CN102025427A - Methods for detecting frequency spectrum, user equipment and fusion equipment - Google Patents

Methods for detecting frequency spectrum, user equipment and fusion equipment Download PDF

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Publication number
CN102025427A
CN102025427A CN2009101777882A CN200910177788A CN102025427A CN 102025427 A CN102025427 A CN 102025427A CN 2009101777882 A CN2009101777882 A CN 2009101777882A CN 200910177788 A CN200910177788 A CN 200910177788A CN 102025427 A CN102025427 A CN 102025427A
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compression sampling
frequency spectrum
user equipment
digital signal
unauthorized user
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汪振兴
杨涛
冯辉
胡波
王可
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Fudan University
Huawei Technologies Co Ltd
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Fudan University
Huawei Technologies Co Ltd
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Abstract

The invention discloses methods and a system for detecting a frequency spectrum, user equipment and fusion equipment. By the methods, frequency spectrum state information can be quickly and accurately acquired in a dynamic broad band sparse frequency spectrum mode. One method for detecting the frequency spectrum comprises the flowing steps of: converting a time domain analog signal into a discrete digital signal; compressing and sampling the discrete digital signal; and sending the result of the compression and sampling to fusion equipment to reconstruct a frequency domain signal. The other method for detecting the frequency spectrum comprises the following steps of: receiving the results of the compression and sampling from all unlicensed user equipment which participates in frequency spectrum detection; and reconstructing the frequency domain signal according to all the results of the compression and sampling. By the embodiment of the invention, the frequency spectrum state information can be quickly and accurately acquired in the dynamic broad band sparse frequency spectrum mode.

Description

The method of frequency spectrum detection and subscriber equipment and fusion device
Technical field
The present invention relates to moving communicating field, relate in particular to a kind of method and subscriber equipment and fusion device of frequency spectrum detection.
Background technology
At present, the frequency spectrum of authorized user device (main subscriber equipment) is not fully used, and as from the propagation characteristic of hundreds of MHz-3GHz preferably the low-frequency range, the availability of frequency spectrum only is 5.2%.So, unauthorized user equipment (cognitive user equipment, inferior subscriber equipment) carries out frequency spectrum share with mode of waiting for an opportunity and authorized user device, be the important channel of improving spectrum efficiency under the existing frequency spectrum policy, its key relates to two aspects: the one, and how non-authorized user device is disturbed and is improved the perception accuracy rate under the environment at the band band of making an uproar; The 2nd, how non-authorized user device is effectively followed the tracks of idle frequency spectrum apace or following idle frequency spectrum is effectively predicted.This is summed up as frequency spectrum state perception (detection) problem in cognitive radio technology.
Existing a kind of frequency spectrum detecting method is to make judgement between following two hypothesis:
x ( t ) = n ( t ) , H 0 hs ( t ) + n ( t ) , H 1 - - - ( 1 )
Wherein, the signal that x (t) receives for time subscriber equipment, s (t) are the signal of main subscriber equipment emission, and n (t) be an additive white Gaussian noise, and h is a link gain, if represent signal to noise ratio with γ, then pass through behind the energy detector about H 0Or H 1The distribution of decision statistic Y can be expressed as:
Y ~ χ 2 TW 2 , H 0 χ 2 TW 2 ( 2 γ ) , H 1 - - - ( 2 )
In the non-fading environment, h is a certainty amount, so can obtain following detection probability P dAnd false alarm probability P f:
P d = P { Y > λ | H 1 } = Q m ( 2 γ , λ ) P f = P { Y > λ | H 0 } = Γ ( m , λ / 2 ) Γ ( m ) - - - ( 3 )
Wherein, Γ (.) and Γ (. .) be fully and non-gamma function completely, Q m(. .) be the Marcum Q-function of broad sense, be defined as follows:
Q m ( a , b ) = ∫ b ∞ x m a m - 1 e - x 2 + a 2 2 I m - 1 ( ax ) dx - - - ( 4 )
Wherein, I M-1(.) is the Bessel function that (m-1) rank are revised.Based on same calculating, can obtain the P under shadow fading and rayleigh fading channel dAnd P fExpression.
Obtain the P of all subscriber equipment dAnd P fAfter, the Chair-Varshney rule that can merge according to optimum decision, i.e. " or " and " with " rule, detection is to the end adjudicated.Adopt " or " during rule, have:
P d = 1 - Π i = 1 k ( 1 - P d , i ) P f = 1 - Π i = 1 k ( 1 - P f , i ) - - - ( 5 )
Adopt " with " during rule, have respectively:
Figure B2009101777882D0000023
With
Figure B2009101777882D0000024
There is the detection fusion center in this method supposition, and each unauthorized user equipment is independent fully, only take " or " and " with " rule, it is limited to detect performance.
Summary of the invention
The embodiment of the invention provides a kind of method of frequency spectrum detection, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of method of frequency spectrum detection comprises:
With the time domain simulation conversion of signals is the discrete digital signal;
Described discrete digital signal is carried out compression sampling;
The result of described compression sampling is sent to fusion device to carry out frequency-region signal reconstruct.
The embodiment of the invention also provides the method for another kind of frequency spectrum detection, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of method of frequency spectrum detection comprises:
Reception is from the compression sampling result of each unauthorized user equipment that participates in frequency spectrum detection, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition;
According to each described compression sampling result, carry out frequency-region signal reconstruct.
The embodiment of the invention also provides the method for another kind of frequency spectrum detection, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of method of frequency spectrum detection comprises:
Determine to have other complementary unauthorized user equipment;
With the time domain simulation conversion of signals is the discrete digital signal;
Described discrete digital signal is carried out compression sampling;
Receive the described compression sampling result that other complementary unauthorized user equipment sends that has, carry out iteration with self compression sampling result.
The embodiment of the invention also provides a kind of subscriber equipment, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of subscriber equipment comprises:
First analog to digital converter, being used for the time domain simulation conversion of signals is the discrete digital signal;
The first compression sampling unit is used for described discrete digital signal is carried out compression sampling;
First interface unit is used for the compression sampling result of the described first compression sampling unit is sent to fusion device to carry out frequency-region signal reconstruct.
