CN116866122B - Blind separation method for interference-containing information of transformation domain signal enhancement - Google Patents
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Abstract
The invention provides a blind separation method for signal enhancement containing noise in a transform domain, which uses the energy aggregation characteristic of the signal after decomposition and transformation to select a signal segment with more concentrated energy as an analysis object, and the signal-to-noise ratio reaches a higher level, so that a separation matrix can be well estimated, and further, the source signal separation is realized. The method can effectively reduce the influence of singular values on the separation result, and the model parameters are less and the fitting phenomenon is not easy to occur. The method solves the technical problems that in the prior art, the model parameters are more, the algorithm is more complex, the model parameters are more sensitive to initial parameters, fitting is easy to pass, and the like.
Description
Technical Field
The invention relates to the technical field of wireless communication and communication anti-interference, in particular to a blind separation method for interference-containing information with enhanced transform domain signals.
Background
Blind source separation is a research hot spot in the field of signal processing in recent years, and can separate mixed signals under the condition that the parameters of a source signal and the parameters of a mixed system are unknown or a small amount of priori information is known, so that effective estimation of an original signal is obtained. Because the blind source separation technology has no special requirements on the power and frequency characteristics of signals, a plurality of expert students in a plurality of attractive professional fields research the blind source separation technology, and the blind source separation technology is widely applied to a plurality of fields such as voice signal processing, image signal processing, communication signal processing, medical signal processing and the like.
According to the relation between the number of source signals and the number of receiving sensors, the mixing model can be divided into underdetermined mixing (the number of source signals is greater than the number of receiving sensors), adaptive mixing (the number of source signals is equal to the number of receiving sensors) and overdetermined mixing (the number of source signals is lower than the number of receiving sensors) models, and according to the transmission response characteristic of a mixing channel, the mixing mode can be divided into linear instantaneous mixing and convolution mixing. Regardless of the hybrid model, current blind source separation theory is mostly based on independent component analysis. However, prior art analysis is a hybrid model without noise, and these algorithms are relatively sensitive to noise. In practical signal processing applications, noise is unavoidable. Thus, to make blind source separation techniques practical, one must consider the blind source separation problem in the presence of noise.
There are two ideas of research regarding blind source separation in noisy situations. One is to eliminate or suppress noise in the received signal by adopting a noise reduction technology, improve the signal-to-noise ratio of the received signal, and then perform blind source separation on the noise-reduced received signal with high signal-to-noise ratio. There are mainly two ways in concrete implementation. Firstly, the noise-containing blind separation problem is solved by utilizing the characteristic that the high-order cumulant of Gaussian distribution is zero. However, since the higher order cumulants are relatively sensitive to singular values, the stability of such methods is not high. The second implementation mode is to perform statistical model modeling on the original signal and the received signal, incorporate noise into the modeling process, and then estimate model parameters and recover the source signal by using a Bayesian inference mode. Generally, such implementations have more model parameters, are more complex algorithms, are more sensitive to initial parameters, and are easier to overfit.
Disclosure of Invention
Considering that the source signals are mostly energy-dispersed time domain signals, the energy-dispersed time domain signals are decomposed and transformed to obtain energy-concentrated transform domain signals. The invention provides a blind separation method of a signal enhancement with noise in a transform domain, which utilizes the energy aggregation characteristic of the signal after decomposition and transformation to select a signal segment with more concentrated energy as an analysis object, and at the moment, the signal to noise ratio reaches a higher level, so that a separation matrix can be well estimated, and further, the source signal separation is realized. The method can effectively reduce the influence of singular values on the separation result, and the model parameters are less and the fitting phenomenon is not easy to occur. Thereby solving the aforementioned problems existing in the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a method for blind separation of a transform domain signal enhanced noise-containing signal, comprising the steps of:
s1, receiving a signal R (t);
s2, decomposing and transforming;
s3, intercepting a signal energy concentration domain;
s4, estimating a separation matrix;
s5, signal separation
Preferably, the process of receiving the signal includes:
is provided with N user signals { s } j (t), j=1, 2, …, N }, the receiving end has M antennas, and the j receiving antenna receives the signal r i (t),i＝1,2,…,M；
The mathematical model of the transmission system is expressed as
R(t)＝HS(t)+n(t) (1)
Wherein S (t) = [ S ] 1 (t)s 2 (t)…s N (t)] T H is a channel transmission matrix with the size of MxN, and the element H thereof ij (i=1, 2, …, M; j=1, 2, …, N) represents the channel transmission attenuation coefficient of the ith antenna receiving the jth source signal.
