CN105763202A - Signal recovery method based on compressed sensing, and apparatus thereof - Google Patents

Abstract

The invention discloses a signal recovery method based on compressed sensing, and an apparatus thereof, and relates to the technical field of satellite communication. The signal recovery method based on compressed sensing comprises the steps: performing Sub-Nyquist sampling on satellite uplink continuous time signal which satisfies sparsity so as to acquire the sampling observation data; based on the sampling mode of the Sub-Nyquist sampling, determining a sampling matrix; and according to the sampling matrix, utilizing a compressed sensing theory to recover an original signal from the sampling observation data. The signal recovery method based on compressed sensing, and the apparatus thereof can perform Sub-Nyquist sampling on the satellite uplink continuous time signal to acquire the sampling observation data, and then can determine the sampling matrix, based on the sampling mode of the Sub-Nyquist sampling, and at last can recover the original signal from the sampling observation data according to the compressed sensing theory, so that the sampling rate is reduced; the signal recovery correct rate is high; and digital channelization satellite borne exchange can be realized.

Description

Signal recovery method and device based on compressed sensing

Technical field

The present invention relates to technical field of satellite communication, particularly to a kind of signal recovery method based on compressed sensing and device.

Background technology

Now, signal reconnaissance is nearly all based upon on star on Digital Signal Processing basis, and analog digital conversion (Analog-to-DigitalConversion, the ADC) process of signal becomes the core of signal reconnaissance.Therefore efficient sampling and restoration methods are most important for signal reconnaissance, have wide engineer applied simultaneously and are worth.

The design of nearly all ADC device is all based on Nyquist-Shannon sampling thheorem, and namely bandwidth is the real signal of BHz, is at least under the uniform sampling of 2Bsps in sample rate, and signal can by Exact recovery.The sample rate of ADC device is more high, and precision (bit number) is more low, and expection often increases the precision (for all of sample rate) of 1.5 bits, it is necessary to the development time of 8 years, this development speed can not meet the demand of association area.For high band (such as Ka or higher) broadband satellite signal, the sample rate that its highest frequency can reach far beyond existing ADC device.Therefore, in ultrashort wave (even higher frequency section) full frequency band signal reconnaissance is applied, ADC encounters serious bottleneck problem, for instance high sample rate.

Sample rate bottleneck problem for above-mentioned ADC, the following two kinds method is taked to tackle in engineering practice at present: first, various structures is adopted to carry out ADC design, such as FlashADC, time-interleaved ADC structure etc., this obtains higher sample rate to a certain extent, but also bringing a lot of problem, the precision such as FlashADC is difficult to improve, because its complexity and precision are exponentially increased relation.Second, adopt conversion method, namely directly wideband input signal is not sampled, but signal spectrum is moved in Low Medium Frequency or zero intermediate frequency, then select existing ADC device to sample.But the method not only can additionally increase hardware device, bring burden, the carrier frequency of input signal and needs know for sure to the volume of system, weight and power consumption etc..Therefore, under the scene that can not obtain any information of carrier frequency, such as broadband radio scouting, electronic warfare etc., the method can not use.

Both the above method is all in the restriction range of Nyquist-Shannon sampling thheorem.Although they solve some engineering problem to a certain extent, but bring immense pressure to follow-up digital signal processing unit.When signal bandwidth is very big, such as ultra-broadband signal etc., current ADC device has been difficult to the analog digital conversion of signal.Therefore, find and propose sampling and restoration methods efficiently, for ultrashort wave full frequency band signal processing, there is very important theory directive significance and engineering practical value.

Summary of the invention

In view of the above problems, it is proposed that the present invention is to provide a kind of a kind of signal recovery method based on compressed sensing and device overcoming the problems referred to above or solving the problems referred to above at least in part.

According to one aspect of the present invention, it is provided that a kind of signal recovery method based on compressed sensing, described method includes:

Time nyquist sampling is carried out, to obtain sampling observation data to meeting openness satellite uplink continuous time signal；

Sample mode based on described nyquist sampling determines sampling matrix；

Compressive sensing theory is utilized to recover primary signal from described sampling observation data according to described sampling matrix.

