CN105553896B - The nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal - Google Patents
The nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03987—Equalisation for sparse channels
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/06—Dc level restoring means; Bias distortion correction ; Decision circuits providing symbol by symbol detection
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Abstract
The nonuniform sampling and method for reconstructing of present invention offer broadband multi-frequency sparse signal, the method includes, signal initial spectral information is calculated by multi-threshold energy detection system, the nonuniform sampling parameter of search signal is distributed using fast search according to acquisition information, establish signal sampling model, signal spectrum information is estimated using subspace estimation method, obtains reconstruction matrix unknown vector, rebuilds original signal.Method of the invention uses multi-threshold energy detection system to estimate signal spectrum information first, chooses the sampling period appropriate, reduces calculating cost, uses the spectrum estimation algorithm based on CAPON again in spectrum estimation, quickly estimates signal spectrum information.Told method sampling multi-threshold energy detection algorithm not only further reduced computation complexity, and accelerate spectrum estimation speed in nonuniform sampling, ensure that numerical robustness of the algorithm under limited signal-to-noise ratio with based on CAPON spectrum estimation algorithm.
Description
Technical field
The present invention relates to signal samplings and algorithm for estimating technical field, and in particular to a kind of broadband multi-frequency sparse signal it is non-
Uniform sampling and method for reconstructing.
Background technique
1) cognitive radio
With wire communication with wireless communication the relevant technologies it is increasingly developed, especially radio communication service is in the world
It is widely applied in range, the bandwidth that wireless communication can be used for signal transmission is being continuously increased, and people's lives are too busy to get away
Wireless communication technique.In order to avoid interfering with each other between all types of user transmission services, radio spectrum resources are divided into difference
Frequency range transmits various businesses, guarantees the reliability of business.But used since more and more wireless traffics are widely accepted,
Directly result in the increasingly in short supply of frequency spectrum resource.
Cognitive radio is a kind of new wireless communication system technologies, research purpose be in limited range as far as possible
Enhanced radio frequency spectrum (RF) the availability of frequency spectrum.
The main target of cognitive radio is optimization spectrum transmissions performance, enhances the availability of frequency spectrum.In order to realize this mesh
Mark, top priority is to study the frequency spectrum detection and perception estimation technique of wireless signal, to identify recovery signal spectrum.It is identifying
After frequency spectrum, using temporal and space gap to transmit information, idle and idle time gap and signal spectrum are utilized
The availability of frequency spectrum is improved in gap.
In radio cognitive process, digital analog converter is needed to carry out signal quick, accurate and stable to signal
It is perceived, in radio cognitive process, needs to carry out information using the frequency spectrum cavity-pocket of certain frequency range first in unauthorized user
Before transmission, exactly before unauthorized user accesses the band transmissions, need to detect to change the time using frequency spectrum perception technology
Whether channel leaves unused.Secondly, occupying this section of time and location after unauthorized user is successfully transmitted using cavity
Frequency spectrum cavity-pocket, in order to avoid the business to the higher authorized user of priority has an impact, there is still a need for the frequency at this moment
Section real-time perfoming perception is that can be timely in priority higher subscriber signal transmitting to prevent interference main business transmission
Perceive signal.So radio-aware technology is very high for real-time and the reliability requirement of signal detection.
2) Undersampling technique
Undersampling technique is to be sampled using the frequency lower than nyquist frequency to signal, to increase sampling speed
Degree, obtains the technology of faster sampling rate.The sampling frequency of signal and of sampled point can be reduced using Undersampling technique
Number, the requirement to hardware is lower, can save hardware cost.
Since Undersampling technique can substantially reduce sampling number, ADC hardware cost is reduced, while reducing sample frequency,
Promote sampling rate.Undersampling technique generally for realized under the target for guaranteeing lesser sample frequency signal without aliasing
It rebuilds.It using specific sampling model and can be tied there are many special sampling and reconstruction mode used for signal model
The specific aim processing to sampled data is closed to realize the full backup of signal.Nonuniform sampling, compressed sensing sampling is all needle
To " sparse " characteristic signals, the part that a small amount of useful information in signal contains main information with lower frequency to signal is chosen
It is chosen or is sampled, to restore signal with less data volume and lower sample frequency.
