shown in FIG. 7.
11 Receive N narrowband signals s with a uniform linear array antenna of M elements n (t), then the mixed signal received by the mth array element isWhere e denotes a natural constant and j denotes a complex number (imaginary unit), i.e.m＝1,2,…,M，f n Is a signal s n Carrier frequency of (t), g m (t) is zero-mean additive white Gaussian noise, τ mn ＝(m-1)dcosφ n C is the time delay of the mth array element for receiving the nth source signal, d is the array element spacing, phi n Is the source signal incident angle;
12 Mixed signal received by mth array elementConversion into a matrix form x (t) = As (t) + g (t), x (t) = [ x = x 1 (t),…,x M (t)] T ，s(t)＝[s 1 (t),…,s N (t)] T And g (t) = [ g = 1 (t),…,g M (t)] T Respectively, the mix signal, the source signal and the noise.Is a complex-valued hybrid matrix with elements ofThe purpose of blind source separation is to estimate the unknown N source signals using only M hybrid signals.
13 In this embodiment, short-Time Fourier Transform (STFT) is used to perform Fourier Transform on both sides of X (t) = As (t) + G (t), and the Time-frequency domain blind source separation model X (t, f) = As (t, f) + G (t, f) is obtained by fully utilizing the sparsity of the signal, where X (t, f) = [ X, X = X 1 (t,f),…,X M (t,f)] T ，S(t,f)＝[S 1 (t,f),…,S N (t,f)] T 。
Step two, extracting prior information of a mixed matrix according to the time-frequency domain blind source separation model obtained in the step one;
extracting a priori information of an analyzed object is an important means for improving the performance of the algorithm in practice. The so-called a priori information is derived from the analytical extraction of the source signal, whereas under the premise of "blind" separation, we assume that no a priori information of the source signal and the mixing process can be obtained. Therefore, the embodiment starts from the mixed signal receiving end, extracts the prior information from the receiving antenna parameters predicted at the receiving end, and assists in performing single source point detection.
According to the time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) obtained in the steps 11) to 13), and the time delay tau of the mth array element for receiving the nth source signal mn ＝(m-1)dcosφ n C and elements of the mixing matrixWriting a mixing matrix into
Wherein the column vectors correspond to N source signals from different directions, i.e. b n (φ n )＝[1,A 2,n ,A 3,n ,…,A M,n ] T Memory for recordingIs the element of the mth row and nth column of the mixing matrix. The first row elements of the mixing matrix are all 1, the remaining elements are complex numbers modulo 1, and the values of each column element exhibit a specific relationship.
The prior information of the mixing matrix a can be summarized as:
the purpose of the mixed matrix estimation is to calculate all the elements in A, and from the summarized prior information, A is m,n (m is more than or equal to 3) can be directly prepared from A 2,n And (4) calculating. Thus, the problem can be simplified to element A of line 2 in A 2,n (N is more than or equal to 1 and less than or equal to N).
Deducing a judgment standard of the single-source time frequency point according to the prior information;
the single source point refers to that only a single source signal appears at the time-frequency point in the time-frequency domain. The underdetermined mixed matrix estimation algorithm based on single-source point detection fully utilizes the sparse characteristic of mixed signals in a time-frequency domain. In order to be able to estimate the mixing matrix, the present embodiment assumes that the source signal and the mixing matrix satisfy the following condition:
assume that 1: any mxm sub-matrix of the mixing matrix a is non-singular. This assumption guarantees the feasibility of the hybrid matrix estimation algorithm and subspace projection method signal separation proposed herein, which was achieved in experiments by assuming that the source signals come from different directions. Assume 2: all source signals in the mixed signal are not completely mixed, and a single-source time frequency point exists.
