CN105553896A - Non-uniform sampling and reconstruction method of broadband multi-frequency sparse signals - Google Patents

Non-uniform sampling and reconstruction method of broadband multi-frequency sparse signals Download PDF

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CN105553896A
CN105553896A CN201510859143.2A CN201510859143A CN105553896A CN 105553896 A CN105553896 A CN 105553896A CN 201510859143 A CN201510859143 A CN 201510859143A CN 105553896 A CN105553896 A CN 105553896A
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sampling
frequency spectrum
gamma
frequency
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CN105553896B (en
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胡斌杰
董飞宏
胡诗玮
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South China University of Technology SCUT
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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
    • 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

Abstract

The present invention provides a non-uniform sampling and reconstruction method of broadband multi-frequency sparse signals. The method comprises: calculating signal initial frequency spectrum information according to a multi-threshold energy detection system; establishing a signal sampling model through adoption of the non-uniform sampling parameter of rapid search emission search signals according to the obtained information; estimating signal frequency spectrum information through adoption of a subspace method of estimation; obtaining a rebuilt matrix unknown vector; and rebuilding an original signal. The method provided by the invention firstly adopts the multi-threshold energy detection system to estimate the signal frequency spectrum information and select an appropriate sampling period, so that the computation cost is reduced; and moreover, a frequency spectrum estimation algorithm based on a CAPON is adopted in the frequency spectrum estimation, so that the signal frequency spectrum information is rapidly estimated. Through adoption of the multi-threshold energy detection algorithm and the frequency spectrum estimation algorithm based on the CAPON, the computation complexity is further reduced, the frequency spectrum estimation speed in the non-uniform sampling is accelerated, and the numerical value robustness of the algorithm in a limited signal to noise ratio is ensured.

Description

The nonuniform sampling of broadband multi-frequency sparse signal and method for reconstructing
Technical field
The present invention relates to signal sampling and algorithm for estimating technical field, be specifically related to a kind of nonuniform sampling and method for reconstructing of broadband multi-frequency sparse signal.
Background technology
1) cognitive radio
Growing along with wire communication and radio communication correlation technique, especially radio communication service worldwide extensive use, radio communication may be used for the bandwidth of Signal transmissions in continuous increase, and the life of people be unable to do without wireless communication technology.In order to avoid the mutual interference between all types of user transport service, radio spectrum resources is divided into different frequency range to transmit miscellaneous service, ensures the reliability of business.But because increasing wireless traffic is widely accepted use, directly results in the day by day in short supply of frequency spectrum resource.
Cognitive radio is a kind of new wireless communication system technologies, and its research purpose is the availability of frequency spectrum of enhanced radio frequency spectrum (RF) as much as possible in limited scope.
The main target of cognitive radio optimizes spectrum transmissions performance, strengthens the availability of frequency spectrum.In order to realize this goal, top priority is frequency spectrum detection and the perception estimation technique of research wireless signal, thus identifies restoring signal frequency spectrum.After identification frequency spectrum, utilize temporal and space, space with transmission information, utilize idle and idle time gap and signal spectrum gap, improve the availability of frequency spectrum.
In radio cognitive process, digital to analog converter is needed to carry out quick, accurate and stable carrying out perception to signal to signal, in radio cognitive process, first need before the frequency spectrum cavity-pocket utilizing certain frequency range carries out information transmission at unauthorized user, exactly before unauthorized user accesses this band transmissions, need to utilize frequency spectrum perception technology for detection to go out to change timeslot channel and whether leave unused.Secondly, successfully utilize after cavity transmits at unauthorized user, occupy the frequency spectrum cavity-pocket in this section of time place, in order to avoid having an impact to the business of the higher authorized user of priority, carve at this moment and still need to carry out perception in real time to this frequency range, to prevent interference main business transmission, be want to perceive signal timely in the subscriber signal transmission that priority is higher.So radio-aware technology requires very high for the real-time of input and reliability.