Preferably, the process of decomposing the transformation includes:
selecting a set of decomposition transformation basesThen obtaining a transformed signal by computing the projection of the signal onto the decomposition transformation matrix
The signal decomposition transformation method has linear characteristics, expressed as:
if it isThen
The received signal in the model type (1) is decomposed and converted into
After the signal is subjected to linear decomposition and transformation, the signal still has the same signal transmission model as the signal in the transformation domain, and the transmission matrix is kept unchanged before and after the signal transformation; i.e. the separation matrix of the transform domain signal pattern (4) is also the separation matrix of the original signal pattern (1).
Preferably, the process of intercepting the signal energy concentration domain includes:
let the observed signal be f (t) =s (t) +n (t), where s (t) is the signal and n (t) is gaussian white noise; firstly, performing discrete sampling on f (t) to obtain M-point discrete signals f (M), wherein m=0, 1, …, M-1, and the discrete wavelet transformation is as follows
Wherein ψ (x) is a wavelet base, j is a scaling factor, k is a panning factor, and W (j, k) is a wavelet coefficient; recursive implementation method for obtaining wavelet transformation by means of double-scale equation
Wherein, l (·) and h (·) are respectively low-pass and high-pass filters corresponding to the wavelet basis ψ (x), W l (j, k) is an approximation coefficient, W h (j, k) is a detail coefficient, and its corresponding reconstruction formula is
Wherein,and->The conjugate transposes of l (-) and h (-) are the coefficients of the reconstruction filter bank, W, respectively l (0, k) is a wavelet representation of f (m); j-layer double-scale wavelet decomposition is carried out on the signal, and the signal energy is mainly concentrated in W l (J-1,k)；
After three layers of wavelet transformation, the energy of noise is mainly distributed in W h (1, k) and W h In (2, k), the energy of the signal is concentrated at W l In (2, k), the magnitude is large relative to the wavelet coefficient generated by the noise.
Preferably, the process of estimating the separation matrix includes:
is obtained from the formula (1), the formula (5) and the formula (6)
Wherein the method comprises the steps of
Preferably, the signal separationThe process of (1) comprises:
on the basis of decomposing and transforming the spatial signal model type (8), adopting an EASI algorithm; the EASI algorithm adopts mutual information quantity as an objective function, and adopts a natural gradient algorithm to iterate and optimize a separation matrix; the iterative updating processing process of the separation matrix in the algorithm comprises the following steps:
after convergence of the separation matrix B (t), use is made ofThe source signal decomposition parameters in the transformation space can be obtained; and (3) reconstructing a source signal by using a signal reconstruction method in the formula (7).
The beneficial effects of the invention are as follows:
the invention uses the energy aggregation characteristic after signal decomposition and transformation, selects the signal segment with more concentrated energy as the analysis object, and has the signal-to-noise ratio reaching higher level, and can better estimate the separation matrix, thereby realizing the source signal separation. The method can effectively reduce the influence of singular values on the separation result, and the model parameters are less and the fitting phenomenon is not easy to occur. Simulation analysis proves that compared with the existing algorithm, the method provided by the invention has the advantage that the separation precision is greatly improved. The method has better performance than the method of directly separating the signal and then denoising. The bit error rate performance obtained by the wavelet noise reduction treatment of the signal after the signal is treated by the method is consistent with the performance obtained by the method only.
Drawings
Fig. 1 is a hybrid model of a multi-antenna transceiver system in an example of the invention;
FIG. 2 is a flow chart of a signal separation method based on signal decomposition transformation in an example of the invention;
FIG. 3 is a schematic view of three exploded layers of a wavelet in an example of the invention;
FIG. 4 is a graph of the performance of the algorithm separation accuracy under different signal-to-noise conditions in an example of the invention;
fig. 5 is a graph of system bit error rate performance under different snr conditions in an example 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.
