CN103457638A - Restraining device and restraining method for burst impulse noise of power line communication channel - Google Patents

Abstract

The invention discloses a restraining device and restraining method for burst impulse noise of a power line communication channel. The restraining device comprises a Fourier transformation module, a masking subcarrier selection module and a compressed sensing estimation module. The restraining method for the burst impulse noise of the power line communication channel is based on compressed sensing and comprises the steps of carrying out Fourier transformation on a received signal to obtain a frequency domain signal, carrying out masking subcarrier selection to obtain a subcarrier only comprising background noise and the burst impulse noise, estimating the burst impulse noise in the power line communication channel by using a signal recover method based on compressed sensing, and finally, removing the impulse noise from the received signal to obtain a signal with noise removed. Due to the facts that the burst impulse noise in the power line communication channel has the characteristic of sparsity, and the OFDM masking subcarrier selection and compressed sensing technologies are applied, the effect of restraining the noise can be remarkably improved, and signal information of positions interfered by burst impulse can be effectively kept.

Description

Suppression device and suppression method for burst pulse noise of power line communication channel

Technical Field

The invention relates to a burst noise suppression technology, in particular to a device and a method for suppressing burst noise of a power line communication channel.

Background

Power Line Communication (PLC) is a Communication using a Power network with low-voltage Power distribution lines as a transmission medium, and has the characteristics of no need of rewiring, wide coverage, low cost, and the like. The low-voltage distribution network is mainly used for transmitting alternating current, data transmission is not considered when the low-voltage distribution network is initially designed, and the communication channel of the low-voltage distribution network has strong noise and has great influence on the performance of power line communication.

The low-voltage power line channel contains various complex noises, which are mainly classified into five categories, specifically as follows:

1. colored background noise, which is a type of noise that is prevalent in power line channels. It is mainly formed by superposition of thermal noise and load harmonic. Its Power Spectral Density (PSD) is small, changes slowly with time, and gradually decreases with increasing frequency.

2. Narrow-band noise, which is a superposition of amplitude-modulated sinusoids, is mainly generated by medium-short wave radio stations and generally has a long interference duration but a low power spectral density.

3. The periodic impulse noise asynchronous with the power frequency of the power grid has low power spectral density and is mainly generated when a switching power supply is switched on or switched off and a television receiver and a computer display perform image field scanning display.

4. The periodic impulse noise synchronized with the power frequency of the power grid is usually 50Hz or 100Hz in period. It is short in duration and its power spectral density decreases with increasing frequency.

5. The asynchronous burst noise is mainly caused by switching on and off of a switch connected to a power distribution network or switching of the power distribution network, the duration time of the asynchronous burst noise is short, but the power spectrum intensity is high and is usually higher than background noise by more than 50dB, and the asynchronous burst noise has a great influence on power line communication.

The above-mentioned types 1-3 of noise belong to slowly varying noise, and generally remain relatively stable for several minutes or even hours, so these three types of noise are called "colored background noise". While class 4-5 noises vary rapidly and are large in amplitude, and are therefore referred to as "burst noise".

The burst noise greatly affects the power line communication performance. In order to ensure the performance of the power line communication system, it is necessary to process burst noise by a noise suppression method before performing processing such as channel estimation and channel equalization.

Zhidkov s, in literature "Analysis and compliance of basic simple impulse simulation schemes for OFDM receivers [ IEEE trans. 5-9] to the power line channel burst pulse noise, a Non-linear clipping (NLC) method is proposed, the basic principle of which is as follows:

let s_kTo transmit signals, u_kIf the noise is in the channel, the noise signal at the receiving end is r_k＝s_k+u_k. First, a received signal r is calculated_kTo obtain | r_kAnd then carrying out amplitude limiting operation by utilizing a nonlinear amplitude limiting technology to obtain a signal with burst pulse noise removed

Namely, it is

${\hat{s}}_k=\left\{\begin{array}{cc}{r}_k,& \left|r_k\right|\&le;{\mathrm{<figure-callout\; id="1"\; label="thr"\; filenames="HDA0000380627380000011.png,HDA0000380627380000051.png"\; state="\{\{state\}\}">thr</figure-callout>}}_1\\ {\mathrm{<figure-callout\; id="1"\; label="thr"\; filenames="HDA0000380627380000011.png,HDA0000380627380000051.png"\; state="\{\{state\}\}">thr</figure-callout>}}_1\&CenterDot;e^{j\arg \left(r_k\right)},& \left|r_k\right|>{\mathrm{<figure-callout\; id="1"\; label="thr"\; filenames="HDA0000380627380000011.png,HDA0000380627380000051.png"\; state="\{\{state\}\}">thr</figure-callout>}}_1\end{array}\right.$

Wherein, | - | represents an absolute value operation, thr₁Is a non-linear clipping threshold.

