CN116388800A - Pulse noise suppression method based on fast Bayes matching pursuit - Google Patents

Abstract

The invention discloses a pulse noise suppression method based on fast Bayes matching pursuit, which comprises the steps of obtaining a discrete time domain signal with pulse noise interference after removing cyclic prefix at a receiving end, and reconstructing the discrete time domain signal by using empty subcarriers in OFDM; introducing a parameter vector to represent pulse noise sparsity; obtaining the relation among the discrete time domain signal, the parameter vector and the impulse noise according to the Bayes criterion, and further obtaining the probability distribution of the impulse noise; according to the Bayes criterion, the posterior probability of the parameter vector is obtained, and then the measure base of the parameter vector is obtained; introducing a measure base increment to update in real time to replace the original measure base update in order to accelerate the calculation process; combining the probability distribution of impulse noise and the measure base increment, and acquiring an optimal set by using a fast Bayes matching tracking algorithm; obtaining an estimated value of impulse noise by utilizing the minimum mean square error solution, and further realizing impulse noise suppression; the method has the advantages of being capable of accurately estimating impulse noise and low in complexity.

Description

Pulse noise suppression method based on fast Bayes matching pursuit

Technical Field

The invention relates to a pulse noise suppression technology under an OFDM (Orthogonal Frequency Division Multiplexing ) system in power line communication (PLC, powerline Communication), in particular to a pulse noise suppression method based on fast Bayesian matching pursuit (Fast Bayesian Matching Pursuit, FBMP) under the OFDM system.

Background

Power line communication is a communication scheme in which carrier transmission is performed using a power line medium. As a well established infrastructure, power line communication can greatly reduce installation time and cost, and has the ability to penetrate longer distance structures, and the use of the power line as a data transmission can greatly reduce communication cost, relative to cables and wireless products. Based on the popularity of power line infrastructure, typical applications of power line communications include: smart grid, real-time quotation, internet of vehicles communication, remote automatic meter reading, intelligent energy management, and the like. In future application designs, transmission of television images, including slow-scan television, video, and audio signals may be accomplished via a power line communication network. Power lines have good development prospects and advantages, but since the power line is designed to transmit unidirectional power in a fixed frequency range instead of being designed for signal transmission, many challenges exist on the line, including channel frequency attenuation, high noise and complex load types, so that high requirements are placed on the anti-interference performance and stability of the device. Among the numerous disturbances in power line communication systems, the effects of noise disturbances are particularly pronounced, with the disturbance effects of impulse noise being the most pronounced. Impulse noise is broadly divided into three types: generalized background noise, asynchronous type, and periodic type. The periodic impulse noise is caused by a power supply and is mainly caused by the switching action of a rectifier diode, and is characterized by long duration, interference peak and periodic appearance in half of power grid main circulation lines; asynchronous impulse noise is mainly caused by switching power supplies among electric appliances and is characterized by short duration and large amplitude, and randomly occurs, thereby causing broadband occupation of up to 11MHz in the frequency domain.

In the power line communication system, because the topology structure is different from the traditional one, there are characteristics of complex channel characteristics and obvious multipath effect. In power line communication, multi-carrier modulation techniques of OFDM are employed to combat inter-symbol interference and fading caused by multipath effects and narrowband interference. Multicarrier communication systems based on OFDM technology are widely used in various communication systems. Although the noise energy of an OFDM system is randomly distributed over a plurality of subcarriers and exhibits a stronger resistance to impulse noise than a single carrier communication system, if the input power exceeds a certain threshold in the time domain, its effect extends to all subcarriers, which results in a dramatic decrease in the performance of the OFDM system. Therefore, in practical applications, an effective impulse noise suppression method is required to be sought under the OFDM system to ensure reliable transmission of the communication system. The impulse noise suppression methods commonly used at present can be divided into two types, namely a parameterized method and a non-parameterized method.

Common parameterization methods include clipping, blanking and joint blanking clipping. Such methods are based mainly on the feature that the amplitude of impulse noise is usually much higher than background noise, and then a threshold is set according to the amplitude, and a signal above the threshold is considered to be the presence of impulse noise. The memory-free nonlinear preprocessor is designed by a blanking or amplitude limiting method to achieve the aim of suppressing impulse noise. The blanking method is to consider a signal above a threshold as an interfering signal and limit it to 0, and the clipping rule limits the signal to a threshold. However, such methods destroy the original signal while suppressing impulse noise, and the performance of the method is highly dependent on the setting of an optimal threshold, which needs a priori statistical information of impulse noise to derive, and this is difficult to obtain in practical applications, and once the a priori information does not match with the assumed model, the communication performance is degraded.

