CN115086116A - DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method - Google Patents
DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method Download PDFInfo
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Abstract
The invention relates to a sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT, belonging to the technical field of power line communication and comprising the following steps: converting frequency domain signals received by a power line receiving end into a vector matrix form, extracting pilot frequency in the received signals, and combining DWT and DCT to construct an observation matrix and an observation vector; uniformly partitioning the observation matrix; initializing a model; starting with an empty model, and performing block addition to obtain sparse solution vectors on the assumption that all signal blocks are not added into the model; taking the front ng row of the sparse solution vector to carry out DCT and DWT to obtain a channel impulse response vector estimated value, and carrying out zero filling FFT to obtain a channel frequency response vector with the length of N; and the ng-ng + N rows of the obtained sparse solution vector are time domain impulse noise estimation vectors, so that a frequency domain symbol with impulse noise removed is obtained.
Description
Technical Field
The invention belongs to the technical field of power line communication, and relates to a sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT
Background
Power Line Communication (PLC) is a communication method that uses an existing power grid for information transmission. Compared with other communication technologies, the communication technology has the advantages of low cost, wide range, stable operation and the like, so that international standards such as PLC G3, PRIME, Home Plug and IEEE P1901 have been proposed. However, due to the complex power line channel environment, the Noise composition and variation are complex, and especially Impulse Noise (IN) degrades the performance of the conventional channel estimation technique. Therefore, accurate CSI acquisition for PLC systems with IN is crucial.
The traditional estimation method such as the least square algorithm does not consider the noise influence, so that the MSE performance is poor, a large amount of pilots are needed for channel estimation, and the frequency band utilization rate is low because the pilots without any useful information occupy the frequency band in the transmission process. Likewise, the channel estimation scheme based on DFT interpolation improves estimation performance by setting a threshold in the time domain to remove noise, but the threshold is difficult to determine due to the complexity and variability of the power line channel environment.
The compressed sensing technology shows that the original signal can be effectively recovered by using a small number of observation values by utilizing the signal sparsity, which means that accurate channel state information can be obtained by using a small number of pilots. Related research has been carried out on jointly estimating impulse noise and channel of a power line communication system by using a compressed sensing technology. But the PLC impulse response is assumed to have sparse characteristics, and the CS theory is directly applied to the time domain PLC channel model. A great deal of research shows that the PLC channel does not have the sparse characteristic in the time domain or the frequency domain, which means that the method which does not carry out sparse representation on the impulse response of the PLC channel can obtain poor performance. In addition, zero filling is also researched on the tail part of the channel impulse response, so that the channel impulse response vector after zero filling can be approximately considered as a sparse vector, and a Bayesian algorithm is applied to channel estimation, but the complexity of the method can be greatly improved along with the increase of the OFDM symbol length.
Disclosure of Invention
In view of the above, the present invention provides a sparse bayesian power line channel and impulse noise joint estimation method based on discrete wavelet sparse transform DCT and discrete cosine transform DWT.
In order to achieve the purpose, the invention provides the following technical scheme:
a sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT comprises the following steps:
s1: converting the frequency domain signal received by the power line receiving end into a vector matrix form;
s2: extracting a pilot frequency in a received signal;
s3: combining DWT and DCT to construct an observation matrix and an observation vector by the extracted pilot symbols based on a compressed sensing model;
s4: uniformly partitioning the observation matrix;
s5: initializing a compressed sensing estimation model of the power line impulse noise and the channel;
s6: starting with an empty model, and performing block addition on the assumption that all signal blocks are not added into the model; iteratively calculating a covariance matrix, block correlation and a correlation structure matrix each time, updating model parameters, and reconstructing the covariance matrix according to the correlation structure matrix until all covariance matrices are obtained;
s7: when the preset condition is met, ending the circulation of S6 to obtain sparse solution vectors;
s8: taking the front ng row of the sparse solution vector obtained in S7 to carry out DCT and DWT to obtain a channel impulse response vector estimated value, and carrying out zero filling FFT to obtain a channel frequency response vector with the length of N;
s9: and the ng-ng + N rows of the obtained sparse solution vector are time domain impulse noise estimation vectors, so that a frequency domain symbol with impulse noise removed is obtained.