3) DOA antenna frequencies algorithm for estimating
The DOA algorithm for estimating of signal is a kind of minimum searching method, that is, is initially formed the function comprising parameter to be estimated,
Then by carrying out peak value searching to the function, obtained extreme value is exactly the direction of arrival of signal.
The signal of array received can be expressed as by matrix equation in model,
X (t)=A (θ) s (t)+n (t)
Wherein θ=[θ1,...,θd]T, the incident angle comprising signal, while s (t)=[s1(t),...,sd(t)]TThere is letter
Number waveform composition.All these DOA equation solution methods are all based on correlation matrix, are defined as,
Correlation matrix R can be broken down into signal and noise subspace two parts, because of the feature vector and matrix of noise
Be it is mutually orthogonal, signal power can by DOA model to the power of signal0≤k≤L-1
It acquires.By threshold judgement it can be concluded that the spectrum distribution of signal.
4) SFS searching algorithm
Before sequence to selection searching algorithm be a kind of simplest greedy search algorithm.Provide first a set L=0,
1 ..., L-1 }, we want that finding a subset closes C={ c1,c2,cp, wherein p < L, to search for the smallest Matrix condition number.
Sequence sweep forward algorithm is while constantly to carry out the minimum to each feature C (i) first since an empty set
The search of conditional number, subclass C is added in one characteristic of selection every time.Algorithm advantage is compared to the speed for being much better than exhaustive search
Degree.
Summary of the invention
For the problem that traditional sampling algorithm sample rate is slow, the present invention provides the non-homogeneous of broadband multi-frequency sparse signal and adopts
Sample and method for reconstructing, the signal based on Fourier transformation owe sample and spectrum estimation algorithm, and this method is first by signal spectrum
The detection pre-estimation of energy goes out the portions of the spectrum information of signal, then chooses nonuniform sampling parameter appropriate by searching algorithm,
Signal spectrum estimation model is established, signal model is estimated by DOA algorithm, signal is finally established according to parameter and spectrum information
Nonuniform sampling reconstructing system, reconstruction signal.
To solve the technical problems existing in the prior art, the present invention is adopted the following technical scheme that.
A kind of nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal, when receiving, spectrum information in channel is complete
After unknown signal, the sampling period is chosen according to the width information of receipt signal frequency spectrum, using multi-threshold energy measuring method, according to
The degree of rarefication of signal sets thresholding, is made decisions by the way of multi-threshold, chooses sampling parameter appropriate to reduce calculating
Complexity reduces computed losses；Signal spectrum is estimated, in signal spectrum estimation, power spectrum signal estimation formulas are as follows:
Wherein a (k) is nonuniform sampling matrix AC(k) kth column vector can reduce signal spectrum using this algorithm and estimate
Computation complexity is counted, signal spectrum estimating speed is faster.For signal sampling correlation matrix, by M
A sample x [n] determines.
Further, for unknown signaling, detection signal is detected using energy detection system, using the judgement of multiple thresholdings
Mode sets m threshold value γ1,γ2...γm, wherein γ1< γ2< ... γm, decision rule is,
Definition judgement coefficient is a,
As Y < γ1When, judgement no user exists, H0,...HmThe user distribution situation of respectively different sparse grades, works as Y
> γmWhen, tight in channel chooses relevant parameter L according to court verdict.
Further, selected when the sampling period, in search sampled point and period when number of samples, sample Xiang Xuan before blind sequence
Select searching algorithm, it is assumed that the effective unit number of frequency spectrum under worst case searches for the more stable sampling of nonuniform sampling equation of sening as an envoy to
Parameter.