The non-parameterization method is used for estimating impulse noise based on the statistical characteristics of signals, does not need a threshold value, does not need to accurately solve the channel characteristic parameters of the power line communication system, and avoids the measurement of the channel characteristic parameters which have no great practical significance. Considering that the occurrence probability of impulse noise in a power line communication system is very low and sparse, the impulse noise can be regarded as a sparse signal in the time domain, so it has been proposed that an unparameterized signal reconstruction algorithm based on a compressed sensing theory can be used for reconstructing and eliminating the impulse noise signal. It is common practice to first use electricityAnd constructing a signal compressed sensing model by empty subcarriers in the power line communication system, then reconstructing the impulse noise signal by adopting a proper compressed sensing reconstruction algorithm, and finally subtracting the impulse noise from the received signal so as to finish the suppression of the impulse noise. The first researchers proposed a least squares-based suppression method, but the accuracy was not high. Researchers have also proposed an Orthogonal Matching Pursuit (OMP) method to estimate and eliminate impulse noise, OMP belongs to a greedy algorithm, the complexity of which depends on the number of iterations, is relatively easy to implement, but its reconstruction accuracy is not high, and its suppression performance is poor. Then, researchers have proposed that impulse noise L is to be solved ₀ The NP-hard problem of norms translates into a smooth L of lower complexity ₀ The norm problem, however, is approximated by a continuous function, which approximates L ₀ An approximate solution to the norm, therefore, is prone to estimation errors at non-impulse noise sampling points, with limited improvement in suppression performance. Researchers also put forward a sparse Bayesian learning method to estimate impulse noise, and compared with other impulse noise suppression algorithms, the Bayesian-based algorithm fully utilizes probability prior information, improves the suppression performance and robustness, but has higher complexity.

Disclosure of Invention

The invention aims to provide a pulse noise suppression method based on fast Bayesian matching pursuit, which can accurately estimate pulse noise and has lower complexity.

The technical scheme adopted for solving the technical problems is as follows: a pulse noise suppression method based on fast Bayesian matching pursuit is characterized by comprising the following steps:

step 1: in the power line communication, a transmitting end of an OFDM system marks an initial binary data sequence of the transmitting end as B; compiling B into a plurality of fixed-length code words, wherein each fixed-length code word contains (N-K) data; then, selecting one fixed-length code word from multiple fixed-length code words, marking the fixed-length code word as C, and expressing C as a column vector form

Mapping C into an OFDM symbol containing (N-K) data by quadrature phase shift keying, supplementing K0 at the end of the OFDM symbol to make the length of the OFDM symbol become N, marking the OFDM symbol after supplementing 0 as D, and representing D as->

Loading the front (N-K) data in the D onto (N-K) subcarriers, wherein the (N-K) subcarriers are data subcarriers, and loading the rear K data in the D onto K subcarriers, wherein the K subcarriers are null subcarriers; meanwhile, performing inverse discrete Fourier transform on D to obtain corresponding discrete time domain signals, namely G, G=F ^H D＝[g ₁ ,g ₂ ,…,g _N ] ^T The method comprises the steps of carrying out a first treatment on the surface of the Finally, adding a cyclic prefix for preventing intersymbol interference to the head of the G, and transmitting the discrete time domain signal added with the cyclic prefix to a receiving end of an OFDM system in power line communication through a channel;

wherein the length of B is at least greater than 2 (N-K), N represents the total number of subcarriers in the OFDM symbol, N > 2,K represents the total number of empty subcarriers in the OFDM symbol, 1 < K < N, and the dimension of C is (N-K). Times.1, symbol "[]"is a vector or matrix representing a symbol, c ₁ ,c ₂ ,…,c _(N-K) Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data in the representation C, and the dimension of D is N multiplied by 1, D ₁ ,d ₂ ,…,d _(N-K) ,d _(N-K)+1 ,…,d _N Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data, the (N-K) +1 st data, … th data, the Nth data in D, the dimension of G is N×1, F represents a discrete Fourier transform Van der Monte matrix of dimension N×N, F ^H Hermite transform as F, g ₁ ,g ₂ ,…,g _N Corresponding to the 1 st data, the 2 nd data, …, the nth data in the G, the superscript "T" represents the transpose of the vector or matrix;

step 2: in a receiver of an OFDM system in power line communication, a receiver is configured to receive a tracking of a header of a discrete time domain signal with impulse noise interferenceThe cyclic prefix is removed, the discrete time domain signal with impulse noise interference after the cyclic prefix is removed is marked as r,

constructing a null sub-carrier matrix with dimension of KxN, which is marked as phi, wherein phi is formed by the N-K+1 row to the N row in F; then at->

Multiplying both sides of the equal sign of (2) by phi at the same time to obtain

Then, based on the orthogonality between the sub-carriers in the OFDM symbol

Conversion to Φr=Φi+Φn; let y=Φr=Φi+Φn, and let v=Φn, convert y=Φi+Φn to y=Φi+v;

wherein the dimension of r is N x 1,

representing a cyclic convolution matrix of channels of dimension nxn,

corresponding to N impulse response values obtained by estimating the channel and normalized, i represents impulse noise signal obeying Bernoulli Gaussian distribution, i is N×1, N represents background noise in OFDM system, N is N×1, y is introduced intermediate variable, y is K×1, v represents variance sigma ² And white noise signals subject to gaussian distribution;

step 3: according to the prior information of the impulse noise sparsity, an independent distribution parameter vector z with the same dimension as i is introduced to reflect the impulse noise sparsity, wherein z= [ z ] ₁ ,...,z _k ,...,z _N ] ^T ，z _k With a value of 1 or 0, when z _k Description of the kth element i in i when=1 _k Is a non-0 element, representing i _k In the presence of impulse noise, when z _k Description of the kth element i in i when=0 _k 0 element represents i _k In the absence of impulse noise, will z _k The probability of =1 is denoted P [ z ] _k ＝1]Will z _k The probability of =0 is denoted P [ z ] _k ＝0]Let Pz _k ＝1]＝p ₁ →i _k ≠0，P[z _k ＝0]＝1-p ₁ →i _k =0; and the relationship between z and i is set, expressed as: p (y|z, i) =p (y|i, z) =p (y|i);

wherein z is ₁ Represents the 1 st element in z, z _k Represents the kth element in z, z _N Represents the Nth element in z, 1.ltoreq.k.ltoreq.N, p (y|z, i) represents the conditional probability of y under the conditions that z and i are known, p (y|i, z) represents the conditional probability of y under the conditions that i and z are known, p (y|z, i) is the same as p (y|i, z), p (y|i) represents the conditional probability of y under the conditions that i is known, p ₁ Representing the probability that the element in z is 1, 0 < p ₁ ＜＜1；