The method mainly has the following problems:

(1) the method carries out nonlinear processing according to a set threshold, so that the selection of the threshold has great influence on the noise suppression performance, and the received signal is damaged if the selection of the threshold is too small; and if the threshold value is selected to be too large, the burst noise cannot be effectively suppressed.

(2) The method only reduces the amplitude of the burst noise, and the residual noise after processing still has great influence on the performance of the communication system.

Zhidkov s, in literature "Analysis and compliance of basic simple impulse simulation schemes for OFDM receivers [ IEEE trans. 5-9]Aiming at the burst pulse noise of the power line channel, a Non-linear null (NLN) method is also provided. The method comprises the following steps of carrying out noise-containing signal r on a receiving end according to the following formula_kCarrying out nonlinear zero setting processing to obtain the signal without burst pulse noise

Is composed of

${\hat{s}}_k=\left\{\begin{array}{cc}{r}_k,& \left|r_k\right|\&le;{\mathrm{<figure-callout\; id="2"\; label="thr"\; filenames="HDA0000380627380000051.png,HDA0000380627380000062.png"\; state="\{\{state\}\}">thr</figure-callout>}}_2\\ 0,& \left|r_k\right|>{\mathrm{<figure-callout\; id="2"\; label="thr"\; filenames="HDA0000380627380000051.png,HDA0000380627380000062.png"\; state="\{\{state\}\}">thr</figure-callout>}}_2\end{array}\right.$

Wherein, | - | is an absolute value operation, thr₂Is a non-linear clipping threshold.

The method mainly has the following problems:

(1) the threshold value selection in the method has great influence on the noise suppression performance.

(2) The method sets the burst noise to zero, which can effectively inhibit the burst noise, but damages the original signal and influences the performance of subsequent processing.

Disclosure of Invention

In order to solve the above problems in the prior art, the present invention is to design a device and a method for suppressing burst noise in a power line communication channel, which can achieve the following objectives:

1. the sparsity characteristic of the burst pulse noise in the power line channel is fully utilized, the effective suppression of the burst pulse noise is realized, and the performance of a power line communication system is improved;

2. when denoising, the signal information at the burst pulse interference position can be effectively reserved.

In order to achieve the purpose, the technical scheme of the invention is as follows:

a power line communication channel burst pulse noise suppression device comprises a Fourier transform module, a masking subcarrier selection module and a compressed sensing estimation module. The input signal of the Fourier transform module is a signal of a channel receiving end containing burst pulse noise, and the output end of the Fourier transform module is connected with the input end of the masking subcarrier selection module; the output end of the masking subcarrier selection module is connected with the input end of the compressed sensing estimation module; and subtracting the signal at the receiving end of the channel from the output end of the compressed sensing estimation module to obtain a de-noised signal.

Based on the suppression principle of the power line channel burst pulse noise of compressed sensing, firstly, Fourier transform is carried out on a received signal to obtain a frequency domain signal of the received signal; then, masking subcarrier selection is carried out to obtain subcarriers only containing background noise and burst pulse noise; then, estimating burst pulse noise in the power line channel by using a signal recovery method based on compressed sensing; finally, the impulse noise is subtracted from the received signal to obtain a noise-cancelled signal.

A suppression method of a suppression device of power line communication channel burst noise comprises the following steps:

A. received signal conversion

Let x (n) be the signal at the transmitting end of the channel, and y (n) be the signal at the receiving end of the channel, then

$y\left(n\right)=x\left(n\right)\&CircleTimes;h\left(n\right)+w\left(n\right)---\left(1\right)$

w(n)＝b(n)+i(n)

Wherein,

representing convolution operation, h (n) is unit impulse response of a channel, w (n) is channel noise, b (n) is colored background noise, and i (n) is burst pulse noise;

the length of unit impulse response h (N) of a channel is set as L, the frame length of a signal y (N) at a receiving end of the channel is set as N, and the formula (1) is written into a matrix form to obtain

Definition of

$\stackrel{\&OverBar;}{y}={[y\left(0\right),y\left(1\right),y\left(2\right),...,y(N-1)]}^T,$

