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

The restraining device of power line communication channel sporadic impulse noise and inhibition method thereof

Technical field

The present invention relates to a kind of sporadic impulse noise inhibition technology, particularly a kind of restraining device of power line communication channel sporadic impulse noise and inhibition method thereof.

Background technology

Power line communication (Power Line Communication, PLC) refers to take the low-voltage power distribution wire as transmission medium, utilizes electric power networks to communicate, and it has without the characteristics such as rewiring, wide coverage, cost be low.Low-voltage network is mainly used in transmitting alternating current, when initial design, does not consider to carry out transfer of data with it, and its communication channel noise is stronger, very large to the performance impact of power line communication.

Contain complicated multiple noise in low voltage power line communication channel, these noises mainly are divided into five classes, specifically are classified as follows:

1, coloured background noise, this is the ubiquitous a kind of noise of power line channel.It mainly is formed by stacking by thermal noise and load harmonic wave.(Power Spectrum Density, PSD) is less for its power spectral density, and temporal evolution is slow, and, along with the increase of frequency, power spectral density reduces gradually.

2, narrow-band noise, it is formed by stacking by some amplitude-modulated sinusoids, mainly by the intermediate waves broadcasting station, is produced, and its duration of disturbance is longer usually, but power spectral density is very low.

3, with the asynchronous recurrent pulse noise of electrical network power frequency, its power spectral density is lower, mainly by Switching Power Supply break-make, television receiver, computer display, is undertaken when picture field scanning shows producing.

The recurrent pulse noise of 4, synchronizeing with the electrical network power frequency, the cycle is 50Hz or 100Hz usually.Its duration is very short, and its power spectral density increases and reduces with frequency.

5, asynchronous sporadic impulse noise, mainly switch on and off or the electrical network switching by the access distribution network causes, and its duration is very short, but power spectrum intensity is very large, and usually than more than the high 50dB of background noise, this is very large on the power line communication impact.

Above-mentioned 1-3 noise like belongs to and becomes slowly noise, usually in a few minutes, even within several hours, all keeps relative stability, so this three noise like is called to " coloured background noise ".And that the 4-5 noise like changes is fast, amplitude greatly, therefore referred to as " sporadic impulse noise ".

Sporadic impulse noise is very large to the power line communication performance impact.In order to guarantee the performance of electric line communication system, before carrying out the processing such as channel estimating, channel equalization, must use noise suppressing method, sporadic impulse noise is processed.

Zhidkov S. is at document " Analysis and comparison of several simple impulsive noise mitigation schemes for OFDM receivers " [IEEE Trans.on Communications, 2008,56 (1): 5-9] in for the power line channel sporadic impulse noise, a kind of non-linear amplitude limit (Non-Linear Clipping is proposed, NLC) method, the basic principle of the method is as follows:

If s _kfor transmitted signal, u _kfor the noise in channel, the receiving terminal signals and associated noises is r _k=s _k+ u _k.At first calculate and receive signal r _kabsolute value, obtain | r _k|, then utilize non-linear limiting technology to carry out the amplitude limit operation, obtain removing the signal after sporadic impulse noise

?

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

Wherein, || mean signed magnitude arithmetic(al), thr ₁for non-linear limiting threshold.

Mainly there is following problem in the method:

(1) the method is carried out Nonlinear Processing according to the threshold value of setting, thus threshold value choose the noise suppressed performance impact greatlyr, threshold value is chosen too small, can destroy the reception signal; And that threshold value is chosen is excessive, can not effectively suppress sporadic impulse noise.

(2) the method has only reduced the amplitude of sporadic impulse noise, and after processing, residual noise still has considerable influence to communication system performance.