Step 4: according to the bayesian criterion, the relationship between z, i and y is obtained, expressed as:

the relationship between z, i and y is then reduced to: p (y, i|z) =p (y|i) p (i|z); next, from p (y, i|z) =p (y|i) p (i|z), a probability distribution of i is obtained, expressed as: />

The probability distribution of i obeys a mean of 0 and a variance of +.>

Is a gaussian distribution of (c); obtaining i according to the probability distribution of i _k |{z _k ＝1}，i _k |{z _k The =1 } obeys a mean of 0 and variance of +.>

Is a gaussian function of (c);

where p (y, i|z) denotes the conditional probability of y and i under the condition that z is known, p (y, i, z) denotes the total probability of y, i and z, p (z) denotes the total probability of z, p (i, z) denotes the total probability of i and z, p (i|z) denotes the conditional probability of i under the condition that z is known,

for the intermediate variables introduced ∈ ->

I _K Represents a K-order identity matrix, R (z) represents a covariance matrix of z, R (z) =e (zz) ^T ) E () represents the expectation that R (z) is a diagonal matrix and the value of the diagonal element of the kth row and kth column is +.>

Representing z _k Variance of (1), when z _k When=1->

Denoted as->

When z _k When=0->

Denoted as->

And->

Step 5: based on the Bayesian criterion, the posterior probability of z is obtained, denoted as p (z|y),

the calculation p (z|y) is then converted intoCalculating p (y|z) p (z); then the logarithm of p (y|z) p (z), denoted ln (p (y|z) p (z)),

then, taking ln (p (y|z) p (z)) as a measure base of z, and recording μ (z) =ln (p (y|z) p (z)); finally, will

Simplified into

Wherein p (z|y) also represents the conditional probability of Z under the condition that y is known, p (y|z) represents the conditional probability of y under the condition that Z is known, Z represents all possible sets of Z, Z ε {0,1} ^N P (y|z ') represents the conditional probability of y under the condition that z' is known, p (z ') represents the full probability of z', "||" is the expression of determinant, exp () represents the exponential function based on natural radix e, det () represents the determinant, and p (z) _k ) Representing z _k Is a function of the full probability of (1), p (r|z) represents the conditional probability of r under the condition that z is known, "| I ₀ "represents 0 norm of the vector, and" = "in μ (z) =ln (p (y|z) p (z)) is an assignment symbol;

step 6: let delta ^(k) (z) represents z _k Modified measure base delta, delta ^(k) (z)＝μ(z ^(k) )-μ(z)，

Then solve for

Then solving by matrix inversion theory

And then obtain

And

according to

and

And

obtaining mu (z) ^(k) ) The relationship with μ (z), described as:

finally according to delta ^(k) (z)＝μ(z ^(k) ) Mu (z) sum

Obtaining

Wherein z is% ^k ) Represents a vector, μ (z ^(k) ) Representing z ^(k) Is a measure of the basis of R (z) ^(k) ) Representing z ^(k) A is a matrix with dimension N x N, and the values of diagonal elements of the kth row and kth column in A are all

While other elements are 0, θ _k A kth column representing Φ;

step 7: acquiring an optimal set Z by using a fast Bayesian matching pursuit algorithm ^* The specific process is as follows:

step 7_1: initializing the initial value of each element in z to be 0; let j represent the iteration number, the initial value of j is 1;

step 7_2: at the jth stackIf j=1, then there are: firstly, generating N-j+1 different z vectors, wherein only one element in each generated z vector is 1 and the other elements are 0; next, the generated N-j+1 different z vectors are respectively substituted

Obtaining N-j+1 measure base increment values; again, the top N is selected from the N-j+1 metric base increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max The Z vectors form a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, executing the step 7_3; wherein N is more than 1 _max ＜N；

At the j-th iteration, if j+.1, then there are: first, for Z ^(j-1) Randomly selecting one element among all 0 elements in the vector to be set to 1, generating N-j+1 different Z vectors for Z ^(j-1) N of (a) _max The z vectors co-produce N _max X (N-j+1) z vectors; second, N will be generated _max X (N-j+1) different z vectors are substituted respectively

In (1) to obtain N _max X (N-j+1) measure base increment values; again, from N _max Selecting the top N from the X (N-j+1) measure-based increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max The Z vectors form a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, executing the step 7_3;

step 7_3: judging whether the value of j reaches the set self-adaptive termination parameter, if so, terminating the iterative process and setting Z ^(j) As the optimal set Z ^* The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let j=j+1, then return to step 7_2 to continue execution; wherein the self-adaptive termination parameter is set as an interval

A positive integer in the range, j=j+1 "=" is an assignment symbol;

step 8: solving using least mean square error

Obtain->

Wherein (1)>

Representing an estimated value of i;

step 9: subtracting r

And obtaining an estimated value of the discrete time domain signal without impulse noise interference, and completing impulse noise suppression.