Further, in step S1, the frequency domain signal received by the power line receiving end is converted into a vector matrix form
Y＝diag(X)H+Fi+G (1)
Wherein X ═ X 1 ,X 2 ,...X N ] T Transmitting symbol vectors for the frequency domain, the OFDM frequency domain symbol vectors having a length N, H ═ H 1 ,H 2 ,...,H N ]F is an N-dimensional fourier transform matrix, i represents time-domain impulse noise, where G-Fg represents frequency-domain background noise and is white gaussian noise, and G represents background noise.
Further, in step S2, a set of positions where pilots are inserted in the transmission signal is defined as P, (·) P is a submatrix formed by index-corresponding rows or elements in the set P, and equation (1) is transformed into:
Y P ＝diag(X P )H p +F p i+G p (2)。
further, in step S3, in combination with the time-domain sparsity of impulse noise, the compressed sensing estimation model of power line impulse noise and channel is:
wherein F p,ng Is a Fourier matrix of P × ng, ng being the guard interval length, DCT ng*ng ，DWT ng*ng Is a matrix of ng by ng dimensions; in the formula, ng 1-dimensional vector h is sparsely represented as:
h＝DCT*a (5)
h＝DWT*b (6)
the formula (3) and the formula (4) are expressed as follows:
Y p ＝ΦX+G p (7)
where Φ is the observation matrix.
Further, in step S4, observation matrix Φ is uniformly partitioned into [ Φ ═ Φ 1 ,Φ 2 ,...Φ m ]The block length is 8, the OFDM length is 1024, the ng length is 256, comb-shaped pilot frequencies are arranged, the comb-shaped pilot frequencies are uniformly distributed, and the number of the comb-shaped pilot frequencies is 64.
Further, the initialization in step S5 takes into account the signal-to-noise ratio SNR<20dB, set beta 0.1Y p || 2 ，
η＝10 -4 M means that the observation vector is divided into m blocks of data, which also corresponds to m observation matrixes, phi i I.e. the observation matrix corresponding to the ith block, wherein m observation matrices are provided in total, eta is an algorithm exit condition, beta refers to the noise variance, iterative computation is needed in the algorithm process, and s i ，q i Is a defined intermediate variable used to calculate the cost function.
Further, in step S6, starting with the null model, all signal blocks X are assumed i Adding the blocks into the model without adding the blocks into the model; the set of bases in the model at the K-th iteration is a k Each iteration carries out the following steps:
s61: computing a covariance matrix
Calculating block correlation gamma i ＝1/d i Tr(A i ) Wherein d is i Is a matrix A i And Tr denotes the trace of the matrix. Computing a correlation structure matrix B i ＝A i /r i Reconstruction of
Wherein r is i Representing the variance of the ith block. Until all A's are obtained i And according to a cost function L ═ log | C | + y T C -1 y, where y denotes the measurement vector input by the algorithm, i.e. the OFDM frequency domain symbol at the input pilot, C ═ β -1 I+ΦΓΦ T I represents an identity matrix, and Γ is a matrix formed by a covariance matrix of the observation block matrix. Computing
And obtainSo that Δ L (i) is maximized
Or the index of the observation block matrix that maximizes Δ l (i);
s62: according to
Whether or not to belong to a k Updating sigma-mu s i q i ；
Further, when | | γ is satisfied in step S7 new - γ |/| | γ | < η, jumping out of the cycle of S6, obtaining a sparse solution vector x ═ μ;
in step S9, the ng-ng + N rows of the sparse solution vector are the time domain impulse noise estimation vectors
The frequency domain symbol with impulse noise removed can be obtained as
Further, in step S62, update Σ μ S using the BSBL-FM algorithm i q i The method specifically comprises the following steps:
(1)
the current block is added to the model, and μ new ＝μ-βΣΦ T Φ i μ i ，
Wherein a ＝-βΣΦ T Φ i Σ ii ，
Wherein e i ＝β(Φ i -βΦΣΦ T Φ i ) Wherein e is i ＝β(Φ i -βΦΣΦ T Φ i ) μ is the mean vector of the probability distribution of the output random vector obeys, Σ is the output vector obeysCovariance vector of probability distribution, mu new Mean vector, Σ, of iterative updates in the reference algorithm new Refers to an iteratively updated covariance vector, μ, in an algorithm i Then it is the ith value in the mean vector, Σ a Only defined intermediate variables, in order to express Σ new Update procedure, s inew ，q inew Representing updated s i ，q i For calculating a new cost function. e.g. of the type i Only intermediate variables derived by an algorithm and no physical meaning are used, and q is conveniently represented inew Update procedure of ∑ ii Is the covariance matrix corresponding to the ith block of data for iteratively updating s i ；