31 Let a = [ b ]) ignoring noise terms in frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) 1 ,b 2 ,…,b N ]Obtaining X (t, f) = AS (t, f) = b 1 S 1 (t,f)+b 2 S 2 (t,f)+…+b N S N (t,f)；
32 Let X (t, f) be at a time-frequency point (t) 1 ,f 1 ) Is that only signal s appears n (t) single-source time-frequency point to obtain X (t) 1 ,f 1 )＝b n S n (t 1 ,f 1 ) Wherein b is n ＝[1,A 2,n ,A 3,n ,…,A M,n ] T ；
33 Obtained by combining the prior information of the mixing matrix ALet A be m,n ＝R m,n +jI m,n Separately calculate X m (t 1 ,f 1 )，S n (t 1 ,f 1 ) And A m,n To obtain complex computed forms thereofAnd respectively and correspondingly equalizing the real part numerical value and the imaginary part numerical value on two sides of the equation to obtain an equation set:
34 Solving the system of equations obtained in step 33) according to the prior information of the mixing matrix A to obtainFurther written in the form of matrix operations
As can be seen from the above derivation, each single-source time-frequency point corresponds to a data pair [ R ] m,n ,I m,n ] T And in the ideal case, R m,n 2 +I m,n 2 =1. However, due to the presence of noise and the effect of calculation errors, R m,n 2 +I m,n 2 The value of (c) is not necessarily exactly equal to 1, and more likely very close to 1.
35 Each single source time-frequency point detection standard formula isThe value range of the parameter epsilon is 0.0001-0.01, | | | · | | non-woven cells 2 The 2 norm of the matrix is calculated. The single-source time-frequency point detection standard shown in the above formula is applicable to linear time delay mixed models of narrow-band and broadband source signals.
Step four, detecting single-source time-frequency points of the time-frequency domain according to the judgment standard;
firstly, extracting a time-frequency domain signal X in a time-frequency domain representation X (t, f) of a mixed signal matrix in the time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) 1 (t, f) and X 2 (t, f), then calculating the time-frequency domain signal X by using the formula of the single-source time-frequency point detection standard 1 (t, f) and X 2 And (t, f) each point in the (t, f) meets the single-source time-frequency point detection standard formula, namely the single-source time-frequency point.
Step five, calculating data pairs corresponding to the detected single-source time-frequency points, automatically clustering the data pairs by adopting a coacervation hierarchical clustering method, and estimating a second row element value of the mixing matrix by utilizing a clustering center;
each single-source time-frequency point corresponds to a data pair R m,n ,I m,n ] T Using the formulaCalculating data pairs corresponding to the single-source time frequency points; automatically clustering the data pairs by adopting a clustering method to obtain a clustering center; the second row of elements in the mixing matrix is estimated.
The clustering method is an improved coacervation hierarchical clustering method, whether two classes are combined or not and whether clustering is finished or not are judged by setting a minimum Euclidean distance threshold d _ threshold between the classes, a threshold N _ threshold is set, and the class with the number of elements larger than the threshold N _ threshold in the classes is selected as a final class.
And step six, according to the special structure of the mixed matrix shown by the prior information obtained in the step two and the second row element value of the mixed matrix obtained in the step four, realizing the reconstruction of all elements of the mixed matrix and finishing the underdetermined blind identification of the mixed matrix.
After the detection of the single-source time-frequency points is finished, each single-source time-frequency point is calculated to obtain a data pair R m,n ,I m,n ] T Theoretically, the element in the corresponding mixing matrix isDue to the fact thatIs a complex number modulo 1 that will be distributed on the same unit circle when the x and y coordinates are set to real and imaginary parts, respectively. Because the incoming wave directions of all source signals are different, the positions of elements in all column vectors of the corresponding mixing matrix distributed on the unit circle are also different, but obvious clustering characteristics are formed in different directions, different data pairs can be separated through a clustering algorithm to obtain a clustering center, and the final mixing is obtained through calculationElements in a matrixA can be known according to prior information m,n ＝(A 2,n ) m-1 (3M M) so that only the mixed signal x needs to be used in the actual calculation process 1 (t) and x 2 (t) time-frequency domain signal X 1 (t, f) and X 2 (t, f) performing a single-source point detection box clustering operation to estimate the second row elements in the mixing matrixAnd (4) finishing. The final mixing matrix may be reconstructed as follows:
the embodiment clusters the single source points by using an improved agglomerative hierarchical clustering method. By "clustering", it is meant that each point to be clustered is individually treated as a class during cluster initialization, and two closest classes are merged at each step. Whether two classes are merged and whether clustering is finished are judged by setting a minimum Euclidean distance threshold (d _ threshold) between the classes. The number of the finally obtained classes is usually larger than the actual number of the source signals, but the center of the actual class has obvious advantages in number, and the classes with the number of elements larger than a threshold (N _ threshold) in the classes are selected as the final classes by setting a proper threshold, so that the estimation of the number of the sources is realized while clustering. The benefit of the agglomerative hierarchical clustering method is that when the clustering is completed, the noise points or the discrete points also respectively occupy one cluster (unless excessive combination is performed), and the discrete classes can be removed by using the threshold value N _ threshold, so that the influence of the discrete classes on the clustering result is reduced.