Alternatively, the sample mode of described nyquist sampling is the sampling of many cosets；

Correspondingly, described carry out time nyquist sampling to meeting openness satellite uplink continuous time signal, observe data obtaining sampling, farther include:

Nyquist sampling is carried out according to preset time period T, to obtain discrete data to meeting openness satellite uplink continuous time signal；

Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

Alternatively, the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\π}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

Alternatively, described according to described sampling matrix utilize compressive sensing theory from described sampling observation data recover primary signal, farther include:

A101: utilize orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\λ}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

A102: according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\‾}{A}}_v=\[{\stackrel{\‾}{A}}_{v-1},A_{{\mathrm{\λ}}_v}\],$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

A103: utilize method of least square, solves optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\‾}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\‾}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

A104: calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

A105: v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then return step A101, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

Alternatively, described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has an effectively frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.

According to another aspect of the present invention, it is provided that a kind of signal recovery device based on compressed sensing, described device includes:

Signal sampling unit, for carrying out time nyquist sampling to meeting openness satellite uplink continuous time signal, observes data obtaining sampling；

Matrix determines unit, determines sampling matrix for the sample mode based on described nyquist sampling；

Signal recovery unit, for utilizing compressive sensing theory to recover primary signal from described sampling observation data according to described sampling matrix.

Alternatively, the sample mode of described nyquist sampling is the sampling of many cosets；

Correspondingly, described signal sampling unit, it is further used for carrying out nyquist sampling according to preset time period T to meeting openness satellite uplink continuous time signal, to obtain discrete data；Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

Alternatively, the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\π}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

Alternatively, described signal recovery unit, farther include:

Index searches subelement, is used for utilizing orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\λ}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

Matrix disposal subelement, for according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\‾}{A}}_v=\[{\stackrel{\‾}{A}}_{v-1},A_{{\mathrm{\λ}}_v}\],$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

Solve recovery subelement, be used for utilizing method of least square, solve optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\‾}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\‾}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

Residual computations subelement, for being calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

From increasing judgment sub-unit, for v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then call described index to search subelement, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

Alternatively, described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has limited frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.

The present invention by carrying out time nyquist sampling to satellite uplink continuous time signal, to obtain sampling observation data, sample mode based on secondary nyquist sampling determines sampling matrix again, compressive sensing theory is utilized to recover primary signal from described sampling observation data finally according to described sampling matrix, thus reducing sample rate, and it is high that signal recovers accuracy, it is possible to realizes the spaceborne exchange of digital channelizing.

Accompanying drawing explanation

Fig. 1 is the flow chart of the signal recovery method based on compressed sensing of one embodiment of the present invention；

Fig. 2 is the spectrum diagram of the up continuous time signal of Ka band satellite；

Fig. 3 is the relation schematic diagram of X (f) and x (f)；

Fig. 4 is the relation schematic diagram that the signal adopting the signal recovery method based on compressed sensing of one embodiment of the present invention to obtain recovers accuracy and sampling observation data length；

Fig. 5 is the structured flowchart of the signal recovery device based on compressed sensing of one embodiment of the present invention.

Detailed description of the invention

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following example are used for illustrating the present invention, but are not limited to the scope of the present invention.

Fig. 1 is the flow chart of the signal recovery method based on compressed sensing of one embodiment of the present invention；With reference to Fig. 1, described method includes:

S101: carry out time nyquist sampling to meeting openness satellite uplink continuous time signal, to obtain sampling observation data；

S102: the sample mode based on described nyquist sampling determines sampling matrix；

S103: utilize compressive sensing theory to recover primary signal from described sampling observation data according to described sampling matrix.

Present embodiment by carrying out time nyquist sampling to satellite uplink continuous time signal, to obtain sampling observation data, sample mode based on secondary nyquist sampling determines sampling matrix again, compressive sensing theory is utilized to recover primary signal from described sampling observation data finally according to described sampling matrix, thus reducing sample rate, and it is high that signal recovers accuracy, it is possible to realizes the spaceborne exchange of digital channelizing.