Compared with the prior art, the invention has the advantages that:

1) The method is based on a sparse compressed sensing theory, the sparsity of impulse noise is utilized, a Bayesian compressed sensing framework is combined for solving, firstly, a parameter vector with the same dimension is introduced to divide the sparse signal into an active part and an inactive part (the parameter vector is only 0 and 1,1 element is considered to be inactive, and 0 element is considered to be active), then a search basis set with high posterior probability is obtained through a fast Bayesian matching tracking algorithm, impulse noise is estimated by utilizing minimum mean square error, and compared with the existing impulse noise sparse Bayesian learning method, the impulse noise estimation method is more accurate.

2) The method of the invention uses the measure base increment to update the parameter estimation rapidly to accelerate the calculation speed when the iterative matching pursuit, compared with the existing impulse noise Orthogonal Matching Pursuit (OMP) algorithm, smooth L ₀ The method has better performance under the condition of low signal-to-noise ratio.

3) The method of the invention is directed to a power lineDifferent situations of communication system, when the total number of empty sub-carriers in one OFDM symbol is changed, compared with the existing least square method, the L is smooth ₀ The method has better estimation performance.

4) Compared with the traditional Bayesian matching pursuit, the method disclosed by the invention has the advantages that the original measure base updating solution is converted into the introduced measure base increment for real-time updating, the updating parameters are simplified, the calculation process is quickened, and the complexity is lower.

Drawings

FIG. 1 is a block diagram of a general implementation of the method of the present invention;

FIG. 2 shows the method (FBMP) of the present invention, the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ A curve comparison schematic diagram of the change curve of the bit error rate along with the number of empty subcarriers in a QPSK modulation system by a norm method (SL 0) and an existing sparse Bayesian learning method (SBL);

FIG. 3 shows the method (FBMP) of the present invention, the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ The change conditions of the system bit error rate under different signal to noise ratios of a norm method (SL 0) and an existing sparse Bayesian learning method (SBL) are compared and shown schematically;

FIG. 4 shows the method (FBMP) of the present invention, the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ And comparing and schematic diagrams of normalized mean square error performance change conditions of a norm method (SL 0) and an existing sparse Bayesian learning method (SBL) under different numbers of empty subcarriers.

Detailed Description

The invention is described in further detail below with reference to the embodiments of the drawings.

The invention provides a pulse noise suppression method based on fast Bayesian matching pursuit in an OFDM system, the general implementation block diagram of which is shown in figure 1, comprising the following steps:

step 1: in the power line communication, a transmitting end of an OFDM system marks an initial binary data sequence of the transmitting end as B; then willB, compiling into a plurality of fixed-length code words, wherein each fixed-length code word contains (N-K) data; then, selecting one fixed-length code word from multiple fixed-length code words, marking the fixed-length code word as C, and expressing C as a column vector form

Mapping C into an OFDM symbol containing (N-K) data by quadrature phase shift keying (Quadrature Phase Shift Keying, QPSK), supplementing K0 at the end of the OFDM symbol to make the length of the OFDM symbol become N, marking the OFDM symbol after supplementing 0 as D, and representing D as column vector form

Loading the front (N-K) data in the D onto (N-K) subcarriers, wherein the (N-K) subcarriers are data subcarriers, and loading the rear K data in the D onto K subcarriers, wherein the K subcarriers are null subcarriers; meanwhile, D is subjected to inverse discrete Fourier transform (Inverse Discrete Fourier Transform, IDFT) to obtain corresponding discrete time domain signals, which are marked as G, G=F ^H D＝[g ₁ ,g ₂ ,…,g _N ] ^T The method comprises the steps of carrying out a first treatment on the surface of the And finally, adding a Cyclic Prefix (CP) for preventing inter-symbol interference to the head of the G, and transmitting the discrete time domain signal added with the Cyclic Prefix to a receiving end of an OFDM system in power line communication through a channel.

Wherein the length of B is at least greater than 2 (N-K), in practice the length of B must be greater than 2 (N-K), N represents the total number of subcarriers in the OFDM symbol, N > 2, n=256 in this embodiment, K represents the total number of empty subcarriers in the OFDM symbol, 1 < K < N, k=120 in this embodiment, the dimension of c is (N-K) ×1, symbol "[ in this embodiment]"is a vector or matrix representing a symbol, c ₁ ,c ₂ ,…,c _(N-K) Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data in the representation C, and the dimension of D is N multiplied by 1, D ₁ ,d ₂ ,…,d _(N-K) ,d _(N-K)+1 ,…,d _N Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data, the (N-K) +1 st data, … in the representation DNth data, G is N1, F represents a discrete Fourier transform (Discrete Fourier Transform, DFT) Van der Waals matrix of N, F ^H Hermite transform as F, g ₁ ,g ₂ ,…,g _N Corresponding to the 1 st data, 2 nd data, …, nth data in G, the superscript "T" indicates a transpose of the vector or matrix.

Step 2: in the receiving end of OFDM system in power line communication, the cyclic prefix of the head of the discrete time domain signal with impulse noise interference received by the receiving end is removed, the discrete time domain signal with impulse noise interference after removing the cyclic prefix is marked as r,

constructing a null sub-carrier matrix with dimension of KxN, which is marked as phi, wherein phi is formed by the N-K+1 row to the N row in F; then at->

Multiplying both sides of the equal sign of (2) by phi at the same time to obtain

Then, based on the orthogonality between the sub-carriers in the OFDM symbol

Conversion to Φr=Φi+Φn; let y=Φr=Φi+Φn again, and let v=Φn, convert y=Φi+Φn to y=Φi+v.