2) Undersampling technique
Undersampling technique adopts to sample to signal lower than the frequency of nyquist frequency, thus increase sample rate, obtains the technology of sampling rate faster.Use Undersampling technique can reduce the sampling frequency of signal and the number of sampled point, lower to the requirement of hardware, can hardware cost be saved.
Because Undersampling technique can reduce sampling number greatly, reduce ADC hardware cost, reduce sample frequency simultaneously, promote sampling rate.Undersampling technique generally for and realize rebuilding without aliasing of signal under the target ensureing less sample frequency.Have the multiple special sampling that adopts for signal model and reconstruction mode, adopt specific sampling model and combine the specific aim process of sampled data thus realize the full backup of signal.Nonuniform sampling, compressed sensing sampling is all for " sparse " characteristic signals, the lower frequency of a small amount of useful information chosen in signal is chosen the part that signal contains main information or samples, thus with less data volume and lower sample frequency restoring signal.
3) DOA antenna frequencies algorithm for estimating
The DOA algorithm for estimating of signal is a kind of minimum searching method, and namely first form the function that comprises parameter to be estimated, then by carrying out peak value searching to this function, the extreme value obtained is exactly the direction of arrival of signal.
In model, the signal of array received can be expressed as by matrix equation,
x(t)＝A(θ)s(t)+n(t)
Wherein θ=[θ 1..., θ d] t, comprise the incident angle of signal, simultaneously s (t)=[s 1(t) ..., s d(t)] tbe made up of the waveform of signal.These all DOA equation solution methods are all based on correlation matrix, and it is defined as,
Correlation matrix R can be broken down into signal and noise subspace two parts, because the characteristic vector of noise and matrix are mutually orthogonal, signal power can by the power to signal in DOA model 0≤k≤L-1 tries to achieve.The spectrum distribution of signal can be drawn by threshold judgement.
4) SFS searching algorithm
Sequence forward direction selects searching algorithm to be the simplest greedy search algorithm of one.First a set L={0 is provided, 1 ..., L-1}, we want to find a subclass C={c 1, c 2, c p, wherein p < L, searches for minimum Matrix condition number.Sequence sweep forward algorithm is first from an empty set, constantly carries out the search of the minimal condition number to each feature C (i) simultaneously, selects a characteristic to add subclass C at every turn.Algorithm advantage compares the speed being much better than exhaustive search.
Summary of the invention
For the problem that traditional sampling algorithm sample rate is slow, the invention provides nonuniform sampling and the method for reconstructing of broadband multi-frequency sparse signal, signal based on Fourier transform owes sample and spectrum estimation algorithm, the method is first by going out the portions of the spectrum information of signal to the detection pre-estimation of signal spectrum energy, suitable nonuniform sampling parameter is chosen again by searching algorithm, set up signal spectrum estimation model, signal model is estimated by DOA algorithm, finally set up signal nonuniform sampling reconstructing system according to parameter and spectrum information, reconstruction signal.
For solving the technical problem existed in prior art, the present invention adopts following technical scheme.
A kind of nonuniform sampling of broadband multi-frequency sparse signal and method for reconstructing, after receiving the completely unknown signal of channel intermediate frequency spectrum information, width information according to Received signal strength frequency spectrum chooses the sampling period, adopt multi-threshold energy measuring method, according to the degree of rarefication setting thresholding of signal, adopt the mode of multi-threshold to adjudicate, choose suitable sampling parameter thus reduce computation complexity, reducing computed losses; Estimate signal spectrum, when signal spectrum is estimated, power spectrum signal estimation formulas is:
Wherein a (k) is nonuniform sampling matrix A ck the kth column vector of (), adopt this algorithm can reduce signal spectrum and estimate computation complexity, signal spectrum estimating speed is faster. for signal sampling correlation matrix, determined by M sample x [n].
Further, for unknown signaling, adopt energy detection system to detect detection signal, adopt the judgement mode of multiple thresholding, set m threshold value γ 1, γ 2... γ m, wherein γ 1< γ 2< ... γ m, decision rule is,
Definition judgement coefficient is a,
As Y < γ 1time, judgement no user exists, H 0... H mbe respectively the user distribution situation of different sparse grade, as Y > γ mtime, tight in channel, chooses relevant parameter L according to court verdict.