The embodiment of the invention also provides a kind of fusion device, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of fusion device comprises:
Second interface unit, be used to receive compression sampling result from each unauthorized user equipment that participates in frequency spectrum detection, wherein, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition;
Integrated unit is used for carrying out frequency-region signal reconstruct according to each described compression sampling result.
The embodiment of the invention also provides another kind of subscriber equipment, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
A kind of subscriber equipment comprises:
Second analog to digital converter, being used for the time domain simulation conversion of signals is the discrete digital signal;
Judging unit is used to determine to have other complementary subscriber equipment, and described information with other complementary subscriber equipment is sent to iteration unit;
The second compression sampling unit is used for described discrete digital signal is carried out compression sampling;
Iteration unit is used for carrying out iteration based on the result and the described compression sampling result with other complementary subscriber equipment transmission of described second compression sampling cell compression sampling.
According to the described detection method of the embodiment of the invention and subscriber equipment and fusion device, owing to can be the discrete digital signal with the time domain simulation conversion of signals, and the discrete digital signal that obtains is handled based on the compression sampling algorithm, and then carry out frequency-region signal reconstruct based on the compression sampling result, signal obtains, the complexity of signal processing so greatly reduce, and can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
Description of drawings
Apparently, the accompanying drawing that describes below only is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.
Fig. 1 is the flow chart of embodiment of the invention frequency spectrum detecting method;
Fig. 2 is a flow chart again of embodiment of the invention frequency spectrum detecting method;
Fig. 3 is the another flow chart of embodiment of the invention frequency spectrum detecting method;
Fig. 4 is the another flow chart of embodiment of the invention frequency spectrum detecting method;
The recovery situation (L=1) of Fig. 5 original sparse signal spectrum during for embodiment of the invention compression sampling point M=55;
The recovery situation (L=1) of Fig. 6 original sparse signal spectrum during for embodiment of the invention compression sampling point M=77;
Fig. 7 during, α=0.5 for embodiment of the invention compression sampling point M=588, the recovery situation of β=1.5 o'clock original sparse signal spectrum;
Fig. 8 during, α=0 for embodiment of the invention compression sampling point M=588, the recovery situation of β=2 o'clock original sparse signal spectrum;
Fig. 9 during, α=1.5 for embodiment of the invention compression sampling point M=588, the recovery situation of β=0.5 o'clock original sparse signal spectrum;
Figure 10 during, α=1 for embodiment of the invention compression sampling point M=588, the recovery situation of β=1 o'clock original sparse signal spectrum;
Figure 11 during, α=2 for embodiment of the invention compression sampling point M=588, the recovery situation of β=0 o'clock original sparse signal spectrum;
The recovery situation of Figure 12 during, β=0 o'clock original sparse signal spectrum for embodiment of the invention compression sampling point M=493;
The recovery situation of Figure 13 during, α=0 o'clock original sparse signal spectrum for embodiment of the invention compression sampling point M=588;
Figure 14 is the another flow chart of embodiment of the invention frequency spectrum detecting method;
Figure 15 is the another flow chart of embodiment of the invention frequency spectrum detecting method;
Figure 16 is the iteration schematic diagram of embodiment of the invention unauthorized user equipment;
Figure 17 is the structure chart of embodiment of the invention subscriber equipment;
Figure 18 is a structure chart again of embodiment of the invention subscriber equipment;
Figure 19 is the structure chart of embodiment of the invention fusion device;
Figure 20 is the another structure chart of embodiment of the invention fusion device;
Figure 21 is the another structure chart of embodiment of the invention fusion device;
Figure 22 is the structure chart of embodiment of the invention frequency spectrum detection system;
Figure 23 is the another structure chart of embodiment of the invention subscriber equipment;
Figure 24 is the another structure chart of embodiment of the invention subscriber equipment;
Figure 25 is another structure chart of embodiment of the invention frequency spectrum detection system.
Embodiment
The embodiment of the invention provides a kind of frequency spectrum detecting method and subscriber equipment and fusion device, can obtain the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
Describe the present invention below in conjunction with accompanying drawing.Described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on the embodiment among the present invention, those of ordinary skills belong to the scope of protection of the invention not making the every other embodiment that is obtained under the creative work prerequisite.
(Compressive Sampling is if echo signal itself has sparse property or can be converted into sparse property by certain transform domain CS) to compression sampling, then this signal can be carried out a kind of signal processing technology of dimensionality reduction.At first the CS principle is made brief analysis below.
Consider the discrete real signal of one dimension finite length
Figure B2009101777882D0000061
X is the discrete vector that non-authorized user device obtains by analog to digital converter sampling broadband wireless signal.X does discrete Fourier transform (DFT) to signal, has:
x = Σ i = 1 N s i ψ i Be x=Ψ s (6)
Wherein, Ψ=[ψ 1| ψ 2| ... | ψ N] be the discrete Fourier orthogonal basis, s i=<x, ψ i〉=ψ i TX is the discrete Fourier coefficient, is the amplitude of respective wireless signal at discrete frequency.If:
T={i:s i≠0}, |T|=K, K<<N (7)
Be that having only K element is non-0 value among the discrete Fourier expansion coefficient vector s of signal x, remaining N-K element is 0, and K<<N, then claim s to satisfy the sparse property of K-.Like this, can be with perception matrix Φ to M value of signal x random sampling, that is:
y i=<x, φ i, i ∈ M is y=Φ x (8)
Wherein, Φ=[φ 1| φ 2| ... | φ N].If M 〉=C μ 2(Φ, Ψ) Slog N, wherein,
Figure B2009101777882D0000063
Then can realize the accurate estimation of s by following optimized Algorithm:
Figure B2009101777882D0000064
Y=Φ x=Φ Ψ s (9) wherein
Make A=Φ Ψ, then matrix A need satisfy appearance such as constraint characteristic.