Further, in ti(n)=(nL+ci) the T moment, 1≤i≤p gathered { c to signal progress nonuniform samplingiPacket
The independent integer of p from set L={ 0,1 ..., L-1 } selection is contained.
Further, signal sampling equation isMatrix indicates
For,
Y (f)=ACS (f),
Wherein y (f) is the vector that length is p, element Xi(ej2πfT), ACIt is p × L dimension matrix；Vector S (f) to
The effective unit of q non-zero is contained only in amount；Signal can be by asking S (f) value to rebuild.
Further, by sampled signal sequence xi[n] obtains x by filteringhi[n] and filtered sequences are folded
Add and combines, the cutoff frequency of interpolation filter h [n]Reconstruction formula are as follows:
Further, the nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal, specifically comprises the following steps:
First, calculate the energy for receiving signal and the general information by detecting frequency band compared with threshold values thresholding.According to
Detection threshold γ decision signal spectrum information, chooses corresponding sampling period L.
Second, sampling model is established, in ti(n)=(nL+ci) the T moment is to signal sampling.Sampling matrix equation passes through in Fu
Leaf transformation can obtainIt can be abbreviated as y (f)=ACS(f),f∈F0。
Third, it is assumed that the frequency spectrum non-zero unit set k under worst case is made by the search of blind SFS searching algorithmSampled point set C={ c as small as possiblei}。
4th, signal spectrum is estimated using DOA Subspace Decomposition method and CAPON spectrum estimation algorithm,
A (k) is matrix AC(k) kth column vector.
5th, according to spectrum estimation as a result, acquiring frequency spectrum non-zero unit set k by threshold judgement.
6th, it is established according to the parameter acquired before and nonuniform sampling is carried out to signal.
7th, non-uniformly sampled signals rebuild and restore original signal
The spectrum information of multi-threshold energy measuring discrimination model detection signal is combined in the step 1.
In the step 3 using blind SFS searching algorithm preset worst case under frequency spectrum k, establish model go forward side by side line frequency spectrum
Estimation.
Covariance matrix is directly sought with without Subspace Decomposition in the step fourFrequency method estimate signal
Frequency spectrum.
The present invention blind non-homogeneous fast signal sampling totally unknown for spectrum information and rebuild, can using with it is quick
ADC device.
Compared with the existing technology, the present invention has the advantage that
(1) combine multi-threshold energy measuring, can direct sampling frequency totally unknown signal, not with traditional lack sampling
Together, it is not necessarily to signal spectrum partial information, type of sampling signal is wider.It is reasonable simultaneously to choose the sampling period, it is effectively reduced non-
The computation complexity of uniform sampling signal model accelerates the spectrum estimation of signal and rebuilds speed.
(2) using forward sequence (SFS) search method when parameter searches element, faster than conventional greedy searching algorithm speed.
(3) empty without carrying out son to signal correlation matrix using modified spectrum estimation algorithm when estimating signal spectrum
Between decompose, can be with the sample rate of promotion signal to accelerate signal spectrum estimating speed.Suitable for very fast sampling device.
Detailed description of the invention
Fig. 1 is signal nonuniform sampling and reconstruction model flow chart based on Fourier transformation；
Fig. 2 is reconstruction signal and original signal spectrum comparison diagram；
Fig. 3 is to improve spectrum estimation algorithm (CAPON) and traditional algorithm (MUSIC) spectrum estimation time comparison diagram；
Fig. 4 is traditional MUSIC algorithm figure compared with the nonuniform sampling reconstruction error of CAPON algorithm.
Fig. 5 is the reconstruction model of non-uniformly sampled signals.
Specific embodiment
It elaborates with reference to the accompanying drawing to specific implementation process of the invention, but the scope of protection of present invention is simultaneously
It is not limited to the range of lower example statement, if it is noted that the following process or parameter for having not special detailed description, is ability
Field technique personnel can refer to the relevant technologies that background technique refers to or the prior art and realize or understand, such as parameter n, t etc. is
Parameter in digital signal technique field in the common expression formula of signal, top right-hand side mark H indicate conjugate transposition etc., without especially saying
Bright meaning.