It should be noted that the sample mode of secondary nyquist sampling can be selected for various ways, in present embodiment, the sample mode of optional time nyquist sampling is the sampling of many cosets；

Correspondingly, step S101, farther include:

Nyquist sampling is carried out according to preset time period T, to obtain discrete data to meeting openness satellite uplink continuous time signal；

Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

It will be appreciated that when the sample mode selecting time nyquist sampling is the sampling of many cosets, the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\π}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

For ensureing the accuracy rate that signal recovers, in present embodiment, step S103 can farther include:

A101: utilize orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\λ}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

A102: according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\‾}{A}}_v=\[{\stackrel{\‾}{A}}_{v-1},A_{{\mathrm{\λ}}_v}\],$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

A103: utilize method of least square, solves optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\‾}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\‾}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

A104: calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

A105: v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then return step A101, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

Carrying out signal recovery owing to satellite uplink continuous time signal needs to meet openness ability by the method for present embodiment, in implementing, described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has limited frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.

It is sampled as example so that the present invention to be described with Ka band satellite signal and many cosets below, but does not limit protection scope of the present invention.The method of the present embodiment comprises the following steps:

By founding mathematical models, the first step, judges whether satellite uplink continuous time signal meets openness；

In scouting application, and in ultrashort wave frequency band, if satellite uplink consecutive hours, the Fourier transform of satellite uplink continuous signal x (t) is:

X (f)=∫ x (t) exp (-j2 π ft) dt (1)

In formula: X (f) is the continuous of frequency f or sectional-continuous function.If x (t) meets following three condition,

(1) x (t) is band-limited signal, and its frequency separation is F=[0,1/T], i.e. X (f)=0,For Ka frequency band signals, its Nyquist (i.e. Nyquist) speed 1/T may be up to tens of Gsps；

(2) X (f) has less than N number of disjoint frequency range on F；

(3) bandwidth of each frequency range is not more than B, i.e. B_n≤ B, n=1,2 ..., N；

Then signal x (t) meets time Nyquist sampling to openness requirement, is referred to as multi-wave signal, as shown in Figure 2.The Nyquist sample rate of recovery signal x (t) correspondence in figure is 1/T, each frequency band [a_i,b_i] uniquely represent.

Secondary Nyquist sample mode based on compressive sensing theory is introduced in satellite system by mathematical abstractions above, to build this theory application framework in Ka band satellite system.From practical application, Ka band bandwidth is up to tens of GHz (20GHz-40GHz), the part being really used only several GHz even less (because also having diversity technique to cause the factor of frequency reuse), the frequency spectrum that namely signal takies meets openness.

Second step: satellite uplink continuous time signal is sampled by many cosets sampling configuration；

If satellite uplink continuous time signal is x (t), initially with Nyquist speed, signal is carried out uniform sampling, obtain sequence { x (nT) }, then this sequence contains all information of x (t).Recycle the sampling of many cosets from { x (nT) }, choose the process of some sampling point, be grouped into p group by sequence { x (nT) }, group often has continuous L sampled point.Define constant set C, c that length is p_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C, then

0≤c₁< c₂< ... < c_p≤L-1.(2)

Definition i-th (1≤i≤p) individual sample sequence is

Under this sample mode, its average oscillation frequency f_avgWith Nyquist sample frequency f_NyqRelation be

$f_{\mathrm{avg}}=\frac{p}{L}{f}_{\mathrm{Nyq}}---\left(4\right)$

By (2) formula it can be seen that f_avg< f_Nyq.

SequenceDiscrete Fourier transform (DFT)And there is relation between Fourier transform X (f) of signal x (t):

$\begin{array}{c}{X}_{c_i}\left(e^{j2\mathrm{\&pi;}fT}\right)=\underset{n=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{x}_{c_i}\exp (-j2\mathrm{\&pi;}fnT)\\ =\frac{1}{LT}\underset{r=0}{\overset{L-1}{\&Sigma;}}\exp \left(j\frac{2\mathrm{\&pi;}}{L}{c}_{i}r\right)X(f+\frac{r}{LT})\end{array}---\left(5\right)$

In formula: 1≤i≤p, and

$f\&Element;F_0=\&lsqb;0,\frac{1}{LT})---\left(6\right)$

So, many cosets sampling process can be expressed as with matrix form

$y\left(f\right)=Ax\left(f\right),\&ForAll;f\&Element;F_0---\left(7\right)$

Wherein, y (f) is the vector with p element, and i-th element isK element of the i-th of matrix A is provided by formula (8)

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\&pi;}}{L}{c}_{i}k\right)---\left(8\right)$

X (f) is the vector with L element, and its i-th element is

$x_i\left(f\right)=X(f+\frac{i}{LT}),0\&le;i\&le;L-1,f\&Element;F_0---\left(9\right)$

Relation between X (f) and x (f) is as shown in Figure 3.