Zhidkov S. is at document " Analysis and comparison of several simple impulsive noise mitigation schemes for OFDM receivers " [IEEE Trans.on Communications, 2008,56 (1): 5-9] in for the power line channel sporadic impulse noise, a kind of non-linear zero setting (Non-Linear Nulling, NLN) method is also proposed.The method is according to following formula, to receiving terminal signals and associated noises r _kcarry out non-linear zero setting processing, obtain removing the signal after sporadic impulse noise

for

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

Wherein, || be signed magnitude arithmetic(al), thr ₂for non-linear slicing threshold value.

Mainly there is following problem in the method:

(1) threshold value in the method is chosen, larger to the noise suppressed performance impact.

(2) the method is by sporadic impulse noise zero setting, and this can effectively suppress sporadic impulse noise, but primary signal has been caused to damage, affects the performance of subsequent treatment.

Summary of the invention

The problems referred to above that exist for solving prior art, the present invention will design a kind of restraining device and inhibition method thereof that can realize the power line communication channel sporadic impulse noise of following purpose:

1, take full advantage of in power line channel the sparse property characteristics that sporadic impulse noise has, realize effective inhibition of sporadic impulse noise, improve the performance of electric line communication system;

2,, when denoising, can effectively retain the signal message at burst interference position place.

To achieve these goals, technical scheme of the present invention is as follows:

A kind of power line communication channel sporadic impulse noise restraining device, comprise Fourier transform module, shelter sub-carrier selection module and compressed sensing estimation module.The input signal of described Fourier transform module is the channel receiving end signal that contains sporadic impulse noise, and its output is connected with the input of sheltering the sub-carrier selection module; The output of sheltering the sub-carrier selection module is connected with the input of compressed sensing estimation module; After the output of compressed sensing estimation module and channel receiving end signal subtract each other, obtain the signal after denoising.

The power line channel sporadic impulse noise that the present invention is based on compressed sensing suppresses principle, carries out at first to received signal Fourier transform, obtains its frequency-region signal; Then sheltered sub-carrier selection, obtained only containing the subcarrier of background noise and sporadic impulse noise; Then use the signal recovery method based on compressed sensing, estimate the sporadic impulse noise in power line channel; Finally, from receive signal, deduct impulsive noise, obtain the signal after de-noising.

A kind of inhibition method of restraining device of power line communication channel sporadic impulse noise comprises the following steps:

A, the conversion of reception signal

If the signal that x (n) is the channel transmitting terminal, y (n) is the channel receiving end signal, has

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

w(n)＝b(n)+i(n)

Wherein,

mean convolution algorithm, the unit impulse response that h (n) is channel, w (n) is interchannel noise, and b (n) is coloured background noise, and i (n) is sporadic impulse noise;

If the length of the unit impulse response h (n) of channel is L, the frame length of channel receiving end signal y (n) is N, is write formula (1) as matrix form, obtains

Definition

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

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

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

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

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

Have

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

Wherein

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

Fourier transform is carried out in formula (3) both sides, 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 diagonal matrix, and F is the Fourier transform battle array

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, shelter sub-carrier selection

If the OFDM symbol is long for the N point, shelters sub-carrier indices and integrate as M=[m _f1, m _f2, m _f3..., m _fq], wherein, M is 1 * q vector, m _fi(i=1,2 ..., q) mean to shelter sub-carrier indices number.

B1, structure are sheltered the sub-carrier selection matrix

At first construct the unit matrix E of N * N dimension, then, according to sheltering sub-carrier indices number, the q in the battle array E of selection unit is capable, forms and shelters the sub-carrier selection matrix

B2, shelter subcarrier place information

Take advantage of respectively and shelter the sub-carrier selection matrix on formula (4) both sides

have

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

Do not send information owing to sheltering subcarrier, therefore

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

So have

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

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

C, utilize compressed sensing signal recovery algorithms estimating burst impulsive noise

Adopt match tracing (Mathing Pursuit, MP) algorithm to the sporadic impulse noise in formula (5)

estimated, the specific implementation step is as follows:

C1, input perception matrix

measure vector and degree of rarefication K.

C2, initialization: surplus

reconstruction signal

indexed set Γ ⁰=φ, atom set iterations n=0.