Fig. 1 is signal nonuniform sampling in the case of unknown signaling, the overall flow frame of spectrum estimation and signal reconstruction.
As example, according to the key step of text classification, to illustrate application of the invention.
1) subscriber signal transmitted in general channel is all the totally unknown signal of information, and is frequently changed.?
In the case that signal band distributed intelligence is unknown, algorithm passes through multi-threshold spectrum energy detection method first, detects signal spectrum
Partial information, allow output signal, input signal and noise signal are respectively x (t), s (t) and w (t).Then output signal can be with
It is expressed as
H0: x (t)=w (t) is not inputted containing only noise
H1: x (t)=s (t)+w (t) has input signal
Calculate detection threshold are as follows:
Using the judgement mode of multiple thresholdings.Assuming that rule of thumb known when gap is not present in channel, threshold value is
γm.Set threshold value γ1,γ2...γm.As Y < γ1When, judgement no user exists, H1,...Hm-1It is respectively different sparse etc.
The user distribution situation of grade, as Y > γmWhen, tight in channel.The sampling period is finally chosen according to court verdict.
2) nonuniform sampling model is established, chooses sampling period LT, T is the nyquist sampling period, in ti(n)=(nL+
ci) the T moment, 1≤i≤p, gathered { c here to signal samplingiP is contained from the only of set L={ 0,1 ..., L-1 } selection
Vertical integer.
3) sampling configuration C is selected by the selection as small as possible of blind SFS searching bar number of packages, conditional number,
When closer 1, the error of signal reconstruction system is smaller.SFS searching algorithm is selected using the method for parameter search one by one
P value appropriate is taken, reduces searching times while by control errors in a certain range, improves parameter search rate.
4) in ti(n)=(nL+ci) the T moment to signal sampling, sampling time interval is increased, to accelerate signal
Sample rate.Nonuniform sampling equation is established,Simplify are as follows:
Y (f)=AC(k) z (f) wherein contains only q non-zero unit in vector z (f),
After acquiring z (f), the domain portion of signal can by each of which part into
Row inverse Fourier transform acquires.
5) signal spectrum index set k contains the information of frequency spectrum non-zero region.First k must be carried out when to signal reconstruction
Estimation.Used here as improving spectrum estimation algorithm, the original spectrum estimating method decomposed based on gross space, need noise and
It disassembles and in the covariance matrix of signal slave sampling side journey.The power spectrum of signal is found out by its mutually orthogonal characteristic again,
To estimate the frequency spectrum of signal.It does not need to decompose the covariance matrix of signal sampling equation in new algorithm, and directly asks
The power spectrum of signal, then signal spectrum information is acquired by threshold judgement.Improve the biggish signal of signal especially information content
Spectrum estimation speed.Accelerate the sampling reconstruction speed of signal.Space power spectrum isWherein a (k)
For matrix AC(k) kth column vector,
Set k is found out according to decision threshold,
6) finally by nonuniform sampling reconstruction model,
Restoration and reconstruction are carried out to the sequence signal after sampling, realize the Fast Inhomogeneous sampling of original signal and are rebuild.
As can be seen from the result of figure 2 that restore signal and input signal x (t) distribution is almost the same, wherein error,
CAPON algorithm calculating speed is much higher than tradition MUSIC algorithm speed as can be seen from Figure 3, so, in the high letter of high speed
It makes an uproar than in the non-homogeneous signal sampling and recovery of channel, improving spectrum estimation algorithm has faster estimating speed, innovatory algorithm
Estimating speed is higher than traditional algorithm about 60%.Time needed for reducing signal estimation, the quick sampling that signal may be implemented are estimated
Meter.
Fig. 4 is the reconstruction average relative error MRE of 21 signal reconstructions.By result above, it is apparent that tradition
MUSIC algorithm is approximate with the nonuniform sampling reconstruction error mean value size of CAPON algorithm, that is, with this condition, two kinds of calculations
Performance in terms of the error of method is approximate.