Because at present from the propagation characteristic of hundreds of MHz-3GHz preferably the low-frequency range, the availability of frequency spectrum only is 5.2%, so the frequency spectrum state can be considered as variable S, use " 0 " and " 1 " expression free time and busy condition respectively, when S is made of small part " 1 " and most of " 0 ", then S has sparse property, and then can be under the CS framework, structure is based on the frequency spectrum detection scheme of CS, so both can implement the N point (in order to obtain result accurately, usually the N value is bigger, and for example value 8962) the fast Fourier computing, can obtain the frequency spectrum state information fast and accurately again.
As shown in Figure 1, a kind of frequency spectrum detecting method that the embodiment of the invention provides comprises:
S11, unauthorized user equipment are the discrete digital signal with the time domain simulation conversion of signals;
For example, can adopt and simulate to the information translation algorithm, with the time domain simulation conversion of signals is the discrete digital signal, simulates to the information translation algorithm and can use far below the desired speed of nyquist sampling theorem and come the sampled analog signal under the situation that guarantee information is not lost.Certainly, other is any can be that the analog-to-digital conversion algorithm of discrete digital signal also all is desirable with the time domain simulation conversion of signals, as long as can satisfy purpose of the present invention.
S12, unauthorized user equipment carry out compression sampling to described discrete digital signal;
S13, unauthorized user equipment send to fusion device to carry out frequency-region signal reconstruct with the result of described compression sampling.
Adopt described frequency spectrum detecting method, because unauthorized user equipment can be the discrete digital signal with the time domain simulation conversion of signals, and the discrete digital signal that obtains is handled based on the compression sampling algorithm, and then the compression sampling result sent to fusion device so that fusion device carries out frequency-region signal reconstruct, signal obtains, the complexity of signal processing so greatly reduce, and can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
As shown in Figure 2, the another kind of frequency spectrum detecting method that provides of the embodiment of the invention comprises:
S21, fusion device receive the compression sampling result from each unauthorized user equipment that participates in frequency spectrum detection, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition;
S22, fusion device carry out frequency-region signal reconstruct according to each described compression sampling result.
Adopt described frequency spectrum detecting method, because fusion device can carry out frequency-region signal reconstruct according to the compression sampling result of each unauthorized user equipment, signal obtains, the complexity of signal processing so greatly reduce, and can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
From above-mentioned analysis to the CS theory as can be known, the enforcement of CS need be to the x inner product operation that to make M length be N to obtain M compression sampling sample, and this relates to extensive matrix multiplication operation, has higher time complexity.Consider the real-time detection requirement of unauthorized user equipment, finish M sampling if adopt M parallel arithmetical unit, the complexity that then can cause the signal processing front end, and frequency spectrum detection is comparatively responsive to the perception time delay, so the series processing of M sampling may be introduced bigger sampling error.To sum up analyze, based on the CS frequency spectrum detection of single unauthorized user equipment have the complexity height, the perception accuracy rate is low and the perception robustness a little less than etc. problem.Because the randomness of unauthorized user device distribution and the homogeneity of perception echo signal, therefore, the embodiment of the invention provides another method of finishing frequency spectrum detection of uniting by all unauthorized user equipment in the given area, as shown in Figure 3, comprising:
Each unauthorized user equipment of S31, participation frequency spectrum detection is the discrete digital signal with the time domain simulation conversion of signals respectively;
For example, can adopt and simulate to the information translation algorithm, with the time domain simulation conversion of signals is the discrete digital signal, simulates to the information translation algorithm and can use far below the desired speed of nyquist sampling theorem and come the sampled analog signal under the situation that guarantee information is not lost.Also can adopt other any can be the algorithm of discrete digital signal with the time domain simulation conversion of signals, as long as can satisfy purpose of the present invention.
Each unauthorized user equipment of S32, participation frequency spectrum detection generates the wherein row element of delegation of perception matrix respectively, and finishes an inner product operation that described discrete digital signal is carried out perception.
Exemplarily, the different rows of the perception matrix Φ in the formula (10) is obtained task and is shared by the different unauthorized user equipment that participates in frequency spectrum detection, that is: unauthorized user equipment 1 generates the first row ψ ' of perception matrix Φ 1=[ψ 11ψ 12ψ 1N], a perception of finishing signal x only needs inner product operation, that is: y one time 1=<x, ψ ' 1.Equally, unauthorized user equipment 2 generates the second row ψ ' of perception matrix Φ 2=[ψ 21ψ 22ψ 2N] and finish a inner product operation to signal x perception.By that analogy, M unauthorized user equipment can obtain M compression sampling (if not authorized user device number greater than M, picked at random M unauthorized user equipment therefrom then).
y = Φx = ψ 11 ψ 12 · · · ψ 1 N ψ 21 ψ 22 · · · ψ 2 N · · · · · · · · · · · · ψ M 1 ψ M 2 · · · ψ MN x 1 x 2 · · · x N - - - ( 10 )
The unauthorized user equipment of S33, each participation frequency spectrum detection result of inner product operation separately sends to fusion device;
S34, fusion device carry out frequency-region signal reconstruct according to the result of each described inner product operation.
Exemplarily, fusion device can carry out the reconstruct of frequency-region signal according to following formula:
Figure B2009101777882D0000085
Wherein, Ψ is the Fourier orthogonal basis, is known and fixing for unauthorized user equipment and fusion device.And perception matrix Φ can produce according to identical rule between unauthorized user equipment and fusion device.Therefore, this perception matrix is known for all unauthorized user equipment and fusion device, and the unauthorized user device just is got wherein corresponding delegation and perceived signal and done an inner product operation (seeing step S32) and get final product.
According to computation complexity, fusion device can adopt multiple different reconfiguration scheme, as combined optimization method, non-protruding optimization, protruding optimization, greedy algorithm etc.Any reconstructing method under formula (11) framework can be adopted.