Wherein the dimension of r is N x 1,

representing a cyclic convolution matrix of channels of dimension nxn,

corresponding to the value obtained by normalizing N impulse response values obtained by estimating the channel, directly estimating the channel by adopting the existing channel estimation technology, normalizing the N impulse response valuesThe method adopts any existing mature normalization processing method, i represents pulse noise signals conforming to Bernoulli Gaussian distribution, i has dimension of N multiplied by 1, N represents background noise in an OFDM system, N has dimension of N multiplied by 1, y is an introduced intermediate variable, y has dimension of K multiplied by 1, v represents variance sigma ² And white noise signal obeying Gaussian distribution, sigma is taken in this embodiment ² ＝0.18。

Step 3: according to the prior information of the impulse noise sparsity, an independent distribution parameter vector z with the same dimension as i is introduced to reflect the impulse noise sparsity, wherein z= [ z ] ₁ ,…,z _k ,…,z _N ] ^T ，z _k With a value of 1 or 0, when z _k Description of the kth element i in i when=1 _k Is a non-0 element, representing i _k In the presence of impulse noise, when z _k Description of the kth element i in i when=0 _k 0 element represents i _k In the absence of impulse noise, will z _k The probability of =1 is denoted P [ z ] _k ＝1]Will z _k The probability of =0 is denoted P [ z ] _k ＝0]Let Pz _k ＝1]＝p ₁ →i _k ≠0，P[z _k ＝0]＝1-p ₁ →i _k =0; and the relationship between z and i is set, expressed as: p (y|z, i) =p (y|i, z) =p (y|i).

Wherein z is ₁ Represents the 1 st element in z, z _k Represents the kth element in z, z _N Represents the Nth element in z, 1.ltoreq.k.ltoreq.N, p (y|z, i) represents the conditional probability of y under the conditions that z and i are known, p (y|i, z) represents the conditional probability of y under the conditions that i and z are known, p (y|z, i) is the same as p (y|i, z), p (y|i) represents the conditional probability of y under the conditions that i is known, p ₁ Representing the probability that the element in z is 1, 0 < p ₁ 1, select 0 p ₁ 1 so that i has few non-0 element values to ensure sparsity, p is taken in this embodiment ₁ ＝0.04。

Step 4: according to the bayesian criterion, the relationship between z, i and y is obtained, expressed as:

then according to zThe relationship between i, i.e., p (y|z, i) =p (y|i, z) =p (y|i), reduces the relationship between z, i and y to: p (y, i|z) =p (y|i) p (i|z); next, from p (y, i|z) =p (y|i) p (i|z), a probability distribution of i is obtained, expressed as: />

The probability distribution of i obeys a mean of 0 and a variance of +.>

Is a gaussian distribution of (c); obtaining i according to the probability distribution of i _k |{z _k ＝1}，i _k |{z _k The =1 } obeys a mean of 0 and variance of +.>

Is a gaussian function of (c).

Where p (y, i|z) denotes the conditional probability of y and i under the condition that z is known, p (y, i, z) denotes the total probability of y, i and z, p (z) denotes the total probability of z, p (i, z) denotes the total probability of i and z, p (i|z) denotes the conditional probability of i under the condition that z is known,

for the intermediate variables introduced ∈ ->

I _K Represents a K-order identity matrix, R (z) represents a covariance matrix of z, R (z) =e (zz) ^T ) E () represents the expectation that R (z) is a diagonal matrix and the value of the diagonal element of the kth row and kth column is +.>

Representing z _k Variance of (1), when z _k When=1->

Denoted as->

When z _k When=0->

Denoted as->

And is also provided with

Step 5: based on the Bayesian criterion, the posterior probability of z is obtained, denoted as p (z|y),

then converting the calculated p (z|y) into calculated p (y|z) p (z) according to the Bayesian criterion; since the set Z is too large, which results in an extremely complex calculation process, the logarithm of p (y|z) p (Z), denoted ln (p (y|z) p (Z)), is then calculated>

Then, taking ln (p (y|z) p (z)) as a measure base of z, and recording μ (z) =ln (p (y|z) p (z)); finally, will

Simplified into

Because μ (z) is a logarithmic relationship with p (z|y), μ (z) is an efficient way to estimate the parameter vector z.

Wherein p (z|y) also represents the conditional probability of Z under the condition that y is known, p (y|z) represents the conditional probability of y under the condition that Z is known, Z represents all possible sets of Z, Z ε {0,1} ^N P (y|z ') represents the conditional probability of y under the condition that z' is known, p (z ') represents the full probability of z', "||" is an expression of determinant, exp () represents an exponential function based on natural radix e, e=2.71 …, det () represents determinant, and p (z) _k ) Representing z _k P (r|z) is expressed inThe conditional probability of r under the condition that z is known, "| I ₀ "represents 0 norm of the vector, and" = "in μ (z) =ln (p (y|z) p (z)) is an assignment symbol.