$\stackrel{\&OverBar;}{h}={[h\left(0\right),h\left(1\right),h\left(2\right),...,h(L-1)]}^T,$

$\stackrel{\&OverBar;}{w}={[w\left(0\right),w\left(1\right),w\left(2\right),...,w(N-1)]}^T,$

$\stackrel{\&OverBar;}{b}={[b\left(0\right),b\left(1\right),b\left(2\right),...,b(N-1)]}^T,$

$\stackrel{\&OverBar;}{i}={[i\left(0\right),i\left(1\right),i\left(2\right),...,i(N-1)]}^T,$

Then there is

$\stackrel{\&OverBar;}{y}=\stackrel{\&OverBar;}{X}\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{w}---\left(3\right)$

Wherein

$\stackrel{\&OverBar;}{w}=\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i}$

Fourier transform is carried out on two sides of the formula (3) to obtain

$\stackrel{\&OverBar;}{Y}=F(\stackrel{\&OverBar;}{X}\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{w})=F\stackrel{\&OverBar;}{X}{F}^{-1}F\stackrel{\&OverBar;}{h}+F\stackrel{\&OverBar;}{w}=\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)F\stackrel{\&OverBar;}{h}+F\stackrel{\&OverBar;}{b}+F\stackrel{\&OverBar;}{i}---\left(4\right)$

Wherein diag (-) is a diagonal matrix and F is a Fourier transform matrix

Here, , $W_N^{\mathrm{nk}}=e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000380627380000051.png,HDA0000380627380000062.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{N}\mathrm{nk}}$

B. masked subcarrier selection

Let the OFDM symbol length be N points, and the masked subcarrier index set be M = [ M =_f1，m_f2，m_f3，…，m_fq]Where M is a 1 xq vector, M_fi(i =1, 2, …, q) denotes a masked subcarrier index number.

B1 constructing a mask subcarrier selection matrix

Firstly, constructing an N multiplied by N dimensional unit array E, then selecting q rows in the unit array E according to the index number of the masking subcarrier to form a masking subcarrier selection matrix

B2, masking information at subcarriers

Multiplying the masked sub-carrier selection matrixes on two sides of the formula (4) respectively

Then there is

$\stackrel{\&OverBar;}{M}\stackrel{\&OverBar;}{Y}=\stackrel{\&OverBar;}{M}\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)F\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{M}F(\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i})$

Since the masked subcarriers do not transmit information, it is possible to reduce the number of subcarriers used for transmission

$\stackrel{\&OverBar;}{M}\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)=0$

Then there are

${\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}=F_{\stackrel{\&OverBar;}{M}}(\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i})\&ap;F_{\stackrel{\&OverBar;}{M}}\stackrel{\&OverBar;}{i}---\left(5\right)$

Wherein, ${\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}=\stackrel{\&OverBar;}{M}\stackrel{\&OverBar;}{Y},F_{\stackrel{\&OverBar;}{M}}=\stackrel{\&OverBar;}{M}F.$

C. estimation of burst noise using compressed sensing signal recovery algorithm

Applying Matching Pursuit (MP) algorithm to impulse noise in formula (5)

The estimation is carried out, and the specific implementation steps are as follows:

c1 input perception matrix

Measurement vectorAnd sparsity K.

C2, initialization: balance of

Reconstructing a signal

Index set Γ⁰= phi, atomic setThe number of iterations n =0.

C3, performing the following iterative calculation

C31 calculation margin and sensing matrix

Inner product of each column in (1)

C32, finding gⁿThe largest element in the group of (1),

c33, updating index set gammaⁿ=Γ^n-1U { k } and atom setWherein

Corresponding to the k column vector in the sensing matrix;

c34, obtaining the approximate solution of the reconstruction signal by using the least square method,

c35, updating the allowance, $r^n={\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}-F_{\stackrel{\&OverBar;}{M}}{\stackrel{\&OverBar;}{i}}^n;$

c36, judging whether the iteration meets the stop condition, namely | rⁿ|<1×10^-10(ii) a If so, stopping the iteration, at which time

I.e. estimated burst noise

Otherwise, jumping to step C31 to continue the iteration;

is provided with

Subtracting the burst noise estimation value from the channel receiving end signal y (n)

Obtaining denoised signals

Is composed of

$\hat{y}\left(n\right)=y\left(n\right)-\hat{i}\left(n\right).$

Compared with the prior art, the invention has the following beneficial effects:

1. according to the characteristic that burst pulse noise in a power line channel has sparsity, the invention estimates the pulse noise by applying a compressed sensing technology, can obviously improve the noise suppression effect, and can effectively reserve signal information at the burst pulse interference position.