Therefore, the recovery problem of x (t) is converted to a typical sparse signal and recovers problem, namely recovers primary signal from sampling observation data.

3rd step: utilize compressive sensing theory to recover primary signal from sampling observation data；

Consider that satellite uplink channel is divided into d sub-channels, if primary signal x (f) takies m sub-channels therein, it is equivalent in signal vector x (f) and only has m nonzero element, the dimension of sampling matrix A is N × d, thus, sampling observation data y (the f)=Ax (f) of N dimension.

Owing to only having m nonzero element in signal vector x (f), therefore sampling observation data y (f) is the linear combination of m row in A.In order to recover signal x (f), it must be determined which row in A are formed with contribution to sampling observation data, once it is determined that, we just know signalThe accurate location of middle nonzero element, corresponds in corresponding sub-channel positions, thus recovering signal x (f).

Detailed step that primary signal recover is given below:

Sampling matrix A=[the A of input parameter: N × d dimension₁,A₂,A₃,…,A_d], then A_{J=1,2,3 ..., d}For N dimensional vector

Sampling observation data y (f) of N dimension

Maximum iteration time V (namely above-mentioned " preset value ")

The recovery signal of output parameter: x (f)

Intermediate parameters: Λ_iFor comprising the index set (manifold) of i element

N dimensional vector y_iApproximation for y (f)

N dimensional vector r_i=y (f)-y_iRepresent data residual error

Data matrix for N × i dimension

Step 1: parameter is initialized, now i=0, make r₀=y (f), index set Λ₀For empty set,For sky, iteration count v=1.

Step 2: utilize orthogonality, finds optimized index λ_vSo that:

${\mathrm{\&lambda;}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|---\left(11\right)$

Step 3: utilize the index λ searched out in step 2_v, vectorManifold and data matrix are processed.

Λ_v=Λ_v-1∪{λ_v}(12)

${\stackrel{\&OverBar;}{A}}_v=\&lsqb;{\stackrel{\&OverBar;}{A}}_{v-1},A_{{\mathrm{\&lambda;}}_v}\&rsqb;---\left(13\right)$

Step 4: utilize method of least square, solves optimization problem, obtains the signal of correspondence:

${\stackrel{\&OverBar;}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\&OverBar;}{A}}_{v}x|{|}_2---\left(14\right)$

Step 5: utilize the result in 4, calculates new observation approximation and data residual error:

$y_v={\stackrel{\&OverBar;}{A}}_v{\stackrel{\&OverBar;}{x}}_v---\left(15\right)$

r_v=y-y_v(16)

Step 6: increase iteration count v=v+1, returns to step 2 and restarts to perform, until enumerator t > V stops.

Step 7: the return signal that step 4 is calculatedAs the primary signal recovered

Ultrashort wave full frequency band signaling protein14-3-3 can be completed according to above step, introduce present invention embodiment in processing satellite uplink signal below by way of concrete data, but do not limit protection scope of the present invention.

First the parameter needing to use is provided in following example:

Table 1 basic parameter table

Star up channel is divided into d=128 sub-channels, signal takies the number m of sub-channel respectively 2,5,10,16,32, the number of observation data y (f) is stepped up d by 2, sample operator matrix A is obtained by standard normal distribution sampling, in signal vector x (f), nonzero element value puts 1, y (f) can be obtained according to formula (7), it is restored signal x further according to y (f), A and above-mentioned algorithm, the signal x relatively recovered and primary signal x (f), it is known that whether correct signal recovers.Program repeats 1000 times and obtains the ratio that signal correctly recovers, and sees Fig. 4.In Fig. 4, abscissa represents the length N of observation data vector, and vertical coordinate represents the accuracy that signal recovers.

As seen from Figure 4, under above-mentioned sample mode and signal recovery algorithms, when signal, to take number of subchannels more many, when namely m is more big, will correctly recover signal, then the N of sampling observation data must be increasing.It is to say, the ratio m/d that signal accounts for whole channel width is more big, namely the sparse degree of signal is more low, then under the observation data qualification of certain length, signal recovers accuracy and reduces, if to improve signal to recover accuracy, need to increase the length of observation data.This is consistent with compressive sensing theory.Therefore, in the method for present embodiment, when carrying out sub-channel division and configuration, to consider " openness " of signal and the dimension of sampling observation data.