(2)
And is
Delete this block from the model and μ new ＝μ+ΔΣβΦ T y，Σ new Σ + Δ Σ, where Δ Σ is ═ Σ i Σ ii -1 Σ i ，
(3)
And is
Reestimating the current block and mu new ＝μ+ΔΣβΦ T y，Σ new ＝Σ+ΔΣ，
The invention has the beneficial effects that: aiming at the defect that the channel impulse response does not directly have the sparse characteristic, the invention provides the sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT, and provides the secondary compression method based on DCT and DWT to sparsely express the channel impulse response, thereby reducing the dimension of the required observation matrix and obtaining better reconstruction performance. In addition, in view of the advantages that the compressed sensing algorithm of the BSBL-FM can effectively recover the original signal only by a small number of observation values and has better re-estimation performance, the BSBL-FM algorithm is applied to channel estimation. Compared with the traditional estimation method, the sparse Bayesian-based channel estimation can obtain an accurate estimation value through a small amount of pilot frequency, and the frequency spectrum utilization rate is improved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
For a better understanding of the objects, aspects and advantages of the present invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of the overall scheme of the present invention;
FIG. 2 is a graph of channel frequency response to which the present invention is directed;
FIG. 3 is a diagram of a channel impulse response referenced by the present invention;
FIG. 4 is a graph of the channel impulse response within ng referenced by the present invention;
fig. 5 is a plot of MSE performance versus the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and embodiments may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
The invention provides a sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT, as shown in figure 1, comprising:
the OFDM frequency domain symbol vector length is N1024, ng is the guard interval length, and is set here to N/4 256. The block length is 8, comb-shaped pilot frequencies are arranged and uniformly distributed, and the number of the comb-shaped pilot frequencies is 64.
S1, converting the frequency domain signals received by the power line receiving end into a vector matrix form;
wherein X ═ X 1 ,X 2 ,...X N ] T Transmitting symbol vectors for the frequency domain, H ═ H 1 ,H 2 ,...,H N ]F is an N-dimensional Fourier transform matrix, i and g respectively represent impulse noise and background noise in a time domain,
representing the hadamard product.
Equation (1) can be written as a matrix-vector product form as follows:
Y＝diag(X)H+Fi+G (2)
where G ═ Fg, represents frequency domain background noise, still gaussian white.
S2, extracting the pilot frequency in the received signal;
defining a set of positions where pilots are inserted in a transmission signal as P, (. cndot.) P is a submatrix formed by corresponding rows or elements of indexes in the set P, and converting the equation (2) into:
Y P ＝diag(X P )H p +F p i+G p (3)
s3, combining with DWT, DCT builds a measuring matrix and an observation vector by the extracted pilot symbols based on a compressed sensing model;
the power line frequency response does not have the sparse characteristic, the prior method assumes that the channel impulse response has the sparse characteristic, and if the channel impulse response is assumed to have the sparse characteristic, the formula (2) can be expressed as follows:
Y P ＝diag(X P )F p,ng h+F p i+G p (4)
in the formula F p,ng Is a Fourier matrix of P × ng, and h is a vector of dimension ng × 1. Considering DCT, the energy compression characteristic of DWT, the h sparsity in equation (4) is expressed as:
h＝DCT*a (5)
h＝DWT*b (6)
then equation 4 can be expressed correspondingly as:
Y P ＝diag(X P )F p,ng DCT ng*ng a+F p i+G p (7)
Y P ＝diag(X P )F p,ng DWT ng*ng b+F p i+G p (8)
where DCT, DWT is a matrix of dimensions ng. The DCT matrix here is represented by the DCT of matlab
The function is obtained, and the DWT matrix is obtained by a discrete wavelet transform matlab program written by an author.