2. The method extracts the background noise and the burst noise of the receiving end by using the characteristics of the power line channel OFDM transmission technology and by selecting the masking subcarrier, so as to improve the estimation precision of the burst noise.

3. The invention adopts the matching tracking algorithm to estimate the burst noise in the compressed sensing, thereby reducing the calculation complexity and facilitating the real-time processing.

4. The invention mainly utilizes the inherent sparsity of burst noise to carry out denoising, has less influence on the statistical property thereof, and can be used for wider application scenes.

Drawings

The invention is shown in the attached figure 11, wherein:

fig. 1 is a schematic block diagram of suppression of power line channel burst noise based on compressed sensing.

Fig. 2 is a flow chart of noise estimation based on compressed sensing.

Fig. 3 is a time domain waveform of a signal at a transmitting end.

Fig. 4 is a time domain waveform of the signal of fig. 3 at the receiving end.

Fig. 5 is a time domain waveform of the signal of fig. 4 after denoising using a nonlinear clipping method.

FIG. 6 is a time domain waveform of the signal of FIG. 4 after denoising using a compressed sensing method.

Fig. 7 is a time domain waveform of the fig. 3 signal with partial amplification.

Fig. 8 is a time domain waveform of the fig. 4 signal with partial amplification.

Fig. 9 is a time domain waveform of the fig. 5 signal with partial amplification.

Fig. 10 is a time domain waveform of the fig. 6 signal at partial amplification.

FIG. 11 is a graph comparing bit error rate performance of a nonlinear amplitude limiting method, a nonlinear zero setting method and a compression sensing denoising method.

Detailed Description

The invention relates to a method for inhibiting burst pulse noise of a power line communication channel, which can obviously reduce the interference caused by the burst pulse noise and effectively improve the transmission performance of a power line communication system. The invention is further described below with reference to the accompanying drawings. Fig. 1 is a functional block diagram of a power line channel burst noise suppression method based on compressive sensing according to the present invention, which includes a fourier transform module, a masking subcarrier selection module, and a compressive sensing estimation module. The method comprises the following specific steps: firstly, transforming a received signal by using Fourier transform of the step A of the invention to obtain a frequency domain signal of the received signal; then, the step B of the invention is used for masking subcarrier selection to obtain the subcarrier only containing background noise and burst pulse noise; then, estimating burst pulse noise in the power line channel by using the signal recovery method based on compressed sensing in the step C of the invention; finally, the estimated impulse noise is subtracted from the received signal, and a pure signal after noise elimination is obtained.

Fig. 2 is a flow chart of the burst noise estimation based on compressed sensing in step C of the present invention.

To verify the effectiveness of the present technique, the following simulation experiment was performed according to the flow chart shown in fig. 1.

In the experiment, the experimental parameters were: the bandwidth of the power line channel is 100MHz, each OFDM symbol of a transmitted signal has 4096 subcarriers, and the length of a cyclic prefix is 1024.

(1) Time domain waveform comparative analysis of nonlinear amplitude limiting method and compressed sensing denoising method

Fig. 3 is a time domain waveform of a signal at a transmitting end, fig. 4 is a time domain waveform of the signal of fig. 3 at a receiving end, fig. 5 is a time domain waveform of the signal of fig. 4 denoised by a nonlinear amplitude limiting method, fig. 6 is a time domain waveform of the signal of fig. 4 denoised by a compressive sensing method, fig. 7 is a time domain waveform of the signal of fig. 3 which is locally amplified, and fig. 8 is a time domain waveform of the signal of fig. 4 which is locally amplified. 3-6, the nonlinear amplitude limiting method and the compressive sensing denoising method can both suppress the power line burst noise. However, after the signal of fig. 3 is partially amplified, it can be seen from observing fig. 7 that the 3021 th sampling point of the transmitted signal is a negative value, but after the point is interfered by the burst noise, the received signal point also becomes a positive value because the burst noise is a positive value and much larger than the transmitted signal at this moment, as shown in fig. 8.