Further, select when the sampling period, search sampled point is with in the cycle during number of samples, and blind sequence forward direction of sampling selects searching algorithm, supposes the effective unit number of frequency spectrum under worst case, searches for the sampling parameter that nonuniform sampling equation of sening as an envoy to is more stable.
Further, at t i(n)=(nL+c i) the T moment carries out nonuniform sampling to signal, 1≤i≤p, set { c icontain p from set L={0,1 ..., the independently integer that L-1} chooses.
Further, signal sampling equation is matrix notation is,
y(f)＝A CS(f)，
Wherein y (f) for length be the vector of p, element is X i(e j2 π fT), A cthat a p × L ties up matrix; Only containing q the effective unit of non-zero in vector S (f) vector; Signal is rebuild by asking S (f) value.
Further, by sampled signal sequence x i[n] obtains x by filtering hi[n] and filtered sequences stack combinations is got up, the cut-off frequency of interpolation filter h [n] reconstruction formula is:
Further, the nonuniform sampling of broadband multi-frequency sparse signal and method for reconstructing, specifically comprise the steps:
The first, calculate Received signal strength energy and by comparing to come the general information of measurement bandwidth with threshold values thresholding.According to detection threshold γ decision signal spectrum information, choose corresponding sampling period L.
The second, set up sampling model, at t i(n)=(nL+c i) the T moment is to signal sampling.Sampling matrix equation can be obtained by Fourier transform y (f)=A can be abbreviated as cs (f), f ∈ F 0.
3rd, suppose the frequency spectrum non-zero unit set k under worst case, made by blind SFS searching algorithm search sampled point set C={c little as far as possible i.
4th, adopt DOA Subspace Decomposition method and CAPON spectrum estimation algorithm to estimate signal spectrum,
A (k) is matrix A cthe kth column vector of (k).
5th, according to spectrum estimation result, try to achieve frequency spectrum non-zero unit set k by threshold judgement.
6th, set up according to the parameter of trying to achieve before and nonuniform sampling is carried out to signal.
7th, reconstruction is carried out to non-uniformly sampled signals and recovers primary signal
In conjunction with the spectrum information of multi-threshold energy measuring discrimination model detection signal in described step one.
Frequency spectrum k under using blind SFS searching algorithm to preset worst case in described step 3, Modling model is gone forward side by side line frequency Power estimation.
Directly covariance matrix is asked with without the need to Subspace Decomposition in described step 4 the method estimated signal frequency spectrum of frequency.
The present invention samples for the blind non-homogeneous fast signal that spectrum information is completely unknown and rebuilds, and can apply and fast A/D C equipment.
Relative to prior art, tool of the present invention has the following advantages:
(1) in conjunction with multi-threshold energy measuring, can the completely unknown signal of Direct Sampling frequency spectrum, different from traditional lack sampling, without the need to signal spectrum partial information, type of sampling signal is wider.Reasonably choose the sampling period simultaneously, effectively reduce the computation complexity of non-uniformly sampled signals model, accelerate the spectrum estimation of signal and the speed of reconstruction.
(2) forward sequence (SFS) search method is used when parameter searches element, faster than conventional greedy searching algorithm speed.
(3), when signal spectrum being estimated, adopting modified model spectrum estimation algorithm, without the need to carrying out Subspace Decomposition to signal correlation matrix, thus accelerating signal spectrum estimating speed, can the sample rate of promotion signal.Be applicable to very fast sampling device.
Accompanying drawing explanation
Fig. 1 is signal nonuniform sampling based on Fourier transform and reconstruction model flow chart;
Fig. 2 is reconstruction signal and original signal spectrum comparison diagram;
Fig. 3 improves spectrum estimation algorithm (CAPON) and traditional algorithm (MUSIC) spectrum estimation time comparison diagram;
Fig. 4 is the nonuniform sampling reconstruction error comparison diagram of traditional MUSIC algorithm and CAPON algorithm.
Fig. 5 is the reconstruction model of non-uniformly sampled signals.