In the present embodiment, each the unauthorized user device just that participates in frequency spectrum detection is done inner product operation one time, and the signal reconstruction computing of complexity is placed on fusion device enforcement, this has reduced the computation complexity of unauthorized user equipment greatly, thereby improved the ability of unauthorized user equipment real-time detection channel, so can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
Yet, in the actual spectrum testing process, the link fading characteristic difference of different spaces, this makes that discrete digital signal " x " no longer is identical for different unauthorized user equipment, and based on this, the embodiment of the invention proposes another frequency spectrum detecting method, as shown in Figure 4, comprising:
Each unauthorized user equipment of S41, participation frequency spectrum detection is the discrete digital signal with the time domain simulation conversion of signals;
For example, can adopt and simulate to the information translation algorithm, with the time domain simulation conversion of signals is the discrete digital signal, simulates to the information translation algorithm and can use far below the desired speed of nyquist sampling theorem and come the sampled analog signal under the situation that guarantee information is not lost.Certainly, other is any can be that the analog-to-digital conversion algorithm of discrete digital signal also all is desirable with the time domain simulation conversion of signals, as long as can satisfy purpose of the present invention.
S42, according to the relative size of the signal to noise ratio of each unauthorized user equipment perception authorized user device signal that participates in frequency spectrum detection, fusion device is for participating in each unauthorized user devices allocation sample number of frequency spectrum detection;
For example, the signal to noise ratio of considering L unauthorized user equipment perception authorized user device signal of participation frequency spectrum detection satisfies
Figure B2009101777882D0000091
Distribute if each unauthorized user equipment has independent choosing decline frequently uniformly, and minimal compression hits Z satisfies Z 〉=C μ 2(then fusion device can be the unauthorized user devices allocation sample number that participates in frequency spectrum detection according to following formula for Φ, Ψ) Slog N:
w i = SNR i Σ j = 1 L SNR j M 1 + M 2 + . . . + M L = Z M 1 w 1 = M 2 w 2 = . . . = M L w L - - - ( 12 )
Wherein, L is the number of the unauthorized user equipment of participation frequency spectrum detection, SNR i(i=1 2...L) is the signal to noise ratio that participates in i unauthorized user equipment of frequency spectrum detection, M i(i=1 is the sample number that participates in i unauthorized user equipment of frequency spectrum detection 2...L), and Z is total sample number.
Formula (12) shows: select fading characteristic if participate in the identical frequency of all unauthorized user equipment obediences of frequency spectrum detection, then unauthorized user equipment is sampled according to the signal to noise ratio size and is shared, promptly under given total compression sample number condition, the sample number that the user that signal to noise ratio is big more shares is many more, thereby obtains compromise between sampling complexity and systematic function.Further, select decline number of sub-bands J known if participate in the frequency of the unauthorized user equipment of frequency spectrum detection, then fusion device need be compromised between signal path decline and choosing decline frequently, with the size of the sample number (line number of Φ) of definite each unauthorized user equipment.Make α, β represent the weight factor of path fading and choosing decline frequently respectively, then fusion device can also be determined the sample number of each unauthorized user equipment of participation frequency spectrum detection according to following formula:
w i = SNR i Σ j = 1 L SNR j , v i = J i Σ j = 1 L J j M 1 + M 2 + . . . + M L = Z M 1 αw 1 + βv 1 = M 2 αw 2 + βv 2 = . . . = M L αw L + βv L α + β = 2 α , β ≥ 0 - - - ( 13 )
Wherein, L is the number of the unauthorized user equipment of participation frequency spectrum detection, SNR i(i=1 2...L) is the signal to noise ratio that participates in i unauthorized user equipment of frequency spectrum detection, M i(i=1 is the sample number that participates in i unauthorized user equipment of frequency spectrum detection 2...L), and Z is total sample number, J i(i=1 is the frequency choosing decline number of sub-bands that participates in i unauthorized user equipment of frequency spectrum detection 2...L), and α is the path fading weight factor, and β selects the decline weight factor frequently.
In this step, greater than L, then fusion device can therefrom select L unauthorized user equipment to participate in frequency spectrum detection at random as if all unauthorized user number of devices.
S43, participate in frequency spectrum detection each unauthorized user equipment respectively based on separately sample number, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals sample number separately.
Each unauthorized user equipment of S44, participation frequency spectrum detection result of inner product operation separately sends to fusion device;
S45, fusion device carry out frequency-region signal reconstruct according to the result of each described inner product operation.But this step refer step S34 repeats no more herein.
The embodiment of the invention has been taken all factors into consideration factors such as link fading characteristic, noise, measurement computation complexity and state reconstruction error, so can reduce that signal obtain, in the signal processing complexity, under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
Below the performance of the embodiment of the invention is carried out simulation analysis.Simulated conditions is as follows: signal length is respectively N=512 and 1024, degree of rarefication K=15, total unauthorized user number of devices L=10 of participation frequency spectrum detection.Interchannel noise Gaussian distributed n~N (0,1), the link decline is respectively path fading and multipath Rayleigh decline, α, β ∈ [0,2].
It is as follows to define the signal indication that satisfies the sparse property of frequency domain K-:
x ( n ) = Σ i = 1 N s i sin ( ( 2 πi ) n ) , n = 1 · · · N - - - ( 14 )
Make T={i, s i≠ 0}, then | T|=K=15.
Orthogonal basis matrix Ψ is:
Ψ = sin 2 π sin 4 π · · · sin 2 Nπ sin 4 π sin 8 π · · · sin 4 Nπ · · · · · · · · · · · · sin 2 Nπ sin 4 Nπ · · · sin NNπ - - - ( 15 )
That is: x=Ψ s.