In combination with the time domain sparse characteristic of the impulse noise, the compressed sensing estimation model of the impulse noise of the power line and the channel is as follows:
the above two equations can be expressed as:
Y p ＝ΦX+G p (11)
s4, evenly partitioning the observation matrix phi into phi [ [ phi ] ] 1 ,Φ 2 ,...Φ m ]The block length is 8;
s5, initialization, considering SNR<20dB, set beta 0.1Y p || 2 ，
η＝10 -4 ；
S6, starting with the null model, assuming all signal blocks X i None were added to the model and block additions were made. At this K iteration the set of bases in the model is a k . Each iteration: 1. computing a covariance matrix
Calculating a block correlation gamma i ＝1/d i Tr(A i ) Where di is the dimension of the matrix Ai, here 8, a correlation structure matrix B is calculated i ＝A i /r i Reconstruction of
Until all A's are obtained i . And according to the cost function L ═ log | C | + y T C -1 y, wherein C ═ β -1 I+ΦΓΦ T Calculating
And obtaining a value such that Δ L (i) is maximized
2. According to
Whether or not to belong to a k Updating sigma-mu s i q i ：
(1)
Add the current block into the model, and μ new ＝μ-βΣΦ T Φ i μ i ，
Wherein a ＝-βΣΦ T Φ i Σ ii ，
Wherein e i ＝β(Φ i -βΦΣΦ T Φ i )
(2)
And is
Delete this block from the model and μ new ＝μ+ΔΣβΦ T y，Σ new ＝Σ+ΔΣ，
Wherein Δ Σ ═ Σ i Σ ii -1 Σ i 。
(3)
And is
Reestimating the current block and mu new ＝μ+ΔΣβΦ T y，Σ new ＝Σ+ΔΣ，
S7, when | | | γ is satisfied new - γ |/| | γ | < η, jumping out of the cycle of S6, obtaining a sparse solution vector x ═ μ;
s8, taking the front ng row of the sparse solution vector obtained in S7 to carry out DCT and DWT to obtain the channel impulse response vector estimated value, and carrying out zero filling FFT to obtain the channel frequency response vector with the length of N
S9, the ng-ng + N rows of the obtained sparse solution vector are time domain impulse noise estimation vectors
The frequency domain symbol with impulse noise removed can be obtained as
If the original signal X is known to be sparse or capable of being sparsely represented (the signal is sufficiently sparse in some transform domain), the difficulty of solving the underdetermined equations can be greatly reduced. Therefore, accurate recovery of the original signal is possible on the premise of sparseness of the signal, and thus the premise of sparseness of the original signal is also a necessary condition for CS signal reconstruction.
In compressed-sensing-based signal reconstruction, discrete wavelet sparse transform (DWT) and Discrete Cosine Transform (DCT) are typically used as sparse decomposition bases for signals. However, the DCT and DWT are not studied to be added to the compressed sensing model to obtain better performance in the PLC channel environment. In addition, the DCT transform is also applied to reduce the energy of the high frequency of the PLC channel frequency response, so that the energy is more concentrated on the low frequency, which means that the energy of the channel impulse response can be more concentrated by the DWT and DCT transform, that is, the energy has a sparse characteristic. In the invention, in a signal reconstruction model based on compressed sensing in a PLC channel environment, discrete wavelet sparse transform (DWT) and Discrete Cosine Transform (DCT) are used as sparse decomposition bases of a channel impulse response vector, the DWT is applied, the DCT performs sparse representation on the channel impulse response, and compressed sensing is applied to estimate a channel and impulse noise. DCT, DWT dimension is only ng, make integral observation matrix phi dimension p ng, need the data bulk of the storage to reduce greatly than the scheme of zero filling.