Suppose U l ＝[R l ,I l ] T (L =1,2, \8230;, L) is a data pair corresponding to the detected L single-source points, defining Q k Are of different classes, each element number being N k I.e. byWhereinDefine the center of class and the distance between classes asAndthe specific steps of the underdetermined mixed matrix blind identification algorithm based on single source point detection and coacervation hierarchical clustering are as follows:
1) For mixed signal x 1 (t) and x 2 (t) performing STFT calculation to obtain a time-frequency domain signal X 1 (t, f) and X 2 (t,f)；
2) Detection of Single Source time-frequency points (t, f) Using equation (12) l And using the single-source time-frequency point to determine the standardCalculating corresponding data pairs U l ＝[R l ,I l ] T (l＝1,2,…,L)；
3) Initializing clusters: setting thresholds d _ threshold and N _ threshold, defining an initial class Q k ＝{U k K =1,2, \ 8230;, L. Calculate the distance between each two classes ask 1 ,k 2 ＝1,2,…L；
4) MergingGet L' new classes, i.e. Q k ,k＝1,2,…,L'；
5) Recalculating the distance between each two classesk 1 ,k 2 ＝12, \8230andL', judgment: if present, isReturning to the step 4) to continue execution, if not existingStep 6) is executed;
6) Q-like with reserved element number larger than N _ threshold n (N =1,2, \8230;, N), the center of each class is calculatedObtaining an estimate of each element of the second row of the mixing matrixFinally according toReconstructing a hybrid matrix
In the experimental process, a voice signal is used as a source signal, and a uniform linear array is used for receiving a mixed signal. Experimental results (fig. 2-9) show that the method proposed in this embodiment can realize the underdetermined blind source separation of linear time delay mixed signals.
The aggregation hierarchical clustering method is actually a self-adaptive clustering process, and the completion of clustering and the determination of target classes are controlled by presetting thresholds d _ threshold and N _ threshold, so that the influence of discrete classes caused by noise or calculation errors is avoided, and the estimation precision of the mixing matrix is improved. Obviously, the selection of the threshold directly determines the performance of the algorithm, when the set distance between the classes is too large, excessive merging of different single source points may be caused, and conversely, if the set distance is too small, the difference between the numbers of various elements is reduced, which is not beneficial to removing scattered points. Fig. 2 shows the effect of setting different d _ threshold on the performance of the hybrid matrix estimation. It can be seen that when the signal-to-noise ratio is low, there is an approximately optimal threshold (about 0.3) to minimize the estimation error of the mixing matrix, and as the signal-to-noise ratio increases, the estimation performance difference of different thresholds becomes smaller, and considering the adaptability to each signal-to-noise ratio level, the minimum inter-class distance threshold d _ threshold is set to 0.3 herein.