Fig. 5 and Fig. 6 are that single unauthorized user equipment, compression sampling point are respectively 44 and 77 o'clock simulation result, and this result shows that sampling number increases, and the signal reconstruction error is more little.Fig. 7~Figure 11 is for participating in the unauthorized user number of devices L=10 of frequency spectrum detection, when path fading and frequency selective fading all exist, according to different α, β combination, in frequency domain reconstruction signal and primary signal respectively in amplitude and locational comparison; State when Figure 12~Figure 13 represents that respectively path fading is only arranged and only frequency selective fading arranged after original signal spectrum and the recovery relatively.From whole reconstruct situation, when only there was specific decline (link decline or choosing decline frequently) in primary signal, the reconstruct effect was better, and the link decline has better reconstruct performance than choosing decline frequently.Than existing frequency spectrum detection scheme, by detecting the compression sampling of front end, effectively reduce the scale of echo signal sampling, improved detection efficiency, reduced the complexity of scheme implementation; And, improved the accuracy rate that detects by the concentrated reconstruct of profile samples and the fusion of part detected state.Simulation result shows: M point by compression sampling and M be during greater than certain critical value (M<<N), still can accurately recover the frequency spectrum state information of signal.
In the Distributed C R system, the difference of consideration space link propagation characteristic, the randomness that subscriber equipment moves and primary and secondary subscriber equipment make different unauthorized user equipment have certain observation error to same observed object in the randomness of spatial distribution.So,, will improve the accuracy rate and the efficient of detection as if serving as that the basis selects unauthorized user equipment to carry out frequency spectrum detection with the complementarity that detects.Based on this, the embodiment of the invention provides the method for another frequency spectrum detection, as shown in figure 14, comprising:
S141, fusion device are classified to all unauthorized user equipment according to frequently selecting fading characteristic, and select a unauthorized user equipment to participate in frequency spectrum detection respectively at least from described each classification;
For example, if not authorized user device has certain selectivity to choosing decline frequently, as part unauthorized user equipment to frequency f 1, f 3Decline, part unauthorized user equipment is to frequency f 2, f 4The decline, then the unauthorized user equipment with same fading characteristic can be sorted out, again with
Figure B2009101777882D0000121
Be the basis, from large to small, carry out the selection of unauthorized user equipment, if only select a unauthorized user equipment from every kind of decline classification, then total cooperation unauthorized user equipment number only depends on the fading characteristic classification.
S142, fusion device are each unauthorized user devices allocation sample number of selected participation frequency spectrum detection.Wherein, but the mode refer step S42 of distribution repeats no more herein.
Each unauthorized user equipment of S143, participation frequency spectrum detection is the discrete digital signal with the time domain simulation conversion of signals;
S144, participate in frequency spectrum detection each unauthorized user equipment respectively based on separately sample number, generate the row element of perception matrix corresponding line, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals sample number separately.
S145, participate in frequency spectrum detection each unauthorized user equipment respectively according to the result of inner product operation separately, carry out frequency-region signal reconstruct and obtain the frequency spectrum state after the reconstruct and send to fusion device;
S146, fusion device obtain overall frequency spectrum state according to each described frequency spectrum state by information fusion.
Adopt the described method of present embodiment, because fusion device can select a unauthorized user equipment to participate in frequency spectrum detection from difference decline classification at least, and selected each unauthorized user equipment is independently implemented frequency-region signal reconstruct, so the frequency spectrum state after the reconstruct is complementary, thereby can obtain the state status of all frequency spectrums in the system by the fusion of fusion device.Like this, though the amount of calculation of small part unauthorized user device end increases, but the unauthorized user equipment of most of bad channel conditions keeps inactive state, in case channel condition improves, can implement sampling and cooperation reconstruct, from system perspective, reduced unnecessary energy consumption, improved detection efficiency and accuracy rate.
Aforementioned each embodiment adopts fusion device to obtain final frequency-region signal, if fusion device breaks down, then whole detection system will quit work.Based on this, the function of fusion device all can be born by unauthorized user equipment, as shown in figure 15, the embodiment of the invention provides another frequency spectrum detecting method, comprising:
S151, other unauthorized user equipment of determining to have complementarity;
For example, feature based on each unauthorized user equipment received signal, according to certain decision criteria (as the mutual information criterion) judge and the complementarity of other unauthorized user equipment for example determine whether have the observation complementarity with other unauthorized user equipment according to the determined threshold value of mutual mutual information.
S152, be the discrete digital signal with the time domain simulation conversion of signals;
For example, can adopt and simulate to the information translation algorithm, with the time domain simulation conversion of signals is the discrete digital signal, simulates to the information translation algorithm and can use far below the desired speed of nyquist sampling theorem and come the sampled analog signal under the situation that guarantee information is not lost.Certainly, other is any can be that the analog-to-digital conversion algorithm of discrete digital signal also all is desirable with the time domain simulation conversion of signals, as long as can satisfy purpose of the present invention.
S153, described discrete digital signal is carried out compression sampling;
S154, receive the described compression sampling result that other complementary unauthorized user equipment sends that has, carry out iteration with self compression sampling result.
Adopt described frequency spectrum detecting method, owing to can determine to have other complementary unauthorized user equipment, and the mode by iteration merges self compression sampling result with the compression sampling result with other complementary unauthorized user equipment, so that obtain final frequency-region signal, so guaranteed the accuracy of frequency spectrum detection; And this frequency spectrum detecting method does not adopt fusion device, has avoided fusion device to break down causing the quit work generation of situation of whole detection system, so robustness strengthens, promptly part unauthorized user equipment perceptional function is damaged the performance that can not influence whole system.So the embodiment of the invention can be obtained the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
Further, but the implementation refer step S32 of step S153.
Certainly, in step S151, can also comprise when determining to have other complementary unauthorized user equipment: with described other unauthorized user equipment interactive information with complementarity, with the sample number of determining to share, wherein, the definite of sample number can be with reference to formula (12) or the described method of formula (13).At this moment, step S153 is specially: based on the sample number that will share, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals described sample number.So just can take all factors into consideration factors such as link fading characteristic, noise, measurement computation complexity and state reconstruction error, thereby improve the accuracy that detects.