According to a zimermann channel model, the time-frequency domain characteristics of a power line reference channel are simulated, the OFDM symbols are 1024 subcarriers, the subcarrier intervals are 24.414KHz, a sampling frequency of 25MHz is adopted, the OFDM time domain length is about 40us, the ng length is about 10us, and the generated amplitude-frequency response and time-domain impulse response of the transmission characteristics frequency domain of the power line channel are shown in figures 2, 3 and 4.
Based on the power line channel impact response obtained by simulation, constructing an observation vector as a frequency domain symbol Y at the pilot frequency of a receiving end P The sum observation matrix is phi, and the power line channel is interfered by background noise, so that the signal-to-noise ratio is continuously increased and changed from 0dB to 20 dB. As shown in fig. 5, compared with compressed sensing channel estimation without sparsification, the MSE performance of the sparse bayesian power line channel and impulse noise joint estimation method based on DCT is improved by 2dB, and the MSE performance of the sparse bayesian power line channel and impulse noise joint estimation method based on DWT is improved by 3 dB. The dimensionality of the memory matrix is reduced 1/4 compared to the zero-padded compressed sensing channel estimation scheme.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Claims (9)
1. A sparse Bayesian power line channel and impulse noise joint estimation method based on DCT and DWT is characterized in that: the method comprises the following steps:
s1: converting the frequency domain signal received by the power line receiving end into a vector matrix form;
s2: extracting a pilot frequency in a received signal;
s3: combining DWT and DCT to construct an observation matrix and an observation vector by the extracted pilot symbols based on a compressed sensing model;
s4: uniformly partitioning the observation matrix;
s5: initializing a compressed sensing estimation model of the power line impulse noise and the channel;
s6: starting with an empty model, and performing block addition on the assumption that all signal blocks are not added into the model; iteratively calculating a covariance matrix, block correlation and a correlation structure matrix each time, updating model parameters, and reconstructing the covariance matrix according to the correlation structure matrix until all covariance matrices are obtained;
s7: when the preset condition is met, ending the circulation of S6 to obtain sparse solution vectors;
s8: taking the front ng row of the sparse solution vector obtained in S7 to carry out DCT and DWT to obtain a channel impulse response vector estimated value, and carrying out zero filling FFT to obtain a channel frequency response vector with the length of N;
s9: and the ng-ng + N rows of the obtained sparse solution vector are time domain impulse noise estimation vectors, so that a frequency domain symbol with impulse noise removed is obtained.
2. The DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method of claim 1, wherein: in step S1, the frequency domain signal received by the power line receiving end is converted into a vector matrix form
Y＝diag(X)H+Fi+G (1)
Wherein X ═ X 1 ,X 2 ,...X N ] T Transmitting symbol vectors for the frequency domain, the OFDM frequency domain symbol vectors having a length N, H ═ H 1 ,H 2 ,...,H N ]F is an N-dimensional fourier transform matrix, i represents time-domain impulse noise, where G-Fg represents frequency-domain background noise and is white gaussian noise, and G represents background noise.
3. The DCT and DWT based sparse bayesian power line channel and impulse noise joint estimation method of claim 2, wherein: in step S2, a set of positions where pilots are inserted in the transmission signal is defined as P, () P is a submatrix formed by index-corresponding rows or elements in the set P, and equation (1) is transformed into:
Y P ＝diag(X P )H p +F p i+G p (2)。
4. the DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method of claim 3, wherein: in step S3, in combination with the time domain sparsity of the impulse noise, the compressed sensing estimation model of the power line impulse noise and the channel is:
wherein F p,ng Is a Fourier matrix of P ng, ng being the guard interval length, DCT ng*ng ，DWT ng*ng Is a matrix of ng by ng dimensions; in the formula, ng 1-dimensional vector h is sparsely represented as:
h＝DCT*a (5)
h＝DWT*b (6)
the formula (3) and the formula (4) are expressed as follows:
Y p ＝ΦX+G p (7)
where Φ is the observation matrix.