Embodiment
Below in conjunction with accompanying drawing, specific embodiment of the invention process is elaborated; but the scope of protection of present invention is not limited to the scope of lower example statement; be pointed out that; if have process or the parameter of not special detailed description below; all correlation techniques or existing techniques in realizing or understanding that those skilled in the art can refer to that background technology mentions; such as parameter n, t etc. are the parameters in the conventional expression formula of signal in digital signal technique field; top right-hand side mark H represents conjugate transpose etc., without the need to illustrating implication.
Fig. 1 is in unknown signaling situation, signal nonuniform sampling, the overall flow framework of spectrum estimation and signal reconstruction.
As an example, according to the key step of text classification, application of the present invention is described.
1) subscriber signal transmitted in general channel is all the signal that information is completely unknown, and frequently changes.When signal band distributed intelligence the unknown, algorithm, first by multi-threshold spectrum energy detection method, detects the partial information of signal spectrum, allows output signal, input signal and noise signal are respectively x (t), s (t) and w (t).Then output signal can be expressed as
H 0: x (t)=w (t), only containing noise, does not input
H 1: x (t)=s (t)+w (t) has input signal
Calculating detection threshold is:
Adopt the judgement mode of multiple thresholding.Suppose rule of thumb known to there is not space in channel, threshold value is γ m.Setting threshold value γ 1, γ 2... γ m.As Y < γ 1time, judgement no user exists, H 1... H m-1be respectively the user distribution situation of different sparse grade, as Y > γ mtime, tight in channel.Finally choose the sampling period according to court verdict.
2) set up nonuniform sampling model, choose sampling period LT, T is the nyquist sampling cycle, at t i(n)=(nL+c i) the T moment, 1≤i here≤p, gathered { c to signal sampling icontain p from set L={0,1 ..., the independently integer that L-1} chooses.
3) sampling configuration C is selected, conditional number by the selection that blind SFS search condition number is little as far as possible,
More close to 1 time, the error of signal reconstruction system is less.SFS searching algorithm adopts the method for parameter search one by one to choose suitable p value, by control errors within the specific limits while decrease searching times, improve parameter search speed.
4) at t i(n)=(nL+c i) the T moment to signal sampling, increase sampling time interval, thus accelerate the sample rate of signal.Set up nonuniform sampling equation, be reduced to:
Y (f)=A ck () z (f), wherein only contains q non-zero unit in vectorial z (f),
after trying to achieve z (f), the domain portion of signal can be tried to achieve by carrying out inverse Fourier transform to its each part.
5) signal spectrum index set k contains the information of frequency spectrum non-zero region.Must first estimate k during signal reconstruction.Here use and improve spectrum estimation algorithm, the original spectrum estimating method decomposed based on gross space, need to decompose in the covariance matrix by noise and signal slave sampling side journey to come.The power spectrum of signal is obtained again by its mutually orthogonal characteristic, thus the frequency spectrum of estimated signal.Do not need in new algorithm to decompose the covariance matrix of signal sampling equation, and directly ask the power spectrum of signal, then try to achieve signal spectrum information by threshold judgement.Improve the spectrum estimation speed of the signal signal that especially amount of information is larger.Accelerate the sampling reconstruction speed of signal.Space power spectrum is wherein a (k) is matrix A cthe kth column vector of (k),
Set k is obtained according to decision threshold,
6) finally by nonuniform sampling reconstruction model,
Restoration and reconstruction are carried out to the sequence signal after sampling, realizes Fast Inhomogeneous sampling and the reconstruction of primary signal.
Can find out that restoring signal and input signal x (t) distribute from Fig. 2 result basically identical, its medial error,
CAPON algorithm computational speed is far above traditional MUSIC algorithm speed as can be seen from Figure 3, so, at the non-homogeneous signal sampling of high speed high s/n ratio channel and in recovering, improve spectrum estimation algorithm and have estimating speed faster, innovatory algorithm estimating speed is higher than traditional algorithm about 60%.Decrease the time needed for Signal estimation, the quick sampling that can realize signal is estimated.