Considering that most of source signals are energy-dispersed time domain signals, the energy-dispersed time domain signals are decomposed and transformed to obtain energy-concentrated transform domain signals, the invention provides a blind separation algorithm based on linear decomposition and transformation of the source signals, and the blind separation algorithm utilizes the energy aggregation characteristic of the signal after decomposition and transformation to select signal fragments with concentrated energy as analysis objects, and at the moment, the signal-to-noise ratio reaches a higher level, so that a separation matrix can be well estimated, and further, the source signal separation is realized. The method can effectively reduce the influence of singular values on the separation result, and the model parameters are less and the phenomenon of fitting is not easy to occur.
1. Description of the problem
Assume that there are N user signals { s j (t), j=1, 2, …, N }, the receiving end has M antennas, and the j receiving antenna receives the signal r i (t), i=1, 2, …, M. The system transmission model is shown in fig. 1.
The mathematical model of the transmission system can be expressed as
R(t)＝HS(t)+n(t) (1)
Wherein S (t) = [ S ] 1 (t)s 2 (t)…s N (t)] T H is a channel transmission matrix with the size of MxN, and the element H thereof ij (i=1, 2, …, M; j=1, 2, …, N) represents the channel transmission attenuation coefficient of the ith antenna receiving the jth source signal. The invention considers the situation that M is not less than N, namely the transmission matrix is not under-timed. n (t) = [ n ] 1 (t)n 2 (t)…n M (t)] T Is a noise vector present in the system and is independent of the source signal vector. R (t) = [ x ] 1 (t)x 2 (t)…x M (t)] T Each path of received signal r i (t) all contain N source signals, which interfere with each other, and it is difficult for the receiving end to correctly demodulate the received signal. Therefore, the receiving end needs to design an interference suppression unit to suppress the interference signal, and generally adopts a band-notch filtering or beam forming method to suppress the interference, but when the source signal is in the same frequency and is in the main lobe frequency band of the receiver, the interference suppression unit is used to suppress the interference signalSome interference suppression methods have poor performance. The blind source separation technology can effectively solve the problems because the blind source separation technology has the capability of separating the source signals from the mixed signals under the condition that the channel transmission parameters are unknown and the source signals are unknown. The main work of blind source separation is to design a unmixing system B at the receiving end, so that after the received signal R (t) is processed by the system, the output signal is the effective estimation of the source signal S (t)Wherein B is also called a separation matrix. The traditional blind source separation method is mainly researched aiming at ideal mixing without external noise, is sensitive to the external noise, and channel noise in wireless communication transmission is unavoidable, and certain special communication systems such as satellite communication can also work under the condition of extremely low signal-to-noise ratio. The invention mainly aims to solve the problem of receiving the multi-user multi-antenna system under the condition of low signal to noise ratio.
2. Design concept
The signal decomposition transformation generally selects a group of decomposition transformation basesThe set of bases may be orthogonal or non-orthogonal. Then, the transformed signal is obtained by computing the projection of the signal onto the set of bases
Such signal decomposition transformation methods generally have linear characteristics, which can be expressed as: if it is Then
The received signal in the mixed model type (1) is decomposed and converted into
As can be seen from the above equation, after the signal is subjected to linear decomposition transformation, the signal still has the same signal transmission model as that of equation (1) in the transformation domain, and the transmission matrix remains unchanged before and after the signal transformation. Therefore, the separation matrix of the transform domain signal model (4) is also the separation matrix of the original signal model (1). For some special transformation methods, the time-domain energy-dispersed signal is made to have energy aggregation characteristics in the transform domain, such as wavelet decomposition transformation, DCT transformation. The energy aggregation characteristic of the signals in the transformation domain enables the signal-to-noise ratio level of the signals to be higher in the energy aggregation area, and if blind source separation is realized in the area, a separation matrix can be estimated better, and signal separation is realized. The signal processing flow diagram is shown in fig. 2.