Further, step S154 can comprise: according to the result of self compression sampling, the reconstructed frequency domain signal obtains the frequency spectrum state after the reconstruct; Receive the described frequency spectrum state that other complementary unauthorized user equipment sends that has, and carry out iteration with the frequency spectrum state of self institute's reconstruct according to compression sampling reconstruct as a result.
Below, be example with Figure 16, the flow process of step S151 to S154 is carried out brief description.Suppose to have 7 unauthorized user equipment CR1 to CR7, each unauthorized user equipment satisfies following perception equation:
Y=HTX+ω (16)
Calculate mutual information between per two unauthorized user equipment by following formula:
M(i,j)=|I(X;Y i)-I(X;Y j)| (17)
0≤i wherein, j≤K, K are the quantity of unauthorized user equipment
Wherein,
Figure B2009101777882D0000141
Therefore can form matrix M K * K, this square is a symmetrical matrix for 20 gusts.Can determine whether connect between each unauthorized user equipment in the following way:
A ( i , j ) = 0 M ( i , j ) < &sigma; 1 M ( i , j ) > &sigma; - - - ( 18 )
As A (i, j)=1 o'clock, show that unauthorized user equipment i is connected with unauthorized user equipment j, thereby can obtain exemplary annexation shown in Figure 16, and just can carry out information sharing between the interconnective unauthorized user equipment, obtain new perception equation:
Y new=H newT newX+ω new
According to the sparse property estimation of Bayesian inference, Hidden Markov method of estimation etc., with arbitrary unauthorized user equipment is basic point, the information of comprehensive its neighbor node, again fusion results is transmitted to connected next unauthorized user equipment, has all participated in fusion until having all complementary unauthorized user equipment of observation.Like this, just can obtain final frequency-region signal by iteration.
If the characteristic of channel of certain unauthorized user equipment changes, then need to recomputate I (X; Y i) and matrix M, the annexation between each unauthorized user equipment that obtains upgrading, and then regain final frequency-region signal by the information sharing between the unauthorized user equipment with annexation.
As shown in figure 17, the embodiment of the invention provides a kind of subscriber equipment 1700, comprises first analog to digital converter 1701, the first compression sampling unit 1702 and first interface unit 1703.Wherein: first analog to digital converter 1701, being used for the time domain simulation conversion of signals is the discrete digital signal; The first compression sampling unit 1702 is used for described discrete digital signal is carried out compression sampling; First interface unit 1703 is used for the compression sampling result of the described first compression sampling unit 1702 is sent to fusion device to carry out frequency-region signal reconstruct.Since simulate to the information translation algorithm can be under the situation that guarantee information is not lost, use far below the desired speed of nyquist sampling theorem and come the sampled analog signal, so first analog to digital converter, 1701 preferred employings are simulated to the information translation algorithm, are the discrete digital signal with the time domain simulation conversion of signals.Certainly, other can realize that the analog-to-digital conversion algorithm of the object of the invention also is desirable.
Adopt described subscriber equipment 1700, because subscriber equipment 1700 can be the discrete digital signal with the time domain simulation conversion of signals, and the discrete digital signal that obtains is handled based on the compression sampling algorithm, and then the compression sampling result sent to fusion device so that fusion device carries out frequency-region signal reconstruct, signal obtains, the complexity of signal processing so greatly reduce, and can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
Further, the 1702 pairs of described discrete digital signals in the first compression sampling unit carry out compression sampling mode can for: generate the wherein row element of delegation of perception matrix, and finish an inner product operation that described discrete digital signal is carried out perception.Like this, just can reduce the computation complexity of each subscriber equipment 1700 greatly, improve the ability of its real-time sounding channel.
Further, first interface unit 1703 also is used to receive the sample number that fusion device distributes, the first compression sampling unit 1702 then, specifically be used for based on described sample number, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals described sample number.Wherein, fusion device can be taken all factors into consideration factors such as link fading characteristic, noise, measurement computation complexity and state reconstruction error, for example when distributing sample to count, the sample number that the big more subscriber equipment of signal to noise ratio 1700 is born is many more, so that improve the accuracy of frequency spectrum detection.
Further, as shown in figure 18, subscriber equipment 1700 can also comprise: processing unit 1801, be used for compression sampling result according to the first compression sampling unit 1702 and carry out frequency-region signal reconstruct and obtain the frequency spectrum state, and described frequency spectrum state is sent to fusion device to carry out the fusion of described frequency spectrum state by first interface unit 1703.
As shown in figure 19, the embodiment of the invention also provides a kind of fusion device 1900, comprise: second interface unit 1901, be used to receive compression sampling result from each unauthorized user equipment that participates in frequency spectrum detection, wherein, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition; Integrated unit 1902 is used for carrying out frequency-region signal reconstruct according to each described compression sampling result.
Adopt described fusion device 1900, owing to can carry out frequency-region signal reconstruct according to the compression sampling result of each unauthorized user equipment, signal obtains, the complexity of signal processing so greatly reduce, and can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
Further, as shown in figure 20, fusion device 1900 also comprises: allocation units 2001 are used to each unauthorized user devices allocation sample number that participates in frequency spectrum detection, and described sample number are sent to corresponding unauthorized user equipment by second interface unit 1901.Wherein, allocation units 2001 can distribute the sample number according to formula (12) or formula (13), have so just taken all factors into consideration factors such as link fading characteristic, noise, measurement computation complexity and state reconstruction error, can improve the accuracy of frequency spectrum detection.
Further, as shown in figure 21, fusion device 1900 can also comprise: selected cell 2101 is used for selecting to participate in each unauthorized user equipment of frequency spectrum detection based on frequently selecting fading characteristic.For example, selected cell 2101 is according to frequently selecting fading characteristic, all unauthorized user equipment are classified, and from described each classification, select a unauthorized user equipment to participate in frequency spectrum detection respectively at least, wherein, but 2101 pairs of all unauthorized user equipment of selected cell are classified and the mode refer step S141 that selects, and repeat no more herein.By all unauthorized user equipment being classified with selection so that the unauthorized user equipment of characteristic complementation participates in frequency spectrum detection, like this, though the amount of calculation of small part unauthorized user equipment increases, but the unauthorized user equipment of most of bad channel conditions keeps inactive state, thereby reduced unnecessary energy consumption, improved detection efficiency and accuracy rate.