After the time domain waveform chart 5 subjected to denoising by the nonlinear amplitude limiting method is locally amplified, the time domain waveform chart is shown in a chart 9; the time domain waveform of the denoised time domain waveform diagram 6 of the compressed sensing method is shown in a figure 10 after the time domain waveform is locally amplified. As can be seen from fig. 9, although the burst noise can be reduced by using the nonlinear slicing method, the difference between the processed signal and the original transmitted signal is large. As can be seen from fig. 10, the compressive sensing method of the present invention not only can suppress the burst noise, but also can recover the original signal information at this point (i.e. point 3021) to some extent, mainly because the burst noise has sparsity, and the compressive sensing technique can estimate the burst noise to perform effective suppression, so that it has better noise suppression performance than the nonlinear amplitude limiting method.

(2) Performance comparison analysis of nonlinear amplitude limiting method, nonlinear clipping method and compressed sensing denoising method

In the power line communication system, the bit error rate performance of the nonlinear amplitude limiting method, the nonlinear zero setting method and the method based on the compressive sensing denoising method are compared as shown in fig. 11. As can be seen from fig. 11, if the receiver does not perform the burst noise suppression, the performance of the communication system is greatly reduced, because the occurrence of the burst noise will seriously interfere with the whole OFDM symbol where it is located, so that the receiver cannot recover the original signal information transmitted by the symbol.

As can be seen from fig. 11, both the nonlinear clipping method and the nonlinear clipping method can suppress the influence of impulse noise, but the selection of the threshold value can greatly affect the suppression effect of impulse noise, thereby affecting the bit error rate performance of the communication system. In a simulation experiment, different thresholds thr are respectively selected according to the characteristics of signals before noise addition, namely a large threshold thr =0.6, an optimal threshold thr =0.06 and a small threshold thr = 0.03. As can be seen from fig. 11, the effect of suppressing the burst noise by the non-linear clipping method is better than that of the non-linear clipping method, mainly because the non-linear clipping method can reduce the influence of the burst noise on the whole OFDM symbol, although the information at the position is lost to some extent, after the information at the impulse interference point is set to zero by the non-linear clipping method, and the non-linear clipping method does not have this function. As can be seen from fig. 11, if the threshold is properly selected, both the nonlinear clipping method and the nonlinear clipping method have better noise suppression performance, but in the actual communication process, due to the factors of channel characteristic variation, modulation mode change, background noise influence, etc., the optimal threshold is difficult to select, and if the threshold is selected too large (for example, thr =0.6 in fig. 11) or too small (for example, thr =0.03 in fig. 11), the denoising performance is reduced.

As can be seen from fig. 11, the compressed sensing denoising method of the present invention fully utilizes the characteristics of impulse noise to effectively estimate burst noise, the noise suppression performance of the method is significantly better than that of the nonlinear amplitude limiting method and the nonlinear clipping method, and the signal information at the burst interference position can be retained to a certain extent; in addition, the method does not relate to the problem of threshold value selection, and is more convenient to apply.

Claims (2)

1. A power line communication channel burst noise suppression device is characterized in that: the device comprises a Fourier transform module, a masking subcarrier selection module and a compressed sensing estimation module; the input signal of the Fourier transform module is a signal of a channel receiving end containing burst pulse noise, and the output end of the Fourier transform module is connected with the input end of the masking subcarrier selection module; the output end of the masking subcarrier selection module is connected with the input end of the compressed sensing estimation module; and subtracting the signal at the receiving end of the channel from the output end of the compressed sensing estimation module to obtain a de-noised signal.

2. A suppression method of a suppression device of power line communication channel burst noise is characterized in that: the method comprises the following steps:

A. received signal conversion

Let x (n) be the signal at the transmitting end of the channel, and y (n) be the signal at the receiving end of the channel, then

$y\left(n\right)=x\left(n\right)\&CircleTimes;h\left(n\right)+w\left(n\right)---\left(1\right)$

w(n)=b(n)+i(n)

Wherein,

representing convolution operation, h (n) is unit impulse response of a channel, w (n) is channel noise, b (n) is colored background noise, and i (n) is burst pulse noise;

the length of the unit impulse response h (N) of the channel is set as L, the length of the signal y (N) at the receiving end of the channel is set as N, the formula (1) is written into a matrix form to obtain

Definition of

$\stackrel{\&OverBar;}{y}={[y\left(0\right),y\left(1\right),y\left(2\right),...,y(N-1)]}^T,$

$\stackrel{\&OverBar;}{h}={[h\left(0\right),h\left(1\right),h\left(2\right),...,h(L-1)]}^T,$