Fig. 4 is the reconstruction average relative error MRE of 21 signal reconstructions.Can obviously be found out by above result, the nonuniform sampling reconstruction error average size of traditional MUSIC algorithm and CAPON algorithm is similar to, and namely with this understanding, the performance of the error aspect of two kinds of algorithms is similar to.
Fig. 5 is the reconstruction model of non-uniformly sampled signals.
The present invention's fast signal be applicable in frequency spectrum perception and other signal sampling fields is sampled and is rebuild.Without the need to learning the prior information of signal, sampling rate is fast, and reconstruction error is little, and hardware cost is low, faster than traditional signal sampling algorithm speed.The spectrum distribution information of signal can be estimated fast.

Claims (6)

1. the nonuniform sampling of a broadband multi-frequency sparse signal and method for reconstructing, it is characterized in that: after receiving the completely unknown signal of channel intermediate frequency spectrum information, width information according to Received signal strength frequency spectrum chooses the sampling period, adopt multi-threshold energy measuring method, according to the degree of rarefication setting thresholding of signal, the mode of multi-threshold is adopted to adjudicate; Estimate signal spectrum, when signal spectrum is estimated, power spectrum signal estimation formulas is:
P = 1 a H ( k ) R ^ - 1 a ( k )
Wherein a (k) is nonuniform sampling matrix A cthe kth column vector of (k), for covariance matrix, determined by M sample x [n].
2. the nonuniform sampling of a kind of broadband multi-frequency sparse signal according to claim 1 and method for reconstructing, is characterized in that for unknown signaling, adopts energy detection system to detect detection signal, adopt the judgement mode of multiple thresholding, set m threshold value γ 1, γ 2... γ m, wherein γ 1< γ 2< ... γ m, decision rule is,
Y < &gamma; 1 H 0 &gamma; 1 < Y < &gamma; 2 H 1 &CenterDot; &CenterDot; &CenterDot; &gamma; m - 1 < Y < &gamma; m H m - 1 &gamma; m < Y H m
Definition judgement coefficient is a,
&gamma; 1 = a &gamma; &gamma; 2 = a 2 &gamma; &CenterDot; &CenterDot; &CenterDot; &gamma; m = a m &gamma;
As Y < γ 1time, judgement no user exists, H 0... H mbe respectively the user distribution situation of different sparse grade, as Y > γ mtime, tight in channel, chooses relevant parameter L according to court verdict.
3. the nonuniform sampling of a kind of broadband multi-frequency sparse signal according to claim 1 and method for reconstructing, it is characterized in that, select when the sampling period, search sampled point and in the cycle during number of samples, blind sequence forward direction of sampling selects searching algorithm, suppose the effective unit number of frequency spectrum under worst case, search is sent as an envoy to the more stable sampling parameter of nonuniform sampling equation.
4. the nonuniform sampling of a kind of broadband multi-frequency sparse signal according to claim 2 and method for reconstructing, is characterized in that: at t i(n)=(nL+c i) the T moment carries out nonuniform sampling to signal, 1≤i≤p, set { c icontain p from set L={0,1 ..., the independently integer that L-1} chooses.
5. the nonuniform sampling of a kind of broadband multi-frequency sparse signal according to claim 2 and method for reconstructing, is characterized in that signal sampling equation is X i ( e j 2 &pi; f T ) = 1 L T &Sigma; r &Element; Z exp ( j 2 &pi; L c i r ) X ( f + r L T ) , Matrix notation is,
y(f)＝A CS(f)，
Wherein y (f) for length be the vector of p, element is X i(e j2 π fT), A cthat a p × L ties up matrix; Only containing q the effective unit of non-zero in vector S (f) vector; Signal is rebuild by asking S (f) value.
6. the nonuniform sampling of a kind of broadband multi-frequency sparse signal according to any one of Claims 1 to 5 and method for reconstructing, is characterized in that, by sampled signal sequence x i[n] obtains x by filtering hi[n] and filtered sequences stack combinations is got up, the cut-off frequency of interpolation filter h [n] reconstruction formula is:
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