Fig. 5 is the reconstruction model of non-uniformly sampled signals.
Fast signal sampling and reconstruction of the present invention suitable for frequency spectrum perception and other signal sampling fields.Without learning
The prior information of signal, sampling rate is fast, and reconstruction error is small, and hardware cost is low, faster than traditional signal sampling algorithm rate.
The spectrum distribution information of signal can quickly be estimated.
Claims (2)
1. a kind of nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal, it is characterised in that: when receiving channel intermediate frequency
After the totally unknown signal of spectrum information, the sampling period is chosen according to the width information of receipt signal frequency spectrum, using multi-threshold energy
Detection method is set thresholding according to the degree of rarefication of signal, is made decisions by the way of multi-threshold；Signal spectrum is estimated,
In signal spectrum estimation, power spectrum signal estimation formulas are as follows:
Wherein a (k) is nonuniform sampling matrix AC(k) kth column vector,For covariance matrix, by M sample x [n]
It determines；For unknown signaling, detection signal is detected using energy detection system, using the judgement mode of multiple thresholdings, sets m
Threshold value γ1,γ2...γm, wherein γ1<γ2<...γm, decision rule is,
Definition judgement coefficient is a,
As Y < γ1When, judgement no user exists, H0,...HmThe user distribution situation of respectively different sparse grades, works as Y > γm
When, tight in channel chooses relevant parameter L according to court verdict；
In ti(n)=(nL+ci) the T moment, 1≤i≤p gathered { c to signal progress nonuniform samplingiP are contained from setThe independent integer chosen；Signal sampling equation isMatrix is expressed as,
Y (f)=ACS (f),
Wherein y (f) is the vector that length is p, element Xi(ej2πfT), ACIt is p × L dimension matrix；In vector S (f) vector only
Contain the effective unit of q non-zero；Signal can be by asking S (f) value to rebuild；By sampled signal sequence xi[n] obtains x by filteringhi
[n] and filtered sequences stack combinations are got up, the cutoff frequency of interpolation filter h [n]It rebuilds public
Formula are as follows:
2. the nonuniform sampling and method for reconstructing of a kind of broadband multi-frequency sparse signal according to claim 1, feature exist
In, when the sampling period is selected, in search sampled point and period when number of samples, sample before blind sequence to selection searching algorithm, it is false
If the effective unit number of frequency spectrum under worst case, the more stable sampling parameter of nonuniform sampling equation of sening as an envoy to is searched for.
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| CN107040296B (en) * | 2017-02-28 | 2020-05-26 | 北京航空航天大学 | Channel estimation method in millimeter wave communication |
| CN109213960B (en) * | 2017-07-03 | 2022-10-28 | 中电科海洋信息技术研究院有限公司 | Method and device for reconstructing periodic non-uniform sampling band-limited signal |
| CN108334932B (en) * | 2017-11-27 | 2022-03-29 | 中科观世（北京）科技有限公司 | Frequency distinguishing method based on target signal characteristics |
| CN108509506B (en) * | 2018-03-06 | 2021-07-13 | 西安大衡天成信息科技有限公司 | Frequency spectrum monitoring data structured representation method |
| CN109298391B (en) * | 2018-08-27 | 2023-08-01 | 南京航空航天大学 | Fixed-place information source positioning system, method and application |
| CN110149118A (en) * | 2019-04-28 | 2019-08-20 | 北京航空航天大学 | A kind of dynamic channelization method based on non-homogeneous filter group |
| CN111884706B (en) * | 2020-07-17 | 2021-02-02 | 北京和德宇航技术有限公司 | Satellite spectrum detection method, device, equipment and storage medium |
| CN113824518B (en) * | 2021-09-16 | 2024-07-09 | 中国电子科技集团公司第二十研究所 | Spectrum-based non-cooperative signal detection method |
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