3. Scrambling blind separation instance based on wavelet decomposition transformation
Let the observed signal be f (t) =s (t) +n (t), where s (t) is the signal and n (t) is gaussian white noise. Firstly, performing discrete sampling on f (t) to obtain M-point discrete signals f (M), wherein m=0, 1, …, M-1, and the discrete wavelet transformation is as follows
Where ψ (x) is the wavelet base, j is the scaling factor, k is the panning factor, and W (j, k) is the wavelet coefficient. Recursion implementation method for obtaining wavelet transformation by means of double-scale equation in practical application
Wherein, l (·) and h (·) are respectively low-pass and high-pass filters corresponding to the wavelet basis ψ (x), W l (j, k) is nearCoefficient of similarity, W h (j, k) is a detail coefficient, and its corresponding reconstruction formula is
Wherein,and->The conjugate transposes of l (-) and h (-) are the coefficients of the reconstruction filter bank, W, respectively l (0, k) is the wavelet representation of f (m). J-layer double-scale wavelet decomposition is carried out on the signal, and the signal energy is mainly concentrated in W l (J-1, k). FIG. 3 is a schematic representation of three-layer wavelet decomposition of f (m) with dual scale.
After three-layer wavelet transformation in fig. 3, the energy of noise is generally distributed in W h (1, k) and W h In (2, k), the energy of the signal is concentrated at W l In (2, k), the magnitude is large relative to the wavelet coefficient generated by the noise.
Is obtained from the formula (1), the formula (5) and the formula (6)
Wherein the method comprises the steps of
Since the expression (8) corresponds to the expressions (1) and (4), the solution mixing system B obtained by the expression (8) is equivalent to the expression (1). In addition, since the energy of noise is mainly concentratedIn (I)>The main bearing of the signal is signal energy, and the signal mixing model represented by the formula (8) has higher signal-to-noise ratio compared with the formula (1), so that better signal separation effect can be obtained.
On the basis of decomposing and transforming the spatial signal model (8), an EASI algorithm with higher robustness is adopted. The EASI algorithm is referred to as an independence-based alike adaptive separation algorithm. The algorithm adopts mutual information as an objective function, and adopts a natural gradient algorithm to iterate and optimize the separation matrix. The iterative updating process of the separation matrix in the algorithm is as follows.
After convergence of the separation matrix B (t), use is made ofThe source signal decomposition parameters in the transform space are obtained. And (3) reconstructing a source signal by using a signal reconstruction method in the formula (7).
4. Simulation analysis
In the simulation, the signal-to-noise ratio (SNR) is defined as the ratio of the energy of the mixed source signal to the energy of the noise in the observed signal, and the calculation formula is
Wherein, the function var (·) represents the energy of the solution.
In order to verify the effectiveness of the invention, experiments adopt one path of BPSK modulation signal as a communication signal and one path of BPSK signal as an interference signal. The BPSK modulated signal employs a root-raised cosine roll-off shaping filter with a roll-off factor of 0.35 and a symbol rate of 128kbps. Figure 4 shows the signal separation accuracy performance curves of the method proposed by the invention under different signal-to-noise ratio conditions. The first comparison algorithm is a classical ICA algorithm, and the second comparison algorithm is to separate signals by wavelet noise reduction and then a classical ICA method. As can be seen from FIG. 4, the method provided by the invention has a larger improvement in separation accuracy compared with the two comparison algorithms.
Figure 5 shows the performance curves of the bit error rate of the separated signals under different signal to noise ratio conditions. The curve of the solid triangle mark is the error rate curve obtained by adopting the classical ICA algorithm to separate the signals, then carrying out wavelet noise reduction treatment on the separated signals, and demodulating. The curve marked by the broken solid circle is a bit error rate curve obtained by performing wavelet noise reduction on a received signal, performing blind separation on the noise reduced signal, performing wavelet noise reduction on the separated signal, and demodulating. As can be seen from fig. 5, the method proposed by the present invention has better performance than the direct separation signal noise reduction. The bit error rate performance obtained by applying wavelet noise reduction treatment to the signal after being treated by the method is consistent with the performance obtained by using the algorithm only.
By adopting the technical scheme disclosed by the invention, the following beneficial effects are obtained:
the invention uses the energy aggregation characteristic after signal decomposition and transformation, selects the signal segment with more concentrated energy as the analysis object, and has the signal-to-noise ratio reaching higher level, and can better estimate the separation matrix, thereby realizing the source signal separation. The method can effectively reduce the influence of singular values on the separation result, and the model parameters are less and the fitting phenomenon is not easy to occur. Simulation analysis proves that compared with the existing algorithm, the method provided by the invention has the advantage that the separation precision is greatly improved. The method has better performance than the method of directly separating the signal and then denoising. The bit error rate performance obtained by the wavelet noise reduction treatment of the signal after the signal is treated by the method is consistent with the performance obtained by the method only.