C3, carry out following iterative computation

C31, calculating surplus and perception matrix

in the inner product of each row

C32, find out g ⁿin greatest member,

C33, renewal indexed set Γ ⁿ=Γ ^n-1∪ { k} and atom set wherein

k row column vector in corresponding perception matrix;

C34, utilize least square method to try to achieve the approximate solution of reconstruction signal,

C35, renewal surplus, $r^n={\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}-F_{\stackrel{\&OverBar;}{M}}{\stackrel{\&OverBar;}{i}}^n;$

C36, judge whether iteration meets stop condition, | r ⁿ|<1 * 10 ^-10; If meet, stop iteration, now

be the sporadic impulse noise of estimation

otherwise, jump to step C31 and continue iteration;

If

deduct the sporadic impulse noise estimated value with channel receiving end signal y (n)

obtain the signal after denoising

for

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

Compared with prior art, the present invention has following beneficial effect:

1, the present invention has the characteristics of sparse property according to sporadic impulse noise in power line channel, and the applied compression cognition technology is estimated impulsive noise, can obviously improve noise suppression effect, and can effectively retain the signal message at burst interference position place.

2, the present invention utilizes the characteristics of power line channel OFDM transmission technology, by sheltering the selection of subcarrier, extracts background noise and the sporadic impulse noise of receiving terminal, to improve the estimated accuracy of sporadic impulse noise.

3, the present invention adopts matching pursuit algorithm estimating burst impulsive noise in compressed sensing, has reduced computation complexity, is convenient to real-time processing.

4, the present invention mainly utilizes the intrinsic sparse property of sporadic impulse noise to carry out denoising, and its statistical property of shorter mention, can be used for wider application scenarios.

The accompanying drawing explanation

11, the total accompanying drawing of the present invention, wherein:

The power line channel sporadic impulse noise that Fig. 1 is based on compressed sensing suppresses theory diagram.

Fig. 2 is based on the noise of compressed sensing and estimates flow chart.

Fig. 3 is the transmitting terminal time domain plethysmographic signal.

Fig. 4 is the time domain waveform of Fig. 3 signal at receiving terminal.

Fig. 5 is the time domain waveform after Fig. 4 signal is used non-linear amplitude limit method denoising.

Fig. 6 is the time domain waveform after Fig. 4 signal is used the compression sensing method denoising.

Fig. 7 is the local time domain waveform of amplifying of Fig. 3 signal.

Fig. 8 is the local time domain waveform of amplifying of Fig. 4 signal.

Fig. 9 is the local time domain waveform of amplifying of Fig. 5 signal.

Figure 10 is the local time domain waveform of amplifying of Fig. 6 signal.

Figure 11 is non-linear margining amplitude technique, non-linear zero setting method, the bit error rate performance comparison diagram based on the compressed sensing Denoising Algorithm.

Embodiment

The present invention is a kind of inhibition method of power line communication channel sporadic impulse noise, can significantly reduce the interference that sporadic impulse noise causes, and effectively improves the transmission performance of electric line communication system.Below in conjunction with accompanying drawing, the present invention is described further.Figure 1 shows that the power line channel sporadic impulse noise based on compressed sensing of the present invention suppresses the methodological function block diagram, comprises Fourier transform module, shelters sub-carrier selection module and compressed sensing estimation module.Concrete steps are: at first with the Fourier transform of steps A of the present invention, converted to received signal, obtain its frequency-region signal; Then sheltered sub-carrier selection with step B of the present invention, obtained only containing the subcarrier of background noise and sporadic impulse noise; Then, with the signal recovery method based on compressed sensing of step C of the present invention, estimate the sporadic impulse noise in power line channel; Finally from receive signal, deduct estimated impulsive noise, obtain the purified signal after de-noising.

The sporadic impulse noise based on compressed sensing that Figure 2 shows that step C of the present invention is estimated flow chart.

For the validity of checking the technology of the present invention, according to the flow chart shown in Fig. 1, carried out following emulation experiment.