Step 6: in order to accelerate the calculation process, a measure base increment is introduced to update in real time to replace the original measure base update, so that delta is caused ^(k) (z) represents z _k The base increment of the measure after the change,

to reduce mu (z) ^(k) ) Then the expression of +.>

Then solving the +.>

And then obtain

And

according to

and

And

obtaining mu (z) ^(k) ) The relationship with μ (z), described as:

finally according to delta ^(k) (z)＝μ(z ^(k) ) Mu (z) sum

Obtaining

Wherein z is% ^k ) Represents a vector, μ (z ^(k) ) Representing z ^(k) Is a measure of the basis of R (z) ^(k) ) Representing z ^(k) A is a matrix with dimension N x N, and the values of diagonal elements of the kth row and kth column in A are all

While other elements are 0, θ _k Represents the kth column of Φ.

Step 7: acquiring an optimal set Z by using a fast Bayesian matching pursuit algorithm ^* The specific process is as follows:

step 7_1: initializing the initial value of each element in z to be 0; let j denote the number of iterations, and the initial value of j be 1.

Step 7_2: at the j-th iteration, if j=1, then there are: firstly, generating N-j+1 different z vectors, wherein only one element in each generated z vector is 1 and the other elements are 0; next, the generated N-j+1 different z vectors are respectively substituted

Obtaining N-j+1 measure base increment values; again, the top N is selected from the N-j+1 metric base increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max The Z vectors form a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, executing the step 7_3; which is a kind ofWherein 1 is less than N _max ＜N。

At the j-th iteration, if j+.1, then there are: first, for Z ^(j-1) Randomly selecting one element among all 0 elements in the vector to be set to 1, generating N-j+1 different Z vectors for Z ^(j-1) N of (a) _max The z vectors co-produce N _max X (N-j+1) z vectors; second, N will be generated _max X (N-j+1) different z vectors are substituted respectively

In (1) to obtain N _max X (N-j+1) measure base increment values; again, from N _max Selecting the top N from the X (N-j+1) measure-based increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max The Z vectors form a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, step 7_3 is performed.

Step 7_3: judging whether the value of j reaches the set self-adaptive termination parameter, if so, terminating the iterative process and setting Z ^(j) As the optimal set Z ^* The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let j=j+1, then return to step 7_2 to continue execution; wherein the self-adaptive termination parameter is set as an interval

The "=" in j=j+1, which is a positive integer in the inner, is the assignment symbol.

Step 8: solving using minimum mean square error (Minimum Mean Square Error, MMSE)

Obtain->

Wherein (1)>

Representing the estimated value of i.

Step 9: subtracting r

And obtaining an estimated value of the discrete time domain signal without impulse noise interference, and completing impulse noise suppression.

To further illustrate the effectiveness and feasibility of the method of the present invention, computer simulations were performed on the method of the present invention.

Computer simulation is performed on complex baseband of OFDM systems in power line communication. In computer simulation, to be able to present a typical noise scenario, the average power ratio of pulse-to-background noise in the bernoulli gaussian model was set to 35 db, and the average power ratio of signal-to-background noise was set to 25 db. The variance of the white noise signal which follows the Gaussian distribution is sigma ² =0.18, the parameter vector active part element probability takes p ₁ =0.04. The Monte Carlo simulation times were set to 1000. The detailed simulation parameters are listed in table 1.

Table 1 list of simulation parameters

Related parameters	Simulation setup
		Modulation scheme	QPSK
Total number of sub-carriers	256
		Total number of data subcarriers	136
Total number of null sub-carriers	120

In order to compare the performance between different impulse noise suppression methods, a bit error rate BER and a normalized mean square error NMSE are defined respectively,

wherein P is _e Representing the number of erroneous bits, P _t Representing the total number of bits of the system>

Represents the NMSE, wherein, "| I ₂ "means the 2-norm of the vector. />

Under the same simulation environment, the method (FBMP) and the existing least squares algorithm (LS), the existing OMP algorithm (OMP) and the existing smooth L are compared ₀ The performance of the norm method (SL 0) and the existing sparse Bayesian learning method (SBL) in terms of bit error rate and normalized mean square error.

FIG. 2 compares the method of the present invention (FBMP), the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ The norm method (SL 0) and the existing sparse Bayesian learning method (SBL) are used for the situation that the bit error rate changes with the number of null subcarriers in a QPSK modulation system. As can be seen from fig. 2, the bit error rates of the five methods all show a decreasing trend with the increase of the number of the null subcarriers, because the observation matrix becomes larger with the increase of the number of the null subcarriers, so that the system obtains more observation values, thereby being capable of accurately estimating impulse noise better and improving estimation inhibition performance. Meanwhile, as can be seen from fig. 2, the method (FBMP) of the present invention is significantly better than other methods, and when the number of empty subcarriers is greater than 130, the bit error rate of the method (FBMP) of the present invention has a significantly reduced tendency, and as the number of empty subcarriers increases, the bit error rate is significantly smaller than that of other methods.

FIG. 3 compares the method of the present invention (FBMP), the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ The norm method (SL 0) and the existing sparse Bayesian learning method (SBL) are used for changing the bit error rate of the system under different signal-to-noise ratios. As can be seen from fig. 3, the bit error rate of the five methods is decreasing with increasing signal-to-noise ratio, and the curve change of the existing least squares algorithm (LS) is not obvious. Meanwhile, the method (FBMP) has some advantages when the signal-to-noise ratio starts from-1 dB, the performance advantage changes obviously when the signal-to-noise ratio starts from 0dB, and the bit error rate of the method (FBMP) is obviously lower than that of other methods when the signal-to-noise ratio exceeds 1 dB.