FIGS. 3 and 4 show the elements of the mixing matrix after the single-source detection method of the present disclosureReal-imaginary scatter plot of. In fig. 3, only scattered points obtained after single-source detection are adopted, and due to the randomness of noise, calculation errors and other reasons, single-source points are distributed on the whole unit circle, although the accurate clustering characteristic cannot be presented, the distribution density is different, and the distribution is dense near the center of an actual position. Fig. 4 shows the clustering result after clustering by the aggregation level, and the threshold is set, and finally three classes are obtained by automatic screening, most of the scatter points on the unit circle are successfully removed, and the class center obtained by final estimation is basically consistent with the actual center, which indicates that each element of the mixing matrix can be successfully estimated.
On the basis of the estimated mixing matrix, by means of a subspace projection algorithm, assuming that the number of non-zero source signals on any time frequency point does not exceed the number of array elements, calculating a local mixing matrix of the time frequency point, and then realizing underdetermined blind source separation through matrix inversion. Fig. 5 to 7 show the effect of underdetermined blind source separation on speech signals according to the present invention, fig. 5 shows four source signals, fig. 6 shows three mixed signals, and fig. 7 shows the separated signals. Experimental results show that the three mixed signals can be used for accurately separating the four source signals, and the signals obtained by separation are basically consistent with the source signal waveforms and have high precision.
The invention further studies the separation effect of the algorithm and the performance of the algorithm in different signal-to-noise ratio environments, and compares the two methods with two traditional methods (TIFROM and h.li). Fig. 8 and 9 show that the proposed algorithm can accurately estimate the complex mixing matrix, especially with better performance in lower signal-to-noise ratio environments. In particular, the estimation error of the mixing matrix becomes smaller as the signal-to-noise ratio increases. This embodiment is generally superior to the TIFROM algorithm, while better performance can be obtained at signal-to-noise ratios below 30dB compared to the h.li hybrid matrix estimation.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (4)
1. An underdetermined blind identification method based on receiving prior and single source point detection is characterized by comprising the following steps:
the method comprises the following steps that firstly, a uniform linear array antenna is used for receiving mixed signals and carrying out time-frequency transformation on the mixed signals to construct a time-frequency domain blind source separation model;
step two, extracting prior information of a mixed matrix according to the time-frequency domain blind source separation model obtained in the step one;
deducing a judgment standard of the single-source time frequency point according to the prior information;
step four, detecting single-source time-frequency points of the time-frequency domain according to the judgment standard;
step five, calculating data pairs corresponding to the detected single-source time-frequency points, automatically clustering the data pairs by adopting a coacervation hierarchical clustering method, and estimating a second row element value of the mixing matrix by utilizing a clustering center;
step six, according to the special structure of the mixed matrix shown by the prior information obtained in the step two and the second row element value of the mixed matrix obtained in the step five, realizing the reconstruction of all elements of the mixed matrix and completing the underdetermined blind identification of the mixed matrix;
the specific steps of the first step comprise:
11 Receive N narrow-band signals s with a uniform linear array antenna of M elements n (t), then the mixed signal received by the mth array element isWherein e represents a natural constant, j represents a complex number, M =1,2, \8230;, M, f n Is a signal s n Carrier frequency of (t), g m (t) is zero-mean additive white Gaussian noise, τ mn ＝(m-1)dcosφ n C is the time delay of the mth array element for receiving the nth source signal, d is the array element spacing phi n Is the source signal incident angle, c is the speed of light;
12 Mixed signal received by mth array elementConversion into a matrix form x (t) = As (t) + g (t), x (t) = [ x = x 1 (t),…,x M (t)] T ，s(t)＝[s 1 (t),…,s N (t)] T And g (t) = [ g = 1 (t),…,g M (t)] T Respectively, a mixed signal, a source signal and noise, A ∈ C M×N Is a complex-valued hybrid matrix with elements of