In experiment, experiment parameter is: the power line channel bandwidth is 100MHz, and the every OFDM symbol of transmitted signal has 4096 subcarriers, and Cyclic Prefix length is 1024.

(1) non-linear margining amplitude technique, the comparative analysis of compressed sensing Denoising Algorithm time domain waveform

Fig. 3 is the time domain waveform of transmitting terminal signal, Fig. 4 is the time domain waveform of Fig. 3 signal at receiving terminal, Fig. 5 is to the time domain waveform after non-linear amplitude limit method denoising for Fig. 4 signal, Fig. 6 is to the time domain waveform after the compression sensing method denoising for Fig. 4 signal, Fig. 7 is the local time domain waveform of amplifying of Fig. 3 signal, and Fig. 8 is the local time domain waveform of amplifying of Fig. 4 signal.From Fig. 3-6, non-linear margining amplitude technique and compressed sensing Denoising Algorithm can suppress the power line sporadic impulse noise.But after Fig. 3 signal is carried out to the part amplification, by observing Fig. 7, can find, the 3021st sampled point of transmitted signal is negative value, but after this point is disturbed by sporadic impulse noise, due to sporadic impulse noise this moment be on the occasion of and much larger than transmitted signal, therefore the signaling point received also become on the occasion of, as shown in Figure 8.

To the time domain waveform Fig. 5 after non-linear amplitude limit method denoising, after amplify part, its time domain waveform is shown in Fig. 9; To the time domain waveform Fig. 6 after compression sensing method denoising of the present invention, after amplify part, its time domain waveform is shown in Figure 10.As seen from Figure 9, though adopt non-linear margining amplitude technique can cut down sporadic impulse noise, signal and former transmitted signal after treatment differ larger.As seen from Figure 10, compression sensing method of the present invention not only can suppress sporadic impulse noise, can also recover to a certain extent the original signal information that this point (i.e. the 3021st point) is located, this is mainly because sporadic impulse noise has sparse property, the compressed sensing technology can estimate sporadic impulse noise, thereby effectively suppress, so it has better noise suppressed performance than non-linear margining amplitude technique.

(2) non-linear margining amplitude technique, non-linear slicing method and the comparative analysis of compressed sensing Denoising Algorithm performance

In electric line communication system, non-linear margining amplitude technique, non-linear zero setting method, the bit error rate performance based on the compressed sensing Denoising Algorithm are more as shown in figure 11.As seen from Figure 11, if do not carry out the inhibition of sporadic impulse noise at receiving terminal, the performance meeting decrease of communication system, this is the whole OFDM symbol because of its place of appearance meeting severe jamming of impulsive noise, thereby causes receiving terminal can't recover the original signal information that this symbol transmits.

As can be seen from Figure 11, the impact that non-linear margining amplitude technique and non-linear slicing method can impulse noise mitigations, but choosing of its threshold value can affect the inhibition of impulsive noise to a great extent, and then affect the bit error rate performance of communication system.In emulation experiment, according to the characteristics that add the front signal of making an uproar, minute three kinds of situations have been chosen respectively different threshold value thr, i.e. large threshold value thr=0.6, optimal threshold thr=0.06, little threshold value thr=0.03.As can be seen from Figure 11, the effect that non-linear slicing method suppresses sporadic impulse noise is better than non-linear margining amplitude technique, this is mainly by after the information zero setting at impulse disturbances point place because of non-linear slicing method, although can lose to a certain extent the information of this position, but can reduce the impact of impulsive noise on whole OFDM symbol, non-linear margining amplitude technique does not have this function.From Figure 11, it can also be seen that, if it is suitable that threshold value is chosen, non-linear margining amplitude technique and non-linear slicing method all have noise suppressed performance preferably, but in the practical communication process, due to factors such as changes in channel characteristics, modulation system change, background noise impacts, excessive (as thr=0.6 situation in Figure 11) that threshold value is chosen or too small (as thr=0.03 situation in Figure 11) make optimal threshold choose very difficult, if all can cause denoising performance to descend.