$\stackrel{\&OverBar;}{w}={[w\left(0\right),w\left(1\right),w\left(2\right),...,w(N-1)]}^T,$

$\stackrel{\&OverBar;}{b}={[b\left(0\right),b\left(1\right),b\left(2\right),...,b(N-1)]}^T,$

$\stackrel{\&OverBar;}{i}={[i\left(0\right),i\left(1\right),i\left(2\right),...,i(N-1)]}^T,$

Then there is

$\stackrel{\&OverBar;}{y}=\stackrel{\&OverBar;}{X}\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{w}$

Wherein

$\stackrel{\&OverBar;}{w}=\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i}$

Fourier transform is carried out on two sides of the formula (3) to obtain

$\stackrel{\&OverBar;}{Y}=F(\stackrel{\&OverBar;}{X}\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{w})=F\stackrel{\&OverBar;}{X}{F}^{-1}F\stackrel{\&OverBar;}{h}+F\stackrel{\&OverBar;}{w}=\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)F\stackrel{\&OverBar;}{h}+F\stackrel{\&OverBar;}{b}+F\stackrel{\&OverBar;}{i}---\left(4\right)$

Wherein diag (-) is a diagonal matrix, F is a Fourier transform matrix,

here, , $W_N^{\mathrm{nk}}=e^{-j\frac{2\mathrm{\&pi;}}{N}\mathrm{nk}}$

B. masked subcarrier selection

Let the OFDM symbol length be N points, and the masked subcarrier index set be M = [ M =_f1，m_f2，m_f3，…，m_fq]Where M is a 1 xq vector, M_fi(i =1, 2, …, q) denotes a masked subcarrier index number;

b1 constructing a mask subcarrier selection matrix

Firstly, constructing an N multiplied by N dimensional unit array E, then selecting q rows in the unit array E according to the index number of the masking subcarrier to form a masking subcarrier selection matrix

B2, masking information at subcarriers

Multiplying the masked sub-carrier selection matrixes on two sides of the formula (4) respectivelyThen there is

$\stackrel{\&OverBar;}{M}\stackrel{\&OverBar;}{Y}=\stackrel{\&OverBar;}{M}\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)F\stackrel{\&OverBar;}{h}+\stackrel{\&OverBar;}{M}F(\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i})$

Since the masked subcarriers do not transmit information, it is possible to reduce the number of subcarriers used for transmission

$\stackrel{\&OverBar;}{M}\mathrm{diag}\left(\stackrel{\&OverBar;}{X}\right)=0$

Then there are

${\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}=F_{\stackrel{\&OverBar;}{M}}(\stackrel{\&OverBar;}{b}+\stackrel{\&OverBar;}{i})\&ap;F_{\stackrel{\&OverBar;}{M}}\stackrel{\&OverBar;}{i}---\left(5\right)$

Wherein, ${\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}=\stackrel{\&OverBar;}{M}\stackrel{\&OverBar;}{Y},F_{\stackrel{\&OverBar;}{M}}=\stackrel{\&OverBar;}{M}F;$

C. estimation of burst noise using compressed sensing signal recovery algorithm

Applying Matching Pursuit (MP) algorithm to impulse noise in formula (5)

The estimation is carried out, and the specific implementation steps are as follows:

c1 input perception matrix

Measurement vector

And sparsity K;

c2, initialization: balance ofReconstructing a signal

Index set Γ⁰= phi, atomic set

The number of iterations n = 0;

c3, performing the following iterative calculation

C31 calculation margin and sensing matrix

Inner product of each column in (1)

C32, finding gⁿThe largest element in the group of (1),

c33, updating index set gammaⁿ=Γ^n-1U { k } and atom set

Wherein

Corresponding to the k column vector in the sensing matrix;

c34, obtaining the approximate solution of the reconstruction signal by using the least square method,

c35, updating the allowance, $r^n={\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}-F_{\stackrel{\&OverBar;}{M}}{\stackrel{\&OverBar;}{i}}^n;$

c36, judging whether the iteration meets the stop condition, namely | rⁿ|＜1×10^-10(ii) a If so, stopping the iteration, at which timeI.e. estimated burst noise

Otherwise, jumping to step C31 to continue the iteration;

is provided with

Subtracting the burst noise estimation value from the channel receiving end signal y (n)

Obtaining denoised signals

Is composed of

$\hat{y}\left(n\right)=y\left(n\right)-\hat{i}\left(n\right).$

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