13 Performing Fourier transform on two sides of X (t) = As (t) + G (t) simultaneously to construct a time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f), wherein X (t, f) = [ X = [) 1 (t,f),…,X M (t,f)] T ，S(t,f)＝[S 1 (t,f),…,S N (t,f)] T ，G(t,f)＝[g 1 (t,f),…,g M (t,f)] T A is a complex valued mixing matrix;
secondly, according to the time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) obtained in the steps 11) to 13), the time delay tau of the mth array element for receiving the nth source signal mn ＝(m-1)d cosφ n C and elements of the mixing matrixWriting a mixing matrix intoThe prior information of the mixing matrix A can be summarized asThe third step comprises the following steps:
31 Let a = [ b ]) ignoring noise terms in frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) 1 ,b 2 ,…,b N ]To obtain X (t, f) = AS (t, f) = b 1 S 1 (t,f)+b 2 S 2 (t,f)+…+b N S N (t,f)；
32 Let X (t, f) be at the time-frequency point (t) 1 ,f 1 ) Is that only the signal s appears n (t) single source time-frequency point to obtain X (t) 1 ,f 1 )＝b n S n (t 1 ,f 1 ) Wherein b is n ＝[1,A 2,n ,A 3,n ,…,A M,n ] T ；
33 Combining the prior information of the mixing matrix A to obtainLet A be m,n ＝R m,n +jI m,n Separately calculate X m (t 1 ,f 1 )，S n (t 1 ,f 1 ) And A m,n To obtain complex calculated forms thereofAnd respectively and correspondingly equalizing the real part numerical value and the imaginary part numerical value on two sides of the equation to obtain an equation set:
34 Solving the system of equations obtained in step 33) according to the prior information of the mixing matrix A to obtainFurther, the method can be used for preparing a novel materialWritten in the form of matrix operations
35 Each single source time-frequency point detection standard formula isThe value range of the parameter epsilon is 0.0001-0.01.
2. The underdetermined blind identification method based on the receive prior and the single source point detection as claimed in claim 1, wherein said step four comprises: firstly, extracting a time-frequency domain signal X in a time-frequency domain representation X (t, f) of a mixed signal matrix in the time-frequency domain blind source separation model X (t, f) = AS (t, f) + G (t, f) 1 (t, f) and X 2 (t, f), then calculating the time-frequency domain signal X by using the formula of the single-source time-frequency point detection standard 1 (t, f) and X 2 And (t, f) each point in the (t, f) meets the single-source time-frequency point detection standard formula, namely the single-source time-frequency point.
3. The underdetermined blind identification method based on the receive prior and the single source point detection as claimed in claim 2, wherein said step five comprises: using formulasCalculating a data pair corresponding to each single-source time frequency point; automatically clustering the data pairs by adopting a clustering method to obtain a clustering center; the second row of elements in the mixing matrix is estimated.
4. The underdetermined blind identification method based on the receive prior and the single source point detection as claimed in claim 3, wherein: the clustering method is an improved aggregation hierarchical clustering method, whether two classes are combined or not and whether clustering is completed or not are judged by setting a minimum Euclidean distance threshold value d _ threshold between the classes, a threshold value N _ threshold is set, and the class with the number of elements larger than the threshold value N _ threshold in the classes is selected as a final class.
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| CN105910701B (en) * | 2016-04-15 | 2019-04-30 | 天津大学 | Characteristic of rotating machines vibration signal blind separating method and device are corrected based on short sample spectra |
| CN106060834B (en) * | 2016-07-26 | 2017-08-01 | 中国人民解放军理工大学 | A kind of design method for the wireless communication system for improving the availability of frequency spectrum |
| CN108108666B (en) * | 2017-11-30 | 2020-09-04 | 电子信息系统复杂电磁环境效应国家重点实验室 | Hybrid matrix estimation method based on wavelet analysis and time-frequency single-source detection |
| CN110060698A (en) * | 2019-04-11 | 2019-07-26 | 哈尔滨工程大学 | A kind of voice signal hybrid matrix estimation method based on improvement potential function |
| CN110336574B (en) * | 2019-07-11 | 2021-02-02 | 中国人民解放军战略支援部队信息工程大学 | Method and device for recovering source signals |
| CN116776108A (en) * | 2023-06-14 | 2023-09-19 | 中国人民解放军空军预警学院 | Underdetermined combined blind source separation method and system based on third-order cumulant and tensor decomposition |
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