As can be seen from Figure 11, compressed sensing denoising method of the present invention takes full advantage of the characteristics of impulsive noise, estimating burst impulsive noise effectively, its noise suppressed performance obviously is better than non-linear margining amplitude technique and non-linear slicing method, and can retain to a certain extent the signal message at burst interference position place; In addition, the inventive method does not relate to the threshold value On The Choice, more convenient in application.

Claims (2)

1. a power line communication channel sporadic impulse noise restraining device, is characterized in that: comprise Fourier transform module, shelter sub-carrier selection module and compressed sensing estimation module; The input signal of described Fourier transform module is the channel receiving end signal that contains sporadic impulse noise, and its output is connected with the input of sheltering the sub-carrier selection module; The output of sheltering the sub-carrier selection module is connected with the input of compressed sensing estimation module; After the output of compressed sensing estimation module and channel receiving end signal subtract each other, obtain the signal after denoising.

2. the inhibition method of the restraining device of a power line communication channel sporadic impulse noise is characterized in that: comprise the following steps:

A, the conversion of reception signal

If the signal that x (n) is the channel transmitting terminal, y (n) is the channel receiving end signal, has

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

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

Wherein,

mean convolution algorithm, the unit impulse response that h (n) is channel, w (n) is interchannel noise, and b (n) is coloured background noise, and i (n) is sporadic impulse noise;

If the length of the unit impulse response h (n) of channel is L, the length of channel receiving end signal y (n) is N, is write formula (1) as matrix form, obtains

Definition

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

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

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

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

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

Have

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

Wherein

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

Fourier transform is carried out in formula (3) both sides, 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 diagonal matrix, and F is the Fourier transform battle array,

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

B, shelter sub-carrier selection

If the OFDM symbol is long for the N point, shelters sub-carrier indices and integrate as M=[m _f1, m _f2, m _f3..., m _fq], wherein, M is 1 * q vector, m _fi(i=1,2 ..., q) mean to shelter sub-carrier indices number;

B1, structure are sheltered the sub-carrier selection matrix

At first construct the unit matrix E of N * N dimension, then, according to sheltering sub-carrier indices number, the q in the battle array E of selection unit is capable, forms and shelters the sub-carrier selection matrix

B2, shelter subcarrier place information

Take advantage of respectively and shelter the sub-carrier selection matrix on formula (4) both sides have

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

Do not send information owing to sheltering subcarrier, therefore

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

So have

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

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

C, utilize compressed sensing signal recovery algorithms estimating burst impulsive noise

Adopt match tracing (Mathing Pursuit, MP) algorithm to the sporadic impulse noise in formula (5)

estimated, the specific implementation step is as follows:

C1, input perception matrix

measure vector

and degree of rarefication K;

C2, initialization: surplus reconstruction signal

indexed set Γ ⁰=φ, atom set

iterations n=0;

C3, carry out following iterative computation

C31, calculating surplus and perception matrix

in the inner product of each row

C32, find out g ⁿin greatest member,

C33, renewal indexed set Γ ⁿ=Γ ^n-1∪ { k} and atom set

wherein

k row column vector in corresponding perception matrix;

C34, utilize least square method to try to achieve the approximate solution of reconstruction signal,

C35, renewal surplus, $r^n={\stackrel{\&OverBar;}{Y}}_{\stackrel{\&OverBar;}{M}}-F_{\stackrel{\&OverBar;}{M}}{\stackrel{\&OverBar;}{i}}^n;$

C36, judge whether iteration meets stop condition, | r ⁿ|<1 * 10 ^-10; If meet, stop iteration, now be the sporadic impulse noise of estimation

otherwise, jump to step C31 and continue iteration;

If

deduct the sporadic impulse noise estimated value with channel receiving end signal y (n)

obtain the signal after denoising

for

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

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