FIG. 4 compares the method of the present invention (FBMP), the existing least squares algorithm (LS), the existing OMP algorithm (OMP), the existing smooth L ₀ The norms (SL 0) and the existing Sparse Bayes Learning (SBL) are normalized in terms of mean square error performance variation under different numbers of empty subcarriers. As can be seen from fig. 4, as the number of null subcarriers increases, the system obtains more observations, so that the normalized mean square error of the five methods all has a decreasing trend. The performance of the method (FBMP) is obviously superior to that of other methods, and the method (FBMP) has lower normalized mean square error under the condition that the number of empty subcarriers is changed from small to large.

Claims (1)

1. A pulse noise suppression method based on fast Bayesian matching pursuit is characterized by comprising the following steps:

step 1: in the power line communication, a transmitting end of an OFDM system marks an initial binary data sequence of the transmitting end as B; compiling B into a plurality of fixed-length code words, wherein each fixed-length code word contains (N-K) data; then, a fixed-length codeword is arbitrarily selected from a plurality of fixed-length codewords, the fixed-length codeword is marked as C, and the C is expressed as C= [ C ] in a column vector form ₁ ,c ₂ ,...,c _(N-K) ] ^T The method comprises the steps of carrying out a first treatment on the surface of the Mapping C into an OFDM symbol containing (N-K) data by quadrature phase shift keying, supplementing K0 at the end of the OFDM symbol to make the length of the OFDM symbol become N, marking the OFDM symbol after supplementing 0 as D, and representing D as D= [ D ] in column vector form ₁ ,d ₂ ,…,d _(N-K) ,d _(N-K)+1 ,…,d _N ] ^T The method comprises the steps of carrying out a first treatment on the surface of the Loading the front (N-K) data in the D onto (N-K) subcarriers, wherein the (N-K) subcarriers are data subcarriers, and loading the rear K data in the D onto K subcarriers, wherein the K subcarriers are null subcarriers; meanwhile, performing inverse discrete Fourier transform on D to obtain corresponding discrete time domain signals, namely G, G=F ^H D＝[g ₁ ,g ₂ ,...,g _N ] ^T The method comprises the steps of carrying out a first treatment on the surface of the Finally, adding a cyclic prefix for preventing intersymbol interference to the head of the G, and transmitting the discrete time domain signal added with the cyclic prefix to a receiving end of an OFDM system in power line communication through a channel;

wherein the length of B is at least greater than 2 (N-K), N represents the total number of subcarriers in the OFDM symbol, N > 2,K represents the total number of empty subcarriers in the OFDM symbol, 1 < K < N, and the dimension of C is (N-K). Times.1, symbol "[]"is a vector or matrix representing a symbol, c ₁ ,c ₂ ,...,c _(N-K) Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data in the representation C, and the dimension of D is N multiplied by 1, D ₁ ,d ₂ ,...,d _(N-K) ,d _(N-K)+1 ,...,d _N Corresponds to the 1 st data, the 2 nd data, …, the (N-K) th data, the (N-K) +1 st data, … th data, the Nth data in D, the dimension of G is N×1, F represents a discrete Fourier transform Van der Monte matrix of dimension N×N, F ^H Hermite transform as F, g ₁ ,g ₂ ,...,g _N Corresponding to the 1 st data, the 2 nd data, …, the nth data in the G, the superscript "T" represents the transpose of the vector or matrix;

step 2: in the receiving end of OFDM system in power line communication, the cyclic prefix of the head of the discrete time domain signal with impulse noise interference received by the receiving end is removed, the discrete time domain signal with impulse noise interference after removing the cyclic prefix is marked as r,

and constructing a null sub-carrier matrix with dimension KxN, denoted as phi from the N-K+1 th row in FAn nth row; then at->

Multiplying both sides of the equal sign of (2) by phi at the same time to obtain +.>

Then based on the orthogonality between the individual sub-carriers in the OFDM symbol +.>

Conversion to Φr=Φi+Φn; let y=Φr=Φi+Φn, and let v=Φn, convert y=Φi+Φn to y=Φi+v;

wherein the dimension of r is N x 1,

a cyclic convolution matrix representing a channel of dimension NxN,>

corresponding to N impulse response values obtained by estimating the channel and normalized, i represents impulse noise signal obeying Bernoulli Gaussian distribution, i is N×1, N represents background noise in OFDM system, N is N×1, y is introduced intermediate variable, y is K×1, v represents variance sigma ² And white noise signals subject to gaussian distribution;

step 3: according to the prior information of the impulse noise sparsity, an independent distribution parameter vector z with the same dimension as i is introduced to reflect the impulse noise sparsity, wherein z= [ z ] ₁ ,...,z _k ,...,z _N ] ^T ，z _k With a value of 1 or 0, when z _k Description of the kth element i in i when=1 _k Is a non-0 element, representing i _k In the presence of impulse noise, when z _k Description of the kth element i in i when=0 _k 0 element represents i _k In the absence of impulse noise, will z _k The probability of =1 is denoted P [ z ] _k ＝1]Will z _k The probability of =0 is denoted P [ z ] _k ＝0]Let Pz _k ＝1]＝p ₁ →i _k ≠0，P[z _k ＝0]＝1-p ₁ →i _k =0; and the relationship between z and i is set, expressed as: p (y|z, i) =p (y|i, z) =p (y|i);

wherein z is ₁ Represents the 1 st element in z, z _k Represents the kth element in z, z _N Represents the Nth element in z, 1.ltoreq.k.ltoreq.N, p (y|z, i) represents the conditional probability of y under the conditions that z and i are known, p (y|i, z) represents the conditional probability of y under the conditions that i and z are known, p (y|z, i) is the same as p (y|i, z), p (y|i) represents the conditional probability of y under the conditions that i is known, p ₁ Representing the probability that the element in z is 1, 0 < p ₁ ＜＜1；