As shown in figure 22, the embodiment of the invention also provides a kind of frequency spectrum detection system 2200, comprising:
A plurality of subscriber equipmenies 2201, it is the discrete digital signal that each subscriber equipment 2201 is respectively applied for the time domain simulation conversion of signals, and described discrete digital signal is carried out compression sampling, and the result of described compression sampling is sent to fusion device 2202;
Fusion device 2202 is used for the result according to each described compression sampling, carries out frequency-region signal reconstruct.
Further, the structure of subscriber equipment 2201 can be the subscriber equipment shown in Figure 17 or 18; Fusion device 2202 can be the fusion device shown in Figure 19,20 or 21.
By adopting described detection system 2200, owing to can be the discrete digital signal with the time domain simulation conversion of signals, and the discrete digital signal that obtains is handled based on the compression sampling algorithm, and then carry out frequency-region signal reconstruct based on the compression sampling result, signal obtains, the complexity of signal processing with regard to reducing greatly like this, so can under the sparse spectrum mode in dynamic broadband, obtain the frequency spectrum state information fast and accurately.
As shown in figure 23, the embodiment of the invention also provides a kind of subscriber equipment 2300 to comprise: second analog to digital converter 2301, and being used for the time domain simulation conversion of signals is the discrete digital signal; Judging unit 2302 is used to judge the complementarity with other each subscriber equipment 2300, and the information that will have other complementary each subscriber equipment 2300 sends to iteration unit 2304; The second compression sampling unit 2303 is used for described discrete digital signal is carried out compression sampling, carries out frequency-region signal reconstruct according to the result of described compression sampling and obtains the frequency spectrum state after the reconstruct and send to iteration unit 2304; Iteration unit 2304, be used for having the frequency spectrum state of complementary 2300 reconstruct of subscriber equipment based on the frequency spectrum state of 2303 reconstruct in the second compression sampling unit and from other, carry out information fusion, and the result that will merge sends to another subscriber equipment 2300 with complementarity to carry out further information fusion.
Since simulate to the information translation algorithm can be under the situation that guarantee information is not lost, use far below the desired speed of nyquist sampling theorem and come the sampled analog signal, so second analog to digital converter, 2301 preferred employings are simulated to the information translation algorithm, are the discrete digital signal with the time domain simulation conversion of signals.Certainly, other can realize that the analog-to-digital conversion algorithm of the object of the invention also is desirable.In addition, for example, judging unit 2302 can be based on the feature of each subscriber equipment 2300 received signals, determine and the observation complementarity of other subscriber equipment 2300 by information interaction, for example determine whether to have the observation complementarity with other subscriber equipment 2300 according to the determined threshold value of mutual mutual information.
Adopt described subscriber equipment 2300, because can be complementary to determine whether having observation alternately mutually with other subscriber equipment 2300, thereby the feasible compression sampling result who participates in each subscriber equipment 2300 of frequency spectrum detection has complementarity; And, can obtain final frequency-region signal according to having complementary compression sampling result by iteration between each subscriber equipment 2300, so the embodiment of the invention can be implemented under the sparse spectrum mode in dynamic broadband, obtains the frequency spectrum state information fast and accurately.
Further, as shown in figure 24, described subscriber equipment 2300 can also comprise:
Interactive unit 2401 is used for having complementary subscriber equipment 2300 interactive information with other, obtaining the sample number that will share, and described sample number is sent to the second compression sampling unit 2303.Wherein, interactive unit 2401 can be obtained the sample number based on formula (12) or formula (13).So just can take all factors into consideration factors such as link fading characteristic, noise, measurement computation complexity and state reconstruction error, for example, the sample number that the subscriber equipment 2300 that signal to noise ratio is big is more shared is many more, thereby can improve the accuracy of frequency spectrum detection.At this moment, the second compression sampling unit 2303, specifically be used for based on received sample number, generate the row element of perception matrix corresponding line, and finish the inner product operation that described discrete digital signal is carried out perception, carry out frequency-region signal reconstruct according to the result of described inner product operation and obtain the frequency spectrum state after the reconstruct and send to described iteration unit 2304.
As shown in figure 25, the embodiment of the invention also provides a kind of frequency spectrum detection system 2500, comprise a plurality of subscriber equipmenies 2501, wherein, each subscriber equipment 2501 is respectively applied for based on the mutual information criterion, judge complementarity with other each subscriber equipment 2501, with the time domain simulation conversion of signals is the discrete digital signal, described discrete digital signal is carried out compression sampling, carry out frequency spectrum state after frequency-region signal reconstruct obtains reconstruct according to the result of described compression sampling, and, obtain overall frequency spectrum state by having the iteration of complementary each subscriber equipment 2501 frequency spectrum state each other.Wherein, frequency spectrum state iterative process example as shown in figure 16.
Wherein, the structure of subscriber equipment 2501 can be the subscriber equipment shown in Figure 23 or 24.
Adopt described detection system 2500,, avoided fusion device to break down and caused the generation of the out-of-work situation of whole detection system owing to do not adopt fusion device.In addition, because the reconstruct of sparse signal is that iteration is finished, so robustness strengthens, promptly certain customers' equipment 2501 perceptional functions are damaged the performance that can not influence whole system.So detection system 2500 can be obtained the frequency spectrum state information fast and accurately under the sparse spectrum mode in dynamic broadband.
One of ordinary skill in the art will appreciate that, realize all or part of flow process in the foregoing description method, be to instruct relevant hardware to finish by computer program, described program can be stored in the computer read/write memory medium, this program can comprise the flow process as the embodiment of above-mentioned each side method when carrying out.Wherein, described storage medium can be magnetic disc, CD, read-only storage memory body (Read-OnlyMemory, ROM) or at random store memory body (Random Access Memory, RAM) etc.