5. The DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method of claim 4, wherein: in step S4, the observation matrix Φ is uniformly partitioned into [ Φ ═ Φ 1 ,Φ 2 ,...Φ m ]The block length is 8, the OFDM length is 1024, the ng length is 256, comb-shaped pilot frequencies are arranged, the comb-shaped pilot frequencies are uniformly distributed, and the number of the comb-shaped pilot frequencies is 64.
6. The DCT and DWT-based sparse Bayesian power line channel and impulse noise joint estimation method of claim 5, wherein: initialization as described in step S5, taking into account the signal-to-noise ratio SNR<20dB, set beta 0.1Y p || 2 ，
η＝10 -4 M denotes the division of the observation vector into m blocks of data, also corresponding to m observation matrices, phi i Representing an observation matrix corresponding to the ith block, wherein eta is an algorithm exit condition, beta refers to a noise variance, iterative computation is needed in the algorithm process, and s i ，q i Is a defined intermediate variable used to calculate the cost function.
7. The DCT and DWT-based sparse Bayesian power line channel and impulse noise joint estimation method of claim 6, wherein: in step S6, starting with the null model, all signal blocks X are assumed i Adding the blocks into the model without adding the blocks into the model; the set of bases in the model at the K-th iteration is a k Each iteration carries out the following steps:
s61: computing a covariance matrix
Calculating a block correlation gamma i ＝1/d i Tr(A i ) Wherein d is i Is a matrix A i Tr denotes the trace of the matrix; computingCorrelation structure matrix B i ＝A i /r i Reconstruction of
Wherein r is i Represents the variance of the ith block; until all A's are obtained i And according to the cost function L ═ log | C | + y T C -1 y, where y represents the measurement vector input by the algorithm, i.e. the OFDM frequency domain symbol at the input pilot; wherein C is beta -1 I+ΦΓΦ T Wherein I represents an identity matrix, and Γ is a matrix formed by covariance matrices of observation block matrices; computing
And obtaining a value such that Δ L (i) is maximized
That is, the index of the observation block matrix that maximizes Δ l (i);
s62: according to
Whether or not to belong to a k Updating sigma-mu s i q i 。
8. The DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method of claim 7, wherein: when | | | γ is satisfied in step S7 new - γ |/| | γ | < η, jumping out of the cycle of S6, obtaining a sparse solution vector x ═ μ;
in step S9, the ng-ng + N rows of the sparse solution vector are the time domain impulse noise estimation vectors
Obtaining a frequency domain symbol with impulse noise removed
9. The DCT and DWT based sparse Bayesian power line channel and impulse noise joint estimation method of claim 7, wherein: in step S62, update Sigma- μ S by BSBL-FM algorithm i q i The method specifically comprises the following steps:
(1)
the current block is added to the model, and μ new ＝μ-βΣΦ T Φ i μ i ，
Wherein a ＝-βΣΦ T Φ i Σ ii ，
Wherein e i ＝β(Φ i -βΦΣΦ T Φ i ) μ is the mean vector of the probability distribution obeyed by the output random vector, ∑ is the covariance vector of the probability distribution obeyed by the output vector, μ new Mean vector, Σ, of iterative updates in the reference algorithm new Covariance vector, μ, referred to as iterative update in the algorithm i Then the ith value in the mean vector, Σ a Is a defined intermediate variable, in order to express sigma new Update procedure, s inew ，q inew Representing updated s i ，q i For calculating a new cost function; e.g. of the type i Is an intermediate variable derived by an algorithm, and is convenient to express q inew Update procedure of ∑ ii Is the covariance matrix corresponding to the ith block of data for iteratively updating s i ；
(2)
And is
Delete this block from the modelAnd mu is combined new ＝μ+ΔΣβΦ T y，Σ new Σ + Δ Σ, where Δ Σ is ═ Σ i Σ ii -1 Σ i ，
(3)
And is
Reestimating the current block and mu new ＝μ+ΔΣβΦ T y，Σ new ＝Σ+ΔΣ，
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