For method embodiment, in order to be briefly described, therefore it is all expressed as a series of combination of actions, but those skilled in the art should know, embodiment of the present invention is not by the restriction of described sequence of movement, because according to embodiment of the present invention, some step can adopt other orders or carry out simultaneously.Secondly, those skilled in the art also should know, embodiment described in this description belongs to preferred implementation, necessary to involved action not necessarily embodiment of the present invention.

Fig. 5 is the structured flowchart of the signal recovery device based on compressed sensing of one embodiment of the present invention；With reference to Fig. 5, described device includes:

Signal sampling unit 501, for carrying out time nyquist sampling to meeting openness satellite uplink continuous time signal, observes data obtaining sampling；

Matrix determines unit 502, determines sampling matrix for the sample mode based on described nyquist sampling；

Signal recovery unit 503, for utilizing compressive sensing theory to recover primary signal from described sampling observation data according to described sampling matrix.

In the optional embodiment of one of the present invention, the sample mode of described nyquist sampling is the sampling of many cosets；

Correspondingly, described signal sampling unit, it is further used for carrying out nyquist sampling according to preset time period T to meeting openness satellite uplink continuous time signal, to obtain discrete data；Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

In the optional embodiment of one of the present invention, the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\&pi;}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

In the optional embodiment of one of the present invention, described signal recovery unit, farther include:

Index searches subelement, is used for utilizing orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\&lambda;}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

Matrix disposal subelement, for according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\&OverBar;}{A}}_v=\&lsqb;{\stackrel{\&OverBar;}{A}}_{v-1},A_{{\mathrm{\&lambda;}}_v}\&rsqb;,$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

Solve recovery subelement, be used for utilizing method of least square, solve optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\&OverBar;}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\&OverBar;}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

Residual computations subelement, for being calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

From increasing judgment sub-unit, for v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then call described index to search subelement, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

In the optional embodiment of one of the present invention, described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has limited frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.

For device embodiments, due to itself and method embodiment basic simlarity, so what describe is fairly simple, relevant part illustrates referring to the part of method embodiment.

It should be noted that, in all parts of assembly of the invention, parts therein have been carried out logical partitioning according to its function to realize, but, the present invention is not only restricted to this, it is possible to as required all parts is repartitioned or combines.

The all parts embodiment of the present invention can realize with hardware, or realizes with the software module run on one or more processor, or realizes with their combination.In this device, equipment or device are remotely controlled by PC by realizing the Internet, control the step of equipment or each operation of device accurately.The present invention is also implemented as part or all the equipment for performing method as described herein or device program (such as, computer program and computer program).It is achieved in that the program of the present invention can store on a computer-readable medium, and the file or document that program produces has and statistically, can produce data report and cpk report etc., power amplifier can be carried out batch testing and add up.The present invention will be described rather than limits the invention to it should be noted above-mentioned embodiment, and those skilled in the art can design replacement embodiment without departing from the scope of the appended claims.In the claims, any reference marks that should not will be located between bracket is configured to limitations on claims.Word " comprises " and does not exclude the presence of the element or step not arranged in the claims.Word "a" or "an" before being positioned at element does not exclude the presence of multiple such element.The present invention by means of including the hardware of some different elements and can realize by means of properly programmed computer.In the unit claim listing some devices, several in these devices can be through same hardware branch and specifically embody.Word first, second and third use do not indicate that any order.Can be title by these word explanations.

Embodiment of above is merely to illustrate the present invention; and it is not limitation of the present invention; those of ordinary skill about technical field; without departing from the spirit and scope of the present invention; can also make a variety of changes and modification; therefore all equivalent technical schemes fall within scope of the invention, and the scope of patent protection of the present invention should be defined by the claims.

Claims (10)

1. the signal recovery method based on compressed sensing, it is characterised in that described method includes:

Time nyquist sampling is carried out, to obtain sampling observation data to meeting openness satellite uplink continuous time signal；

Sample mode based on described nyquist sampling determines sampling matrix；

Compressive sensing theory is utilized to recover primary signal from described sampling observation data according to described sampling matrix.