Should be appreciated that the concrete order of each step in any disclosed process or the example that level is illustrative methods.Should be appreciated that based on design preference, can when keeping falling into scope of the present invention, rearrange the concrete order or the level of these process steps.In addition, claim to a method has been introduced the element of various steps with example sequence, but is not intended to be limited to concrete order or the level of being introduced.
The above; only be the specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; can expect easily changing or replacing, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the described protection range of claim.

Claims (15)

1. the method for a frequency spectrum detection is characterized in that, comprising:
With the time domain simulation conversion of signals is the discrete digital signal;
Described discrete digital signal is carried out compression sampling;
The result of described compression sampling is sent to fusion device to carry out frequency-region signal reconstruct.
2. method according to claim 1 is characterized in that, describedly described discrete digital signal is carried out compression sampling comprises:
Generate the wherein row element of delegation of perception matrix, and finish an inner product operation that described discrete digital signal is carried out perception;
Perhaps describedly described discrete digital signal carried out compression sampling comprise:
Receive the sample number that described fusion device distributes;
Based on described sample number, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals described sample number.
3. method according to claim 1 and 2 is characterized in that, described result with described compression sampling sends to fusion device and comprises to carry out frequency-region signal reconstruct:
Carry out frequency spectrum state after frequency-region signal reconstruct obtains reconstruct according to the result of described compression sampling;
Frequency spectrum state after the described reconstruct is sent to described fusion device to carry out frequency-region signal reconstruct and fusion.
4. the method for a frequency spectrum detection is characterized in that, comprising:
Reception is from the compression sampling result of each unauthorized user equipment that participates in frequency spectrum detection, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition;
According to each described compression sampling result, carry out frequency-region signal reconstruct.
5. method according to claim 4 is characterized in that, also comprises before the compression sampling result of described reception from each unauthorized user equipment that participates in frequency spectrum detection:
Based on frequently selecting fading characteristic, select each unauthorized user equipment of described participation frequency spectrum detection.
6. the method for a frequency spectrum detection is characterized in that, comprising:
Determine to have other complementary unauthorized user equipment;
With the time domain simulation conversion of signals is the discrete digital signal;
Described discrete digital signal is carried out compression sampling;
Receive the described compression sampling result that other complementary unauthorized user equipment sends that has, carry out iteration with self compression sampling result.
7. method according to claim 6 is characterized in that, described method also comprises:
With described other unauthorized user equipment interactive information, determine the sample number that to share with complementarity;
Describedly described discrete digital signal is carried out compression sampling comprise: based on the sample number that will share, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals described sample number.
8. according to claim 6 or 7 described methods, it is characterized in that described reception is described to have a compression sampling result that other complementary unauthorized user equipment sends, carry out iteration with self compression sampling result and comprise:
According to the compression sampling result of self, the reconstructed frequency domain signal obtains the frequency spectrum state after the reconstruct;
Receive the described frequency spectrum state that other complementary unauthorized user equipment sends that has, and carry out iteration with the frequency spectrum state of self reconstruct according to compression sampling reconstruct as a result.
9. a subscriber equipment is characterized in that, comprising:
First analog to digital converter, being used for the time domain simulation conversion of signals is the discrete digital signal;
The first compression sampling unit is used for described discrete digital signal is carried out compression sampling;
First interface unit is used for the compression sampling result of the described first compression sampling unit is sent to fusion device to carry out frequency-region signal reconstruct.
10. subscriber equipment according to claim 9 is characterized in that, described first interface unit also is used to receive the sample number that described fusion device distributes;
The described first compression sampling unit, specifically be used for based on described sample number, generate the row element of corresponding line in the perception matrix, and finish the inner product operation that described discrete digital signal is carried out perception, the line number of wherein said corresponding line equals described sample number.
11., it is characterized in that described subscriber equipment also comprises according to claim 9 or 10 described subscriber equipmenies:
Processing unit, be used for compression sampling result according to the described first compression sampling unit and carry out frequency-region signal reconstruct and obtain the frequency spectrum state, and described frequency spectrum state is sent to described fusion device to carry out the fusion of described frequency spectrum state by described first interface unit.
12. a fusion device is characterized in that, comprising:
Second interface unit, be used to receive compression sampling result from each unauthorized user equipment that participates in frequency spectrum detection, wherein, described compression sampling result is the discrete digital signal by described unauthorized user equipment with the time domain simulation conversion of signals, and described discrete digital signal is carried out the compression sampling acquisition;
Integrated unit is used for carrying out frequency-region signal reconstruct according to each described compression sampling result.
13. fusion device according to claim 12 is characterized in that, described fusion device also comprises:
Selected cell is used for selecting each unauthorized user equipment of described participation frequency spectrum detection based on frequently selecting fading characteristic.
14. a subscriber equipment is characterized in that, comprising:
Second analog to digital converter, being used for the time domain simulation conversion of signals is the discrete digital signal;
Judging unit is used to determine to have other complementary subscriber equipment, and described information with other complementary subscriber equipment is sent to iteration unit;
The second compression sampling unit is used for described discrete digital signal is carried out compression sampling;
Iteration unit is used for carrying out iteration based on the result and the described compression sampling result with other complementary subscriber equipment transmission of described second compression sampling cell compression sampling.
15. subscriber equipment according to claim 14 is characterized in that, described subscriber equipment also comprises:
Interactive unit is used for and describedly has other complementary subscriber equipment interactive information, determines the sample number that will share, and described sample number is sent to the described second compression sampling unit;
The described second compression sampling unit, specifically be used for based on received sample number, generate the row element of perception matrix corresponding line, and finish the inner product operation that described discrete digital signal is carried out perception, carry out frequency-region signal reconstruct according to the result of described inner product operation and obtain the frequency spectrum state after the reconstruct and send to described iteration unit.
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CN102445691B (en) * 2011-10-11 2013-07-24 北京航空航天大学 Multichannel spaceborne synthetic aperture radar azimuth spectrum sparse reconstruction method
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