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 method for blind separation of a transform domain signal enhanced noise-containing signal, comprising the steps of:
s1, receiving a signal R (t);
s2, decomposing and transforming;
s3, intercepting a signal energy concentration domain;
s4, estimating a separation matrix;
s5, signal separation
The process of intercepting the signal energy concentration domain comprises the following steps:
let the observed signal be f (t) =s (t) +n (t), where s (t) is the signal and n (t) is gaussian white noise; firstly, performing discrete sampling on f (t) to obtain M-point discrete signals f (M), wherein m=0, 1, L and M-1, and the discrete wavelet transformation is as follows
Wherein ψ (x) is a wavelet base, j is a scaling factor, k is a panning factor, and W (j, k) is a wavelet coefficient; recursive implementation method for obtaining wavelet transformation by means of double-scale equation
Wherein, l (·) and h (·) are respectively low-pass and high-pass filters corresponding to the wavelet basis ψ (x), W l (j, k) is an approximation coefficient, W h (j, k) is a detail coefficient, and its corresponding reconstruction formula is
Wherein,and->The conjugate transposes of l (-) and h (-) are the coefficients of the reconstruction filter bank, W, respectively l (0, k) is a wavelet representation of f (m); j-layer double-scale wavelet decomposition is carried out on the signal, and the signal energy is mainly concentrated in W l (J-1,k)；
After three layers of wavelet transformation, the energy of noise is mainly distributed in W h (1, k) and W h In (2, k), the energy of the signal is concentrated at W l In (2, k), the magnitude is large relative to the wavelet coefficient generated by the noise.
2. The method of blind separation of enhanced noise-containing signals of claim 1 wherein said process of receiving signals comprises:
is provided with N user signals { s } j (t), j=1, 2, L, N }, the receiving end has M antennas, and the j receiving antenna receives the signal r i (t),i＝1,2,L,M；
The mathematical model of the transmission system is expressed as
R(t)＝HS(t)+n(t) (1)
Wherein S (t) = [ S ] 1 (t)s 2 (t)L s N (t)] T H is a channel transmission matrix with the size of MxN, and the element H thereof ij (i=1, 2, l, m; j=1, 2, l, n) represents the channel transmission attenuation coefficient of the ith antenna receiving the jth source signal; n (t) = [ n ] 1 (t)n 2 (t)L n M (t)] T Is a noise vector present in the system and is independent of the source signal vector.
3. The method of blind separation of noisy signals with enhanced transform domain signal according to claim 2, wherein said process of decomposing the transform comprises:
selecting a set of decomposition transformation basesThen obtaining transformed signals by calculating the projection of the signals on the decomposition transformation baseNumber (number)
The signal decomposition transformation method has linear characteristics, expressed as:
if it isThen
The received signal in the model type (1) is decomposed and converted into
After the signal is subjected to linear decomposition and transformation, the signal still has the same signal transmission model as the signal in the transformation domain, and the transmission matrix is kept unchanged before and after the signal transformation; i.e. the separation matrix of the transform domain signal pattern (4) is also the separation matrix of the original signal pattern (1).
4. The method of blind separation of noisy signals with enhanced transform domain signal according to claim 1, wherein said process of estimating a separation matrix comprises:
is obtained from the formula (1), the formula (5) and the formula (6)
Wherein the method comprises the steps of
5. The method of blind separation of transform domain signal enhancement with noise according to claim 4, wherein said signal separationThe process of (1) comprises:
on the basis of decomposing and transforming the spatial signal model type (8), adopting an EASI algorithm; the EASI algorithm adopts mutual information quantity as an objective function, and adopts a natural gradient algorithm to iterate and optimize a separation matrix; the iterative updating processing process of the separation matrix in the algorithm comprises the following steps:
after convergence of the separation matrix B (t), use is made ofThe source signal decomposition parameters in the transformation space can be obtained; and (3) reconstructing a source signal by using a signal reconstruction method in the formula (7).
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