2. the method for claim 1, it is characterised in that the sample mode of described nyquist sampling is the sampling of many cosets；

Correspondingly, described carry out time nyquist sampling to meeting openness satellite uplink continuous time signal, observe data obtaining sampling, farther include:

Nyquist sampling is carried out according to preset time period T, to obtain discrete data to meeting openness satellite uplink continuous time signal；

Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

3. method as claimed in claim 2, it is characterised in that the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\&pi;}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

4. the method as according to any one of claims 1 to 3, it is characterised in that described according to described sampling matrix utilize compressive sensing theory from described sampling observation data recover primary signal, farther include:

A101: utilize orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\&lambda;}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

A102: according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\&OverBar;}{A}}_v=\&lsqb;{\stackrel{\&OverBar;}{A}}_{v-1},A_{{\mathrm{\&lambda;}}_v}\&rsqb;,$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

A103: utilize method of least square, solves optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\&OverBar;}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\&OverBar;}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

A104: calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

A105: v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then return step A101, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

5. method as claimed in claim 2, it is characterised in that described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has limited frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.

6. the signal recovery device based on compressed sensing, it is characterised in that described device includes:

Signal sampling unit, for carrying out time nyquist sampling to meeting openness satellite uplink continuous time signal, observes data obtaining sampling；

Matrix determines unit, determines sampling matrix for the sample mode based on described nyquist sampling；

Signal recovery unit, for utilizing compressive sensing theory to recover primary signal from described sampling observation data according to described sampling matrix.

7. device as claimed in claim 6, it is characterised in that the sample mode of described nyquist sampling is the sampling of many cosets；

Correspondingly, described signal sampling unit, it is further used for carrying out nyquist sampling according to preset time period T to meeting openness satellite uplink continuous time signal, to obtain discrete data；Described discrete data is carried out the sampling of many cosets, to obtain described sampling observed data.

8. device as claimed in claim 7, it is characterised in that the elements A of the i-th row kth row in described sampling matrix A_ikDetermined by following formula,

$A_{ik}=\frac{1}{LT}\exp \left(j\frac{2\mathrm{\&pi;}}{L}{c}_{i}k\right)$

Wherein, L is array length during many cosets sampled packet, c_iFor the i-th parameter in constant set C, described parameter is for reflecting its position in described constant set C.

9. the device as according to any one of claim 6～8, it is characterised in that described signal recovery unit, farther includes:

Index searches subelement, is used for utilizing orthogonality, finds optimum index λ by following formula_v,

${\mathrm{\&lambda;}}_v=\arg {\max }_{j=1,2,...,d}\left|r_{v-1}^{*}{A}_j\right|,$

Wherein, * is conjugate transpose symbol, A_jFor the vector that the jth column element in sampling matrix A forms, r_v-1For the data residual error that the last time calculates, d is the columns of element in sampling matrix A；

Matrix disposal subelement, for according to described index λ_vBy following formula, data matrix is processed,

${\stackrel{\&OverBar;}{A}}_v=\&lsqb;{\stackrel{\&OverBar;}{A}}_{v-1},A_{{\mathrm{\&lambda;}}_v}\&rsqb;,$

Wherein,For the data matrix of this calculating,For the last time calculate data matrix,For the λ in sampling matrix A_tThe vector of column element composition,For inciting somebody to actionIt is added intoIn calculating symbol；

Solve recovery subelement, be used for utilizing method of least square, solve optimization problem by following formula, to obtain the recovery signal of this calculating

${\stackrel{\&OverBar;}{x}}_v=\arg {\min }_x\left|\right|y-{\stackrel{\&OverBar;}{A}}_{v}x|{|}_2,$

Wherein, y is sampling observation data；

Residual computations subelement, for being calculated this data residual error by following formula,

r_v=y-y_v,

Wherein,y_vFor observation approximation；

From increasing judgment sub-unit, for v is carried out auto-adding operation, it is judged that whether v reaches preset value, if it is not, then call described index to search subelement, otherwise by the recovery signal of this calculatingAs the primary signal recovered.

10. device as claimed in claim 7, it is characterised in that described satellite uplink continuous time signal meets openness when meeting following 3 conditions:

(1) described satellite uplink continuous time signal x (t) is band-limited signal, and its frequency separation is [0,1/T]；

(2) described satellite uplink continuous time signal x (t) has limited frequency range on frequency domain, and non-intersect between each frequency range；

(3) described satellite uplink continuous time signal x (t) bandwidth of all frequency ranges on frequency domain is finite width, and less than 1/T.