Step 4: according to the bayesian criterion, the relationship between z, i and y is obtained, expressed as:

the relationship between z, i and y is then reduced to: p (y, i|z) =p (y|i) p (i|z); next, from p (y, i|z) =p (y|i) p (i|z), a probability distribution of i is obtained, expressed as:

the probability distribution of i obeys a mean of 0 and a variance of +.>

Is a gaussian distribution of (c); obtaining i according to the probability distribution of i _k |{z _k ＝1}，i _k |{z _k The =1 } obeys a mean of 0 and variance of +.>

Is a gaussian function of (c);

wherein, p (y,i|z) represents the conditional probability of y and i under the condition that z is known, p (y, i, z) represents the total probability of y, i and z, p (z) represents the total probability of z, p (i, z) represents the total probability of i and z, p (i|z) represents the conditional probability of i under the condition that z is known,

for the intermediate variables introduced ∈ ->

I _K Represents a K-order identity matrix, R (z) represents a covariance matrix of z, R (z) =e (zz) ^T ) E () represents the expectation that R (z) is a diagonal matrix and the value of the diagonal element of the kth row and kth column is +.>

Representing z _k Variance of (1), when z _k When=1->

Denoted as->

When z _k When=0->

Denoted as->

And->

Step 5: based on the Bayesian criterion, the posterior probability of z is obtained, denoted as p (z|y),

then converting the calculated p (z|y) into calculated p (y|z) p (z) according to the Bayesian criterion; then the logarithm of p (y|z) p (z) is calculated, denoted ln (p (y|z) p (z)),/j>

Then, taking ln (p (y|z) p (z)) as a measure base of z, and recording μ (z) =ln (p (y|z) p (z)); finally, will

Simplified into

Wherein p (z|y) also represents the conditional probability of Z under the condition that y is known, p (y|z) represents the conditional probability of y under the condition that Z is known, Z represents all possible sets of Z, Z ε {0,1} ^N P (y|z ') represents the conditional probability of y under the condition that z' is known, p (z ') represents the full probability of z', "||" is the expression of determinant, exp () represents the exponential function based on natural radix e, det () represents the determinant, and p (z) _k ) Representing z _k Is a function of the full probability of (1), p (r|z) represents the conditional probability of r under the condition that z is known, "| I ₀ "represents 0 norm of the vector, and" = "in μ (z) =ln (p (y|z) p (z)) is an assignment symbol;

step 6: let delta ^(k) (z) represents z _k Modified measure base delta, delta ^(k) (z)＝μ(z ^(k) )-μ(z)，

Then solve +.>

Then solving by matrix inversion theory

And get->

And->

According to

and

And

obtaining mu (z) ^(k) ) The relationship with μ (z), described as:

finally according to delta ^(k) (z)＝μ(z ^(k) ) Mu (z) sum

Obtain->

Wherein z is ^(k) Represents a vector, μ (z ^(k) ) Representing z ^(k) Is a measure of the basis of R (z) ^(k) ) Representing z ^(k) A is a matrix with dimension N x N, and the values of diagonal elements of the kth row and kth column in A are all

While other elements are 0, θ _k A kth column representing Φ;

step 7: acquiring an optimal set Z by using a fast Bayesian matching pursuit algorithm ^* The specific process is as follows:

step 7_1: initializing the initial value of each element in z to be 0; let j represent the iteration number, the initial value of j is 1;

step 7_2: at the j-th iteration, if j=1, then there are: firstly, generating N-j+1 different z vectors, wherein only one element in each generated z vector is 1 and the other elements are 0; next, the generated N-j+1 different z vectors are respectively substituted

Obtaining N-j+1 measure base increment values; again, the top N is selected from the N-j+1 metric base increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max The Z vectors form a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, executing the step 7_3; wherein N is more than 1 _max ＜N；

At the j-th iteration, if j+.1, then there are: first, for Z ^(j-1) Randomly selecting one element among all 0 elements in the vector to be set to 1, generating N-j+1 different Z vectors for Z ^(j-1) N of (a) _max The z vectors co-produce N _max X (N-j+1) z vectors; second, N will be generated _max X (N-j+1) different z vectors are substituted into s respectively

In (1) to obtain N _max X (N-j+1) measure base increment values; again, from N _max Selecting the top N from the X (N-j+1) measure-based increment values _max The largest measure base increment value is found out _max N corresponding to the largest measure base increment value _max Z vectors, N _max Z vectorsForm a set, denoted as Z ^(j) The method comprises the steps of carrying out a first treatment on the surface of the Finally, executing the step 7_3;

step 7_3: judging whether the value of j reaches the set self-adaptive termination parameter, if so, terminating the iterative process and setting Z ^(j) As the optimal set Z ^* The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, let j=j+1, then return to step 7_2 to continue execution; wherein the self-adaptive termination parameter is set as an interval

A positive integer in the range, j=j+1 "=" is an assignment symbol;

step 8: solving using least mean square error

Obtain->

Wherein (1)>

Representing an estimated value of i;

step 9: subtracting r

And obtaining an estimated value of the discrete time domain signal without impulse noise interference, and completing impulse noise suppression.

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